diff --git a/research/coupled-provider-independent-audit/.gitattributes b/research/coupled-provider-independent-audit/.gitattributes new file mode 100644 index 0000000000..fa1385d99a --- /dev/null +++ b/research/coupled-provider-independent-audit/.gitattributes @@ -0,0 +1 @@ +* -text diff --git a/research/coupled-provider-independent-audit/CLAIMS.json b/research/coupled-provider-independent-audit/CLAIMS.json new file mode 100644 index 0000000000..0f45425eb1 --- /dev/null +++ b/research/coupled-provider-independent-audit/CLAIMS.json @@ -0,0 +1,60 @@ +{ + "admitted_kappa": null, + "canonical_main": "1ec1119972c9aefe42525172d07b332fcff81cb4", + "clifford": { + "finite_oracle": "bounded implementation evidence only", + "full_provider_replay": false, + "fusion_census_replayed": false, + "head": "848cdce9003262c4b6e02ec4558f302e4fae56ad", + "positive_compact_equality_independent_certificate": false, + "pr": 5376, + "written_all_n_criterion": "sound under fixed-coefficient exact dyadic-Clifford hypotheses" + }, + "closure_budget": { + "actual_extra_autonomous_H8_admitted": 0, + "closure_constructed": false, + "hypothetical_unearned_extra_H8": 144, + "paid_144_H8_cancels_hypothetical_credit": true, + "providers": 18, + "status": "conditional necessary comparison only", + "unpriced_terms": [ + "closure paid calls", + "lost targets", + "changed main/idle profile", + "physical ordinary work", + "full caller precision and compiler/outer funding" + ] + }, + "completed_caller": false, + "local_envelope": { + "copy_count": 16, + "full_caller_precision_admitted": false, + "head": "3348fccea855082786d5f0fc5558b73d4974e745", + "joint_field_l2_exponent": 19012, + "max_field_l2_exponent": 18996, + "scope": "one-provider abstract scalar/unitary transcript; arbitrary contiguous intervals and suffixes; local residuals measured in the same stated field norm" + }, + "new_unconditional_or_formal_kernel_theorem": false, + "provider": { + "admission": "independent partial coupled component", + "arbitrary_owned_inputs": 9, + "autonomous_credit_from_coupled_helpers": 0, + "autonomous_helpers": 400, + "coupled_helpers": 8, + "head": "3348fccea855082786d5f0fc5558b73d4974e745", + "original_inputs": 632, + "owned_outputs_zero": 9, + "paid": { + "1": 2193, + "2": 412, + "3": 510, + "4": 127, + "5": 40 + }, + "phase_bindings": 1240, + "pr": 5402 + }, + "review_status": "READY_FOR_COLD_REPLAY", + "schema_version": 1, + "selected_record_changed": false +} diff --git a/research/coupled-provider-independent-audit/COMMANDS.json b/research/coupled-provider-independent-audit/COMMANDS.json new file mode 100644 index 0000000000..91a7ac5d6c --- /dev/null +++ b/research/coupled-provider-independent-audit/COMMANDS.json @@ -0,0 +1,75 @@ +{ + "author_pair": "Frozen authenticated root normal/-O receipt only; never rerun by this schedule.", + "commands": [ + { + "argv": [ + "--out", + "agents/algebra/FRESH.json" + ], + "drop": [ + "runtime_seconds" + ], + "engine": "agents/algebra/check_provider.py", + "expected": "reports/algebra/REPLAY-EXPECTED.json", + "name": "algebra", + "result": "agents/algebra/FRESH.json", + "timeout_seconds": 180 + }, + { + "argv": [ + "--out", + "agents/algebra/FRESH-MUTANT.json" + ], + "drop": [ + "runtime_seconds" + ], + "engine": "agents/algebra/check_same_chart_cache_mutant.py", + "expected": "reports/algebra/SAME-CHART-CACHE-MUTANT.json", + "name": "same-chart-control", + "result": "agents/algebra/FRESH-MUTANT.json", + "timeout_seconds": 15 + }, + { + "argv": [ + "--moments", + "--output", + "agents/budget/FRESH.json" + ], + "drop": [ + "runtime" + ], + "engine": "agents/budget/screen_v3.py", + "expected": "reports/budget/RESULT-v3.json", + "name": "budget", + "result": "agents/budget/FRESH.json", + "timeout_seconds": 15 + }, + { + "argv": [ + "--output", + "agents/budget/FRESH-ENVELOPE.json" + ], + "drop": [ + "runtime" + ], + "engine": "agents/budget/independent_local_envelope.py", + "expected": "reports/budget/LOCAL-ENVELOPE-v1.json", + "name": "local-envelope", + "result": "agents/budget/FRESH-ENVELOPE.json", + "timeout_seconds": 15 + }, + { + "argv": [], + "drop": [ + "elapsed_seconds" + ], + "engine": "agents/clifford-proof/independent_audit.py", + "expected": "reports/clifford-proof/RESULT.json", + "name": "clifford-proof", + "result": "agents/clifford-proof/RESULT.json", + "timeout_seconds": 30 + } + ], + "custody": "Source guard freshly verifies raw origin objects, source rows, nested pins and all working input bytes before any package execution.", + "optimization_policy": "Registered wrapper normal/-O modes each run all five commands serially. The adapter explicitly compiles unchanged mathematical source at optimize=0 in both modes, preserving scientific assert checks under -O." +} diff --git a/research/coupled-provider-independent-audit/README.md b/research/coupled-provider-independent-audit/README.md new file mode 100644 index 0000000000..4b517de5a4 --- /dev/null +++ b/research/coupled-provider-independent-audit/README.md @@ -0,0 +1,68 @@ +# Independent coupled-provider and closure-budget audit + +This focused review accepts **#5402 as a partial coupled provider**, supplies a conditional budget for closing it, and records a companion bounded review of #5376's Clifford proof/certificate implementation. It supplies no completed consumer, no autonomous credit for the eight coupled H outputs and no new κ. + +The candidate heads are #5402 `3348fccea855082786d5f0fc5558b73d4974e745` and #5376 `848cdce9003262c4b6e02ec4558f302e4fae56ad`. Canonical main at assignment is `1ec1119972c9aefe42525172d07b332fcff81cb4`. Raw commit/tree/blob membership proofs are vendored under `custody/`; the older #5376 base and its missing non-runtime contributor document remain explicit in that provenance. These side-head objects are evidence, not publication-history parents. + +## Accepted component and remaining interface + +The independent checker derives the actual early cache rows and both basis matrices from the original source, replays 632 arbitrary original inputs and nine arbitrary owned inputs, checks all nine final owned zero rows, and verifies 1,240 phase-sensitive physical identities. It compares complete Pauli action and a full zero-state phase anchor. Its partial block is + +``` +X = D x - R y + R W h +Y = D y +H = D(h - Z y), ZW = 14 I8, WZ = I-C. +``` + +The eight H outputs retain independent Y terms. Only the other 400 helpers receive autonomous credit. Ordered native words, explicit charts, all original directions and all owned fields remain part of the contract. The exact paid profile is `{1:2193,2:412,3:510,4:127,5:40}`. Unchanged native/helper implementations are inherited from the pinned source; this review does not flatten their entire physical tape realization. + +The original semantic controls cover endpoint/basis mutation, ownership, phase, order, false zero retags and false autonomous credit. The cache-source substitution is a frame-contract rejection. An additional legal same-chart `SCALE -1` after the actual cache COPY reaches the native algebra and rejects because a required zero row becomes nonzero. See `reports/algebra/SAME-CHART-CACHE-MUTANT.json` and the raw root run. + +## Conditional closure budget + +The budget lane reconstructs the complete #5398 eighteen-body comparator and requires exact agreement with the prior independent #5400 invoice. Its local paid/helper profiles already match the comparator. The deleted eight H8 plus eight H1 calls are savings against the original raw source, so they cannot be claimed again against this comparator. + +Granting eight **new, unearned autonomous H8 targets per provider** gives 144 hypothetical targets. At `t=1-κ`, the exact comparison is + +``` +margin_new = margin_reference + 144*8^t - M(K) - M(L) + M(Delta). +``` + +K is added paid closure work; L is lost productive work; Delta is every other signed main/idle/caller change. All remain unknown until a typed caller is supplied. If K is exactly 144 H8 jobs and L=Delta=0, the signed histogram equals the comparator at every rank and hence at every t. Any further positive paid job without compensating targets makes the incremental moment worse. This is a conditional budget, with no universal controller obstruction or autonomous credit for coupled H. + +The literal boundary inventory per provider is 17,917 ADD, 1,204 SCALE, 16 COPY, 40 CLEAR, eight whole-field swaps and 464 monomial maps. The exact inherited scalar tariff is 175,022 units, including 42 exterior boundary units; physical monomial work, closure, routing/storage, precision and compiler/outer funding remain open. The earlier checker failure used the wrong original-source subtotal (158,744 versus the actual 158,168). The failed raw receipt is retained as a diagnostic; final source and successful result are the corrected version. No failed construction claim follows. A later literal-scale audit found that the stored output `cache_scalar` already is the final factor. The earlier checker took its reciprocal again, yielding a conservative 16-unit overcount. `screen_v3.py` uses the emitted factor directly. Recursive profiles, field counts and moment budgets are unchanged; old results remain diagnostics. + +The separate local-envelope checker derives exponent **18,996** in the author's maximum-over-fields Euclidean norm and **19,012** in the joint Euclidean norm across fields. The latter includes a factor of two for each of sixteen COPY gates; COPY is nonexpansive in the former norm. It bounds the literal one-provider abstract scalar/unitary transcript, all contiguous subintervals and all suffixes at a fixed width. Local residuals must be measured in the same stated norm. It does not supply coordinate-to-field residual conversion or complete caller precision, storage, movement or compiler funding. + +## Companion Clifford review + +`reports/clifford-proof/REVIEW.md` reviews the all-n criterion under fixed coefficients, exact phase-bearing dyadic Clifford operators, fixed programs and arbitrary roles. The trace alphabet, exact Gram identity, filter and eight-copy invariant supply the written implication. The finite oracle independently builds Fraction-pair matrices: 25 entries, four traces, seven conditional inners, 24 programs, 64 tiny tensor-width cases, seventeen witnesses and 68 rejected witness mutations. It also constructs the 96 one-axis matrices, modular Gram rank and Reynolds checks. + +These finite checks support only their tested implementation cases. The literal witness checker certifies a negative nonzero entry; compact positive equality still relies on trusted exact expansion/trace/merge execution, shares expansion helpers and has no separate small positive proof receipt. We did not replay the complete #5376 provider programs, 7,000 recipe classes, 30,328 fusion census, or its six registered commands. The inherited five framework premises and physical/precision/stock/analytic recovery remain outside this bundle. + +## Reproduction + +Python 3.10+ and its standard library are sufficient on Linux/POSIX. From the repository root: + +```sh +python3 -B scripts/research_package.py --package research/coupled-provider-independent-audit +``` + +A Git-free, read-only export can run either registered wrapper directly, from any working directory: + +```sh +python3 -I -B /absolute/path/coupled-provider-independent-audit/verify.py +python3 -I -O -B /absolute/path/coupled-provider-independent-audit/verify.py +``` + +Each command freshly authenticates every working input and raw origin proof, then serially executes independent algebra, the same-chart control, the corrected conditional exact budget, the two-norm local envelope and the bounded Clifford oracle. The frozen original root author normal/-O pair (51.350 seconds) is authenticated historical evidence only and is not rerun. `COMMANDS.json` declares the actual fresh schedule. Full stable mathematical result objects are compared with frozen receipts; only named runtime fields are ignored. The original main algebra receipt remains unchanged at `reports/algebra/RESULT.json`. Its derived `REPLAY-EXPECTED.json` adds only the authenticated SHA256 inventory row for the later same-chart control file: the unchanged main checker inventories every adjacent Python file, even this unused helper. `REPLAY-EXPECTED-PROVENANCE.json` records that exact transformation, and the source guard requires full equality to the original object plus that one row. No mathematical or other provenance fields are dropped or replaced from fresh output. Fresh outputs and logs go to a private temporary tree; `--output /outside/package/REPLAY.json` selects a new receipt path. `--bindings-only` performs custody/input checks without scientific execution. + +The wrapper re-executes through a built-in-only `sys`/`posix` isolated bootstrap, pins its helper/manifest bytes, rejects symlinks, hardlinks, undeclared files and bytecode, and verifies source bytes again after replay. Local imported Python source is loaded from authenticated private scratch, with a fresh cache path. Mathematical engines remain byte-for-byte frozen. Both wrapper modes deliberately compile scientific source at **optimize=0** so assert-based oracle checks remain active under wrapper `-O`; this does not claim an unprotected direct `-O` run of the assert-based oracle. Standard-library loaders are unchanged. The exported wrapper is the trust anchor; hashes provide integrity and origin binding, not a formal proof kernel. + +## Open next questions + +1. Emit one portable typed closure: exact A/S or alternative operators, their ordered physical words/charts, helper-tail updates, arbitrary-input/owned endpoints, and all added paid/lost-target terms. The reported private continuation is not a replayable input. +2. Test that closure against the complete signed histogram and ordinary/precision/compiler ledger. The conditional 144-H8 cancellation identifies a useful stopping test before another large search. +3. For compact positive Clifford equality, supply a small independent positive proof receipt and an explicit conversion contract for native versus dense witness schemas. Keep it separate from the bounded negative-witness checks. + +Construction and predecessor credit remains with Ali Romman and the source-pinned native, provider, controller, Clifford and compiler contributors. The independent dyadic and exact-price engines retain prior attribution. This independent audit is Chris R/Clear1nsight with substantial OpenAI Codex assistance; it claims no independent human or formal-kernel acceptance. New material is under Apache-2.0. 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bless changed scientific claims." +} diff --git a/research/coupled-provider-independent-audit/SOURCES.json b/research/coupled-provider-independent-audit/SOURCES.json new file mode 100644 index 0000000000..75b7c6846e --- /dev/null +++ b/research/coupled-provider-independent-audit/SOURCES.json @@ -0,0 +1,24 @@ +{ + "base_commit": "1ec1119972c9aefe42525172d07b332fcff81cb4", + "files": [ + { + "git_blob": "b288ae44032fd84dd5564243422836cbcd29835e", + "path": "certificates/selected-result.json", + "sha256": "f9ed52bb642cd1e1486cf2743557ac5fa23cf1514a3277d786a644e39a565038", + "usage": "provenance" + }, + { + "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602", + "path": "docs/research/agent-task-catalog.json", + "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72", + "usage": "provenance" + } + ], + "review_sources": { + "clifford5376": "848cdce9003262c4b6e02ec4558f302e4fae56ad", + "provider5402": "3348fccea855082786d5f0fc5558b73d4974e745" + }, + "schema_version": 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Final registered and read-only export execution remain root-owned gates.", + "novel_coverage": "Reconstruct actual source caches, complete original/owned formal rows, ordered physical phases, changed literal cost census and complete comparator ledger; isolate missing closure targets and positive certificate boundaries.", + "open_questions": [ + { + "blocked_by": "Missing portable closure definitions, paid jobs, lost targets and caller precision/compiler/outer funding.", + "first_step": "Publish exact ordered A/S or alternative physical words, charts, helper-tail schedule and all arbitrary-input/owned endpoints.", + "question": "Can an actual typed caller close the eight coupled outputs within a fully charged profile?", + "why_it_matters": "The current coupled H fields earn zero autonomous credit and conditional budgets do not construct a consumer." + }, + { + "blocked_by": "No separate small positive proof certificate currently supplied.", + "first_step": "Specify a positive receipt plus exact native/dense schema conversion and source binding.", + "question": "Can compact positive Clifford equality have a small independently checked positive proof receipt?", + "why_it_matters": "The existing literal witness checker proves negative nonzero entries; positive equality trusts expansion and trace/merge execution." + } + ], + "original_card": { + "acceptance_gate": "Demonstrate independence, source binding, positive cases and semantic failure controls. Name the existing checks and the missing coverage. More digits or another equivalent evaluation of an unchanged root is not by itself new verification coverage.", + "allowed_variations": [ + "Reconstruct either a source ledger or a numeric enclosure with a different method." + ], + "bottleneck_link": "Independent pricing prevents unsupported frontier claims and can reveal genuine accounting slack.", + "existing_checks": [ + { + "evidence": "research/staged544-mixed-fourth-entry/README.md", + "remaining": "Independent binding of changed construction to paid histogram, distinct from full admission.", + "scope": "PR #4088: mixed local/owner/phase ledger and moment reported.", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129", + "source_commit": "72d7efc181edb21806a878f174847c96dd410ab0", + "status": "author-checked" + }, + { + "evidence": "research/staged-fourth-mixture-ceiling/README.md", + "remaining": "Validate dual, exhaustive pattern scope and exact source equivalence before applying to newer fills.", + "scope": "PR #4091: sharp pooled ceiling proposed for fixed THREE/FOUR words and inventory.", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129", + "source_commit": "a29bdd8f56cd18b805917775cdec09ff935eddc4", + "status": "author-checked" + }, + { + "evidence": "research/r437-two-window-carrier/README.md", + "remaining": "Independent full cost delta; remaining caller/precision/stock obligations are separate.", + "scope": "PR #4067: paid (2,2) to (1,3) exchange and fixed OQ4 host reported.", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129", + "source_commit": "a95f11c52e3ca1e4c5171b3c20d8f4b0815aee2e", + "status": "author-checked" + } + ], + "first_experiment": "Independently reconstruct one changed ledger or pooled certificate with a positive case and a semantic failure control. Compare exact sources and name what existing checks miss. Keep this separate from supplier-boundary-audit (ordinary/outer dispatch) and uniform-transfer-audit (all-size proof). Stop after the chosen implication; more digits of an unchanged root are not additional mechanism coverage.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Choose one uncovered implication in #4088 literal mixed fill, #4091 pooled dual/model binding or #4067 changed frame/host bill. #4091 pins an earlier #4088 head: validate word, capacity and stock equivalence before applying that ceiling to the later fill.", + "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately." + }, + "id": "independent-moment", + "methods": [ + "Independently reconstruct one changed paid ledger or pooled dual with exact source and model binding.", + "Check a genuinely uncovered moment implication with a different enclosure method and semantic controls." + ], + "overlap_terms": [ + "independent moment", + "rank histogram", + "exact enclosure", + "2979", + "rank7 joint endframes", + "paired extraction", + "joint lowering", + "4088", + "4091", + "4067", + "staged544-mixed-fourth-entry", + "staged-fourth-mixture-ceiling", + "r437-two-window-carrier" + ], + "question": "Does a new paid-profile or mixture-ceiling claim have independent source-bound coverage of its actual changed ledger?", + "scope_change_triggers": [ + "Importing the primary function and calling its output independent verification.", + "Calling an aggregate histogram or source archive an independently accepted physical supplier." + ], + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/staged544-mixed-fourth-entry/README.md", + "research/staged-fourth-mixture-ceiling/README.md", + "research/r437-two-window-carrier/README.md" + ] + }, + "outcome": "partial", + "priority_revision": 7, + "publication_transport_status": "Pending final registered normal/optimized, committed-byte/source-history/export and root acceptance gates.", + "schema_version": 1, + "scope_change_reason": "Direct donor assignment selected the changed provider and closure ledger instead of the historical card examples; parallel bounded Clifford proof review was explicitly authorized.", + "scope_status": "refined", + "stop_rule": "Stop at one independent partial-component admission plus typed conditional budget and bounded companion review; do not invent or search an unpriced closure.", + "task_id": "independent-moment" +} diff --git a/research/coupled-provider-independent-audit/VERIFY.json b/research/coupled-provider-independent-audit/VERIFY.json new file mode 100644 index 0000000000..d1a7ec06e6 --- /dev/null +++ b/research/coupled-provider-independent-audit/VERIFY.json @@ -0,0 +1,351 @@ +{ + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-B", + "{package}/verify.py" + ], + "checks": "Fresh actual-byte/source-origin custody; serial independent provider algebra, legal same-chart content mutant, corrected conditional closure moments, two-norm local envelope and bounded Clifford oracle. 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b/research/coupled-provider-independent-audit/capsule/agents/algebra/check_provider.py @@ -0,0 +1,237 @@ +#!/usr/bin/env python3 +"""Independent provider algebra, ownership, basis and physical phase audit.""" +import argparse, copy, gzip, hashlib, json, time +from collections import Counter +from fractions import Fraction as F +from pathlib import Path +from prior_dyadic_engine import require, initial, linear, rational_row, warped +from provider_rows import interpret +import phase_exact as ph + +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1]/'repository' +P=ROOT/'research/native-rank8-helper-provider' +MODE=[224,225,227,229,240,241,256,257] +SOURCE='research/native-center-free-code/SOURCE-WORD.json.gz' + +def add(a,b,q=F(1)): + for j,v in b.items(): + a[j]=a.get(j,F(0))+q*v + if not a[j]:del a[j] + +def scalar(row): + rr=rational_row(row) + require(all(not word and role[0]=='L' for role,word in rr), 'row retains native word or owned dirt') + return {role[1]:v for (role,word),v in rr.items()} + +def basis(program,rows,c,frame): + out=[dict(r) for r in rows] + for e in program: + tag,dst=e[:2] + require(224<=dst<632 and c['start' if frame==0 else 'final'][dst]==frame,'basis physical chart') + if tag=='add': + src,q=e[2],F(e[3]);require(dst!=src and 224<=src<632 and c['start' if frame==0 else 'final'][src]==frame,'basis source chart') + require(q.denominator&(q.denominator-1)==0,'basis ADD dyadic') + add(out[dst],out[src],q) + else: + require(tag=='scale','basis cannot erase or borrow scratch') + q=F(e[2]);require(q and abs(q.numerator)&(abs(q.numerator)-1)==0 and q.denominator&(q.denominator-1)==0,'basis SCALE signed power of two') + out[dst]={j:q*v for j,v in out[dst].items() if q*v} + return out + +def decode(source,changed): + old=source['programs']['backward'];j=0;caches={};centers={};zeros={} + for i,e in enumerate(old): + require(j0: + a,b=changed[j:j+2];slot=tuple(a[1][1]);frame=a[2] + require(slot not in caches and b[0]=='scalar' and b[1][:2]==['copy',list(slot)] and b[2]==frame,'cache production') + caches[slot]={'event':i,'role':tuple(b[1][2]),'frame':frame};j+=2 + require(j==len(changed),'unexpected trailing native traffic') + require(len(caches)==len(centers)==len(zeros)==8 and set(caches)=={('C',i) for i in range(1,9)},'eight independent caches and deletions') + require(max(r['event'] for r in caches.values())=224: + for i in range(112): + a=-sum(B[k][j-224]*M[k][i] for k in range(8)) + if a:want[112+i]=a + require(cf[j]==want,'source-derived full centerfree coupling') + E=[None]*8;cache_modes={};identities=[] + for slot,r in caches.items(): + row=scalar(observed[r['event']][r['role']]);coeff={j-224:a for j,a in row.items() if j>=224} + projection=[sum(a*B[k][j] for j,a in coeff.items()) for k in range(8)] + require(sum(bool(v) for v in projection)==1,'source cache selects exactly one mode') + k=next(k for k,v in enumerate(projection) if v);f=projection[k] + require(E[k] is None,'cache modes independent') + E[k]={j:a/f for j,a in coeff.items()} + want={224+j:f*a for j,a in E[k].items()} + for j in range(112): + if M[k][j]:want[112+j]=-f*M[k][j] + require(row==want,'entire actual source cache identity') + cache_modes[slot]=(k,f) + require(all(sum(a*B[l][j] for j,a in E[k].items())==int(k==l) for k in range(8) for l in range(8)),'E B transpose identity') + deltas={} + for i,r in centers.items(): + cache=caches[r['slot']];delta=linear(observed[i][('C',0)],observed[cache['event']][cache['role']],-1) + d=scalar(delta);require(d and all(j>=224 for j in d),'center delta uses scalar helpers only') + deltas[r['frame']]=delta + identities.append({'center_source_event':i,'cache_source_event':cache['event'],'frame':r['frame'],'scalar_relation':{str(j):str(v) for j,v in d.items()}}) + for i,r in zeros.items():require(observed[i][r['role']]==linear(({},0),deltas[r['frame']],-1),'actual later row negative center delta') + owned={('C',i) for i in range(9)} + raw,_,bill=interpret(c,program,owned,require_owned_return=False) + require(not raw[('C',0)][0],'center owner already zero') + rawrows=[scalar(raw[('L',j)]) for j in range(632)]+[scalar(raw[('C',j)]) for j in range(9)] + require(Counter(oldbill['paid'])==Counter(bill['paid'])+Counter({1:8,8:8}),'eight H8 plus eight H1 deletions') + require(bill['paid']=={1:2193,2:412,3:510,4:127,5:40},'complete paid histogram') + active=sorted(set(j for r in B for j,a in enumerate(r) if a)|set(j for r in E for j in r));roles=[224+j for j in active] + require(len(active)==122 and artifact['basis_roles']==roles and artifact['mode_owners']==MODE,'122 common-chart basis roles') + L=[{j:F(1)} for j in range(632)] + for j in roles:L[j]={} + for k,owner in enumerate(MODE): + for r in active: + if B[k][r]:L[224+r][owner]=B[k][r] + for owner in roles: + if owner in MODE:continue + for r in active: + a=F(224+r==owner)-sum(B[k][r]*E[k].get(owner-224,F(0)) for k in range(8)) + if a:L[224+r][owner]=a + identity=[{j:F(1)} for j in range(632)] + entered=basis(artifact['input_basis_program'],identity,c,0);require(entered==L,'literal entrance equals derived L') + require(basis(artifact['output_basis_program'],entered,c,1)==identity,'literal inverse basis product') + # Square left inverse implies full inverse over Q; also test reverse product. + inverse=basis(artifact['output_basis_program'],identity,c,1) + require(basis(artifact['input_basis_program'],inverse,c,0)==identity,'literal reverse inverse product') + endpoint=[] + for row in rawrows: + dest={} + for j,a in row.items():add(dest,entered[j],a) + endpoint.append(dest) + endpoint=basis(artifact['output_basis_program'],endpoint,c,1) + for j in range(632): + want={} if j in MODE else {j:F(1)} + if j<112: + want[112+j]=F(-1) + for k in range(8): + if M[k][j]:want[MODE[k]]=F(M[k][j],4) + require(endpoint[j]==want,'complete composed persistent endpoint '+str(j)) + for slot,(k,f) in cache_modes.items(): + want={MODE[k]:f} + for j in range(112): + if M[k][j]:want[112+j]=-f*M[k][j] + require(endpoint[632+slot[1]]==want,'complete composed cache endpoint') + records=artifact['mode_boundaries'];require(len(records)==8,'eight boundary records') + K=[];NN=[];F8=[] + frame=lambda j:ph.frame(c['frames'][j]) + back=lambda j:ph.conjugate(frame(j)) + D=tuple(('C',1<0);mutated[idx][1][2][1]+=1 + reject('actual_cache_source_changed',lambda:interpret(c,mutated,owned,require_owned_return=False)) + mutated=copy.deepcopy(program);idx=next(i for i,e in enumerate(mutated) if e[0]=='scalar' and e[1][0]=='clear');mutated[idx][1][1]=['L',224] + reject('actual_borrowed_erasure',lambda:interpret(c,mutated,owned,require_owned_return=False)) + mutated=copy.deepcopy(artifact['input_basis_program']);idx=next(i for i,e in enumerate(mutated) if e[0]=='add');mutated[idx][3]=str(F(mutated[idx][3])+1) + reject('actual_basis_ADD_changed',lambda:require(basis(mutated,identity,c,0)==L,'derived basis matrix changed')) + reject('same_tableau_wrong_global_phase',lambda:require(ph.equal(K[0]+F8[0]+NN[0]+(('phase',1),),D),'global phase mismatch')) + reject('wrong_operator_order',lambda:require(ph.equal(NN[0]+F8[0]+K[0],D),'reversed noncommuting factors')) + reject('false_autonomous_H8_credit',lambda:require(all(not any(112<=j<224 for j in endpoint[owner]) for owner in MODE),'H contains nonzero independent Y columns')) + reject('false_zero_retag_original_input',lambda:interpret(c,[['zero_retag',224,c['start'][224],c['final'][224]]],owned,require_owned_return=False)) + # The ordinary source mutation runs through the actual same interpreter. + mutated=copy.deepcopy(program);idx=next(i for i,e in enumerate(mutated) if e[0]=='scalar' and e[1][0]=='add');mutated[idx][1][3]+=1 + def wrong_add(): + rr,_,_=interpret(c,mutated,owned,require_owned_return=False) + require(rr==raw,'actual source ADD changes complete endpoint') + reject('actual_native_ADD_changed',wrong_add) + a=initial(('L',0)) + reject('free_generators_do_not_commute',lambda:require(warped(warped(a,1),2)==warped(warped(a,2),1),'distinct native generators retain order')) + result={'status':'PASS_INDEPENDENT_COUPLED_PROVIDER_COMPONENT','candidate_head':'3348fccea855082786d5f0fc5558b73d4974e745','all_original_inputs':632,'arbitrary_owned_inputs':9,'owned_outputs_zero':9,'autonomous_helpers':400,'coupled_helpers_without_target_credit':8,'paid':bill['paid'],'source_16_identities':identities,'native_replay':bill,'physical_phase_bindings':dict(counts),'source_derived_E':[{str(j+224):str(a) for j,a in row.items()} for row in E],'basis_roles':roles,'ordinary_basis_counts':{'input':dict(Counter(e[0] for e in artifact['input_basis_program'])),'output':dict(Counter(e[0] for e in artifact['output_basis_program']))},'controls':controls,'consumed_sha256':consumed,'checker_files_sha256':{p.name:hashlib.sha256(p.read_bytes()).hexdigest() for p in HERE.glob('*.py')},'runtime_seconds':round(time.monotonic()-start,6),'claims':['X=D x-R y+R W h','Y=D y','H=D(h-Z y)','ZW=14 I8','WZ=I-C'],'limitations':['No autonomous target credit for coupled H.','No caller, kappa, inverse/transpose schedule or outer budget.','Native realization and unchanged helper physical implementations inherited from pinned source.','Phase proof is exact Pauli action plus full zero-column anchor, not flattened all-column physical tape.']} + out.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n');print(json.dumps({'status':result['status'],'phase_bindings':1240,'controls':list(controls),'seconds':result['runtime_seconds']})) + +if __name__=='__main__': + ap=argparse.ArgumentParser();ap.add_argument('--out',type=Path,default=HERE/'RESULT.json');main(ap.parse_args().out) diff --git a/research/coupled-provider-independent-audit/capsule/agents/algebra/check_same_chart_cache_mutant.py b/research/coupled-provider-independent-audit/capsule/agents/algebra/check_same_chart_cache_mutant.py new file mode 100644 index 0000000000..973ba63cdf --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/agents/algebra/check_same_chart_cache_mutant.py @@ -0,0 +1,44 @@ +#!/usr/bin/env python3 +"""Actual same-chart cache coefficient mutant through frozen native interpreter. + +This is an additional semantic control. It intentionally bypasses the literal +source zipper to test native row content after preserving frame/ownership rules. +""" +import argparse,copy,gzip,hashlib,json,time +from pathlib import Path +from prior_dyadic_engine import require +from provider_rows import interpret + +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1]/'repository' +FROZEN={'check_provider.py':'3774c5742b565ea9007af90d10e43d38a3e675c2074583c8c365799fc256baaf', +'phase_exact.py':'15e90b63c5659090f02902cb38951ec4ab252352fb0b967b411ed547c501e2ba', +'provider_rows.py':'c7e579939d89709d72457d5fa213173b3b492c3cc3de7546afc3ed6a6fb32f0c', +'prior_dyadic_engine.py':'3ee4ae79a55188d5abf2306f678179f4aafb799602ffb970fc1bc8f76cb061d9'} + +def main(out): + started=time.monotonic() + for name,digest in FROZEN.items():require(hashlib.sha256((HERE/name).read_bytes()).hexdigest()==digest,'frozen engine changed') + source=ROOT/'research/native-center-free-code/SOURCE-WORD.json.gz' + candidate=ROOT/'research/native-rank8-helper-provider/WORD.json.gz' + sraw=source.read_bytes();raw=candidate.read_bytes() + c=json.loads(gzip.decompress(sraw))['canonical'] + original=json.loads(gzip.decompress(raw))['word'];mutated=copy.deepcopy(original) + i=next(i for i,e in enumerate(mutated) if e[0]=='scalar' and e[1][0]=='copy' and e[1][1]==['C',1]) + frame=mutated[i][2] + require(mutated[i-1]==['scalar',['clear',['C',1]],frame],'actual cache COPY already preceded by same-chart owned CLEAR') + event=['scalar',['scale',['C',1],-1,1],frame] + mutated.insert(i+1,event) + require(mutated[:i+1]==original[:i+1] and mutated[i+2:]==original[i+1:],'exactly one legal scalar event inserted') + # SCALE -1 is a legal ordinary signed power-of-two on the same current + # physical chart. It neither reads another owner nor erases any owner. + rejection=None + try:interpret(c,mutated,{('C',j) for j in range(9)},require_owned_return=False) + except ValueError as e:rejection=str(e) + require(rejection=='zero retag requires complete exact zero row','mutant must reject for nonzero algebraic content, not frames or ownership') + require(source.read_bytes()==sraw and candidate.read_bytes()==raw,'source changed') + result={'status':'PASS_SAME_CHART_CACHE_CONTENT_MUTANT_REJECTED','mutation_source_event':i,'inserted_event':event,'preserved':'same chart, all owned CLEAR/COPY rules, no borrowed erasure; one legal SCALE -1 on retained C1 only','rejection':rejection,'runtime_seconds':round(time.monotonic()-started,6),'source_raw_sha256':hashlib.sha256(sraw).hexdigest(),'candidate_raw_sha256':hashlib.sha256(raw).hexdigest(),'frozen_engine_sha256':FROZEN,'checker_sha256':hashlib.sha256(Path(__file__).read_bytes()).hexdigest()} + out.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n');print(json.dumps(result)) + +if __name__=='__main__': + ap=argparse.ArgumentParser();ap.add_argument('--out',type=Path,default=HERE/'SAME-CHART-CACHE-MUTANT.json');main(ap.parse_args().out) diff --git a/research/coupled-provider-independent-audit/capsule/agents/algebra/phase_exact.py b/research/coupled-provider-independent-audit/capsule/agents/algebra/phase_exact.py new file mode 100644 index 0000000000..4959f78b9f --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/agents/algebra/phase_exact.py @@ -0,0 +1,110 @@ +"""Independent nine-bit signed-Pauli and exact anchor circuit evaluator. + +No submitted or source evaluator import. Equality is the complete 18-generator +Pauli action plus the full image of |0>, which fixes the scalar phase. +""" +from functools import lru_cache + +N=9 + +def parity(x): return x.bit_count()%2 + +def mv(rows,x): return sum(parity(r&x)<>j)&1)<>j&1) + a[j],a[k]=a[k],a[j] + for i in range(N): + if i!=j and a[i]>>j&1:a[i]^=a[j] + if [x&511 for x in a]!=[1<>N for x in a) + +def rank(rows): + basis={} + for x in rows: + while x: + k=x.bit_length()-1 + if k not in basis:basis[k]=x;break + x^=basis[k] + return len(basis) + +def freeze(word):return tuple(tuple(tuple(x) if isinstance(x,list) else x for x in e) for e in word) + +def adjoint(word): + result=[] + for e in reversed(word): + if e[0]=='P':result.append(('P',invert(e[1]))) + elif e[0]=='D':result.append(('D',e[1],tuple(-v%4 for v in e[2]))) + elif e[0]=='C':result.append(('C',e[1],-e[2])) + elif e[0]=='phase':result.append(('phase',-e[1]%4)) + else:result.append(e) + return tuple(result) + +def conjugate(word): + return tuple(('D',e[1],tuple(-v%4 for v in e[2])) if e[0]=='D' else + ('C',e[1],-e[2]) if e[0]=='C' else + ('phase',-e[1]%4) if e[0]=='phase' else e for e in word) + +def polynomial(e,x): + Q,alpha=e[1:] + return (sum(alpha[j] for j in range(N) if x>>j&1)+ + 2*sum(parity(Q[j]&x&~((1<<(j+1))-1)) for j in range(N) if x>>j&1))%4 + +def pauli(word,x,z,p=0): + for e in word: + if e[0]=='P':x,z=mv(e[1],x),mv(transpose(invert(e[1])),z) + elif e[0]=='X':p+=2*parity(z&e[1]) + elif e[0]=='D': + q=polynomial(e,x) + z^=sum((((polynomial(e,x^(1<len(basis):basis.append(q) + G=transpose(basis);gi=invert(G);cols=transpose(gi) + Q=tuple((1<>j)&1 for j in range(N)))) + return adjoint(K)+tuple(('C',1<> shift for k, v in d.items()} + return d, exponent - shift + +def linear(a, b, numerator=1, denominator=1): + # Source rationals may carry the sign on either integer, including + # SCALE [2,-1]. Normalize the rational sign before dyadic validation. + if denominator < 0: + numerator, denominator = -numerator, -denominator + require(denominator > 0 and denominator & (denominator - 1) == 0, 'non-dyadic scalar') + exp_b = b[1] + denominator.bit_length() - 1 + exp = max(a[1], exp_b) + d = {k: v << (exp - a[1]) for k, v in a[0].items()} + for k, v in b[0].items(): + d[k] = d.get(k, 0) + numerator * (v << (exp - exp_b)) + return norm(d, exp) + +def scaled(a, numerator, denominator): + return linear(({}, 0), a, numerator, denominator) + +def initial(role): + return ({(role, ()): 1}, 0) + +def warped(a, symbol): + # Left action: cancel only an adjacent inverse. Distinct symbols never + # commute and the scalar coefficient is kept outside the word. + d = {} + for (role, word), v in a[0].items(): + key = (role, word[1:] if word and word[0] == -symbol else (symbol,) + word) + d[key] = d.get(key, 0) + v + return norm(d, a[1]) + +def rational_row(row): + return {k: Fraction(v, 1 << row[1]) for k, v in row[0].items()} + +def rref(relations, preferred_pivots=()): + """Conventional matrix elimination, with fixed increasing column order.""" + all_columns = {h for d in relations for h in d} + require(set(preferred_pivots) <= all_columns, 'prepared pivot absent from derived relation system') + columns = list(preferred_pivots) + sorted(all_columns - set(preferred_pivots)) + matrix = [[Fraction(d.get(h, 0)) for h in columns] for d in relations] + rank, pivots = 0, [] + for j, h in enumerate(columns): + k = next((k for k in range(rank, len(matrix)) if matrix[k][j]), None) + if k is None: + continue + matrix[rank], matrix[k] = matrix[k], matrix[rank] + q = matrix[rank][j] + matrix[rank] = [v / q for v in matrix[rank]] + for i in range(len(matrix)): + if i != rank and matrix[i][j]: + q = matrix[i][j] + matrix[i] = [a - q * b for a, b in zip(matrix[i], matrix[rank])] + pivots.append(h) + rank += 1 + if rank == len(matrix): + break + return {p: {h: q for h, q in zip(columns, matrix[i]) if q} for i, p in enumerate(pivots)} + +def decode_edits(source, candidate): + """Read the literal word delta without WITNESS.json or expected outputs.""" + old, new = source['programs']['backward'], candidate['programs']['backward'] + j = next(i for i, e in enumerate(new) if e == old[0]) + preparation = new[:j] + snapshots, centers, zeros = {}, {}, {} + for i, event in enumerate(old): + if new[j] == event: + j += 1 + elif event[0] == 'center': + a, b, c = new[j:j + 3] + frame = event[3] + require(a == ['scalar', ['clear', ['C', 0]], frame], 'center clear') + require(b[0] == 'scalar' and b[1][:2] == ['copy', ['C', 0]] and b[2] == frame, 'center COPY gauge') + slot = tuple(b[1][2]) + require(c == ['scalar', ['clear', list(slot)], frame], 'snapshot consumption') + centers[i] = {'slot': slot, 'frame': frame} + j += 3 + else: + require(event[0] == 'climb', 'unexpected source edit') + role, oldframe, newframe = ('L', event[2]), event[3], event[4] + require(new[j] == ['zero_retag', list(role), oldframe, newframe], 'zero edit exact frames') + zeros[i] = {'role': role, 'frame': oldframe, 'rank': event[5]} + j += 1 + if j + 1 < len(new) and new[j][0] == 'scalar' and new[j][1][0] == 'clear' and new[j][1][1][0] == 'C' and new[j][1][1][1] > 0: + a, b = new[j:j + 2] + slot, frame = tuple(a[1][1]), a[2] + require(b[0] == 'scalar' and b[1][:2] == ['copy', list(slot)] and b[2] == frame, 'snapshot COPY') + require(slot not in [x['slot'] for x in snapshots.values()], 'snapshot slot reused') + snapshots[i] = {'slot': slot, 'role': tuple(b[1][2]), 'frame': frame} + j += 2 + trailing = new[j:] + require(len(snapshots) == len(centers) == len(zeros) == 8, 'eight of each edit') + require(len({x['slot'] for x in centers.values()}) == 8, 'eight independent snapshot slots') + require(max(snapshots) < min(centers), 'all eight snapshots simultaneously live') + for i, x in centers.items(): + match = [k for k, s in snapshots.items() if s['slot'] == x['slot']] + require(len(match) == 1 and match[0] < i and snapshots[match[0]]['frame'] == x['frame'], 'chronological same-frame snapshot') + x['snapshot'] = match[0] + require(candidate['programs']['forward'] == source['programs']['forward'], 'unchanged entire forward word') + canonical = dict(source['canonical']); canonical.pop('local_profile') + require(candidate['canonical'] == canonical, 'unchanged actual native operators and frames') + return preparation, snapshots, centers, zeros, trailing + +def replay(canonical, program, owned, source_sites=None): + roles = {('L', i) for i in range(632)} | set(owned) + rows = {r: initial(r) for r in roles} + frames = {('L', i): f for i, f in enumerate(canonical['start'])} + frames.update({r: None for r in owned if r[0] == 'C'}) + observed, spaces = {}, {} + paid = {} + max_terms = 1 + def space(frame): + if frame not in spaces: + s = {0} + for v in canonical['frames'][frame]: + s |= {u ^ v for u in tuple(s)} + require(len(s) == 1 << len(canonical['frames'][frame]), 'independent binary frame') + spaces[frame] = s + return spaces[frame] + for i, event in enumerate(program): + tag = event[0] + touched = None + if tag == 'scalar': + op, f = event[1:] + action, dst = op[0], tuple(op[1]); touched = dst + require(dst in roles and 0 <= f < len(canonical['frames']), 'scalar declaration') + if action == 'clear': + require(dst in owned, 'borrowed erasure') + rows[dst] = ({}, 0); frames[dst] = f + else: + require(frames[dst] == f, 'destination gauge') + if action in ('add', 'copy'): + src = tuple(op[2]) + require(src in roles and dst != src and frames[src] == f, 'source gauge') + if action == 'copy': + require(dst in owned and not rows[dst][0], 'COPY requires clean owned destination') + rows[dst] = (dict(rows[src][0]), rows[src][1]) + else: + rows[dst] = linear(rows[dst], rows[src], op[3], op[4]) + else: + require(action == 'scale', 'unknown scalar') + rows[dst] = scaled(rows[dst], op[2], op[3]) + elif tag == 'warp': + _, role, symbol, old, new = event + dst = tuple(role); touched = dst + require(frames[dst] == old and 1 <= abs(symbol) <= len(canonical['warps']), 'warp source gauge') + rows[dst] = warped(rows[dst], symbol); frames[dst] = new + elif tag in ('center', 'climb'): + if tag == 'center': + _, idx, old, new, rank = event; dst = ('C', idx) + require(space(old) < space(new) or space(new) < space(old), 'center nested spaces') + else: + _, _, idx, old, new, rank = event; dst = ('L', idx) + require(space(old) < space(new), 'climb nested spaces') + require(frames[dst] == old and rank == abs(len(canonical['frames'][old]) - len(canonical['frames'][new])), 'paid exact frame and rank') + frames[dst] = new; paid[rank] = paid.get(rank, 0) + 1 + elif tag == 'zero_retag': + _, role, old, new = event; dst = tuple(role) + require(frames[dst] == old and not rows[dst][0], 'physical identity requires complete zero row') + frames[dst] = new + else: + require(tag in ('phase', 'adapter'), 'unrecognized native event') + if touched is not None: + max_terms = max(max_terms, len(rows[touched][0])) + if source_sites and i in source_sites: + observed[i] = {r: (dict(rows[r][0]), rows[r][1]) for r in source_sites[i]} + for i in range(632): + r = ('L', i) + require(frames[r] == canonical['final'][i], 'retained final frame') + if r not in owned: + want = initial(r) + if i < 112: + want = linear(want, initial(('L', i + 112)), -1) + require(rows[r] == want, 'retained exact endpoint L' + str(i)) + require(all(not rows[r][0] for r in owned), 'arbitrary owned entry must erase and return zero') + return observed, {'events': len(program), 'paid': paid, 'max_live_row_terms': max_terms, + 'independent_retained_inputs': 632 - sum(r[0] == 'L' for r in owned), + 'arbitrary_owned_entry_inputs': len(owned)} + +def serialize(d): + return {str(k): str(v) for k, v in sorted(d.items())} + +def verify_preparation(prep, basis): + pivots = set(basis) + expected = [] + for pivot, row in sorted(basis.items()): + expected.append(['scalar', ['clear', ['L', pivot]], 0]) + for h, q in sorted(row.items()): + if h != pivot: + require(h not in pivots and q.denominator & (q.denominator - 1) == 0, 'independent dyadic preparation') + expected.append(['scalar', ['add', ['L', pivot], ['L', h], -q.numerator, q.denominator], 0]) + require(prep == expected, 'actual simultaneous pivot preparation differs from independently derived RREF') + +def main(): + ap = argparse.ArgumentParser(); ap.add_argument('--out', type=Path, default=HERE / 'RESULT.json') + ap.add_argument('--candidate', type=Path, default=ROOT / CANDIDATE) + ap.add_argument('--candidate-pr', type=int, default=5383) + ap.add_argument('--candidate-head', default='4bd6efa51a495a7c7b7754915cf0244e7e60969e') + args = ap.parse_args() + source_raw = (ROOT / SOURCE).read_bytes() + candidate_raw = args.candidate.read_bytes() + source_payload, candidate_payload = map(gzip.decompress, (source_raw, candidate_raw)) + source, candidate = map(json.loads, (source_payload, candidate_payload)) + prep, snapshots, centers, zeros, trailing = decode_edits(source, candidate) + sites = {} + for i, s in snapshots.items(): sites.setdefault(i, set()).add(s['role']) + for i in centers: sites.setdefault(i, set()).add(('C', 0)) + for i, z in zeros.items(): sites.setdefault(i, set()).add(z['role']) + observed, before = replay(source['canonical'], source['programs']['backward'], {('C', 0)}, sites) + relations, identities, by_frame = [], [], {} + for i, x in sorted(centers.items()): + s = snapshots[x['snapshot']] + diff = linear(observed[i][('C', 0)], observed[x['snapshot']][s['role']], -1) + qrow = rational_row(diff) + require(qrow and all(r[0] == 'L' and 224 <= r[1] < 632 and not word for (r, word) in qrow), 'derived relation must contain only scalar helper inputs') + relation = {r[1]: q for (r, _), q in qrow.items()} + require(all(source['canonical']['start'][h] == 0 and source['canonical']['final'][h] == 1 for h in relation), 'cold full-ended relation domain') + relations.append(relation); by_frame[x['frame']] = diff + identities.append({'center_event': i, 'snapshot_event': x['snapshot'], 'snapshot_role': s['role'], 'frame': x['frame'], 'center_minus_snapshot': serialize(relation)}) + require(len(by_frame) == 8, 'distinct center frames') + for i, z in sorted(zeros.items()): + require(z['frame'] in by_frame and z['rank'] == 1, 'zero site belongs to named rank-one center frame') + require(observed[i][z['role']] == scaled(by_frame[z['frame']], -1, 1), 'unrestricted later row equals negative center-minus-snapshot') + identities.append({'zero_event': i, 'role': z['role'], 'frame': z['frame'], 'unrestricted_row_is_negative_center_delta': True}) + canonical_basis = rref(relations) + require(len(canonical_basis) == 8, 'joint relation rank eight') + prepared_pivots = [e[1][1][1] for e in prep if e[0] == 'scalar' and e[1][0] == 'clear' and e[1][1][0] == 'L'] + require(len(prepared_pivots) == len(set(prepared_pivots)) == 8, 'eight distinct actual prepared pivots') + basis = rref(relations, sorted(prepared_pivots)) + require(set(basis) == set(prepared_pivots), 'actual chosen pivots not independent in joint relation system') + verify_preparation(prep, basis) + require(trailing == [['scalar', ['clear', ['L', h]], 1] for h in sorted(basis)], 'all pivot outputs returned zero') + owned = {('L', h) for h in basis} | {('C', i) for i in range(9)} + require({tuple(r) for r in candidate['owned']['backward']} == owned, 'actual owned declarations') + _, after = replay(candidate['canonical'], candidate['programs']['backward'], owned) + # Controls are exact local propositions applied to independently derived + # rows, rather than rerunning or relying on author's rejection controls. + controls = {} + def rejects(name, fn): + try: fn() + except ValueError as e: controls[name] = str(e) + else: raise ValueError('accepted negative control ' + name) + mutant = json.loads(json.dumps(prep)); mutant[1][1][3] += 1 + rejects('wrong_preparation_coefficient', lambda: verify_preparation(mutant, basis)) + mutant2 = json.loads(json.dumps(prep)); mutant2[1][1][3] *= -1 + rejects('wrong_preparation_sign', lambda: verify_preparation(mutant2, basis)) + mutant3 = json.loads(json.dumps(prep)); mutant3[0][1][1][1] = 226 + rejects('wrong_pivot', lambda: verify_preparation(mutant3, basis)) + # Swapping distinct saved values must change the unrestricted center delta. + cs = list(sorted(centers)); x, y = centers[cs[0]], centers[cs[1]] + sx, sy = snapshots[x['snapshot']], snapshots[y['snapshot']] + wrong_delta = linear(observed[cs[0]][('C', 0)], observed[y['snapshot']][sy['role']], -1) + rejects('wrong_snapshot', lambda: require(wrong_delta == by_frame[x['frame']], 'snapshot changes unrestricted identity')) + wrong_gauge = json.loads(json.dumps(candidate)); ci = next(i for i,e in enumerate(wrong_gauge['programs']['backward']) if e[0]=='scalar' and e[1][:2]==['copy',['C',0]]) + wrong_gauge['programs']['backward'][ci][2] = 0 + rejects('wrong_copy_gauge', lambda: decode_edits(source, wrong_gauge)) + zi = min(zeros); z = zeros[zi] + wrong_zero = linear(observed[zi][z['role']], initial(('L', 224))) + rejects('wrong_zero_row', lambda: require(wrong_zero == scaled(by_frame[z['frame']], -1, 1), 'nonzero retained column at zero site')) + fake_rank = dict(basis); fake_rank.pop(min(fake_rank)) + rejects('drop_independent_relation', lambda: require(len(fake_rank)==8, 'rank seven cannot fund eight pivots')) + result = {'status': 'PASS_INDEPENDENT_JOINT_ALGEBRA', 'author_credit': 'Ali Romman; source word Cao Yifan', + 'candidate_pr': args.candidate_pr, 'candidate_head': args.candidate_head, + 'source_file': str(ROOT / SOURCE), 'candidate_file': str(args.candidate.resolve()), + 'source_raw_sha256': hashlib.sha256(source_raw).hexdigest(), + 'source_payload_sha256': hashlib.sha256(source_payload).hexdigest(), + 'candidate_raw_sha256': hashlib.sha256(candidate_raw).hexdigest(), + 'candidate_payload_sha256': hashlib.sha256(candidate_payload).hexdigest(), + 'checker_sha256': hashlib.sha256(Path(__file__).read_bytes()).hexdigest(), + 'relation_rank': 8, 'independently_derived_pivots': list(sorted(basis)), + 'independently_derived_rref': {str(p): serialize(d) for p,d in sorted(basis.items())}, + 'unconstrained_canonical_rref': {str(p): serialize(d) for p,d in sorted(canonical_basis.items())}, + 'source_identities': identities, 'source_replay': before, 'candidate_replay': after, + 'simultaneous_snapshot_count': 8, 'all_16_unrestricted_identities_checked': True, + 'forward_entire_word_unchanged': True, 'canonical_operators_frames_unchanged': True, + 'negative_controls': controls, + 'limitations': ['No new absolute-phase lowering or physical all-size proof.', 'Forward replay unchanged and reused; this checker independently replays backward words only.', 'Cost, compiler, outer inequalities are separate review responsibilities.']} + args.out.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + print(json.dumps({'status': result['status'], 'pivots': sorted(basis), 'controls': list(controls)})) + +if __name__ == '__main__': main() diff --git a/research/coupled-provider-independent-audit/capsule/agents/algebra/provider_rows.py b/research/coupled-provider-independent-audit/capsule/agents/algebra/provider_rows.py new file mode 100644 index 0000000000..06f0fd7d9b --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/agents/algebra/provider_rows.py @@ -0,0 +1,101 @@ +"""Independent source-word interpreter for provider audit. + +Arithmetic is explicitly reused from our frozen #5383 dyadic engine, whose +unmodified copy is retained beside this file. No author module is imported. +Every original field and every owned field starts with arbitrary input dirt. +Native generator order is free, with adjacent inverse cancellation only. +""" +from prior_dyadic_engine import initial, linear, scaled, warped, require + + +def interpret(canonical, program, owned, observations=(), require_owned_return=True): + roles = {('L', i) for i in range(632)} | set(owned) + rows = {r: initial(r) for r in roles} + frames = {('L', i): f for i, f in enumerate(canonical['start'])} + frames.update({r: None for r in owned if r[0] == 'C'}) + spaces, seen, events, paid = {}, {}, {}, {} + writes = {r: [] for r in roles} + reads = {r: [] for r in roles} + live_owners, max_live = set(), 0 + def space(f): + if f not in spaces: + values = {0} + for axis in canonical['frames'][f]: + values |= {x ^ axis for x in tuple(values)} + require(len(values) == 1 << len(canonical['frames'][f]), 'dependent binary frame') + spaces[f] = values + return spaces[f] + for index, event in enumerate(program): + tag = event[0] + events[tag] = events.get(tag, 0) + 1 + if tag == 'scalar': + op, frame = event[1:] + action, dst = op[0], tuple(op[1]) + require(dst in roles and 0 <= frame < len(canonical['frames']), 'undeclared scalar role/frame') + if action == 'clear': + require(dst in owned, 'borrowed erasure') + rows[dst], frames[dst] = ({}, 0), frame + live_owners.discard(dst) + else: + require(frames[dst] == frame, 'destination scalar frame') + if action in ('copy', 'add'): + src = tuple(op[2]) + require(src in roles and src != dst and frames[src] == frame, 'source scalar frame') + reads[src].append(index) + if action == 'copy': + require(dst in owned and not rows[dst][0], 'COPY requires cleared owned destination') + rows[dst] = (dict(rows[src][0]), rows[src][1]) + else: + rows[dst] = linear(rows[dst], rows[src], op[3], op[4]) + else: + require(action == 'scale', 'unknown scalar opcode') + q, d = op[2:] + require(q and d and abs(q) & (abs(q)-1) == 0 and abs(d) & (abs(d)-1) == 0, 'physical SCALE must be signed power of two') + reads[dst].append(index) + rows[dst] = scaled(rows[dst], q, d) + if dst in owned and rows[dst][0]: + live_owners.add(dst) + writes[dst].append((index, action)) + elif tag == 'warp': + _, role, symbol, old, new = event + dst = ('L', role) if isinstance(role, int) else tuple(role) + require(dst in roles and frames[dst] == old and 1 <= abs(symbol) <= len(canonical['warps']), 'native warp declaration/frame') + rows[dst] = warped(rows[dst], symbol) + frames[dst] = new + writes[dst].append((index, tag)); reads[dst].append(index) + elif tag in ('center', 'climb'): + if tag == 'center': + _, field, old, new, rank = event + dst = ('C', field) + require(space(old) < space(new) or space(new) < space(old), 'center physical nested spaces') + else: + _, label, field, old, new, rank = event + dst = ('L', field) + require(space(old) < space(new), 'climb physical nested spaces') + require(frames[dst] == old, 'paid source frame') + require(rank == abs(len(canonical['frames'][old])-len(canonical['frames'][new])), 'paid exact rank') + frames[dst] = new + paid[rank] = paid.get(rank, 0) + 1 + writes[dst].append((index, tag)); reads[dst].append(index) + elif tag == 'zero_retag': + _, role, old, new = event + dst = ('L', role) if isinstance(role, int) else tuple(role) + require(frames[dst] == old and not rows[dst][0], 'zero retag requires complete exact zero row') + frames[dst] = new + writes[dst].append((index, tag)); reads[dst].append(index) + else: + require(tag in ('phase', 'adapter'), 'unknown word event') + if index in observations: + seen[index] = {r: (dict(rows[r][0]), rows[r][1]) for r in observations[index]} + max_live = max(max_live, len(live_owners)) + for i in range(632): + require(frames[('L', i)] == canonical['final'][i], 'wrong final borrowed frame') + for role in owned if require_owned_return else (): + require(not rows[role][0], 'owned return has dependence on arbitrary entry') + require(writes[role] and writes[role][-1][1] == 'clear', 'owned final write must clear') + return rows, seen, {'events': len(program), 'event_counts': events, + 'paid': paid, 'max_live_owned_rows': max_live, + 'original_inputs': 632, 'arbitrary_owned_inputs': len(owned), + 'owner_lifetimes': {str(r): {'first_write': writes[r][0], + 'last_write': writes[r][-1], 'last_read': max(reads[r], default=-1)} + for r in sorted(owned)}} diff --git a/research/coupled-provider-independent-audit/capsule/agents/budget/envelope-inputs/PHYSICAL.md b/research/coupled-provider-independent-audit/capsule/agents/budget/envelope-inputs/PHYSICAL.md new file mode 100644 index 0000000000..da8837ba67 --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/agents/budget/envelope-inputs/PHYSICAL.md @@ -0,0 +1,71 @@ +# Real physical normalizers for the coded producer + +This is local constructive research on canonical/pr4929, not a completed supplier or exponent claim. Source code and Gaussian conventions retain the original authors' credit. + +Let n=9 and let q be any of the source's 112 port vectors (weight 3 or 7). Let e0=1. Construct an orthogonal binary matrix G taking e0 to q. If q_0=0, use the orthogonal transvection T_(e0+q). If q_0=1, select j>0 with q_j=0 and use T_(ej+q) T_(e0+ej). Here T_v(x)=x+(v dot x)v; both v have even weight, hence T_v is orthogonal. Such j exists because q is not the all-ones vector. + +For row j of G put z_j=(wt(row_j G)-1)/2 modulo 2. Define K=Z_z P_G. It is a real signed permutation. The full Gaussian R has entries alpha*(-i)^wt(x+y), with alpha=(1+i)^9/2^9. Orthogonality gives + +wt(G^-1 d)-wt(d) = 2 z dot d (mod 4). + +Indeed the degree-two coefficients vanish modulo four because distinct columns of G^-1 have even dot product; the linear coefficient is the weight of that column minus one. Therefore K R K^-1=R exactly, including absolute phase. K also maps the central line to span(q), and its orthogonal complement to q-perp, at the canonical-frame Lagrangian level. All these statements tensor to every positive digit-column count. + +Let Q be the central C gate, D the product of the other eight C gates, so R=DQ. Let E_i and S_i be the actual retained entrance-line and exit-hyperplane frame operators. With the operator convention that rightmost applies first, use + +input X: E_i K_i Q^-1 +input Y: K_i +output X: K_i^-1 +output Y: D K_i^-1 S_i^-1. + +All four wrappers are monomial. Their Lagrangian incidences prove this for every port, and the scratch verifier checks exact tableaus and absolute phases at every one of the 112 source ports. With A from PR4929, define C_ij= A_ij K_i^-1 K_j. Then the full main endpoint is + +F = diag(D,D) [[I,0],[C Q^-1,I]]. + +C is a physically implementable fixed owner recoding: apply K_i to each owner, apply A among the owners at common physical coordinates, and apply K_i^-1. Its inverse uses A^-1=(A+12I)/13. Since each K_i is real orthogonal and A is real symmetric, C^T=C. Since K_i commutes with R, C commutes with R. The polynomial C^2+12C-13I=0 follows by similarity. The 408 independent helper jobs and every paid Gaussian child are unchanged. + +For the actual raw inverse transpose, F^-T=diag(D^-1,D^-1) [[I,-Q^-1 C],[0,I]], since Q,D are symmetric. Multiply both outputs by D^2, then conjugate the physical X bank by Q^2 (input Q^-2 and output Q^2). These are explicit monomial powers. The result is + +B = diag(D,D) [[I,-Q C],[0,I]]. + +The old source convention using Y-only Q^2 conjugation cannot simply be copied for noncommuting C. The X-only convention above is exact. + +For a prior code B0 commuting with the current D, set G(B0)=diag(B0,Q^-1 B0 Q). The following two constructive local identities hold without requiring C and Q to commute: + +(post X C) F (pre Y C) = G(C B0) F_standard G(B0)^-1, +(post X C^-1) B (pre Y C^-1) = G(C^-1 B0) B_standard G(B0)^-1. + +They use [C,DQ]=0 and [B0,D]=0. Every additional operation on the left is physically cheap fixed recoding. For disjoint fresh blocks, codes from earlier stages commute with the current D. These identities do not yet settle interstage ADD/IDLE compatibility, terminal gauges, productive jobs, or the complete moment. + +## Literal recoding and complete local bill + +The source code has an exact factorization A=I-MM^T/4 with M a 112-by-8 matrix having entries 0,+1,-1 and M^T M=56I. Each mode column has 56 nonzero entries, and each owner row has four. The mode columns are emitted in NORMALIZERS.json and all 12,544 entries are checked against the pinned CODE.json. This factorization is used here as a constructive scalar program, without relying on any common physical address chart for separate Gaussian mode transformations. + +To execute A on arbitrary independent owner fields x, allocate eight owned zero fields t. Compute t=M^T x with 448 signed ADDs; update x-=M t/4 with 448 scaled ADDs; clear the eight owned temporaries. Reading x is finished before any x is updated. Hence no input field is overwritten before its last source read. For A^-1 use the same program with coefficient -1/52, since A^-1=I-MM^T/52. Both are exact rational linear programs. The helper fields of the native producer are never used as scratch, copied as free credit, or erased. + +Conjugating this scalar program by the 112 K_i and their inverses implements C or C^-1. This pays 224 monomial field maps, 896 scalar ADDs and 16 owned CLEARs per recoding, with eight owned fields reusable sequentially. The two additional recodings in either local gauge identity therefore cost at most 448 monomial maps, 1,792 scalar ADDs and 32 CLEARs, with no recursive Gaussian child. The four actual port normalizers contribute 448 monomial maps per native invocation. The displayed backward conversion contributes at most 448 further monomial maps (112 input X powers, 112 output X powers and 224 output D-squares); fusing maps can reduce this upper bound but is not assumed. + +These are field-level operation counts. A lifted K_i is an explicit binary map on nine f-bit address blocks together with signs given by block parity. Its constants, indexed movement and phase passes use the retained native monomial implementation. It is therefore a fixed finite O(V polylog p) nonrecursive operation under that caller's precision/address ABI, not a zero-work instruction. Each fixed rational ADD is likewise charged at its actual scalar precision. In particular the inverse denominator 52 must be implemented and rounded; no free exact real-division oracle is assumed. This lemma makes no independent TM tariff or outer-budget claim. + +The maximum exact component-l1 prefix bound for the scalar A program, including its temporaries, is 57. For A^-1 it is 56 (the output-only bound is 69/13). Signed monomial maps preserve component magnitude. A fixed local sequence has a fixed suffix bound obtained by multiplying elementary bounds 1+|coefficient|; owned CLEAR has bound one. This gives a finite bound for local rounding propagation. The number of local uses, compiler precision and complete outer error allocation still belong to the caller theorem. + +The normalized producer still has its exact PR4929 paid profile + + {1:2201, 2:412, 3:510, 4:127, 5:40} + +and independent helper profile + + {4:28, 7:7, 8:47, 9:326}. + +No productive main ranks are asserted merely from the coupled central ABI. Those depend on the completed caller, its initial/final gauges and every paid correction. + +## Universal scope and reproducible evidence + +PR4929 supplies the arbitrary-input logical identity over Q[FreeGroup72] for its emitted center-free word with ground-chart helper pre-compensation. Its normalized main endpoint is L(A), its raw dual is L(A)^-T, and every one of the 408 helper endpoints is autonomous. This proof is an inherited premise with exact source pins, not a consequence of this normalizer checker. The present wrappers and owner recodings act exclusively on the 224 main fields; new scratch is explicitly owned. Thus the helper block remains autonomous and its independent inputs, requested transforms and paid profile remain unchanged. + +For every f>=1, assign the shared native letters their actual consistent invertible lifted operators. Evaluation of the source free-group algebra is a homomorphism and gives the source logical identity. Independently lift each K_i as its f-fold tensor product, retaining spectator coordinates; its signed-permutation word, the two direct frame identities and its commutation with R lift by operator composition. In every compiled monomial word, P and X act columnwise on the f-bit blocks, D sums its Z4 polynomial over the f columns, and a one-column scalar phase i^gamma becomes i^(f*gamma). Reusing the one-column global phase unchanged would be incorrect. Finally form the owner matrix C_f with entries A_ij K_i,f^-1 K_j,f. One does not tensor the whole 224-by-224 owner matrix and does not assert that tensor powers preserve sums. Instead the finite scalar owner program is evaluated directly in the algebra of these lifted address operators. This proves the central ABI and local gauge identities at every positive width. + +Run `python3 -I -B research/coded-native-caller/normalizers.py` or its optimized `-O` form. The checker authenticates the decompressed actual native payload, CODE.json and retained Clifford source before executing the latter. It verifies all 112 real signed normalizers, 57,344 explicit weight-congruence addresses, 896 forward/backward monomial wrappers and eight exact frame/block identities per port, including absolute phase. Each emitted wrapper is separately lowered to a literal P/D/X/phase-only word and checked against its defining expression by exact tableau and absolute-phase state. No C gate remains in an emitted wrapper. The independent incoming-column and outgoing-row identities imply all 5,824 nonzero off-diagonal code blocks, without sampling those pairs. It also executes the eight-mode recoding on all 112 arbitrary-input basis columns in both directions. Omitting the essential signed phase is rejected at every affected port. The default command compares a regenerated mathematical receipt and performs no writes; `--write` is the explicit authoring path. + +Source pins: canonical main 624de9dc66858af0945e5f8a0942488d62280d43, `research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz`, decompressed SHA-256 cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd; PR4929 head 361f5d4100640177d6a983dd2f336021c75bfd5e, `research/native-center-free-code/CODE.json`, SHA-256 8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0; canonical `research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py`, SHA-256 2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962. Gzip container bytes are not substituted for decompressed source identity. + +Credit Dugongue's PR4929 for the coded producer and stable code; Cinna Davis's PR4694/4698 and the original cache/helper construction; Cao Yifan's PR4610 native word; the retained zxv, Jacob Alan Sussman, Cinna Davis and Clifford/native/compiler lineage. The exact canonical-frame implementation and phase conventions are retained source material. The constructive real centralizing normalizers, their explicit lifted words, X-only raw-dual convention and costed local code gauges are the additions here. New work is Apache-2.0 and has substantial OpenAI Codex assistance; no formal-kernel or independent human acceptance is asserted. diff --git a/research/coupled-provider-independent-audit/capsule/agents/budget/envelope-inputs/SOURCES.json b/research/coupled-provider-independent-audit/capsule/agents/budget/envelope-inputs/SOURCES.json new file mode 100644 index 0000000000..5be363adf2 --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/agents/budget/envelope-inputs/SOURCES.json @@ -0,0 +1,20 @@ +[ + { + "head": "3348fccea855082786d5f0fc5558b73d4974e745", + "source_path": "research/coded-native-caller/clifford_exact.py", + "local": "envelope-inputs/clifford_exact.py", + "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962" + }, + { + "head": "3348fccea855082786d5f0fc5558b73d4974e745", + "source_path": "research/coded-native-caller/PHYSICAL.md", + "local": "envelope-inputs/PHYSICAL.md", + "sha256": "4321b159ff8d3fe705419adaaa1beef75606e869e34341bda553f17d598a6078" + }, + { + "head": "3348fccea855082786d5f0fc5558b73d4974e745", + "source_path": "research/native-rank8-helper-provider/verify.py", + "local": "envelope-inputs/verify.py", + "sha256": "121d87787c0f76bd530b6e1682704a311e96dfb33d787bea2ba29a1d0e5ee23e" + } +] diff --git a/research/coupled-provider-independent-audit/capsule/agents/budget/envelope-inputs/clifford_exact.py b/research/coupled-provider-independent-audit/capsule/agents/budget/envelope-inputs/clifford_exact.py new file mode 100644 index 0000000000..166841a037 --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/agents/budget/envelope-inputs/clifford_exact.py @@ -0,0 +1,149 @@ +"""Small exact Gaussian-dyadic Clifford compiler, independent of gx internals. +Paulis use i^p X^x Z^z. State vectors use integer Gaussian numerators / 2^d. +The tableau is supplemented by a literal circuit, so global phases are kept. +""" +from dataclasses import dataclass + +def parity(x):return x.bit_count()&1 +def rank(rows): + p={} + for x in rows: + while x: + b=x.bit_length()-1 + if b not in p:p[b]=x;break + x^=p[b] + return len(p) +def transpose(rows,n):return tuple(sum(((rows[j]>>i)&1)<>j&1);a[j],a[k]=a[k],a[j] + for i in range(n): + if i!=j and a[i]>>j&1:a[i]^=a[j] + assert [r&((1<>n for r in a) +def basis_extend(cols,n): + out=[] + for x in list(cols)+[1<len(out):out.append(x) + assert len(out)==n + return tuple(out) +def nullspace(rows,n): + a=list(rows);p=[];k=0 + for j in range(n): + t=next((i for i in range(k,len(a)) if a[i]>>j&1),None) + if t is None:continue + a[t],a[k]=a[k],a[t] + for i in range(len(a)): + if i!=k and a[i]>>j&1:a[i]^=a[k] + p.append(j);k+=1 + return tuple((1<>j)&1)<>i&1:out=pmul(out,T[i]) + for i in range(n): + if z>>i&1:out=pmul(out,T[n+i]) + return out +def compose(A,B):return tuple(apply(A,p) for p in B) +def inverse(T): + n=len(T)//2;cols=[x|(z<>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4)) + return tuple(out) +def qvalue(Q,alpha,x,n): + return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4 +def mul_i(a,p): + x,y=a;p%=4 + return [(x,y),(-y,x),(-x,-y),(y,-x)][p] +@dataclass +class Op: + n:int + tab:tuple + circuit:list + def then(self,b): + assert self.n==b.n + return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit) + def adjoint(self): + circ=[] + for e in reversed(self.circuit): + if e[0]=='P':circ.append(('P',inv(e[1],self.n))) + elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2]))) + elif e[0]=='C':circ.append(('C',e[1],-e[2])) + elif e[0]=='phase':circ.append(('phase',(-e[1])%4)) + else:circ.append(e) + return Op(self.n,inverse(self.tab),circ) + def zero_state(self,basis=0): + N=1<>i)&1 for i in range(n)) + assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n)) + return Op(n,tuple([(1<>i&1 else 0,1<>i&1 else 0) for i in range(n)]),[('C',q,sgn)]) +def xgate(n,b):return Op(n,tuple([(1<>i)&1)) for i in range(n)]),[('X',b)]) +def fourier(n,axes=None): + out=ident(n) + for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<len(selected):picks.append(j);selected.append(x) + assert len(picks)==r and all(x>>r==0 for x in Bcols) + Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1<= 632, 'persistent CLEAR forbidden') + dirt = {k: v for k, v in rows[dst].items() if k[0] >= 632} + if dirt: + dirt_clears.append((dst, dirt)) + rows[dst], charts[dst] = {}, chart + else: + need(charts[dst] == chart, 'destination chart') + if op[0] in ('copy', 'add'): + src = addr(op[2]) + need(charts[src] == chart, 'source chart') + if op[0] == 'copy': + need(dst >= 632 and not rows[dst], 'COPY must fill owned zero') + rows[dst] = dict(rows[src]) + else: + need(dst != src, 'ADD self alias') + add(rows[dst], rows[src], F(op[3], op[4])) + else: + need(op[0] == 'scale', 'unknown scalar operation') + factor = F(op[2], op[3]) + rows[dst] = {k: v * factor for k, v in rows[dst].items() if v * factor} + elif kind == 'warp': + _, ref, warp, old, new = e + dst = addr(ref) + need(charts[dst] == old, 'warp chart') + symbol = (1 if warp > 0 else -1) * (abs(warp) + 1000000) + after = {} + for (owner, word), value in rows[dst].items(): + word = word[1:] if word and word[0] == -symbol else (symbol,) + word + add(after, {(owner, word): value}) + rows[dst], charts[dst] = after, new + elif kind in ('climb', 'center'): + if kind == 'climb': + _, _, dst, old, new, rank = e + expected = len(c['frames'][new]) - len(c['frames'][old]) + else: + _, dst, old, new, rank = e + dst += 632 + expected = abs(len(c['frames'][new]) - len(c['frames'][old])) + need(charts[dst] == old and rank == expected and rank > 0, + 'paid child chart/rank') + charts[dst] = new + paid[rank] += 1 + elif kind == 'zero_retag': + _, dst, old, new = e + need(charts[dst] == old and not rows[dst], 'zero retag has nonzero input') + zeros.append([event, dst, old, new]) + charts[dst] = new + else: + # Inherited source annotations / physical boundary bindings. The + # predecessor's normalized-row convention treats these as no row + # update; they remain byte-for-byte records in the emitted word. + # New physical boundaries are checked separately below, with phase. + need(kind in ('phase', 'adapter', 'residual_adapter'), 'unknown source record') + for at, owner in snapshots: + if event == at: + saved[(at, owner)] = (charts[owner], dict(rows[owner])) + return rows, charts, paid, scalar, zeros, dirt_clears, saved + + +def scalar(row): + need(all(not word for _, word in row), 'endpoint has unreduced native word') + return {j: a for (j, _), a in row.items()} + + +def rewrite(source, witness): + centers = {r['event']: i for i, r in enumerate(witness)} + late = {r['zero_event']: i for i, r in enumerate(witness)} + caches = {r['cached_event']: i for i, r in enumerate(witness)} + need(len(centers) == len(late) == len(caches) == 8, 'distinct eight sites') + need(max(caches) < min(centers), 'caches must precede all replacements') + word = [] + for event, op in enumerate(source['programs']['backward']): + if event in centers: + i = centers[event] + frame = witness[i]['frame'] + need(op == ['center', 0, 0, frame, 8], 'center source binding') + word += [['scalar', ['clear', ['C', 0]], frame], + ['scalar', ['copy', ['C', 0], ['C', i + 1]], frame]] + elif event in late: + r = witness[late[event]] + need(op == ['climb', 'warp_retimed', r['zero_role'], r['frame'], 1, 1], + 'late H1 source binding') + word.append(['zero_retag', r['zero_role'], r['frame'], 1]) + else: + word.append(op) + if event in caches: + i = caches[event] + r = witness[i] + word += [['scalar', ['clear', ['C', i + 1]], r['frame']], + ['scalar', ['copy', ['C', i + 1], ['L', r['cached_role']]], r['frame']]] + return {'source_sha256': SOURCE_HASH, 'direction': 'backward', 'word': word} + + +def inverse(matrix): + n = len(matrix) + a, b, ops = [dict(r) for r in matrix], [{j: F(1)} for j in range(n)], [] + for j in range(n): + k = next((i for i in range(j, n) if a[i].get(j)), None) + need(k is not None, 'singular basis') + if k != j: + a[j], a[k], b[j], b[k] = a[k], a[j], b[k], b[j] + ops.append(['swap', j, k]) + factor = 1 / a[j][j] + if factor != 1: + a[j] = {k: factor * v for k, v in a[j].items()} + b[j] = {k: factor * v for k, v in b[j].items()} + ops.append(['scale', j, str(factor)]) + for i in range(n): + if i == j or not a[i].get(j): + continue + factor = -a[i][j] + add(a[i], a[j], factor) + add(b[i], b[j], factor) + ops.append(['add', i, j, str(factor)]) + need(a == [{j: F(1)} for j in range(n)], 'basis reduction') + return b, ops + + +def ordinary(ops, roles, reverse=False): + out = [] + for e in reversed(ops) if reverse else ops: + if e[0] == 'swap': + a, b = roles[e[1]], roles[e[2]] + out += [['add', a, b, '1'], ['add', b, a, '-1'], + ['add', a, b, '1'], ['scale', b, '-1']] + elif e[0] == 'scale': + v = F(e[2]) + out.append(['scale', roles[e[1]], str(1 / v if reverse else v)]) + else: + v = F(e[3]) + out.append(['add', roles[e[1]], roles[e[2]], str(-v if reverse else v)]) + return out + + +def apply_ordinary(program, rows): + rows = [dict(r) for r in rows] + for e in program: + if e[0] == 'add': + need(e[1] != e[2], 'ordinary ADD alias') + add(rows[e[1]], rows[e[2]], F(e[3])) + else: + need(e[0] == 'scale', 'ordinary operation') + rows[e[1]] = {j: a * F(e[2]) for j, a in rows[e[1]].items() if a * F(e[2])} + return rows + + +def authenticate(): + pins = json.loads((HERE / 'SOURCES.json').read_text()) + for r in pins['files']: + if r['usage'] == 'input': + need(sha256((ROOT / r['path']).read_bytes()).hexdigest() == r['sha256'], + 'changed scientific input: ' + r['path']) + raw = gzip.decompress((ROOT / 'research/native-center-free-code/SOURCE-WORD.json.gz').read_bytes()) + need(sha256(raw).hexdigest() == SOURCE_HASH, 'native payload') + need(sha256((HERE / 'WITNESS.json').read_bytes()).hexdigest() == WITNESS_HASH, + 'Ali verbatim candidate provenance') + cp = ROOT / 'research/coded-native-caller/clifford_exact.py' + spec = importlib.util.spec_from_file_location('rank8_provider_clifford', cp) + ce = importlib.util.module_from_spec(spec) + sys.modules[spec.name] = ce + spec.loader.exec_module(ce) + return json.loads(raw), json.loads((HERE / 'WITNESS.json').read_text()), ce + + +def main(emit=False): + started = time.monotonic() + source, witness, ce = authenticate() + c = source['canonical'] + normal = json.loads((ROOT / 'research/coded-native-caller/NORMALIZERS.json').read_text()) + M = normal['mode_columns'] + A = [[F(a) for a in r] for r in json.loads((ROOT / 'research/native-center-free-code/CODE.json').read_text())['A']] + need(c['start'][112:224] == [0] * 112, 'main Y inputs have ground chart') + need(len(M) == 8 and all(len(r) == 112 for r in M), 'M dimensions') + need(all(sum(M[k][i] * M[l][i] for i in range(112)) == 56 * int(k == l) + for k in range(8) for l in range(8)), 'M Gram') + need(all(A[i][j] == F(i == j) - sum(F(M[k][i] * M[k][j], 4) for k in range(8)) + for i in range(112) for j in range(112)), 'A factorization') + original = replay(source['programs']['backward'], c, 633, + [(r['cached_event'], r['cached_role']) for r in witness]) + oldrows, oldcharts, oldpaid, oldscalar = original[:4] + expected = [{(j, ()): F(1)} for j in range(632)] + for j in range(112): + expected[j][(j + 112, ())] = F(-1) + need(oldrows[:632] == expected and not oldrows[632], 'original 632-row endpoint') + need(oldcharts[:632] == c['final'], 'original exit charts') + + centerfree = [['scalar', ['clear', ['C', e[1]]], e[3]] if e[0] == 'center' else e + for e in source['programs']['backward']] + cf = replay(centerfree, c, 633) + cfrows = [scalar(r) for r in cf[0]] + need(cf[1][:632] == c['final'] and not cfrows[632], 'center-free charts/owned') + P = [[-cfrows[j + 224].get(i + 112, F(0)) for i in range(112)] for j in range(408)] + B = [[sum(P[j][i] * M[k][i] for i in range(112)) / 56 for j in range(408)] for k in range(8)] + need(all(P[j][i] == sum(B[k][j] * M[k][i] for k in range(8)) + for j in range(408) for i in range(112)), 'full native coupling factorization') + for j in range(632): + row = {j: F(1)} + if j < 112: + for i in range(112): + if A[i][j]: + row[i + 112] = -A[i][j] + elif j >= 224: + for i, a in enumerate(P[j - 224]): + if a: + row[i + 112] = -a + need(cfrows[j] == row, 'center-free complete scalar endpoint') + + delta = [{j - 224: F(a) for j, a in r['relation']} for r in witness] + coupling = [[sum(a * B[k][j] for j, a in d.items()) for k in range(8)] for d in delta] + need(all(sum(bool(a) for a in r) == 1 and set(r) <= {F(0), F(1), F(-1)} + for r in coupling), 'candidate is not a signed retraction') + perm = [next(k for k, a in enumerate(r) if a) for r in coupling] + sign = [coupling[i][perm[i]] for i in range(8)] + need(sorted(perm) == list(range(8)), 'retraction permutation') + E = [{} for _ in range(8)] + for i, k in enumerate(perm): + E[k] = {j: sign[i] * a for j, a in delta[i].items()} + row = {(j + 224, ()): F(witness[i]['zero_factor']) * a for j, a in delta[i].items()} + for j in range(112): + a = -F(witness[i]['zero_factor']) * sign[i] * M[k][j] + if a: + row[(j + 112, ())] = a + need(original[6][(witness[i]['cached_event'], witness[i]['cached_role'])] + == (witness[i]['frame'], row), 'fresh original cached row binding') + need(all(sum(a * B[l][j] for j, a in E[k].items()) == int(k == l) + for k in range(8) for l in range(8)), 'E B^T identity') + active = sorted(set(j for r in B for j, a in enumerate(r) if a) | set(j for r in E for j in r)) + roles, index = [224 + j for j in active], {j: i for i, j in enumerate(active)} + need(len(active) == 122 and all(c['start'][j] == 0 and c['final'][j] == 1 for j in roles), + 'basis requires 122 actual cold H9 owners') + J = [j - 224 for j in MODE] + L = [{} for _ in active] + for k, j in enumerate(J): + for r in active: + if B[k][r]: + L[index[r]][index[j]] = B[k][r] + for j in active: + if j in J: + continue + for r in active: + a = F(r == j) - sum(B[k][r] * E[k].get(j, F(0)) for k in range(8)) + if a: + L[index[r]][index[j]] = a + Li, ops = inverse(L) + for left, right in ((L, Li), (Li, L)): + for i, row in enumerate(left): + product = {} + for j, a in row.items(): + add(product, right[j], a) + need(product == {i: F(1)}, 'two-sided basis inverse') + for k, row in enumerate(E): + product = {} + for j, a in row.items(): + add(product, L[index[j]], a) + need(product == {index[J[k]]: F(1)}, 'E L mode selection') + need(all(sum(a * B[k][active[j]] for j, a in row.items()) == int(i == index[J[k]]) + for i, row in enumerate(Li) for k in range(8)), 'Li B mode embedding') + need(all(a.denominator & (a.denominator - 1) == 0 + for matrix in (L, Li) for row in matrix for a in row.values()), 'dyadic basis') + entrance, exitword = ordinary(ops, roles, True), ordinary(ops, roles) + identity = [{j: F(1)} for j in range(632)] + entered = apply_ordinary(entrance, identity) + def check_basis(rows): + for i, j in enumerate(roles): + need(rows[j] == {roles[k]: a for k, a in L[i].items()}, 'literal L program') + check_basis(entered) + need(apply_ordinary(exitword, entered) == identity, 'literal Li program') + need(Counter(e[0] for e in entrance) == Counter(add=822, scale=12), 'basis program bill') + need(Counter(e[0] for e in exitword) == Counter(add=822, scale=12), 'inverse program bill') + + changed = rewrite(source, witness) + frozen_word = json.loads(gzip.decompress((HERE / 'WORD.json.gz').read_bytes())) + need(changed == frozen_word, 'committed exact word differs from source rewrite') + result = replay(changed['word'], c, 641) + rawrows, charts, paid, scalars, zeros, dirt = result[:6] + need(charts[:632] == c['final'] and not rawrows[632], 'changed persistent charts/C0') + need(paid == PAID and oldpaid == paid + Counter({1: 8, 8: 8}), 'paid children') + need(scalars == oldscalar + Counter(clear=16, copy=16), 'source ordinary delta') + need(len(zeros) == 8, 'eight exact zero retags') + need(len(dirt) == 9 and {j for j, _ in dirt} == set(range(632, 641)) + and all(d == {(j, ()): F(1)} for j, d in dirt), 'all arbitrary owned dirt cleared') + need(not any(j >= 632 for row in rawrows for j, _ in row), 'owned dirt leaked') + need(sum(rawrows[j] != oldrows[j] for j in range(632)) == 218, 'changed endpoint count') + endpoint = [] + for row in rawrows: + out = {} + for j, a in scalar(row).items(): + add(out, entered[j], a) + endpoint.append(out) + endpoint = apply_ordinary(exitword, endpoint) + for j in range(632): + expected = {} if j in MODE else {j: F(1)} + if j < 112: + expected[j + 112] = F(-1) + for k in range(8): + if M[k][j]: + expected[MODE[k]] = F(M[k][j], 4) + need(endpoint[j] == expected, 'composed all-owner endpoint at ' + str(j)) + def check_cache(i, row): + r, k = witness[i], perm[i] + factor = F(r['zero_factor']) * sign[i] + expected = {MODE[k]: factor} + for j in range(112): + if M[k][j]: + expected[j + 112] = -factor * M[k][j] + need(row == expected and charts[633 + i] == r['frame'], 'composed retained cache') + for i in range(8): + check_cache(i, endpoint[633 + i]) + first_cache = dict(endpoint[633]) + + def conjugate(op): + circuit = [] + for e in op.circuit: + if e[0] == 'D': + circuit.append(('D', e[1], tuple((-x) % 4 for x in e[2]))) + elif e[0] == 'C': + circuit.append(('C', e[1], -e[2])) + elif e[0] == 'phase': + circuit.append(('phase', (-e[1]) % 4)) + else: + circuit.append(e) + return ce.Op(9, tuple((x, z, -p % 4) for x, z, p in op.tab), circuit) + + @lru_cache(None) + def frame(j, back=False): + op = ce.canonical_frame(9, c['frames'][j]) + return conjugate(op) if back else op + + def literal(word): + op = ce.ident(9) + for e in word: + if e[0] == 'P': + part = ce.perm(9, tuple(e[1])) + elif e[0] == 'D': + part = ce.diag(9, tuple(e[1]), tuple(e[2])) + elif e[0] == 'X': + part = ce.xgate(9, e[1]) + elif e[0] == 'phase': + part = ce.Op(9, ce.identity(9), [('phase', e[1])]) + else: + raise ValueError('boundary contains a Gaussian gate') + op = op.then(part) + return op + + def equal(a, b): + return a.tab == b.tab and a.zero_state() == b.zero_state() + + def rank(op): + return ce.rank([x for x, _, _ in op.tab[9:]]) + + def receipt(op): + vec, den = op.zero_state() + j = next(j for j, a in enumerate(vec) if a != (0, 0)) + return {'literal_word': op.circuit, 'signed_tableau': op.tab, + 'zero_column_anchor': {'index': j, 'gaussian_numerator': vec[j], + 'denominator_power2': den}} + + def compile_monomial(op): + need(rank(op) == 0, 'nonmonomial boundary map') + compiled, _ = ce.monomial(op) + need(equal(compiled, op) and equal(literal(compiled.circuit), op), + 'literal phase-correct monomial compilation') + return compiled + + R, D = frame(1), ce.fourier(9, range(1, 9)) + Km, N = [None] * 8, [None] * 8 + records = [None] * 8 + for i, r in enumerate(witness): + k = perm[i] + candidates = [q for q in range(1, 512) + if all(ce.parity(q & v) == 0 for v in c['frames'][r['frame']])] + need(len(candidates) == 1, 'rank-eight missing line') + q = candidates[0] + need(q.bit_count() % 2 == 1 and q != 511, 'odd noncharacteristic line') + if not q & 1: + transvections = [1 ^ q] + else: + j = next(j for j in range(1, 9) if not q >> j & 1) + transvections = [1 ^ (1 << j), (1 << j) ^ q] + cols = [] + for j in range(9): + x = 1 << j + for v in transvections: + x ^= v if ce.parity(x & v) else 0 + cols.append(x) + G = ce.transpose(cols, 9) + z = sum((((row.bit_count() - 1) // 2) & 1) << j for j, row in enumerate(G)) + K = ce.perm(9, G).then(ce.diag(9, (0,) * 9, tuple(2 * ((z >> j) & 1) for j in range(9)))) + need(equal(K.then(R), R.then(K)), 'mode K/R absolute phase') + need(all((ce.mv(ce.transpose(G, 9), x).bit_count() - x.bit_count() + - 2 * ce.parity(z & x)) % 4 == 0 for x in range(512)), 'K weight congruence') + F8 = frame(r['frame'], True) + need(rank(F8) == 8, 'actual cache rank') + Km[k] = compile_monomial(K) + N[k] = compile_monomial(K.then(F8).adjoint().then(D)) + records[k] = {'mode': k, 'owner': MODE[k], 'cache_slot': 633 + i, + 'witness_row': i, 'frame': r['frame'], 'missing_line': q, + 'cache_scalar': str(1 / (2 * F(r['zero_factor']) * sign[i])), + 'input_K': receipt(Km[k]), 'output_N': receipt(N[k])} + Kp = [literal(r['K_word']) for r in normal['ports']] + checks = Counter() + for j, port in enumerate(normal['ports']): + need(port['port'] == j and rank(Kp[j]) == 0 and equal(Kp[j].then(R), R.then(Kp[j])), + 'port K binding and R commutation') + wrappers = port['compiled_wrappers'] + BX, BY, OX, OY = [literal(wrappers[key]['word']) for key in + ('backward_input_X', 'backward_input_Y', 'backward_output_X', 'backward_output_Y')] + birth, final, finalY = frame(c['start'][j], True), frame(c['final'][j], True), frame(c['final'][112 + j], True) + need(equal(BX.then(birth.adjoint()).then(final).then(OX), D), 'X diagonal physical block') + need(equal(BY.then(finalY).then(OY), D), 'Y diagonal physical block') + need(equal(BY.then(final).then(OX), R), 'main shear physical block') + checks['main_diagonal_and_shear'] += 3 + for k in range(8): + if not M[k][j]: + continue + need(equal(Km[k].then(final).then(OX), Km[k].then(Kp[j].adjoint()).then(R)), + 'helper-to-main physical coupling') + F8 = frame(records[k]['frame'], True) + need(equal(BY.then(F8).then(N[k]), Kp[j].then(Km[k].adjoint()).then(D)), + 'main-to-helper physical coupling') + checks['two_coupling_directions'] += 2 + for k in range(8): + need(equal(Km[k].then(frame(records[k]['frame'], True)).then(N[k]), D), + 'helper diagonal physical block') + checks['helper_diagonal'] += 1 + need(dict(checks) == {'main_diagonal_and_shear': 336, 'two_coupling_directions': 896, + 'helper_diagonal': 8}, '1,240 physical bindings') + autonomous = Counter(len(c['frames'][c['final'][j]]) - len(c['frames'][c['start'][j]]) + for j in range(224, 632) if j not in MODE) + need(autonomous == Counter({4: 28, 7: 7, 8: 47, 9: 318}), '400 retained native helper jobs') + # Physical normalization precedes a complete-field SWAP, including chart tags. + for r in records: + owner, cache = r['owner'], r['cache_slot'] + need(not endpoint[owner], 'SWAP destination must be identically zero') + endpoint[owner], endpoint[cache] = endpoint[cache], endpoint[owner] + need(all(not endpoint[j] for j in range(632, 641)), 'all owned outputs clean') + + # Failure controls invoke the same predicates as the construction. + controls = [] + bad_c = dict(c) + bad_c['start'] = c['start'][:] + bad_c['start'][0] = 0 + try: + replay([['zero_retag', 0, 0, 1]], bad_c, 641) + except ValueError as e: + need(str(e) == 'zero retag has nonzero input', 'wrong rejection') + controls.append('nonzero zero-retag rejected') + need(len(controls) == 1, 'zero-retag control accepted') + corrupted = [e[:] for e in entrance] + mutated = next(e for e in corrupted if e[0] == 'add') + mutated[3] = str(F(mutated[3]) + 1) + try: + check_basis(apply_ordinary(corrupted, identity)) + except ValueError as e: + need(str(e) == 'literal L program', 'wrong basis rejection') + controls.append('one altered basis ADD coefficient rejected') + need(len(controls) == 2, 'basis coefficient mutation accepted') + badN = ce.Op(9, N[0].tab, N[0].circuit + [('phase', 1)]) + need(badN.tab == N[0].tab and not equal(Km[0].then(frame(records[0]['frame'], True)).then(badN), D), + 'phase-only error escaped') + controls.append('same-tableau phase-only cache error rejected') + wrong = dict(first_cache) + add(wrong, {MODE[perm[0]]: F(1)}) + try: + check_cache(0, wrong) + except ValueError as e: + need(str(e) == 'composed retained cache', 'wrong cache rejection') + controls.append('one altered saved-cache coefficient rejected') + need(len(controls) == 4, 'saved-cache coefficient mutation accepted') + + # An explicit, conservative local error-amplification bound for this finite + # schedule. Gaussian and monomial field maps have Euclidean norm one. + def log2_bound(a): + a, exponent = max(F(1), a), 0 + while a > 1: + a /= 2 + exponent += 1 + return exponent + amplification = 0 + for e in changed['word']: + if e[0] == 'scalar': + op = e[1] + if op[0] == 'add': + amplification += log2_bound(1 + abs(F(op[3], op[4]))) + elif op[0] == 'scale': + amplification += log2_bound(abs(F(op[2], op[3]))) + for e in entrance + exitword: + amplification += log2_bound(1 + abs(F(e[3]))) if e[0] == 'add' else log2_bound(abs(F(e[2]))) + amplification += 8 * log2_bound(F(2)) + amplification += sum(log2_bound(abs(F(r['cache_scalar']))) for r in records) + + artifact = { + 'schema_version': 1, 'source_payload_sha256': SOURCE_HASH, + 'candidate_witness_sha256': WITNESS_HASH, + 'word_payload_sha256': sha256(gzip.decompress((HERE / 'WORD.json.gz').read_bytes())).hexdigest(), + 'basis_roles': roles, 'mode_owners': MODE, + 'candidate_mode_permutation': perm, 'candidate_mode_signs': list(map(str, sign)), + 'canonical_retraction_E': [enc(row) for row in E], + 'input_basis_program': entrance, 'output_basis_program': exitword, + 'mode_boundaries': records, + 'ordered_schedule': [ + 'Main input wrappers: NORMALIZERS.ports[j].compiled_wrappers.backward_input_X/Y.', + 'On each mode owner apply input_K and scalar 2; run input_basis_program.', + 'Run every instruction of WORD.json.gz; C0..C8 initially arbitrary.', + 'Run output_basis_program on the 122 persistent common-chart helpers.', + 'For each mode apply cache_scalar and output_N to its owned cache; SWAP the whole field and chart with its zero original owner; CLEAR the owned zero.', + 'Main output wrappers: NORMALIZERS.ports[j].compiled_wrappers.backward_output_X/Y.' + ], + 'paid': dict(sorted(paid.items())), 'autonomous_native_helpers': dict(sorted(autonomous.items())), + 'owned_fields': {'count': 9, 'initial_values': 'arbitrary', 'final_values': 'zero', 'productive_credit': 0}, + 'added_ordinary_work_vs_original_raw_source': { + 'ADD': 1644, 'SCALE': 40, 'COPY': 16, 'CLEAR': 24, 'whole_field_SWAP': 8, + 'monomial_field_maps': 464, + 'monomial_breakdown': {'fused_inherited_main_standardizers': 448, 'mode_inputs': 8, 'cache_outputs': 8}}, + 'local_error_amplification_power2_bound': amplification, + 'source_original_scalar_counts': dict(sorted(oldscalar.items())), + 'source_changed_scalar_counts': dict(sorted(scalars.items())), + 'physical_phase_bindings': dict(checks), 'exact_zero_retags': zeros, + 'formula': {'X': 'D x - R y + R W h', 'Y': 'D y', 'H': 'D (h - Z y)', + 'W': 'diag(K_port^-1) M diag(K_mode)/2', + 'Z': 'diag(K_mode^-1) M^T diag(K_port)/2'}, + 'failure_controls': controls, + 'scope': 'Changed coupled backward provider. No autonomous credit for eight coupled outputs; no completed caller, inverse/transpose implementation, new kappa or selected-result change.' + } + artifact = json.loads(json.dumps(artifact)) + path = HERE / 'PROVIDER.json' + if emit: + path.write_text(json.dumps(artifact, indent=2) + '\n') + else: + need(json.loads(path.read_text()) == artifact, 'committed boundary recipe differs from replay') + print('PASS_NATIVE_RANK8_HELPER_PROVIDER ' + json.dumps({ + 'original_inputs': 632, 'arbitrary_owned_inputs': 9, 'owned_outputs_zero': 9, + 'autonomous_helpers': 400, 'coupled_helpers': 8, 'paid': dict(sorted(paid.items())), + 'phase_bindings': sum(checks.values()), 'seconds': round(time.monotonic() - started, 3)})) + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--emit', action='store_true', help='regenerate the package-local boundary recipe') + main(parser.parse_args().emit) diff --git a/research/coupled-provider-independent-audit/capsule/agents/budget/independent_local_envelope.py b/research/coupled-provider-independent-audit/capsule/agents/budget/independent_local_envelope.py new file mode 100644 index 0000000000..fa33ce8e35 --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/agents/budget/independent_local_envelope.py @@ -0,0 +1,92 @@ +#!/usr/bin/env python3 +"""Fresh literal one-provider envelope, two norms; no submitted Python execution. +Max-field Euclidean norm matches the author's stated geometry. Joint-field +Euclidean norm requires a COPY factor. No caller/compiler/precision admission. +Chris R/Clear1nsight with substantial OpenAI Codex assistance; retain source credit. +""" +from pathlib import Path +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +import argparse,gzip,json,resource,time +HERE=Path(__file__).resolve().parent + +def need(v,s): + if not v:raise ValueError(s) +def load(p): + b=p.read_bytes();return json.loads(gzip.decompress(b)if p.suffix=='.gz'else b) +def ceil_log2(q): + q=max(Q(1),q);e=0 + while q>1:q/=2;e+=1 + return e + +def rank(rows): + piv={} + for x in rows: + while x: + b=x.bit_length()-1 + if b in piv:x^=piv[b] + else:piv[b]=x;break + return len(piv) +def exponent(g,geometry): + if g[0]=='add':return ceil_log2(1+abs(Q(g[-2],g[-1]))) + if g[0]=='scale':return ceil_log2(abs(Q(g[-2],g[-1]))) + if g[0]=='copy':return int(geometry=='joint_field_l2') + need(g[0]in('clear','swap','unitary','zero_retag','annotation'),'unknown geometry gate') + return 0 + +def main(): + ap=argparse.ArgumentParser();ap.add_argument('--output',type=Path,required=True);args=ap.parse_args();start=time.monotonic();resource.setrlimit(resource.RLIMIT_AS,(128*1024*1024,128*1024*1024)) + pins=load(HERE/'inputs/ALL-PINS.json')+load(HERE/'envelope-inputs/SOURCES.json') + for pin in pins:need(sha256((HERE/pin['local']).read_bytes()).hexdigest()==pin['sha256'],'changed norm input '+pin['local']) + a=load(HERE/'inputs/PROVIDER.json');word=load(HERE/'inputs/WORD.json.gz')['word'];source=load(HERE/'inputs/SOURCE-WORD.json.gz');n=load(HERE/'inputs/NORMALIZERS.json');c=source['canonical'] + # Every frame is an independent subspace basis within the same nine-axis field. + need(all(len(v)<=9 and rank(v)==len(v)and all(00,'nonpositive denominator interval');return mul(a,(1/b[1],1/b[0])) +def difference(a,b):return a[0]-b[1],a[1]-b[0] +def logsmall(x): + z=(x-1)/(x+1);need(0<=z<=Q(1,3),'logsmall outside [1,2]') + term=z;s=Q(0) + for j in range(60):s+=2*term/(2*j+1);term*=z*z + return down(s),up(s+2*term/(121*(1-z*z))) +@lru_cache(None) +def logint(n): + need(isinstance(n,int) and n>=1,'rank must be positive integer') + k=n.bit_length()-1;a,b=logsmall(Q(n,2**k));c,d=logsmall(Q(2));return a+k*c,b+k*d +def exponential(x): + if x<0: + a,b=exponential(-x);return down(1/b),up(1/a) + shift=0 + while x>Q(1,32):x/=2;shift+=1 + term=s=Q(1) + for j in range(1,33):term*=x/j;s+=term + a,b=down(s),up(s+term*x/33/(1-x/34)) + for _ in range(shift):a,b=down(a*a),up(b*b) + return a,b +@lru_cache(None) +def power(rank,exponent): + exponent=Q(exponent);l,h=logint(rank);l,h=sorted((l*exponent,h*exponent));return exponential(l)[0],exponential(h)[1] +def profile(p): + for k,v in p.items(): + need((type(k) is int or type(k) is str and k.isdigit()) and type(v) is int,'rank/count must be exact integers') + p={int(k):v for k,v in p.items()};need(all(k>0 and v>=0 for k,v in p.items()),'invalid rank/count');return {k:v for k,v in p.items() if v} +def moment(p,e):return tuple(sum((n*power(r,Q(e))[i] for r,n in p.items()),Q(0)) for i in (0,1)) +def ledger(p): + k,b,a,q,ep,be,r,st,la=(p[x] for x in ['kappa','b','a','q','epsilon','beta','r0','stop','layout']) + si,ta=1-b,1-a;it=ta+(1-st)*max(si-ta,Q(0));lf=si+st*(1-si) + lm=1-(q+a)/2;xi=ep*(1+q)-Q(3,32)+la;key=be+1-ep + m=dict(main_transform=ep*q,global_coordinate_router=a,fused_gaussian=1-ep+q*be,group_bit_router=1-ep+a*be,group_scans=1-ep+be,boundary_algebraic_matrix=Q(3,32)+xi-ep,sparse_union_movement=xi+Q(1,2)-ep,polynomial_products=ep,microbox_face_corrections=1-(ep+be+48-128+2)) + c=dict(actual_bit_above_effective=p['bit_saving']-a,complex_above_effective=b-a,q_positive=q,complex_endpoint=b-q,q_below_effective=a-q,stop_positive=st,stop_below_one=1-st,leaf_saving_above_effective=(1-st)*b-a,q_below_internal=1-it-q,q_below_leaf=1-lf-q,lambda_above_tau=lm-ta,lambda_above_sigma=lm-si,lambda_above_internal=lm-it,lambda_prime_above_lambda=1-q-lm,lambda_prime_above_leaf=1-q-lf,epsilon_positive=ep,epsilon_below_one=1-ep,cap_above_band=xi-Q(1,2),cap_below_cell=ep-xi,group_positive=be,group_below_dimension=ep-be,support_router_span=1-be,group_gauge_power_slack=1-(2*xi-2)-r-be,actual_logarithmic_group_guard=1-(2*xi-2)-be,global_gamma_power_slack=1-ep-r,actual_logarithmic_gamma_guard=1-ep,alpha_logarithm_absorption=r,group_key_fits_record=1-key,membership_arithmetic_fits_record=1-be-2*(1-ep),microbox_halo_volume=128-48-be,positive_layout_slack=la,short_record_fallback=ep-a,complex_below_one_over_32=Q(1,32)-b,strassen_integer_power_gap=Q(2**45-7**16),theta_positive_polynomial_power=Q(2),cap_below_phase_cell_power=2-xi,halo_covers_generic_inverse_radius=Q(5),union_tag_work_per_visit_fits_record=1-be,union_header_fits_record=1-be,source_axis_superpolynomial=1-ep,gaussian_above_main=m['fused_gaussian']-m['main_transform'],new_complex_uniform_saving_above_b=p['complex_uniform_saving']-b,improvement_over_user_baseline=k-Q('.001730970419199163702738'),new_semantic_guard_with_C1_one=1-ep,fine_prime_halo_umbrella=Q(7,2)) + c.update({n+'_above_kappa':v-k for n,v in m.items()}) + f=dict(new_semantic_group_guard=1-be,new_BIT_row_stock_sublinear_in_active_group=be*Q(997,1000),fixed_halo_explicit_metadata_branch=128-48-ep-be-1,actual_new_BIT_stock_sublinear=be*(1-p['bit_atom'])) + return m,c,f + +def enc(x): + if isinstance(x,Q):return str(x) + if isinstance(x,dict):return {str(k):enc(v) for k,v in x.items()} + if isinstance(x,(tuple,list)):return [enc(v) for v in x] + return x + +def evaluate(targets,paid,config): + """Exact arithmetic only. Caller must bind invoice and prove source applicability. + + Supports the one fixed, source-certified tuple only. It does not promote a + model/profile or generic precision argument to physical/funded admission. + """ + start=time.monotonic();T,P=profile(targets),profile(paid) + need(T and P and max(T)==145 and max(P)<=145,'OUTSIDE_PROVED_DOMAIN: ambient rank145') + need(config['model']==MODEL,'OUTSIDE_PROVED_DOMAIN: model') + need(config['tuple']=={'power':1024,'cutoff':20,'floor':21,'tail_offset':'1/5','theta':'63/64','logarithm_power':1000},'OUTSIDE_PROVED_DOMAIN: tuple') + k,s=Q(config['kappa']),Q(config['tested']);lo,hi=map(Q,config['root_bracket']);reserve=Q(config['reserve']);t=1-s + need(00>signs[1][1],'strict root bracket fails') + signed={r:T.get(r,0)-P.get(r,0) for r in T.keys()|P.keys()} + der=[];away=[] + for i in range(16): + a,b=Q(i,320),Q(i+1,320);lower=Q(0) + for r,n in signed.items(): + z=mul(power(r,1-b if n>0 else 1-a),logint(r));lower+=n*z[0 if n>0 else 1] + der.append(lower) + for i in range(128): + a,b=Q(1,20)+Q(19*i,2560),Q(1,20)+Q(19*(i+1),2560) + away.append(sum(n*power(r,1-a if n>0 else 1-b)[1 if n>0 else 0] for r,n in signed.items())) + need(min(der)>0 and max(away)<0,'fixed-profile ceiling not established') + target,payment=moment(T,t),moment(P,t) + ratios={'alpha':divide(payment,target),'gamma':divide(moment(P,t+Q(1,5)),mul(power(20,Q(1,5)),target)),'delta':divide((Q(sum(T.values())*21),)*2,mul(power(20,s),target))} + need(reserve>0 and ratios['alpha'][1]<1-reserve,'unfunded reserve') + need(t+Q(1,5)>=1,'tail moment outside source domain') + need(ratios['gamma'][1]theta**1000,'initial_range':power(145,1024*s)[1]<2**1000} + gap=(s-k)/7;need(gap.numerator==1,'non-unit grid not supported') + step=gap.denominator + def wins(j):return (step*j+1)**1000<2**j + left,right=1,2 + while not wins(right):left,right=right,2*right + while right-left>1: + j=(left+right)//2 + if wins(j):right=j + else:left=j + j=right;H=step*j + capacity.update(height_domain=H>8*1024,height_success=wins(j),preceding_grid_fails=not wins(j-1)) + need(all(capacity.values()),'compiler capacity failure') + bit=config['ordinary_BIT'];atom,after,admitted=map(Q,(bit['atom'],bit['after_cover'],bit['admitted'])) + ordinary=(1-atom)*after+atom*Q('.0000384599') + need(atom==Q('.004') and ordinary==Q(bit['ordinary_saving']) and atom>ordinary>admitted>s and atom<1-ordinary,'BIT conversion/stock domain fails') + params=dict(kappa=k,tested_saving=s,complex_uniform_saving=k+6*gap,b=k+5*gap,a=k+4*gap,q=k+3*gap,bit_saving=admitted,bit_atom=atom,epsilon=1-gap,beta=1-3*gap,r0=gap/10,stop=gap,layout=gap,d=gap) + margins,strict,functional=ledger(params) + need(len(strict)==54 and len(functional)==4 and min(strict.values())>0 and min(functional.values())>0,'outer predicate failure') + controls={} + for n,patch in [('old_BIT',{'bit_saving':Q('.0027')}),('closed_uniform',{'complex_uniform_saving':params['b']}),('tested_as_final_endpoint',{'kappa':s}),('closed_epsilon',{'epsilon':Q(1)}),('missing_layout',{'layout':Q(0)}),('group_full_dimension',{'beta':params['epsilon']})]: + _,bad,func=ledger(dict(params,**patch));controls[n]=[x for x,v in (bad|func).items() if v<=0];need(controls[n],'mutation accepted: '+n) + controls['excess_reserve']=ratios['alpha'][0]>1-Q(1,10**7) + controls['insufficient_reserve_completion']=1/(1+1024*Q(1,10**13))+Q(4,2**32)>1 + controls['power128_tail_envelope']=1/(1+128*reserve)+4*Q(97,100)**128>1 + controls['preceding_grid_rejected']=not wins(j-1) + controls['raw_upper_has_negative_moment']=signs[1][1]<0 + need(all(controls.values()),'one arithmetic negative control failed') + return enc({'status':'PASS_INDEPENDENT_EXACT_ARITHMETIC_ONLY','model':MODEL,'targets':T,'paid':P,'productive_count':sum(T.values()),'paid_count':sum(P.values()),'rank_mass_surplus':sum(r*n for r,n in T.items())-sum(r*n for r,n in P.items()),'kappa':k,'tested':s,'root':{'bracket':[lo,hi],'width':hi-lo,'strict_signs':signs,'decreasing_domain':['0','1/20'],'derivative_upper':-min(der),'remaining_domain':['1/20','1'],'remaining_moment_upper':max(away),'scope':'necessary fixed-profile moment ceiling on 00 and d&(d-1)==0,'nonzero dyadic tariff') + if g[0]=='scale': + need(n&(n-1)==0,'scale is dyadic unit') + return 2*(abs(n.bit_length()-d.bit_length())+int(q<0)) + need(g[0]=='add','scalar tariff alphabet') + return 2*(3+n.bit_length()-1+n.bit_count()+d.bit_length()-1) +def basis_gate(g): + q=Q(g[-1]);return [g[0],g[1],g[2],q.numerator,q.denominator]if g[0]=='add'else[g[0],g[1],q.numerator,q.denominator] +def static(): + pins=read('ALL-PINS.json') + for p in pins: + need(sha256((HERE/p['local']).read_bytes()).hexdigest()==p['sha256'],'changed input: '+p['local']) + a,w,s,n=read('PROVIDER.json'),read('WORD.json.gz')['word'],read('SOURCE-WORD.json.gz'),read('NORMALIZERS.json') + original=s['programs']['backward'];c=s['canonical']; paid=Counter(e[-1]for e in w if e[0]in('climb','center')) + raw_orig=Counter(e[-1]for e in original if e[0]in('climb','center')) + mode=set(a['mode_owners']);need(len(mode)==8,'eight distinct mode owners') + helpers=Counter(len(c['frames'][c['final'][r]])-len(c['frames'][c['start'][r]])for r in range(224,632)if r not in mode) + need(paid==Counter({1:2193,2:412,3:510,4:127,5:40}),'literal paid census') + need(helpers==Counter({4:28,7:7,8:47,9:318}),'autonomous remainder frame census') + scalars=[e[1]for e in w if e[0]=='scalar']; old=[e[1]for e in original if e[0]=='scalar'] + bp=[a['input_basis_program'],a['output_basis_program']] + basis=[basis_gate(g)for p in bp for g in p] + # Boundary exterior factors: input 2; emitted cache_scalar is ALREADY output1/(2*f_i). + boundary=[] + for m in a['mode_boundaries']: + for q in [Q(2),Q(m['cache_scalar'])]:boundary.append(['scale',m['owner'],q.numerator,q.denominator]) + full=scalars+basis+boundary+[['clear',['C',i]]for i in range(1,9)] + counts=Counter(g[0]for g in full);need(counts==Counter(add=17917,scale=1204,copy=16,clear=40),'complete field operation census') + oldcounts=Counter(g[0]for g in old);delta=counts-oldcounts + # Read all monomial words literally; native physical validation belongs to another lane. + wrappers=[p['compiled_wrappers'][k]['word']for p in n['ports']for k in ['backward_input_X','backward_input_Y','backward_output_X','backward_output_Y']] + words=wrappers+[m[k]['literal_word']for m in a['mode_boundaries']for k in ['input_K','output_N']] + need(len(words)==464,'complete boundary monomial count') + gates=Counter(g[0]for w0 in words for g in w0);need(set(gates)<=set(['D','P','X','phase']),'monomial word alphabet') + kinds=Counter(e[0]for e in w);need(kinds['zero_retag']==8,'retag census') + units=sum(tariff(g)for g in full)+8*26 + need(sum(tariff(g)for g in old)==158168,'original raw source scalar tariff binding') + return dict(status='PASS_STATIC_LITERAL_BUDGET_INVENTORY',head=HEAD,paid=paid,autonomous_helpers=helpers,paid_calls=sum(paid.values()),paid_rank_mass=sum(r*v for r,v in paid.items()),autonomous_count=sum(helpers.values()),autonomous_rank_mass=sum(r*v for r,v in helpers.items()),coupled=dict(owners=8,diagonal_rank=8,autonomous_credit=0),original_paid=raw_orig,removed_paid=raw_orig-paid,original_scalar=oldcounts,changed_word_scalar=Counter(g[0]for g in scalars),basis_counts=[Counter(g[0]for g in p)for p in bp],basis_scalar_units=[sum(tariff(basis_gate(g))for g in p)for p in bp],boundary_scalar_units=sum(tariff(g)for g in boundary),complete_scalar=counts,added_scalar=delta,whole_field_swaps=8,monomial_maps=len(words),monomial_primitive_gates=gates,scalar_tariff_units_including_swaps=units,scalar_tariff_units_added=units-158168,retained_native_word_records=kinds,owned_fields=9,owned_credit=0,unknown_costs=['ordinary monomial maps at machine/tape level','retained native warps/adapters/phase annotations and recursive primitive internals','consumer closure recursive invoice and changed/lost targets','caller query/idles/boundaries/main diagonal','full caller finite precision/movement/storage/compiler/outer funding'],scope='Static literal census and inherited scalar tariff only; source equation, endpoint and physical admission are separate gates') +def full_profile(paid,helpers): + ref=read('REFERENCE-5400-INVOICE.json');ctl=read('REFERENCE-5398-CONTROLLER.json');P,T=Counter(),Counter();events=Counter();idles=Counter() + for e in ctl['physical_events']: + events[e[0]]+=1 + if e[0]=='LOCAL':need(e[3] is True,'all comparison providers backward');P.update(paid);T.update(helpers) + elif e[0]=='QUERY_SHEAR':P[1]+=112 + elif e[0]=='IDLE':need(len(set(e[2]))==len(e[2]),'distinct idle stage incidence');r=8*len(e[2]);P[r]+=224;idles[r]+=224 + else:need(e[0]in('ADD','SIGNED_SWAP','Q_POWER'),'comparison caller ordinary alphabet') + main=Counter() + for term in ctl['diagonal']: + need(abs(term[0])==1 and all(x in(0,1)for x in term[1:]),'comparison main diagonal');main[1+8*sum(term[1:])]+=112 + T.update(main) + need((P,T)==tuple(Counter({int(k):v for k,v in ref['histograms'][name].items()})for name in ['paid','productive']),'reconstructed complete comparison invoice differs') + need(events['LOCAL']==18 and sum(P.values())==64116 and sum(T.values())==10784,'full comparison census') + optimistic=T.copy();optimistic[8]+=8*18 + equal_paid=P.copy();equal_paid[8]+=8*18 + bct={side:Counter(g[0]for g in ctl['boundaries'][side+'_program'])for side in ['left','right']} + return dict(reference_head='174fb211493b43a42210434083e9702b4fb7a2ce',reference_paid=P,reference_targets=T,main_targets=main,whole_idles=idles,caller_events=events,boundary_program_events=bct,hypothetical_paid=P,hypothetical_targets=optimistic,hypothetical_paid_count=sum(P.values()),hypothetical_target_count=sum(optimistic.values()),hypothetical_rank_mass_surplus=sum(r*v for r,v in optimistic.items())-sum(r*v for r,v in P.items()),hypothetical_added_target_profile={8:144},eight_paid_H8_per_provider=dict(paid=equal_paid,targets=optimistic,signed_profile_equals_reference={r:optimistic[r]-equal_paid[r]for r in optimistic.keys()|equal_paid.keys()}=={r:T[r]-P[r]for r in T.keys()|P.keys()}),unproved_contract='All 18 providers must close to standard B main outputs, preserve400 ordinary helpers each, and supply8 new autonomous H8 each; no source proves this contract. Closure paid jobs/lost targets and ordinary overhead are unknown, not zero.',ordinary_provider_subtotal_for_18={k:18*v for k,v in dict(ADD=17917,SCALE=1204,COPY=16,CLEAR=40,SWAP=8,monomial_field_map=464).items()},ordinary_caller_scope='The literal caller and left/right boundary record counts are retained; ADD, SIGNED_SWAP and Q_POWER each act on112 fields. QUERY_SHEAR recursive costs are included in P. Consumer closure operations and their finite movement/storage/precision costs remain unknown.') +def screen(): + from independent_price_engine import power,moment,difference + ref=read('REFERENCE-5400-INVOICE.json')['histograms'];P={int(r):v for r,v in ref['paid'].items()};T={int(r):v for r,v in ref['productive'].items()} + rows=[] + for k in [Q('.00302728823'),Q('.00302728824'),Q('.00302728825')]: + t=1-k;base=difference(moment(T,t),moment(P,t));u=power(8,t);credit=(8*u[0],8*u[1]);ratios={} + for r in [1,2,3,4,5,8,9,16,32,64,145]: + v=power(r,t);lo,hi=(Q(8),Q(8)) if r==8 else (credit[0]/v[1],credit[1]/v[0]) + # Strict incremental budget requires m < ratio; equality is not gain. + maximum=(lo.numerator-1)//lo.denominator + need(maximum < lo and maximum+1>=hi,'integer budget separated') + ratios[r]=dict(ratio_interval=(lo,hi),max_identical_paid_jobs_for_strict_incremental_gain=maximum) + rows.append(dict(kappa=k,reference_target_minus_paid=base,hypothetical_credit_per_provider=credit,identical_paid_jobs=ratios,reference_full_calls=18,hypothetical_p16_credit=(18*credit[0],18*credit[1]))) + return dict(status='PASS_CONDITIONAL_CLOSURE_NECESSARY_SCREEN_NO_CALLER_NO_KAPPA',new_kappa=None,rows=rows,contract='For any completed comparator at t=1-kappa: margin_new=margin_reference+sum(extra_target_count[r]*r^t)-sum(closure_paid_count[r]*r^t)-sum(lost_target_count[r]*r^t)+main_idle_other_delta. Unknown terms never default to zero.',relaxation='Reference p16 invoice plus n times eight autonomous H8, all other paid/productive jobs unchanged. Coupled5402 H fields do NOT supply this credit; physical reachability is unproved.',stop_test='If all other changes vanish and per-provider closure costs eight H8 plus any positive paid job, its incremental margin is strictly negative for every 0>j)&1) for j,a in enumerate(alpha)) + e+=2*sum(((y>>j)&1)*((y>>k)&1) for j in range(n) for k in range(j+1,n) if (rows[j]>>k)&1) + out[y][y]=power(I,e%4) + elif k=='C': + q,s=g[1:];a=(F(1,2),F(s,2));b=conj(a) + out[y][y]=add(out[y][y],a);out[y^q][y]=add(out[y^q][y],b) + else:raise ValueError(k) + return tuple(tuple(r) for r in out) +def circuit(n,gs): + out=eye(1<>j)&1==bit for j,bit in enumerate(xp))) + assert external(dutq.partial_inner(path,inv,xp,yp))==expect;counts['conditional_inners']+=1 + def op(kind,dst=0,**kw):return {'op':kind,'dst':dst,**kw} + cases=[] + for n in range(3): + ops={'I':[],'phase':[['phase',1]],'C':[['C',(1<0 else '')+str(b)+'i' +if __name__=='__main__':main() diff --git a/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/ADVANCES-MUTATIONS.json b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/ADVANCES-MUTATIONS.json new file mode 100644 index 0000000000..cadc0398be --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/ADVANCES-MUTATIONS.json @@ -0,0 +1,45 @@ +{ + "cases": [ + { + "mutation": "conjugate native C factor", + "optimized": false, + "rejection": "Native trace phase" + }, + { + "mutation": "conjugate native C factor", + "optimized": true, + "rejection": "Native trace phase" + }, + { + "mutation": "ignore native inverse sign", + "optimized": false, + "rejection": "Native entry phase" + }, + { + "mutation": "ignore native inverse sign", + "optimized": true, + "rejection": "Native entry phase" + }, + { + "mutation": "omit output prefix constraint", + "optimized": false, + "rejection": "Native partial inner product" + }, + { + "mutation": "omit output prefix constraint", + "optimized": true, + "rejection": "Native partial inner product" + }, + { + "mutation": "omit final native return", + "optimized": false, + "rejection": "Compact complete endpoint" + }, + { + "mutation": "omit final native return", + "optimized": true, + "rejection": "Compact complete endpoint" + } + ], + "status": "PASS_CLIFFORD_ADVANCE_MUTATIONS" +} diff --git a/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/ADVANCES-RESULT.json b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/ADVANCES-RESULT.json new file mode 100644 index 0000000000..2e8e73ba23 --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/ADVANCES-RESULT.json @@ -0,0 +1,50 @@ +{ + "code_fourier_values": 256, + "complete_programs": 48, + "controls": [ + "singular permutation", + "diagonal parity", + "asymmetric diagonal", + "wrong C sign", + "unknown gate", + "coordinate out of range", + "invalid prefix", + "negative axes" + ], + "exact_native_relations": 9, + "exhaustive_quadratic_forms": 640, + "filter_axis_counts": 65, + "general_test_widths": "8n-3 through 8n+4 for n>=2", + "large_native_programs": [ + { + "axes": 64, + "base_dimension": "18446744073709551616", + "equivalent": false + }, + { + "axes": 65, + "base_dimension": "36893488147419103232", + "equivalent": true + } + ], + "literal_witnesses": 48, + "native_entries": 3328, + "native_traces": 128, + "native_words": 128, + "one_axis": { + "group_sha256": "32481fd502c5f388244bcd56d20fbc0e0ca3933f47dbbdbbd8215397cea0238d", + "image_of_i": 256, + "prime": 65537, + "rank": 96, + "widths": [ + 5, + 6, + 7, + 8 + ] + }, + "partial_inner_products": 304, + "scalar_phase_traps": 1, + "stable_separation": "75/76", + "status": "PASS_CLIFFORD_ADVANCES_NO_NEW_KAPPA" +} diff --git a/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/ADVANCES.md b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/ADVANCES.md new file mode 100644 index 0000000000..340c54f752 --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/ADVANCES.md @@ -0,0 +1,251 @@ +# Fewer widths and exact computation without dense matrices + +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. + +This note extends [PROOF.md](PROOF.md). It uses the same group C_n, exact +global phases, complete register endpoints and coefficients that do not +depend on the positive tensor width f. Set D=2^n. No result changes kappa. + +## 1. Eight widths suffice for every axis count + +For n>=1, a fixed residual vanishes at every positive width if and only if +it vanishes at the eight widths + + 8n-3, 8n-2, ..., 8n+4. + +For n=0, use widths 1,2,3,4. For n=1, Section 3 improves the test to +widths 5,6,7,8. The number of tests and the largest tested width are +different quantities. The general maximum 8n+4 has not decreased. + +Let E be the binary code generated by the four length-eight rows +11111111, 11110000, 11001100 and 10101010. It has dimension four. Its +weights are 0,4,8, and E=E-perp for the binary dot product. Define T_n +in (C^D) tensor-power 8 by summing the basis vectors whose n binary rows +all belong to E. This vector is nonzero. + +The vector T_n is fixed by the eighth tensor power of each native generator: + +- S on one axis contributes i to the power of that row's weight. This is 1. +- CNOT adds one code row to another. It permutes the summands. +- The native Hadamard is ((1+i)/2) times the binary Fourier matrix. + Its eighth tensor power has coefficient 1/16. The Fourier sum of E + is 16 times the indicator of E-perp=E. Thus it fixes T_n, with phase 1. +- The scalar iI has eighth power 1. + +These gates generate C_n. Here is a direct reduction argument. The image +of Z_1 under a Clifford is a nonidentity Pauli. Single-axis H and S gates +convert each nonzero component to Z. CNOT gates reduce the resulting +nonempty Z string to Z_1. An X gate corrects its sign. The image of X_1 +then anticommutes with Z_1. CNOT and controlled-Z gates with control 1 +remove its components on the other axes. An S gate removes its remaining +Z_1 component, and Z_1 corrects its sign. These changes preserve Z_1. +The remaining operator fixes X_1 and Z_1, so it has the form I tensor V. +Repeat on V. The final scalar is a dyadic Gaussian unit of absolute value +one, hence one of 1,i,-1,-i, as proved in PROOF.md. Replace each ordinary +H in this argument by the native Hadamard. The Pauli action is unchanged; +the final scalar still belongs to the same four-element group. + +Normalize T_n to a unit vector tau. The injection J_f(v)=v tensor tau +satisfies + + (sum_g c_g g^(tensor(f+8))) J_f + = J_f (sum_g c_g g^(tensor f)). + +Thus vanishing at f+8 implies vanishing at f. Every integer from 1 to +F=8n+4 can be increased by a multiple of eight to a member of F-7,...,F. +The first theorem in PROOF.md now gives the stated eight-width test. +Apply the argument separately to every input and output role. + +This argument does not transfer the dimension-free stability constant +to the eight selected widths. The bound in Section 2 uses all widths +1,...,8n+4. A direct restriction argument loses powers of D. + +The code invariant is classical. See Runge's prior results as credited in +[Nebe, Rains and Sloane, The invariants of the Clifford groups, Sections 4 +and 6](https://arxiv.org/pdf/math/0001038). The contribution here is its +use in the fixed-coefficient endpoint test, with the native phase checked. + +## 2. Uniform separation improves from 14/15 to 75/76 + +For distinct exact operators and M=sum_g |c_g|^2, let +E_f=D^(-f)||sum_g c_g g^(tensor f)||_HS^2. Then + + max_(1<=f<=8n+4) E_f >= (75/76) M. + +Use the same filter as PROOF.md. Write r=-1/4, m=2n and + + P_m(t) = product_(j=1..m) (t-r^j)/(1-r^j), + q_n(z) = (z+z^2+z^3+z^4) P_m(z^4)/4. + +The four residue classes of coefficients do not overlap. Therefore the +sum of absolute coefficients of q_n equals that of P_m. + +In descending degree, the coefficient with index l has sign +s_l=(-1)^(l(l+3)/2), namely ++--++--. To check this, the elementary +symmetric function in r,...,r^m equals + + r^(l(l+1)/2) product_(k=1..l) (1-r^(m-l+k))/(1-r^k). + +This identity follows by separating subsets that contain the last root; +the empty product gives the initial case. Every factor in the product +is positive. Include the coefficient sign (-1)^l to get s_l. + +Let u_l be the absolute coefficients of P_(2n), L their sum, and U_odd +their sum over odd l. Add the next two roots -a,b, where +b=16^(-(n+1)) and a=4b. The new factor is +(t^2+(a-b)t-ab)/((1+a)(1-b)). The sign rule gives + + L_new - L = [2ab L - 2(a-b) U_odd]/((1+a)(1-b)). + +For n>=1, the unnormalized coefficient of t^(2n-1) has magnitude +(1-16^(-n))/5 >=3/16. The sum of the unnormalized absolute coefficients +is at most product_j(1+4^(-j)) <=3/2. The last inequality follows by +expanding the product and bounding it by the geometric series whose +ratio is sum_j 4^(-j)<=1/3. Hence U_odd/L>=1/8. On the other hand, +ab/(a-b)=4b/3<=1/192. Thus L_new=1. + +For n=1, P_2(t)=(64t^2+12t-1)/75, so L=77/75. For n=0, L=1. +Consequently the positive coefficient mass of q_n is at most +(1+77/75)/2=76/75. The exact identity sum_f b_f E_f=M and E_f>=0 +give the claimed bound. This is a bound for this filter; optimality of +the operator stability constant is not claimed. + +The implementation forms the integer numerator +product_j(4^j t-(-1)^j) and the common denominator +product_j(4^j-(-1)^j) first. It reduces fractions only when it emits q_n. +This gives the same polynomial and avoids repeated large rational reductions. + +## 3. The one-axis maximum cutoff is exactly eight + +The frozen native C and S gates generate all 96 exact operators of C_1. +Their closure and phases are checked in verify.py. Let + + K[g,h] = sum_(f=5..8) (tr(g* h)/2)^f. + +The file [ONE-AXIS-RANK.json](ONE-AXIS-RANK.json) contains an inverse of K +after reduction to F_65537 with i mapped to 256. The checker reconstructs +K, checks that 65537 is prime and 256^2=-1, and multiplies K by this +inverse. It does not use the elimination routine to check the inverse. +All original denominators are powers of two. A nonzero reduced determinant +therefore proves that the characteristic-zero determinant is nonzero. +The positive semidefinite Gram sum K has zero kernel. This proves that +widths 5,6,7,8 suffice for every fixed residual on C_1. + +The Reynolds example in PROOF.md vanishes at widths 1 through 7 and is +nonzero at width 8. The maximum cutoff eight is therefore sharp. +At least four tested widths are required: for each residue r modulo four, +the four scalar operators give the residual + + sum_(k=0..3) i^(-rk) (i^k I)^(tensor f). + +It vanishes unless f is congruent to r modulo four. A test set that omits +one residue cannot detect this residual. Thus four is also the minimum +number of widths for a fixed universal test on C_1. Neither conclusion +establishes a sharp cutoff for n>=2. + +## 4. A phase-exact quadratic path calculation + +[quadratic.py](quadratic.py) accepts the frozen native P, X, D, C and +phase gate grammar. It keeps a list of binary affine output bits and a +phase polynomial modulo four. The polynomial has arbitrary linear +coefficients and even cross coefficients. It also keeps an exact Gaussian +scalar factor. It never allocates an array indexed by the 2^n base states. + +Start with n input variables. P and X change only the affine output bits. +D adds its stated linear and even quadratic phase. For C(q,s), use + + C(q,s) = ((1+s i)/2) (I + i^(-s) X_q). + +Add one binary path variable a, multiply the scalar factor by (1+s i)/2, +add -s a to the phase and add a q to the output bits. Keep the literal +phase gate. The formula also covers q=0. The number of variables is +m=n+h, where h is the number of C gates in the literal word. + +An affine parity has, modulo four, its constant and linear terms plus +even pair terms. Terms of degree at least three vanish modulo four. +Twice a product of parities needs only the product over F_2. Thus every +gate preserves this representation, including affine translations. + +An entry fixes the input and output bits. A trace equates them. Binary +elimination either rejects inconsistent equations or gives an affine +parametrization with one assignment per solution. Substitute this map +in the phase. The remaining unconstrained sum is evaluated as follows: + +- For an odd linear coefficient a of variable x, write its part as + a x+2 x L. Summing x gives (1+i^a) i^(-a L). Remove x and add the + indicated parity phase. This keeps the same quadratic form class. +- If every linear coefficient is even and a cross term remains, sum one + variable x. The result is twice the sum subject to a binary affine + constraint on its neighbors. Eliminate that constraint. +- If no cross terms remain, a linear coefficient 2 makes the sum zero. + Otherwise each remaining variable supplies a factor two. + +Each step removes at least one variable. The code uses direct polynomial +substitution. A conservative bound is O(m^5) arithmetic operations per +sum, plus O(L m^4) to build a path form for L native gates. It uses +polynomial space. This bound is not a +claim of optimal stabilizer simulation or constant-time integer arithmetic. +Coefficient bit lengths are polynomial in the literal word length. + +The use of binary quadratic forms for Clifford operations is classical; +see [Dehaene and De Moor, Sections III-V](https://arxiv.org/pdf/quant-ph/0304125). +The new implementation derives its phases directly from the pinned native +kernel. The dense frozen kernel remains a separate finite test oracle. + +## 5. Bitwise witness extraction removes the D^2 scan + +For two operators g,h and fixed prefixes of the output and input bits, +define B(g,h) as the sum of conjugate(g[x,y])h[x,y] over the unspecified +bits. Combine two path sums, negate the left phase, equate their input +and output bits, and impose the prefix equations. Section 4 computes B +in polynomial time, with at most the sum of both path-variable counts. + +With r tensor factors still after the current factor, the conditional +squared norm is + + sum_(g,h) conjugate(c_g)c_h B(g,h) (tr(g* h)/D)^r. + +It is real and nonnegative. The two choices for the next coordinate bit +partition its sum. Choose the larger child. After 2n choices, the current +base coordinate pair is fixed; multiply each coefficient by g[x,y] and +continue with the next tensor factor. There are 2nf bit choices, each +with two children, instead of fD^2 coordinate trials. + +At the start of one factor the conditional norm is D E. The 2n splits +lose at most D^2. Induction gives the same final entry bound as PROOF.md: + + |entry|^2 >= E_f D^(-f). + +[compact.py](compact.py) also expands complete register endpoints as +signed native words. It retains every input and return role. It merges +two unitary words exactly when tr(g* h)/D=1; the identity +||g-h||_HS^2=2D-2 Re tr(g* h) proves this test. Global phases stay inside +the operator keys, not in coefficients outside the tensor power. + +For expanded support s and a maximum literal path size m, pair traces +cost O(s^2 poly(m)). A witness costs O(n f s^2 poly(m)) arithmetic +operations, with polynomial space in these parameters. No 2^n matrix or +2^(nf) tensor is built. The symbolic support s can still grow exponentially +in the register-program length. This result does not remove that obstacle. + +## Verification and limits + +[verify_advances.py](verify_advances.py) checks the code invariant, exact +filter bounds, modular inverse certificate, exhaustive small quadratic +sums, frozen native entries and traces, conditional inner products, and +complete programs against the original dense compiler. It checks larger +native examples without a dense matrix. ADVANCES-RESULT.json records the +executed counts. Normal and optimized Python must produce the same receipt. + +The proofs above are written arguments, not proof-kernel certificates. +The code invariant and quadratic-form method have classical predecessors. +The sparse full-program adapter, finite-width refinements and native phase +bindings are the present contribution. No complete current provider or +physical cost invoice has been run. No selected frontier changes here. + +## Open next questions + +1. Prove a sharper maximum cutoff for n>=2, or give a matching obstruction. +2. Bound support growth on one complete current provider before a large run. +3. Derive a useful stability constant for the eight selected widths. +4. Improve the quadratic elimination cost after a measured provider needs it. diff --git a/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/LICENSE b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/MUTATIONS.json new file mode 100644 index 0000000000..9263be8739 --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/MUTATIONS.json @@ -0,0 +1,45 @@ +{ + "cases": [ + { + "mutation": "omit final trace root", + "optimized": false, + "rejection": "Polynomial endpoints" + }, + { + "mutation": "omit final trace root", + "optimized": true, + "rejection": "Polynomial endpoints" + }, + { + "mutation": "ignore inverse", + "optimized": false, + "rejection": "Signed-word complete endpoint" + }, + { + "mutation": "ignore inverse", + "optimized": true, + "rejection": "Signed-word complete endpoint" + }, + { + "mutation": "omit final return", + "optimized": false, + "rejection": "Zero-axis scalar group" + }, + { + "mutation": "omit final return", + "optimized": true, + "rejection": "Zero-axis scalar group" + }, + { + "mutation": "remove Gram normalization", + "optimized": false, + "rejection": "Independent dense norm" + }, + { + "mutation": "remove Gram normalization", + "optimized": true, + "rejection": "Independent dense norm" + } + ], + "status": "PASS_CLIFFORD_GRAM_MUTATIONS" +} diff --git a/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/ONE-AXIS-RANK.json b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/ONE-AXIS-RANK.json new file mode 100644 index 0000000000..6138b717d1 --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/ONE-AXIS-RANK.json @@ -0,0 +1,9422 @@ +{ + "group_sha256": "32481fd502c5f388244bcd56d20fbc0e0ca3933f47dbbdbbd8215397cea0238d", + "image_of_i": 256, + "inverse": [ + [ + 32344, + 51075, + 51075, + 43700, + 17417, + 17417, + 43700, + 60702, + 38637, + 38637, + 38637, + 38637, + 38637, + 60702, + 7672, 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b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/PROOF.md @@ -0,0 +1,268 @@ +# A finite and stable tensor test for dyadic Clifford programs + +The [continuation](ADVANCES.md) reduces the number of tested widths, +improves 14/15 to 75/76, proves the sharp one-axis cutoff, and supplies +a compact native implementation. This note retains the original proof. + +## Result + +Let R = Z[i,1/2], let D = 2^n, and let C_n be the unitary matrices in +M_D(R) that normalize the n-axis Pauli group. Keep their exact global phase. +This class includes the source Gaussian gate + + C_v = (1+i)I/2 + (1-i)X_v/2, + +its inverse, quadratic phase gates, affine binary permutations and the +source Hadamard gate. It is larger than the monomial subgroup. + +Consider two finite scalar register programs. Each role has an independent +arbitrary input in (C^D)^(tensor f). Instructions can add a scalar multiple +of one role to another, scale a role, exchange roles, or apply U^(tensor f) +for U in C_n. Queries can add c U^(tensor f) v_s to v_d. Self queries are +permitted. Both programs and their scalar coefficients are fixed as f varies. +Every input and return role is part of the contract. + +**Theorem.** The complete endpoints agree for every positive integer f if +and only if they agree for f = 1,...,8n+4. There is no program-length or +support-size term in this cutoff. This is not a claim that these widths are +minimal, or that dense tensor matrices can be tested at low cost. + +There is a stronger quantitative statement. In one endpoint entry, combine +equal exact native matrices and write the residual as + + A_f = sum_(g in S) c_g g^(tensor f), + +where the matrices in S are distinct. Set + + M = sum_g |c_g|^2, + E_f = D^(-f) ||A_f||_HS^2. + +Then + + max_(1 <= f <= 8n+4) E_f >= (14/15) M. (1) + +The proof gives explicit rational weights b_f such that + + sum_(f=1)^(8n+4) b_f E_f = M. (2) + +Each E_f can be computed from base-dimension pair traces. It does not require +a tensor matrix. A nonzero E_f gives an exact nonzero tensor entry by a finite +sequence of conditional norm tests. The executable uses Q(i); the theorem +allows arbitrary complex scalar coefficients. + +This result changes an infinite algebraic obligation into a finite test for +this native class. It does not supply a native layout, a physical cost bound, +rounding, stock, a recursive supplier, or a change to the complete kappa. + +## 1. The exact trace alphabet + +Use Hermitian Paulis P_v, labelled by v in F_2^(2n), as an orthogonal basis +of M_D(C). A Clifford U acts by + + U P_v U* = epsilon(v) P_(S v), + +where S is symplectic and each epsilon(v) is 1 or -1. On the fixed space +L = ker(S-I), the signs form an additive character. Indeed, multiplication +P_u P_v = gamma(u,v) P_(u+v), followed by conjugation, cancels the same +nonzero gamma on both sides and gives epsilon(u+v)=epsilon(u)epsilon(v). + +The trace of conjugation on all matrices is |tr U|^2. The Pauli basis gives +the same trace as sum_(v in L) epsilon(v). A nontrivial sign character sums +to zero; the trivial character sums to |L|. Thus + + |tr U|^2 is zero or 2^d, with 0 <= d <= 2n. (3) + +We also need the phase of this trace. C_n is a finite group. Its conjugation +action on the finite Pauli group has finite image. Its kernel consists of +scalar matrices: commuting with all Z generators forces a diagonal matrix, +and commuting with all X generators makes that diagonal constant. A scalar +in R with absolute value one is in {1,i,-1,-i}. To see this, write it as +(a+bi)/2^k. Unique factorization in Z[i], with 2=-i(1+i)^2, shows that a +Gaussian rational with denominator a power of two and norm one is a unit. +The kernel therefore has four elements. + +Every U has finite order. Its eigenvalues are roots of unity, so its trace +is an algebraic integer. The trace is also in Q(i). The ring of integers of +Q(i) is Z[i], so tr U is a Gaussian integer. Factoring its norm in (3) now +shows + + tr U in {0} union {i^k (1+i)^d : 0 <= k < 4, + 0 <= d <= 2n}. (4) + +The same statement holds for U*V. In particular, no arbitrary rational +unit-circle phase may be admitted. For example (3+4i)I/5 is unitary and +normalizes Paulis, but is outside the dyadic hypothesis. + +Finally tr(U*V)=D holds exactly when U=V. All eigenvalues of U*V have absolute +value one. Equality in their sum being the positive real number D forces +every eigenvalue to be one; a unitary matrix with those eigenvalues is I. + +## 2. An explicit polynomial that selects the identity + +Let z = tr U / D. In addition to zero and the four scalar values 1,i,-1,-i, +every possible z satisfies + + z^4 = (-1)^j 4^(-j), for some 1 <= j <= 2n. + +Define the rational polynomial + + q_n(z) = z(1+z+z^2+z^3)/4 + * product_(j=1)^(2n) + (z^4 - (-1)^j 4^(-j))/(1 - (-1)^j 4^(-j)). (5) + +It has zero constant term, degree 8n+4, and q_n(1)=1. It vanishes at every +other value in the trace alphabet. Therefore, for exact matrices U,V in C_n, + + q_n(tr(U*V)/D) = 1 if U=V, and 0 otherwise. (6) + +Write q_n(z)=sum_f b_f z^f. The triangle inequality for polynomial +coefficient norms gives a dimension-independent bound. The first factor +has coefficient norm one. Each odd-j factor has nonnegative coefficients +whose sum is one. The norm of the even factor j=2k is + + (1+16^(-k))/(1-16^(-k)). + +For nonnegative a,b with a+b<1, + + [(1+a)/(1-a)] [(1+b)/(1-b)] + = (1+t)/(1-t), where t=(a+b)/(1+ab) <= a+b. + +Induction and sum_(k>=1) 16^(-k)=1/15 show + + sum_f |b_f| <= product_(k=1)^n (1+16^(-k))/(1-16^(-k)) < 8/7. (7) + +For n=0 the norm is one and the same strict bound holds. Also sum_f b_f=1. +It follows that the sum of the positive coefficients is less than 15/14. + +## 3. The Gram identity and stable separation + +The Hilbert-Schmidt inner product is multiplicative under tensor products. +Thus + + E_f = sum_(g,h in S) conjugate(c_g)c_h (tr(g^* h)/D)^f, (8) + +where g* denotes the adjoint, so the trace argument is g* h. Apply (6) to +(8) and sum against b_f. All terms with g != h vanish and the diagonal +terms give M. This proves (2). + +Each E_f is a nonnegative real number. Terms with b_f<0 can be removed from +the right side of (2) when taking an upper bound. Hence + + M <= (sum_(b_f>0) b_f) max_f E_f < (15/14) max_f E_f + +when M>0. The weaker non-strict form (1) also covers M=0. If the first 8n+4 +residual matrices vanish, (2) forces M=0. Every exact coefficient c_g is then +zero, so A_f vanishes at every positive width. The reverse implication is +immediate. Apply this argument to each input/output entry to obtain the full +dirty-register theorem. + +This proof uses only pair traces and a rational polynomial. It does not need +an irreducible character table or a census of C_n. Burnside-Brauer supplies +a related classical tensor-generation argument; (5)-(8) give the explicit +native cutoff, quantitative bound and computational certificate used here. + +## 4. Extract a tensor entry without a tensor matrix + +Suppose E_f>0. For one output coordinate x and input coordinate y in the +first tensor factor, put c'_g=c_g g[x,y]. The remaining tensor operator is +sum_g c'_g g^(tensor (f-1)). Its normalized squared norm is obtained from +the same pair-trace matrix by (8). The sum of these conditional norms over +the D^2 choices of (x,y) is D E_f. At least one choice is positive, and a +maximizing choice is at least E_f/D. + +Repeat until no tensor factors remain. The final scalar is exactly the +chosen entry of A_f. It is nonzero and its squared absolute value is at +least E_f/D^f. Start at a width attaining the maximum in (1) to obtain + + |entry|^2 >= (14/15) M D^(-f). (9) + +The independent witness checker uses a separate signed-word interpreter, +multiplies the base matrices in their literal order, and computes this one +entry as a product of base entries. It does not use traces, the cutoff, +the interpolation polynomial, or the producer's register compiler. + +## 5. Cost, input validation and trust + +For s distinct residual operators supplied as D-by-D matrices, all pair +traces cost O(s^2 D^2) exact scalar operations. Equal traces can be collected +into at most 8n+5 buckets, including zero. The full norm sequence then costs +O(n^2+s^2) further scalar operations after the pair traces, apart from +coefficient storage. Coefficient bit sizes are not bounded by this count. + +The direct entry extractor uses O(f D^2 s^2 log(f+1)) scalar operations in the +worst case, with base matrices and their Gram matrix in memory. The logarithm +accounts for repeated squaring of pair traces. It never allocates +a D^f-by-D^f matrix. Word support can grow exponentially during compilation; +the program compiler is not asserted to be polynomial in instruction count. +The base dimension D itself is exponential in n. No practical full-supplier +speedup is inferred from these bounds. + +The frontend checks every supplied matrix for dyadic entries, unitarity and +Pauli normalization on all 2n generators. The last check is sufficient: +the generators generate the Pauli group, and invertible conjugation gives +an injective map of that finite group into itself. Products and adjoints +remain in C_n. Exact matrix keys include global phase. Scalar coefficients +remain outside tensor powers. The checker does not move a scalar phase +from an operator into a coefficient. + +The actual source kernel uses precisely the gates in the first section. +Its C formula has eigenvalues 1 and i. Its Hadamard convention is S C S, +so H^2=iI, not I. The retained source bytes and the independent column +formula are checked in verify.py. These checks bind the algebraic grammar; +they do not run a complete native supplier or its physical implementation. + +The proof is written mathematics. Python, the compiler, the frozen Gaussian +arithmetic and the native-source transcription remain trusted. The direct +tensor, signed-word and source-column checks test different implications. +They are not an independent human review or a proof-assistant theorem. + +## 6. A finite test that misses a real failure + +The one-axis source C and S gates generate a group G of 96 exact matrices. +There are at most 24 signed images of an ordered anticommuting Pauli pair, +and at most four scalar lifts of each image. Thus this group is the complete +one-axis dyadic normalizer, not just a proper subgroup used for calibration. +Let one dirty target receive + + y <- y + (1/96) sum_(g in G) g^(tensor f) x. + +The source x is unchanged. The average is an orthogonal projector, so its +trace equals its rank. Complete exact enumeration gives rank zero at widths +1 through 7 and rank 15 at width 8. The all-zero input/output tuple has +entry 5/24 at width 8. Thus seven full small-width checks can all accept +a false all-width identity. The registered example and literal witness +checker reproduce this counterexample without building its tensor matrix. + +## 7. Scope and credit + +The program must have fixed scalar coefficients and a fixed native word as +width changes. This theorem does not cover a different program at each f, +arbitrary continuous phases, nonunitary scaled operators, non-Clifford gates, +positive characteristic, nonlinear leaves or physical aliasing. A caller +with restricted clean inputs needs its own input contract. Rounded equality +is not exact equality. No complete multiplication theorem or kappa changes. + +The finite-group algebra viewpoint is prior work. The repository's +projection-recursion-check already uses positive-width Burnside-Brauer +separation, following Jacob Alan Sussman's engine model. The free-word +tensor audit of Cinna Davis's programs and the certificates by zxv and +Krzysztof Wojt retain their separate contributions. Chris R's retained-helper +and passive-query proofs already use finite Clifford alphabets and tensor +Gram separation. For fixed scalar coefficients, this package supplies the +explicit filter and dimension-independent stability constant above. It does +not replace their statements about width-dependent coefficients. The +concurrent PR #5369 targets the smaller +affine-quadratic monomial class with four selected widths. This package does +not claim its result. README.md links these related sources. + +Classical provenance: Burnside and Brauer's tensor-generation theorem, as +reviewed by Benjamin Steinberg in +[On the Burnside-Brauer-Steinberg theorem](https://arxiv.org/abs/1409.7632), +the Pauli conjugation basis, Gaussian-integer factorization, polynomial +interpolation and Gram identities. No global mathematical priority is +claimed. The new package provides the explicit dyadic-Clifford trace +filter, stable bound, complete program frontend, compressed failure +certificate and source-bound checks. The exact source and credit map is +in README.md and SOURCES.json. + +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. diff --git a/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/PROVIDER.md b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/PROVIDER.md new file mode 100644 index 0000000000..7b7dfa9e48 --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/PROVIDER.md @@ -0,0 +1,281 @@ +# Complete selected-provider check and a pair-fusion obstruction + +The new verifier passes the complete local provider selected from PR4610. +It also excludes **30,328 fixed pair fusions at every positive tensor width**. +This contribution does not increase kappa. The paid profile does not change. + +The provider is the exact word at main commit +`1ec1119972c9aefe42525172d07b332fcff81cb4`. Its author head is +`20bb93cd990d2ff683e4d0fc56b87a42cd5d3296`. The paid catalogue comes from +the independent PR5241 admission at +`13efb5fc5f3b7c14ec2cfa181dd9eb6480972cf2`. +`provider/SOURCES.json` binds each copied input to its source Git object and +SHA-256. Frozen source files are not changed. + +## Result and coverage + +Each direction has 21,449 source events, 632 independent persistent inputs, +and one independent owned input. Every persistent output is checked. The owned +output must be zero. All 408 helper inputs remain arbitrary. Their outputs +have their specified native frame changes; they are not assumed to be zero. + +The new quadratic-sum engine checks 7,000 oriented recipe classes: + +| Class | Checks | Coverage | +| --- | ---: | --- | +| Paid transitions | 5,710 | All 6,596 event instances across both directions | +| Native warps | 360 | All 480 signed event instances | +| Helper boundaries | 34 | All 408 roles in each direction | +| Main adapters | 896 | All 448 adapter events in each direction | + +These counts refer to labelled classes. They do not count distinct matrices. +For two unitary circuits U,V on D=512 coordinates, the checker requires +`tr(U* V)/D = 1`. Here `*` is the conjugate transpose. This equality proves +U=V, including absolute phase. Each circuit then has the same tensor power at +every positive width. A recipe's stored PASS status is not an input to this +test. The main adapter generator only proposes data. Acceptance does not +import or execute that generator or its native compiler. + +The complete physical programs are also passed directly to `compact.certify`. +Their references contain every input and output role. The result is equality +at every positive width, with no nonzero endpoint entry. The complete sparse +expansion gives these measured support counts: + +| Direction | Scalar/native instructions | Native symbols | Peak total terms | Peak terms in one row | Final terms | +| --- | ---: | ---: | ---: | ---: | ---: | +| Forward | 24,827 | 1,297 | 22,331 | 156 | 744 | +| Backward | 24,819 | 1,297 | 12,930 | 148 | 744 | + +These are counts for this fixed provider. General program support can still +grow exponentially. No dense tensor matrix is made. The separate check of +the displayed failure witnesses uses base-space vectors with 512 entries. + +## Exact boundary and translation + +Let F_U be the source canonical frame, C_q the source Gaussian gate, and +F_full the full frame. Write E_i for the entrance frame of persistent role i +and H_i for its exit frame. In the forward orientation: + +- For 0<=i<112, E_i=C_(q_i) and H_i=F_full. +- For 112<=i<224, E_i=I and H_i=F_full C_(q_(i-112))^-1. +- For 224<=i<632, E_i=F_(start_i) and H_i=F_(final_i). + +The backward orientation uses the entrywise conjugate of each native frame +and operator. A negative warp uses the inverse before this conjugation. +Conjugation is not replaced by the adjoint. + +In these logical coordinates, the forward endpoint is +`L_(112+j) <- L_(112+j) + L_j` for 0<=j<112. The backward endpoint is +`L_j <- L_j - L_(112+j)`. All other persistent logical coordinates return +unchanged. Thus the persistent physical endpoint is + + diag(H_i^tensor f) T diag((E_i^-1)^tensor f). + +This operator is invertible for every positive f. The owned input is erased, +and its output is zero. All scalar coefficients remain outside tensor powers. + +The importer expands a paid transition a->b as F_b F_a^-1. A signed warp +becomes F_b K_signed F_a^-1. A scalar ADD retains its literal rational +coefficient. Owned CLEAR becomes scalar multiplication by zero. Owned COPY +becomes CLEAR followed by ADD. Borrowed CLEAR and COPY are rejected. + +The 448 main adapter markers are included. An entrance adapter is +F_start E_i^-1. An exit adapter is H_i F_final^-1. There is a source detail +that must not be hidden: some identity exit markers precede the final climb. +The importer permits a marker at a different current frame only when the +adapter circuit is exactly the identity. A nonidentity marker must use its +actual current frame. +Every nonidentity entrance adapter must precede all uses of its role. Every +nonidentity exit adapter must follow all uses. The word audit checks both +conditions. Thus an adapter inside a candidate interval changes its endpoint +frame and has the identity logical map. + +The sparse interpreter expands all independent inputs together. The existing +`compact.certify` interpreter expands one input at a time. Both complete +endpoints agree with the same explicit physical reference. The earlier +PR5241 free-group argument already proves this provider's algebraic lift. +The new contribution here is an executable application of the new Gram +engine, complete support measurements, and the obstruction below. It is not +a priority claim for that earlier lift argument. + +## Fusion class + +For each persistent role, list its paid climbs in chronological order. Take +every pair in this list, at all positive ranks. Paid events on the same role +or on other roles may occur between the two climbs. Native warps, scalar contacts, +adapters and complete owned-center windows may also occur between them. +There are **7,582 pairs per direction**. No adjacency or common middle-frame +condition is imposed. The domain includes all 2,658 adjacent pairs, including +all 1,363 adjacent rank-one pairs, per direction. + +Let A and B be the literal physical operators of the first and second climb. +Let T be the complete interval between them. The original local map is BTA. +Two replacements are tested: + +- Early fusion: apply BA at the first slot and remove the second slot. The + local map becomes TBA. +- Late fusion: remove the first slot and apply BA at the second slot. The + local map becomes BAT. + +Every other physical operation is fixed. In particular, no scalar contact +is changed to a new native query. The product BA is used with its exact +phase, even when the middle frames differ. This gives 2*2*7582=30,328 candidate +rewrites. The domain does not include a new intermediate placement, a +changed pair of operators, simultaneous fusions, or a pair on different roles. + +The initial invoice opportunity was two H1 jobs replaced by one H2 job. +For a legal replacement in each of 18 local calls, the complete delta would +be -36 H1 +18 H2. This is the physical-pair gap in the PR5243 handoff. +The proof also applies to the other rank pairs. The endpoint obstruction +rejects every candidate before a new complete pricing step. +No such saving is charged to the complete kappa calculation. + +## Closed-cut lemma + +At every persistent climb in this source, the owned register is either +unused and about to be initialized before any read, or is zero after a +completed lifetime. The word audit checks this property. It also checks +that only the owned register can be overwritten and that all reads occur +after initialization. + +Set the unused owned entry to zero. At either end of each candidate interval, +the state is therefore determined by the 632 persistent fields. Each prefix, +interval and suffix defines a square linear map on those fields. This remains +true when the interval contains a whole owned-center window. + +For a fixed positive f, write the complete baseline as S(BTA)P on persistent +fields. The complete endpoint above is invertible. A product of square +matrices over Q(i) can be invertible only when every factor is invertible. +Thus P and S are invertible. It follows that + + S(C-BTA)P = 0 if and only if C-BTA = 0. + +A nonzero interval defect therefore survives to the complete provider's +return. This argument does not require the persistent prefix or suffix to +be unitary. It does not carry a numerical norm bound through those maps. +It would fail at a cut with live owned information omitted from the state. + +## A quantitative contact obstruction + +Use the moving logical frames at the interval boundaries. Let M be the +interval's logical matrix. Frame changes and adapter changes are identity +maps in these coordinates. Scalar instructions remain scalar instructions. +Each native warp is the corresponding phase-bearing K operator. + +For each candidate, the saved certificate gives an off-diagonal block of M +that touches the changed role r. That block is exactly + + M_(r,j) = q U^tensor f or M_(j,r) = q U^tensor f, j != r, + +where q is a nonzero rational and U is a signed word of native unitary maps. +The coefficient is obtained by exact free-group arithmetic. It is not a +sampled equality and holds for all positive f. The second replay checks every +saved coefficient with the earlier independent-input engine. A separate +role-list census checks that the saved pairs cover the entire declared class. + +For early fusion, let G1 and G2 be the diagonal physical frames immediately +after A and immediately before B. Let G3 be the frame immediately after B. +Then the changed logical interval is L M R, where + + L = G3^-1 G2, + R = G1^-1 B G1. + +Both corrections act only on role r. Their r-blocks are conjugates of B^-1 +and B. For late fusion the corresponding corrections have r-blocks conjugate +to A and A^-1. These formulas do not require the two middle frames to agree. + +On the saved off-diagonal block, only one correction acts. The defect is a +unitary left or right multiple of q(V^tensor f-I), where V is a conjugate of +the relevant paid operator or its inverse. Let + + tau = tr(V)/D, D=512. + +The normalized squared Hilbert-Schmidt defect of this block is exactly + + q^2 (2 - 2 Re(tau^f)). + +The new quadratic-sum engine calculates every required trace with exact +Gaussian rational arithmetic. In every case it checks + + Re(tau) <= 1/2, |tau|^2 <= 1/2. + +For f=1, the first inequality gives Re(tau^f)<=1/2. For f>=2, the second +gives |tau|^f<=1/2. The same bounds hold for the inverse, whose trace is the +complex conjugate. Consequently every saved block has normalized squared +defect at least **q^2>0 at every positive width**. The closed-cut lemma lifts +this obstruction to the complete provider. +The smallest saved q^2 is **1/256**, which is a uniform lower bound on the +selected cut-block defects. It is not a lower bound on the full-provider +defect after multiplication by its prefix and suffix. + +`provider/FUSIONS.json.gz` contains all 15,164 contact certificates, the exact +event positions, ranks, four frame IDs, native word, scalar coefficient and two +traces. Each certificate excludes the early and late replacement. +`provider/WITNESSES.json` also gives twelve literal width-one basis witnesses +from the complete physical programs. They cover both directions, both +placements, equal and unequal middle frames, and nonadjacent pairs with a +higher-rank climb. The native source +amplitude evaluator checks each value without Gram traces or quadratic sums. + +## Verification and limits + +From the repository root, with Python 3.12 and the standard library: + +```sh +python3.12 -I -W error -B research/clifford-tensor-gram/verify_provider.py +python3.12 -I -O -W error -B research/clifford-tensor-gram/verify_provider.py +``` + +Expected final line: + +```text +PASS_COMPLETE_PR4610_PROVIDER_AND_30328_FUSION_OBSTRUCTIONS +``` + +The replay checks source bytes, every recipe class, both complete programs, +the complete pair census, every contact coefficient, exact trace bounds and +the full-program witnesses. Negative controls cover an omitted paid class, +a wrong absolute phase, borrowed erasure, a cut with live owned data and a +missing contact. An identity interval is a positive control: no obstruction +is inferred merely from the presence of two paid operations. + +The local paid profile remains `{1:2201,2:412,3:510,4:127,5:40,8:8}`: 3,298 jobs +and rank mass 5,327 per direction. The complete selected kappa remains +0.0030217758. This work does not reprice the controller, run a new outer +admission, or change the selected record. The five selected framework +assumptions remain. The result covers this ideal finite local provider and +its tensor substitution; it does not prove physical tape, precision, stock, +analytic recovery or the complete multiplication theorem. + +The obstruction does not exclude changed contacts, joint use of several +fields, simultaneous rewrites, interior placement, owned-center pairs, +new operators or later source providers. In particular, it does not +subsume the separate frozen eight-relation row argument in PR5393. + +## Open next questions + +1. Can a changed scalar contact supply the missing transformed operand at a + lower complete cost? Start from a saved contact certificate. Replace that + actual contact, retain dirty restoration, and price the replacement query. +2. Can several coordinated fusions cancel their endpoint defects? Start with + a small explicit set of saved pairs. Run the complete native endpoint test; + individual rejection does not prove joint rejection. +3. Can the eight-width criterion help with a complete program whose endpoint + cannot first be reduced by free-group identities? This provider gives a + manageable support example, not a bound for other programs. + +## Credit + +Cao Yifan / intqwq supplies the selected PR4610 construction. Chris R / +Clear1nsight supplies the PR5241 independent paid catalogue, complete admission +and earlier quantified lift proof. Cinna Davis / 1337isnot1337 supplies the +retained controller, native warp and helper chain. zxv, Jacob Alan Sussman, +Dugongue, Rohan Arun, Jeremy Kothe, icekylinx, DreamingOfClouds and chafreaky +retain credit for the relevant native, frame, helper and adapter sources. +The source notices and `provider/NOTICE.md` give the source links. The scalar +arithmetic and frozen native kernel retain their existing notices. + +The new provider importer, Gram application, cut proof, complete pair census +and receipts are by Ali Romman with substantial OpenAI Codex assistance. +The checks are author checks. Independent human review and a proof-kernel +verification are not claimed. Apache-2.0. diff --git a/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/README.md b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/README.md new file mode 100644 index 0000000000..9f6cdf24c5 --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/README.md @@ -0,0 +1,234 @@ +# Finite, stable tensor tests for the full dyadic Clifford group + +**A uniform algebraic interface theorem and an exact verifier; no new kappa.** +For fixed scalar register programs on n binary axes, with unitary dyadic +Clifford operators and every dirty input/return retained, equality at the +**eight widths 8n-3 through 8n+4 implies equality at every positive width** +for n>=2. For one axis, **widths 5,6,7,8 suffice**, and both the maximum +cutoff eight and the number of tests four are sharp. For zero axes use +widths 1,2,3,4. This +covers Gaussian and Hadamard gates as well as phase-monomial maps. The cutoff +does not depend on program length or expanded support. + +The [original proof](PROOF.md) and [extensions](ADVANCES.md) give a stable test. +Let M be the squared coefficient +norm after equal exact native operators are combined. Some tested width has +normalized squared Hilbert-Schmidt residual at least **(75/76)M** among all +widths 1 through 8n+4. An explicit +rational polynomial recovers M from the finite norm sequence. Base-space pair +traces suffice. The compact implementation uses exact quadratic sums and +bitwise conditional norms. It builds **neither a dense base matrix nor a +tensor matrix**, and it removes the original D^2 coordinate scan. + +For the source's nine binary axes, **eight tests at widths 69 through 76** suffice. +This is an algebraic bound, not a full supplier replay or a minimal cutoff. +The complete kappa calculation and selected frontier are unchanged. + +The [complete-provider application](PROVIDER.md) now passes both directions +of the selected PR4610 local provider: all 633 inputs and returns, 7,000 +oriented native recipe classes, and the full physical programs. It also +excludes **30,328 early/late pair fusions at every positive tensor width**. +The domain contains every pair of paid climbs on one persistent role, at +all ranks and without an adjacency condition. The [result](provider/RESULT.json), +[full-program witnesses](provider/WITNESSES.json), and +[research notes](provider/RESEARCH-NOTES.md) preserve the evidence and limits. +No paid job is removed and kappa does not increase. + +## A concrete small-width trap + +The [Reynolds example](examples/reynolds.json) adds the average of the 96 +one-axis native group operators to a dirty target. It preserves the source. +Its complete endpoint is the identity at widths **1 through 7**, but fails at +width **8**, with a literal entry **5/24**. The +[certificate](examples/reynolds.certificate.json) gives the roles and coordinates. +This example uses the full group, not a numerical sample. + +## Use + +Python 3.12 and the standard library suffice. From the repository root: + +```sh +python3.12 -B scripts/research_package.py --package research/clifford-tensor-gram +``` + +The registered commands print `PASS_CLIFFORD_TENSOR_GRAM_NO_NEW_KAPPA` and +`PASS_CLIFFORD_ADVANCES_NO_NEW_KAPPA` in normal and optimized Python. +The provider commands also print +`PASS_COMPLETE_PR4610_PROVIDER_AND_30328_FUSION_OBSTRUCTIONS`. +Direct commands also work in a Git-free export: + +```sh +python3.12 -I -W error -B research/clifford-tensor-gram/verify.py +python3.12 -I -O -W error -B research/clifford-tensor-gram/verify.py +python3.12 -I -W error -B research/clifford-tensor-gram/verify_advances.py +python3.12 -I -O -W error -B research/clifford-tensor-gram/verify_advances.py +python3.12 -I -W error -B research/clifford-tensor-gram/verify_provider.py +python3.12 -I -O -W error -B research/clifford-tensor-gram/verify_provider.py +python3.12 -I -B research/clifford-tensor-gram/compact.py \ + research/clifford-tensor-gram/examples/native-64.json +python3.12 -I -B research/clifford-tensor-gram/certify.py \ + research/clifford-tensor-gram/examples/native-relation.json +python3.12 -I -B research/clifford-tensor-gram/check_witness.py \ + research/clifford-tensor-gram/examples/reynolds.json \ + research/clifford-tensor-gram/examples/reynolds.certificate.json +python3.12 -I -B research/clifford-tensor-gram/audit_mutations.py +python3.12 -I -B research/clifford-tensor-gram/audit_advances.py +``` + +The producer prints JSON. Read `equivalent_at_all_positive_widths`; a successful +process means the decision completed, and a counterexample is a valid result. +The independent witness checker prints `PASS_LITERAL_TENSOR_WITNESS 5/24`. +Relative to the original dense producer, it uses a separate signed-word +interpreter and literal matrix entries, with +no producer import, trace calculation or interpolation argument. Only the +frozen scalar arithmetic is shared. +It checks the literal nonzero entry, not the claimed norms or the universal +cutoff theorem. + +The compact producer reuses that signed-word expansion. Its differential +checks use the original dense compiler, frozen source matrices and literal +entries. It is not an independent checker of itself. The research record is +saved in [RESEARCH-NOTES.md](RESEARCH-NOTES.md). + +## Input contract + +`compact.py` uses the same roles and instructions below, but each value in +`operators` is a literal native circuit. See the +[64-axis example](examples/native-64.json) and +[65-axis phase relation](examples/native-65.json). The native gate forms are +`["P", rows]`, `["X", offset]`, `["D", rows, alpha]`, `["C", mask, sign]` +and `["phase", exponent]`. Binary matrix rows are integer masks. Diagonal +alpha values belong to 0,1,2,3 and have the diagonal row parity. C signs +are +1 or -1. The parser checks the native gate conditions. + +The compact certificate records the reduced decision widths. For a negative +result it still computes all 8n+4 norm values to use the stronger stability +bound and select its witness. The eight-width theorem alone does not give +that dimension-free bound on the selected eight norms. + +The [native relation example](examples/native-relation.json) gives the format. +`axes` is n; `roles` counts arbitrary independent inputs and returns. +`operators` contains exact 2^n-by-2^n matrices, with integer entries or +Gaussian-rational strings such as `1/2-1/2i`. Floats are rejected. The frontend +checks dyadic entries, unitarity and normalization of all Pauli generators. +`program` and `reference` are complete instruction lists. An empty reference +is identity on every role. + +| Instruction | Required fields | Action | +| --- | --- | --- | +| `add` | `src`, `dst` | Add a scalar multiple of a role | +| `query` | `src`, `dst`, `symbol` | Add an operator image of a role | +| `apply` | `dst`, `symbol` | Apply an operator to a role | +| `scale` | `dst`, `coefficient` | Scale a role | +| `swap` | `src`, `dst` | Exchange roles | + +`add` and `query` accept an optional `coefficient`, default one. `query` and +`apply` accept Boolean `inverse`, default false. Self queries read the previous +value. Global phase stays inside the tensor power; scalar coefficients stay +outside. The source convention has H^2=iI. Replacing that operator with scalar +scaling by i passes width one and fails width two, as the +[phase example](examples/phase-trap.json) shows. Scalar coefficients need not +be dyadic. + +## Evidence and limits + +[ADVANCES-RESULT.json](ADVANCES-RESULT.json) records the continuation: +256 code Fourier values, exact filter bounds for n=0,...,64, a rank-96 +modular inverse certificate, 640 exhaustive small quadratic sums, 3,328 +native entries, 128 native traces, 304 partial inner products, 48 complete +program comparisons and literal witnesses, nine exact native relations, +a scalar-phase trap and eight rejection controls. The large cases use +64 and 65 axes. Their base dimensions are 2^64 and 2^65; no dense base +array is allocated. The 64-axis witness is the exact entry 1/4294967296. +The 65-axis relation retains H^2=iI as a native operator identity. + +[RESULT.json](RESULT.json) records 96 group elements, 689 exact trace-filter +values, 2,124 source columns, 48 entangling trace cases, 60 explicit tensor +norms, 72 complete endpoint comparisons, 24 full tensor program comparisons, +16 random literal witnesses, two zero-axis boundary cases and 20 controls. +The source columns include both +orientations of an actual nine-axis Gaussian gate. Controls reject nonunitary +inputs, non-dyadic phases, Toffoli, malformed instructions, wrong tensor phases, +missing helper returns and false witnesses. Source hashes are checked before +the replay imports the frozen files. + +[MUTATIONS.json](MUTATIONS.json) records four private-copy defects rejected in +both Python modes: a missing trace factor, an ignored inverse, an omitted +dirty return and a missing Gram normalization. The audit prints +`PASS_CLIFFORD_GRAM_MUTATIONS`. The local runs used CPython 3.12.13 on macOS +with no third-party packages. + +[ADVANCES-MUTATIONS.json](ADVANCES-MUTATIONS.json) records four additional +defects rejected in both modes: a wrong native C phase, an ignored native +inverse sign, a missing prefix constraint and an omitted dirty return. +The audit prints `PASS_CLIFFORD_ADVANCE_MUTATIONS`. + +The written proof supplies the universal quantifiers. Finite tests corroborate +it. This is author-checked with substantial AI assistance, not independent +human or proof-kernel acceptance. Compilation can expand exponentially many +terms. The compact path and witness algorithms use polynomial work in the +axis count, literal word length, tensor width and expanded support. The +original dense frontend still uses base dimension 2^n. No polynomial-time claim in instruction +length or practical full-supplier speedup follows. The provider application +checks the complete selected local word and its native recipes. A selected +controller/compiler cold replay, new admission, Lean and Docker are not run. +Physical storage, tapes, stock, precision and outer recovery remain separate. +Programs that change with f, non-Clifford gates, continuous phases, nonunitary +native operators, rounded leaves and restricted clean-input contracts are excluded. + +## Sources and credit + +Base: canonical main `7c472563474e60185e6ca101a17622133d047e56`, priority 7. +[SOURCES.json](SOURCES.json) binds exact sources. No predecessor is modified. +The provider application has the separate current-main pin +`1ec1119972c9aefe42525172d07b332fcff81cb4`; its source copies and full credit +are in [provider/SOURCES.json](provider/SOURCES.json) and +[provider/NOTICE.md](provider/NOTICE.md). +Rohan Arun supplies the retained native compiler, following Jeremy Kothe and +the native lineage. Tekalign's retention and Cinna Davis's borrowing work keep +their credit. The complete [notice](vendor/NATIVE-LINEAGE-NOTICE) accompanies +the byte-identical kernel. + +zxv's [PR #5235](https://github.com/CrocSwap/integer-mult-bounds/pull/5235) +supplies the independent-symbol interface and frozen Gaussian arithmetic. +Krzysztof Wojt's [PR #5262](https://github.com/CrocSwap/integer-mult-bounds/pull/5262) +supplies the inverse-aware interface and native-relation handoff. lm1909's +[projection-recursion check](https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/research/projection-recursion-check/README.md) +already uses positive-width group separation, following Jacob Alan Sussman's +engine model. Cinna Davis, ToikY, Sagar Thakrar, roger-sato and the retained +free-word/tensor audits keep their earlier results and attribution. + +Chris R's [PR #4928](https://github.com/CrocSwap/integer-mult-bounds/pull/4928) +and [PR #4978](https://github.com/CrocSwap/integer-mult-bounds/pull/4978) +already use finite Clifford alphabets and tensor Gram separation. Their +[general separation proof](https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/research/two-full-retained-helper-ceiling/science/PROOF.md) +and [passive-query clarification](https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/research/passive-saved-query-ceiling/evidence/frozen/pr4948-saved-query-macro-gate/UNIFORM-ALPHABET-ADDENDUM.md) +retain that credit. This package adds an explicit linear cutoff and constant +stability bound for fixed scalar coefficients in the full dyadic class. + +Concurrent [PR #5369](https://github.com/CrocSwap/integer-mult-bounds/pull/5369) +proves a four-width criterion for affine-quadratic monomial maps. +Its scope excludes Hadamard gates. The +[coordination claim](https://github.com/CrocSwap/integer-mult-bounds/discussions/5236#discussioncomment-19153620) +records this package's larger class, Gram test and stability claim. Public +PR/Discussion bodies and relevant main notes were checked. Historical diffs +and unpublished work remain outside coverage. + +Classical ingredients are credited in [PROOF.md](PROOF.md). No new general +Burnside-Brauer theorem, general circuit identity algorithm or global priority +is claimed. The contribution is the explicit native trace filter, stable +cutoff, program frontend, compact witness and source-bound validation. +The code invariant follows Runge and Nebe, Rains and Sloane. The binary +quadratic-form method follows Dehaene and De Moor. [ADVANCES.md](ADVANCES.md) +links those sources and derives the native phase conventions used here. + +## Open next questions + +1. Find the sharp maximum cutoff for n>=2. The one-axis maximum eight is + now sharp. The general eight-width test still reaches 8n+4. +2. Prove a useful stability constant on the eight selected widths. The + present 75/76 bound uses the full range 1,...,8n+4. +3. Bind a complete current provider and measure support growth. Retain every + input/return and native phase. Physical admission and a full bill remain open. + +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. diff --git a/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/RESEARCH-NOTES.md b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/RESEARCH-NOTES.md new file mode 100644 index 0000000000..dc3244e15d --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/RESEARCH-NOTES.md @@ -0,0 +1,133 @@ +# Continuation research record + +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. + +## Starting point + +The first result is commit 0db0609042d3bee25028ef6515fcee40a33e958d in +[PR #5376](https://github.com/CrocSwap/integer-mult-bounds/pull/5376). +It proves the 8n+4 positive-width cutoff and a 14/15 separation bound. +Both local modes, the export, mutation checks and hosted CI passed. +The continuation refresh found main at +1ec1119972c9aefe42525172d07b332fcff81cb4. Priority revision 7 and both +consumed kernels are unchanged. The selected kappa is not part of this work. + +## Questions and acceptance tests + +1. Can a degree-eight invariant reduce the number of widths to eight? + Prove invariance under a complete native generating set. Prove the + resulting kernel inclusion, with all width and coefficient quantifiers. +2. Can the filter bound improve from 14/15 to 75/76? + Prove the coefficient signs and control their total absolute value for + every n. Numerical samples do not establish the uniform bound. +3. What is the sharp one-axis positive-width cutoff? + Combine an exact full-rank Gram certificate with an explicit lower-bound + example. Do not generalize a one-axis result to other axis counts. +4. Can exact traces and entries avoid a dense 2^n base matrix? + Derive a phase-exact quadratic-sum algorithm. Compare it with the frozen + source and independent dense cases, including inverses and zero traces. + Preserve possible exponential growth in expanded circuit support. + +## Initial observations, not yet new accepted results + +For n=1,...,12, exact filter coefficient sums give reciprocal positive mass +at least 75/76. The n=1 value is exactly 75/76. The later values increase +toward approximately 0.9887179563. These samples suggest a monotonicity +proof; they do not prove it. + +The extended binary Hamming code of length eight is self-dual and doubly +even. Its row-code tensor is a candidate invariant for every axis count. +The classical code-invariant construction is prior work of Runge and +Nebe, Rains and Sloane, not a new invariant discovered here. + +The original direct witness search examines all D^2 coordinate pairs at +each tensor factor. Even a compact trace routine alone does not remove +that search. A complete scalable extractor needs a separate argument. + +## Results of the continuation + +The proofs and algorithms are saved in [ADVANCES.md](ADVANCES.md), +[quadratic.py](quadratic.py) and [compact.py](compact.py). + +1. The length-eight code invariant gives kernel inclusion from f+8 to f. + Eight selected widths now suffice. For nine axes these are 69 through 76. +2. The coefficient sign pattern ++-- gives a monotonicity proof for the + filter norm. Its maximum is 77/75 at n=1. Positive mass is at most 76/75, + so the stable separation improves from 14/15 to 75/76. +3. The one-axis Gram sum at widths 5,6,7,8 has rank 96. A saved inverse + over F_65537 proves this rank in characteristic zero. The previous + Reynolds example proves that the maximum cutoff eight is sharp. + Central scalar characters also prove that four widths are necessary. +4. Exact quadratic path sums retain the native global phase. Conditional + sums with coordinate prefixes give a bitwise witness extractor. This + removes both the dense base matrix and the D^2 coordinate scan. + +The first modular experiment gave cumulative ranks modulo 65537 of +4,14,34,57,77,91,95,96 at widths 1 through 8. These are modular ranks; +the lower-width values alone are not characteristic-zero rank certificates. +The final proof uses the rank-96 inverse and the separate Reynolds obstruction. + +The replay includes 640 exhaustive small quadratic sums, every one-axis +native group word, entangling two- and three-axis words, complete register +programs and exact positive relations. The large cases certify an explicit +64-axis entry and the phase relation on 65 axes. Full counts and literal +certificates are saved with the package. + +## Performance correction + +The initial filter routine repeatedly reduced rational coefficients. The +continuation instead multiplies integer numerator factors and keeps one +denominator. A direct comparison with the function from commit +0db0609042d3bee25028ef6515fcee40a33e958d gave identical coefficient lists +at n=0,1,2,9,16,32. One local CPython 3.14.7 measurement at n=32 took +0.283 seconds before and 0.0149 seconds after. This is one measurement of +the filter builder, not a full-verifier or provider speed claim. +The registered validation uses CPython 3.12.13 and checks the original +receipts as well as the new results. + +The first read-only continuation replay found a receipt-comparison defect: +native gate tuples serialize as JSON arrays. Comparing the loaded arrays +with in-memory tuples fails even when the serialized bytes agree. The +receipt check now compares canonical serialized bytes. This fixes the +serialization boundary without changing mathematical values or certificates. + +## Limits and routes not established + +The eight-width embedding does not preserve the dimension-free stability +constant. The 75/76 bound still uses all widths from 1 through 8n+4. A +trace routine alone would not remove the coordinate search; the conditional +two-path sum is needed for that step. The general maximum cutoff is not +proved sharp, and the one-axis result cannot be extrapolated to n>=2. + +The code invariant and binary quadratic-form method are classical. No +literature priority claim is made for those methods. The native phase +derivation, program binding, width refinements and reproducible certificates +are the contribution here. Symbolic word support can still be exponential. +No complete current provider, physical invoice or kappa improvement follows. +The written proofs remain author-checked with substantial AI assistance. + +The final upstream refresh kept main at +1ec1119972c9aefe42525172d07b332fcff81cb4. The selected result and source +pins did not change. The canonical Discussion claim remains the coordination +point. This continuation updates the same focused PR. + +## Local verification closeout + +The registered runner passed all four commands on CPython 3.12.13: +the original replay and the continuation replay, each in normal and +optimized mode. One complete local run took 88.42 seconds. The original +receipts remain unchanged after the integer filter optimization. + +Both mutation audits passed. Each of eight defects was rejected in both +Python modes, for 16 negative runs. The new defects change a native phase, +an inverse sign, a coordinate constraint and a dirty return. The metadata +and pinned-source check also passed. Exact commands are in README.md. + +The final advisory overlap refresh at 2026-10-23 21:12 UTC covered 337 +open PRs and 4,676 Discussion records, with complete remote pagination. +The new-term matches were this contribution and an unrelated occurrence +of 75/76 in a prior pencil-selection note. The sparse local checkout covers +only 16 of 7,269 note paths. Relevant predecessor proofs were read +separately. Historical diffs and unpublished work remain outside coverage. +The concurrent monomial PR remains at its previously reviewed head and +has not been changed by this work. diff --git a/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/RESULT.json b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/RESULT.json new file mode 100644 index 0000000000..bd440a4b06 --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/RESULT.json @@ -0,0 +1,98 @@ +{ + "closure_edges": 192, + "complete_endpoint_comparisons": 72, + "controls": [ + "wrong witness value", + "wrong witness width", + "wrong certificate schema", + "wrong certificate problem_sha256", + "wrong certificate axes", + "wrong certificate cutoff", + "nonunitary", + "continuous rational phase", + "wrong shape", + "floating scalar", + "non-Clifford dyadic unitary", + "invalid instruction 11", + "invalid instruction 12", + "invalid instruction 13", + "invalid instruction 14", + "invalid instruction 15", + "invalid instruction 16", + "omitted helper return detected", + "noncommuting order detected", + "phase outside tensor detected" + ], + "cutoff": "8n+4", + "dense_norm_cases": 60, + "entangling_trace_cases": 48, + "full_tensor_programs": 24, + "native_source_columns": 2124, + "one_axis_group_order": 96, + "polynomial_values": 689, + "random_literal_witnesses": 16, + "reynolds": { + "coefficient_norm_squared": "1/96", + "first_nonzero_width": 8, + "input_role": 0, + "normalized_squared_norms": [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "15/256", + "0", + "0", + "0", + "155/4096" + ], + "output_role": 1, + "support": 96, + "trace_buckets": 13, + "witness": { + "discrepancy": "5/24", + "input_tuple": [ + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1 + ], + "output_tuple": [ + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1 + ], + "width": 8 + } + }, + "separation": "14/15", + "status": "PASS_CLIFFORD_TENSOR_GRAM_NO_NEW_KAPPA", + "trace_histogram": { + "-1": 8, + "-1+1i": 6, + "-1-1i": 6, + "-2": 1, + "0": 36, + "0+1i": 8, + "0+2i": 1, + "0-1i": 8, + "0-2i": 1, + "1": 8, + "1+1i": 6, + "1-1i": 6, + "2": 1 + }, + "zero_axis_cases": 2 +} diff --git a/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/SOURCES.json b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/SOURCES.json new file mode 100644 index 0000000000..874eb9c3f4 --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/SOURCES.json @@ -0,0 +1,141 @@ +{ + "schema_version": 1, + "base_commit": "7c472563474e60185e6ca101a17622133d047e56", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "c35482cd9035843b15a634cc8276a7e1e40e8395", + "sha256": 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"c5907050a9a7fa36d4fcba3ad4fe440d1bec2063360c095013891785ba65c3ce" + } + ], + "attribution": "Rohan Arun and the retained native lineage supply the exact kernel; Tekalign retained its source. zxv supplies fields.py. Krzysztof Wojt supplies the inverse-interface handoff. lm1909 and Jacob Alan Sussman supply the prior positive-width group-separation use. See README.md and the retained notice. New material by Ali Romman with substantial OpenAI Codex assistance; Apache-2.0. Chris R / Clear1nsight supplies the related finite-alphabet tensor separation in PR4928 and PR4978. The current provider application retains Cao Yifan / intqwq, Chris R / Clear1nsight, Cinna Davis and all source frame/helper/adapter credit in provider/NOTICE.md. Current source bytes are copied and authenticated inside the package; their source paths are provenance pins." +} diff --git a/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/TASK.json b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/TASK.json new file mode 100644 index 0000000000..220174d087 --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/TASK.json @@ -0,0 +1,133 @@ +{ + "schema_version": 1, + "task_id": "formal-interface-lemma", + "priority_revision": 7, + "base_commit": "7c472563474e60185e6ca101a17622133d047e56", + "original_card": { + "id": "formal-interface-lemma", + "question": "Can one uncovered interface implication be formalized with exact caller and certificate bindings?", + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/gate-operand-parity-lean/README.md", + "research/staged544-certified-endpoint/README.md", + "research/unconditional-batched-crt/README.md" + ], + "methods": [ + "Formalize a missing boundary lemma identified by the selected review.", + "Audit a formal theorem-to-certificate binding independently." + ], + "acceptance_gate": "State the exact formalized proposition and remaining assumptions; avoid duplicate arithmetic formalizations already present.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Inventory the gate-operand parity lemma (#3807) and certified endpoint arithmetic (#3857). Neither is a full multiplication proof. For #4100, audit the compact-switch statement and its hypotheses before formalizing it.", + "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately." + }, + "first_experiment": "Write one missing statement with quantified hypotheses, actual caller and existing coverage. A compact-switch lemma is a candidate only after its mathematical contract is reviewed. Establish a bounded proof plan before a separately budgeted proof-assistant build; do not rerun large Lean jobs as orientation.", + "bottleneck_link": "A missing interface proof can reduce the conditional gap even if it does not change kappa.", + "allowed_variations": [ + "Narrow to one formal lemma or one theorem-to-certificate binding." + ], + "scope_change_triggers": [ + "Formalizing already-covered arithmetic and claiming the full multiplication theorem." + ], + "overlap_terms": [ + "hyperplane end", + "formal interface", + "Lean binding", + "3807", + "3857", + "4100", + "gate-operand-parity-lean", + "staged544-certified-endpoint", + "unconditional-batched-crt" + ], + "existing_checks": [ + { + "scope": "PR #3807: scoped gate-operand parity formalization.", + "evidence": "research/gate-operand-parity-lean/README.md", + "remaining": "Exact theorem-to-caller binding and genuinely uncovered interface lemmas.", + "status": "author-checked", + "source_commit": "4c3530f42a6abcc48e7a6bcffd6c901911dc8269", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #3857: certified real-power moment/endpoint arithmetic.", + "evidence": "research/staged544-certified-endpoint/README.md", + "remaining": "Uniform algorithmic implications, not another endpoint digit.", + "status": "author-checked", + "source_commit": "ef4315b8caa605e47a2515004845eb2d2ed71a86", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4100: compact-switch formalization proposed as future validation.", + "evidence": "research/unconditional-batched-crt/README.md", + "remaining": "Audit the statement and assumptions before a formal proof campaign.", + "status": "author-checked", + "source_commit": "337d04939571a637aeab54a0f58f54fde811663a", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + }, + "scope_status": "changed", + "actual_scope": "Eight-width full dyadic Clifford tests, compact exact native certificates, complete selected-provider replay and a uniform obstruction to all 30328 early/late fusions of two paid climbs on one persistent role.", + "scope_change_reason": "Supply a written native-relation interface theorem and executable certificate rather than repeat a formal arithmetic endpoint.", + "bottleneck_link": "A fixed native program needs an all-width endpoint proof. The trace filter supplies a uniform finite test and a quantified failure certificate for the full dyadic Clifford class.", + "budget_minutes": 60, + "stop_rule": "Prove the stated cutoff and stability bound, check source and independent tensor fixtures, then publish one scoped package. No supplier or selected-frontier update.", + "outcome": "completed", + "evidence": "PROOF.md, ADVANCES.md, PROVIDER.md, all result and mutation receipts, source-bound complete provider inputs and registered normal/optimized replays.", + "author": "Ali Romman with substantial OpenAI Codex assistance", + "ai_assistance": "Substantial OpenAI Codex assistance in derivation, implementation, self-review, validation and publication. No independent human or proof-kernel review.", + "open_questions": [ + { + "question": "What is the sharp maximum cutoff for n>=2?", + "why_it_matters": "Eight tests still reach width 8n+4.", + "first_step": "Find a smaller representation-theoretic bound or a matching explicit residual.", + "blocked_by": "The one-axis modular certificate does not generalize." + }, + { + "question": "Can the eight selected widths retain a dimension-free stability constant?", + "why_it_matters": "The 75/76 bound uses the full range of widths.", + "first_step": "Bound the selected-width Gram spectrum.", + "blocked_by": "The invariant embedding alone loses powers of the base dimension." + }, + { + "question": "Can a changed contact provide the transformed operand at lower complete cost?", + "why_it_matters": "Every fixed pair fusion retains a nonzero contact defect.", + "first_step": "Use one saved contact certificate and replace its literal scalar contact with a priced native query.", + "blocked_by": "Whole-caller endpoint, dirty restoration and full cost remain." + }, + { + "question": "Can coordinated pair rewrites cancel their defects?", + "why_it_matters": "The obstruction covers one pair at a time.", + "first_step": "Name a small joint rewrite and run its complete native endpoint.", + "blocked_by": "No joint-rewrite or physical invoice certificate exists." + } + ], + "coordination": "https://github.com/CrocSwap/integer-mult-bounds/discussions/5236#discussioncomment-19153620", + "continuation": { + "user_requested": true, + "main_checkpoint": "1ec1119972c9aefe42525172d07b332fcff81cb4", + "previous_result": "0db0609042d3bee25028ef6515fcee40a33e958d", + "source_pins_changed": false, + "notes": "RESEARCH-NOTES.md" + }, + "provider_application": { + "user_requested": true, + "main_checkpoint": "1ec1119972c9aefe42525172d07b332fcff81cb4", + "verifier_predecessor": "5370f4465388dbbfff3ba45d5d6ae99d447b1766", + "scope": "Complete selected local provider in both directions, then early/late fusion of every pair of paid persistent climbs on one role. All positive tensor widths.", + "decision": "Narrow after the full fixed pair-fusion domain fails. Changed contacts or coordinated rewrites require a new test.", + "outcome": "No kappa improvement; complete provider certificates and a uniform scoped obstruction.", + "paid_profile_changed": false, + "unknown_costs": "No changed physical, compiler or outer cost is assumed zero. All candidate rewrites fail the algebraic endpoint.", + "notes": "provider/RESEARCH-NOTES.md", + "sources": "provider/SOURCES.json" + } +} diff --git a/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/VERIFY.json b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/VERIFY.json new file mode 100644 index 0000000000..b41360ab97 --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/VERIFY.json @@ -0,0 +1,87 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py", + "research/universal-dirty-certificates/fields.py" + ], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-W", + "error", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 90, + "checks": "Exact trace filter, complete one-axis group, source columns, independent tensor norms and endpoints, literal witnesses and rejection controls." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-W", + "error", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 90, + "checks": "Exact trace filter, complete one-axis group, source columns, independent tensor norms and endpoints, literal witnesses and rejection controls." + }, + { + "argv": [ + "{python}", + "-I", + "-W", + "error", + "-B", + "{package}/verify_advances.py" + ], + "timeout_seconds": 90, + "checks": "Code invariant, stronger filter bound, one-axis rank certificate, quadratic sums, complete native programs, bitwise witnesses and large-axis phase cases." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-W", + "error", + "-B", + "{package}/verify_advances.py" + ], + "timeout_seconds": 90, + "checks": "Code invariant, stronger filter bound, one-axis rank certificate, quadratic sums, complete native programs, bitwise witnesses and large-axis phase cases." + }, + { + "argv": [ + "{python}", + "-I", + "-W", + "error", + "-B", + "{package}/verify_provider.py" + ], + "timeout_seconds": 420, + "checks": "All 7000 native recipe classes, both complete selected provider directions, all 30328 pair fusions, separate contact and coverage replays, literal full-program witnesses and controls." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-W", + "error", + "-B", + "{package}/verify_provider.py" + ], + "timeout_seconds": 420, + "checks": "All 7000 native recipe classes, both complete selected provider directions, all 30328 pair fusions, separate contact and coverage replays, literal full-program witnesses and controls." + } + ] +} diff --git a/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/audit_advances.py b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/audit_advances.py new file mode 100644 index 0000000000..0429c569ab --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/audit_advances.py @@ -0,0 +1,58 @@ +"""Reject compact-computation defects in private package copies. + +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +""" +import argparse +import json +from pathlib import Path +import shutil +import subprocess +import sys +import tempfile + +HERE = Path(__file__).resolve().parent +MUTATIONS = [ + ("conjugate native C factor", "quadratic.py", "G.pair(1, sign)/2", "G.pair(1, -sign)/2", "Native trace phase"), + ("ignore native inverse sign", "quadratic.py", "out.append((kind, gate[1], -gate[2]))", + "out.append((kind, gate[1], gate[2]))", "Native entry phase"), + ("omit output prefix constraint", "quadratic.py", + "equations += [left.outputs[j] ^ x for j, x in enumerate(output_prefix)]", + "equations += []", "Native partial inner product"), + ("omit final native return", "compact.py", "enumerate(zip(left, right))", + "enumerate(zip(left[:-1], right[:-1]))", "Compact complete endpoint"), +] + + +def audit(write=False): + results = [] + for label, filename, old, new, expected in MUTATIONS: + for optimized in (False, True): + with tempfile.TemporaryDirectory(prefix="clifford-advance-mutation-") as directory: + target = Path(directory) / "package" + shutil.copytree(HERE, target, ignore=shutil.ignore_patterns("__pycache__")) + source = target / filename + original = source.read_text(encoding="utf-8") + if original.count(old) != 1: + raise ValueError("Mutation target is not unique: "+label) + source.write_text(original.replace(old, new), encoding="utf-8") + command = [sys.executable, "-I", "-W", "error", "-B"] + if optimized: + command.append("-O") + command += [str(target / "verify_advances.py"), "--write"] + run = subprocess.run(command, text=True, capture_output=True, timeout=180) + if run.returncode == 0 or "ValueError: "+expected not in run.stderr: + raise ValueError("Mutation did not fail at its semantic check: "+label+"\n"+run.stdout+run.stderr) + results.append({"mutation": label, "optimized": optimized, "rejection": expected}) + receipt = {"status": "PASS_CLIFFORD_ADVANCE_MUTATIONS", "cases": results} + path = HERE / "ADVANCES-MUTATIONS.json" + if write: + path.write_text(json.dumps(receipt, indent=2, sort_keys=True)+"\n", encoding="utf-8") + elif json.loads(path.read_text(encoding="utf-8")) != receipt: + raise ValueError("Committed advance mutation receipt mismatch") + print(receipt["status"]) + + +if __name__ == "__main__": + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--write", action="store_true", help="Regenerate the advance mutation receipt") + audit(parser.parse_args().write) diff --git a/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/audit_mutations.py b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/audit_mutations.py new file mode 100644 index 0000000000..11fd235740 --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/audit_mutations.py @@ -0,0 +1,57 @@ +"""Check that semantic defects fail in private package copies. + +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +""" +import argparse +import json +from pathlib import Path +import shutil +import subprocess +import sys +import tempfile + +HERE = Path(__file__).resolve().parent +MUTATIONS = [ + ("omit final trace root", "range(1, 2*n+1)", "range(1, 2*n)", "Polynomial endpoints"), + ("ignore inverse", "adjoint(operators[symbol]) if inverse else operators[symbol]", + "operators[symbol]", "Signed-word complete endpoint"), + ("omit final return", "enumerate(zip(left, right))", "enumerate(zip(left[:-1], right[:-1]))", + "Zero-axis scalar group"), + ("remove Gram normalization", "G(0))/d\n for right", "G(0))\n for right", + "Independent dense norm"), +] + + +def audit(write=False): + results = [] + for label, old, new, expected in MUTATIONS: + for optimized in (False, True): + with tempfile.TemporaryDirectory(prefix="clifford-gram-mutation-") as directory: + target = Path(directory) / "package" + shutil.copytree(HERE, target, ignore=shutil.ignore_patterns("__pycache__")) + source = target / "certify.py" + original = source.read_text(encoding="utf-8") + if original.count(old) != 1: + raise ValueError("Mutation target is not unique: "+label) + source.write_text(original.replace(old, new), encoding="utf-8") + command = [sys.executable, "-I", "-W", "error", "-B"] + if optimized: + command.append("-O") + command += [str(target / "verify.py"), "--write"] + run = subprocess.run(command, text=True, capture_output=True, timeout=180) + if run.returncode == 0 or "ValueError: "+expected not in run.stderr: + raise ValueError("Mutation did not fail at its semantic check: "+label+"\n"+run.stdout+run.stderr) + results.append({"mutation": label, "optimized": optimized, "rejection": expected}) + receipt = {"status": "PASS_CLIFFORD_GRAM_MUTATIONS", "cases": results} + path = HERE / "MUTATIONS.json" + if write: + path.write_text(json.dumps(receipt, indent=2, sort_keys=True)+"\n", encoding="utf-8") + elif json.loads(path.read_text(encoding="utf-8")) != receipt: + raise ValueError("Committed mutation receipt mismatch") + print(receipt["status"]) + + +if __name__ == "__main__": + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--write", action="store_true", help="Regenerate the mutation receipt") + audit(parser.parse_args().write) diff --git a/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/certify.py b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/certify.py new file mode 100644 index 0000000000..95c1cbf710 --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/certify.py @@ -0,0 +1,329 @@ +"""Decide complete tensor identities for dyadic Clifford register programs. + +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +The trace interpolation proof is in PROOF.md. No tensor matrix is built. +""" +import argparse +from fractions import Fraction as Q +import hashlib +import json +from pathlib import Path +import sys + +sys.path.insert(0, str(Path(__file__).resolve().parent / "vendor")) +from fields import Gaussian as G + + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def conjugate(z): + return G.pair(z.real, -z.imag) + + +def norm2(z): + return z.real*z.real + z.imag*z.imag + + +def power(z, k): + result = G(1) + while k: + if k & 1: + result = result*z + z = z*z + k //= 2 + return result + + +def scalar(x): + require(type(x) in (str, int), "Use an integer or an exact Gaussian string") + return G(x) + + +def identity(d): + return tuple(tuple(G(int(i == j)) for j in range(d)) for i in range(d)) + + +def adjoint(a): + return tuple(tuple(conjugate(a[j][i]) for j in range(len(a))) for i in range(len(a))) + + +def multiply(a, b): + d = len(a) + out = [[G(0) for _ in range(d)] for _ in range(d)] + sparse_b = [[(j, x) for j, x in enumerate(row) if x] for row in b] + for i, row in enumerate(a): + for k, x in enumerate(row): + if x: + for j, y in sparse_b[k]: + out[i][j] = out[i][j] + x*y + return tuple(tuple(row) for row in out) + + +def key(a): + return tuple(tuple((z.real, z.imag) for z in row) for row in a) + + +def pauli(n, x, z, phase=0): + d = 1 << n + unit = power(G("i"), phase % 4) + return tuple( + tuple(unit*(-1 if (z & j).bit_count() % 2 else 1) if i == j ^ x else G(0) + for j in range(d)) for i in range(d)) + + +def pauli_signature(a): + """Return the exact X/Z/phase label, or reject a non-Pauli matrix.""" + d = len(a) + n = d.bit_length()-1 + first = [(i, row[0]) for i, row in enumerate(a) if row[0]] + require(len(first) == 1, "Conjugated generator is not a Pauli") + x, unit = first[0] + units = [G(1), G("i"), G(-1), G("-i")] + require(unit in units, "Conjugated generator has a non-Pauli phase") + z = 0 + for j in range(n): + value = a[x ^ (1 << j)][1 << j] + require(value in (unit, -unit), "Conjugated generator is not a Pauli") + if value == -unit: + z |= 1 << j + phase = units.index(unit) + require(a == pauli(n, x, z, phase), "Conjugated generator is not a Pauli") + return x, z, phase + + +def validate_operator(a, n): + d = 1 << n + require(len(a) == d and all(len(row) == d for row in a), "Operator shape") + for row in a: + for value in row: + for part in (value.real, value.imag): + den = part.denominator + require(den & (den-1) == 0, "Operator entry is not dyadic") + star = adjoint(a) + require(multiply(star, a) == identity(d), "Operator is not unitary") + return [pauli_signature(multiply(multiply(a, pauli(n, x, z)), star)) + for x, z in [(1 << j, 0) for j in range(n)] + [(0, 1 << j) for j in range(n)]] + + +def parse_problem(problem): + require(type(problem) is dict and set(problem) == {"axes", "roles", "operators", "program", "reference"}, + "Problem keys") + n, r = problem["axes"], problem["roles"] + require(type(n) is int and n >= 0 and type(r) is int and r > 0, "Axes or roles") + require(type(problem["operators"]) is dict, "Operators must be an object") + matrices = {} + for name, rows in problem["operators"].items(): + require(type(name) is str and bool(name) and type(rows) is list and + all(type(row) is list for row in rows), "Operator format") + a = tuple(tuple(scalar(x) for x in row) for row in rows) + validate_operator(a, n) + matrices[name] = a + return n, r, matrices + + +def accumulate(out, label, coefficient): + value = out.get(label, G(0)) + coefficient + if value: + out[label] = value + else: + out.pop(label, None) + + +def compile_difference(problem): + """Keep phases in matrix keys and keep scalar coefficients outside them.""" + n, roles, operators = parse_problem(problem) + eye = identity(1 << n) + bank = {key(eye): eye} + products = {} + + def execute(instructions): + require(type(instructions) is list, "Instruction list") + rows = [{(i, key(eye)): G(1)} for i in range(roles)] + for instruction in instructions: + require(type(instruction) is dict, "Instruction object") + kind = instruction.get("op") + allowed = {"add": {"op", "src", "dst", "coefficient"}, + "scale": {"op", "dst", "coefficient"}, + "swap": {"op", "src", "dst"}, + "apply": {"op", "dst", "symbol", "inverse"}, + "query": {"op", "src", "dst", "symbol", "inverse", "coefficient"}} + require(kind in allowed and set(instruction) <= allowed[kind], "Instruction keys") + dst = instruction.get("dst") + require(type(dst) is int and 0 <= dst < roles, "Destination role") + src = instruction.get("src", dst) + require(type(src) is int and 0 <= src < roles, "Source role") + if kind in ("add", "query", "swap"): + require("src" in instruction, "Missing source role") + if kind == "swap": + rows[src], rows[dst] = rows[dst], rows[src] + continue + if kind == "scale": + coefficient = scalar(instruction["coefficient"]) + rows[dst] = {k: coefficient*v for k, v in rows[dst].items() if coefficient*v} + continue + image = rows[src].copy() + if kind in ("apply", "query"): + symbol = instruction.get("symbol") + inverse = instruction.get("inverse", False) + require(type(inverse) is bool and type(symbol) is str and symbol in operators, "Operator reference") + a = adjoint(operators[symbol]) if inverse else operators[symbol] + image = {} + for (i, old), coefficient in rows[src].items(): + cache_key = symbol, inverse, old + if cache_key not in products: + product = multiply(a, bank[old]) + new = key(product) + bank[new] = product + products[cache_key] = new + accumulate(image, (i, products[cache_key]), coefficient) + if kind == "apply": + rows[dst] = image + else: + coefficient = scalar(instruction.get("coefficient", 1)) + updated = rows[dst].copy() + for label, value in image.items(): + accumulate(updated, label, coefficient*value) + rows[dst] = updated + return rows + + left, right = execute(problem["program"]), execute(problem["reference"]) + result = [] + for output, (a, b) in enumerate(zip(left, right)): + row = a.copy() + for label, coefficient in b.items(): + accumulate(row, label, -coefficient) + for input_role in range(roles): + terms = [(coefficient, bank[operator]) for (i, operator), coefficient in row.items() if i == input_role] + if terms: + result.append((output, input_role, terms)) + return n, result + + +def cutoff_polynomial(n): + require(type(n) is int and n >= 0, "Nonnegative axis count") + coefficients, denominator = [1], 1 + for j in range(1, 2*n+1): + scale, sign = 4**j, (-1)**j + new = [0]*(len(coefficients)+1) + for degree, coefficient in enumerate(coefficients): + new[degree] -= sign*coefficient + new[degree+1] += scale*coefficient + coefficients = new + denominator *= scale-sign + return [Q(0)]+[Q(a, 4*denominator) for a in coefficients for _ in range(4)] + + +def gram(matrices): + d = len(matrices[0]) + return [[sum((conjugate(a)*b for row_a, row_b in zip(left, right) + for a, b in zip(row_a, row_b)), G(0))/d + for right in matrices] for left in matrices] + + +def energy(coefficients, inner, width): + value = sum((conjugate(a)*b*power(inner[i][j], width) + for i, a in enumerate(coefficients) for j, b in enumerate(coefficients)), G(0)) + require(value.imag == 0 and value.real >= 0, "Invalid squared residual norm") + return value.real + + +def trace_buckets(coefficients, inner): + out = {} + for i, a in enumerate(coefficients): + for j, b in enumerate(coefficients): + value = inner[i][j] + accumulate(out, (value.real, value.imag), conjugate(a)*b) + return out + + +def bucket_energies(buckets, cutoff): + powers = {label: G(1) for label in buckets} + answer = [] + for _ in range(cutoff): + for label in powers: + powers[label] = powers[label]*G.pair(*label) + value = sum((coefficient*powers[label] for label, coefficient in buckets.items()), G(0)) + require(value.imag == 0 and value.real >= 0, "Invalid bucket norm") + answer.append(value.real) + return answer + + +def tensor_entry(coefficients, matrices, output, input_tuple): + answer = G(0) + for coefficient, a in zip(coefficients, matrices): + value = coefficient + for x, y in zip(output, input_tuple): + value = value*a[x][y] + answer = answer+value + return answer + + +def entry_witness(coefficients, matrices, inner, width): + """Choose an entry by exact conditional squared norms.""" + d = len(matrices[0]) + initial = energy(coefficients, inner, width) + require(initial > 0, "The requested width has zero residual") + current = list(coefficients) + output, input_tuple = [], [] + for remaining in range(width-1, -1, -1): + best = None + for x in range(d): + for y in range(d): + candidate = [c*a[x][y] for c, a in zip(current, matrices)] + value = energy(candidate, inner, remaining) + if best is None or value > best[0]: + best = value, x, y, candidate + require(best[0] > 0, "Conditional tensor norm lost the witness") + _, x, y, current = best + output.append(x) + input_tuple.append(y) + value = sum(current, G(0)) + require(norm2(value)*d**width >= initial, "Tensor entry lower bound") + return {"width": width, "output_tuple": output, "input_tuple": input_tuple, + "discrepancy": str(value)} + + +def analyze(n, terms): + """Analyze distinct validated Clifford matrices with nonzero coefficients.""" + coefficients, matrices = zip(*terms) + require(len(set(key(a) for a in matrices)) == len(matrices), "Merge equal exact operators first") + inner = gram(matrices) + polynomial = cutoff_polynomial(n) + buckets = trace_buckets(coefficients, inner) + energies = bucket_energies(buckets, len(polynomial)-1) + mass = sum(norm2(c) for c in coefficients) + require(sum(b*v for b, v in zip(polynomial[1:], energies)) == mass, "Trace interpolation failed") + require(max(energies) >= Q(14, 15)*mass, "Stable separation failed") + width = 1 + max(range(len(energies)), key=energies.__getitem__) + witness = entry_witness(coefficients, matrices, inner, width) + return {"support": len(terms), "trace_buckets": len(buckets), "coefficient_norm_squared": str(mass), + "normalized_squared_norms": [str(x) for x in energies], + "first_nonzero_width": 1+next(i for i, x in enumerate(energies) if x), + "witness": witness} + + +def certify(problem): + n, residuals = compile_difference(problem) + digest = hashlib.sha256(json.dumps(problem, sort_keys=True, separators=(",", ":")).encode()).hexdigest() + result = {"schema": "clifford-tensor-gram/v1", "problem_sha256": digest, + "axes": n, "cutoff": 8*n+4, "equivalent_at_all_positive_widths": not residuals, + "nonzero_endpoint_entries": len(residuals)} + if residuals: + output, input_role, terms = residuals[0] + result["failure"] = {"output_role": output, "input_role": input_role, **analyze(n, terms)} + return result + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("problem", type=Path) + args = parser.parse_args() + result = certify(json.loads(args.problem.read_text(encoding="utf-8"))) + print(json.dumps(result, indent=2, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/check_witness.py b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/check_witness.py new file mode 100644 index 0000000000..a3bca57b43 --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/check_witness.py @@ -0,0 +1,150 @@ +"""Check a tensor entry by a separate signed-word interpreter. + +This module does not import the certificate producer or use Gram traces. +It shares only the frozen exact scalar arithmetic. Word support can grow. +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +""" +import argparse +import hashlib +import json +from pathlib import Path +import sys + +sys.path.insert(0, str(Path(__file__).resolve().parent / "vendor")) +from fields import Gaussian as G + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def star(a): + return tuple(tuple(G.pair(a[j][i].real, -a[j][i].imag) + for j in range(len(a))) for i in range(len(a))) + + +def product(a, b): + return tuple(tuple(sum((x*y for x, y in zip(row, column)), G(0)) + for column in zip(*b)) for row in a) + + +def eye(d): + return tuple(tuple(G(int(i == j)) for j in range(d)) for i in range(d)) + + +def add_term(row, word, coefficient): + row[word] = row.get(word, G(0))+coefficient + if not row[word]: + del row[word] + + +def word_endpoint(problem, instructions, input_role): + r = problem["roles"] + rows = [{(): G(1)} if j == input_role else {} for j in range(r)] + for instruction in instructions: + kind, d = instruction["op"], instruction["dst"] + need(type(d) is int and 0 <= d < r, "Destination role") + s = instruction.get("src", d) + need(type(s) is int and 0 <= s < r, "Source role") + if kind == "swap": + rows[d], rows[s] = rows[s], rows[d] + continue + if kind == "scale": + coefficient = G(instruction["coefficient"]) + rows[d] = {w: coefficient*c for w, c in rows[d].items() if coefficient*c} + continue + image = rows[s].copy() + if kind in ("query", "apply"): + symbol, inverse = instruction["symbol"], instruction.get("inverse", False) + need(symbol in problem["operators"] and type(inverse) is bool, "Operator reference") + letter = (symbol, inverse) + image = {} + for word, coefficient in rows[s].items(): + if word and word[0] == (symbol, not inverse): + new_word = word[1:] + else: + new_word = (letter,)+word + add_term(image, new_word, coefficient) + if kind == "apply": + rows[d] = image + else: + need(kind in ("add", "query"), "Instruction kind") + coefficient = G(instruction.get("coefficient", 1)) + updated = rows[d].copy() + for word, value in image.items(): + add_term(updated, word, coefficient*value) + rows[d] = updated + return rows + + +def matrices(problem): + d = 1 << problem["axes"] + bank = {} + for name, rows in problem["operators"].items(): + a = tuple(tuple(G(x) for x in row) for row in rows) + need(len(a) == d and all(len(row) == d for row in a), "Matrix shape") + inverse = star(a) + need(product(a, inverse) == eye(d), "Inverse requires a unitary matrix") + bank[name, False], bank[name, True] = a, inverse + return bank + + +def evaluate_word(word, bank, d): + out = eye(d) + for letter in word: + out = product(out, bank[letter]) + return out + + +def discrepancy(problem, output_role, input_role, output_tuple, input_tuple): + width = len(output_tuple) + d, r = 1 << problem["axes"], problem["roles"] + need(width > 0 and len(input_tuple) == width, "Positive tensor width") + need(all(type(x) is int and 0 <= x < d for x in output_tuple+input_tuple), "Tensor coordinate") + need(type(output_role) is int and 0 <= output_role < r and + type(input_role) is int and 0 <= input_role < r, "Endpoint role") + bank = matrices(problem) + left = word_endpoint(problem, problem["program"], input_role)[output_role] + right = word_endpoint(problem, problem["reference"], input_role)[output_role] + words = left.copy() + for word, coefficient in right.items(): + add_term(words, word, -coefficient) + answer = G(0) + for word, coefficient in words.items(): + a = evaluate_word(word, bank, d) + value = coefficient + for x, y in zip(output_tuple, input_tuple): + value = value*a[x][y] + answer = answer+value + return answer + + +def check(problem, certificate): + need(certificate.get("schema") == "clifford-tensor-gram/v1", "Certificate schema") + digest = hashlib.sha256(json.dumps(problem, sort_keys=True, separators=(",", ":")).encode()).hexdigest() + need(certificate.get("problem_sha256") == digest, "Problem digest") + need(type(certificate.get("axes")) is int and certificate["axes"] == problem["axes"], "Axis count") + need(type(certificate.get("cutoff")) is int and certificate["cutoff"] == 8*problem["axes"]+4, "Cutoff") + need(certificate["equivalent_at_all_positive_widths"] is False, "Expected a negative certificate") + failure = certificate["failure"] + witness = failure["witness"] + need(type(witness["width"]) is int and 1 <= witness["width"] <= certificate["cutoff"], "Witness width") + need(witness["width"] == len(witness["input_tuple"]) == len(witness["output_tuple"]), "Width mismatch") + value = discrepancy(problem, failure["output_role"], failure["input_role"], + witness["output_tuple"], witness["input_tuple"]) + need(value != 0 and value == G(witness["discrepancy"]), "The literal discrepancy does not match") + return str(value) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("problem", type=Path) + parser.add_argument("certificate", type=Path) + args = parser.parse_args() + value = check(json.loads(args.problem.read_text()), json.loads(args.certificate.read_text())) + print("PASS_LITERAL_TENSOR_WITNESS", value) + + +if __name__ == "__main__": + main() diff --git a/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/compact.py b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/compact.py new file mode 100644 index 0000000000..aa83f0f565 --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/compact.py @@ -0,0 +1,182 @@ +"""Certify complete native programs with quadratic sums and bitwise witnesses. + +Program support can grow exponentially. No base or tensor matrix is built. +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +""" +import argparse +from fractions import Fraction as Q +import hashlib +import json +from pathlib import Path +import sys + +sys.path.insert(0, str(Path(__file__).resolve().parent)) +import certify as c +from check_witness import word_endpoint, add_term +from quadratic import Paths, partial_inner, inverse_circuit + + +def decision_widths(n): + if n == 0: + return list(range(1, 5)) + if n == 1: + return list(range(5, 9)) + return list(range(8*n-3, 8*n+5)) + + +def validate(problem): + c.require(type(problem) is dict and set(problem) == {"axes", "roles", "operators", "program", "reference"}, + "Native problem keys") + n, roles = problem["axes"], problem["roles"] + c.require(type(n) is int and n >= 0 and type(roles) is int and roles > 0, "Axes or roles") + c.require(type(problem["operators"]) is dict, "Native operators") + bank = {} + for name, circuit in problem["operators"].items(): + c.require(type(name) is str and bool(name) and type(circuit) is list, "Native operator format") + Paths(n, circuit) + bank[name, False] = circuit + bank[name, True] = inverse_circuit(n, circuit) + allowed = {"add": {"op", "src", "dst", "coefficient"}, + "scale": {"op", "dst", "coefficient"}, "swap": {"op", "src", "dst"}, + "apply": {"op", "dst", "symbol", "inverse"}, + "query": {"op", "src", "dst", "symbol", "inverse", "coefficient"}} + for instructions in (problem["program"], problem["reference"]): + c.require(type(instructions) is list, "Native instruction list") + for op in instructions: + c.require(type(op) is dict and op.get("op") in allowed, "Instruction object") + kind = op["op"] + c.require(set(op) <= allowed[kind], "Instruction keys") + c.require(type(op.get("dst")) is int and 0 <= op["dst"] < roles, "Destination role") + if kind in ("add", "query", "swap"): + c.require(type(op.get("src")) is int and 0 <= op["src"] < roles, "Source role") + if kind in ("query", "apply"): + c.require(type(op.get("symbol")) is str and op["symbol"] in problem["operators"] and + type(op.get("inverse", False)) is bool, "Operator reference") + if kind == "scale": + c.require("coefficient" in op, "Scale coefficient") + if "coefficient" in op: + c.scalar(op["coefficient"]) + return bank + + +def merge_terms(coefficients, paths): + """For unitary matrices, normalized inner product one means equality.""" + d = 1 << paths[0].n + inner = [[partial_inner(a, b)/d for b in paths] for a in paths] + representatives, merged = [], [] + for j, coefficient in enumerate(coefficients): + i = next((i for i, k in enumerate(representatives) if inner[k][j] == 1), None) + if i is None: + representatives.append(j) + merged.append(coefficient) + else: + merged[i] = merged[i]+coefficient + keep = [i for i, coefficient in enumerate(merged) if coefficient] + indices = [representatives[i] for i in keep] + return ([merged[i] for i in keep], [paths[j] for j in indices], + [[inner[i][j] for j in indices] for i in indices]) + + +def residuals(problem): + bank = validate(problem) + n = problem["axes"] + paths = {} + out = [] + for input_role in range(problem["roles"]): + left = word_endpoint(problem, problem["program"], input_role) + right = word_endpoint(problem, problem["reference"], input_role) + for output_role, (a, b) in enumerate(zip(left, right)): + words = a.copy() + for word, coefficient in b.items(): + add_term(words, word, -coefficient) + if not words: + continue + for word in words: + if word not in paths: + circuit = [gate for letter in reversed(word) for gate in bank[letter]] + paths[word] = Paths(n, circuit) + coefficients, operators, inner = merge_terms(list(words.values()), [paths[word] for word in words]) + if coefficients: + out.append((output_role, input_role, coefficients, operators, inner)) + return out + + +def entry_witness(coefficients, paths, inner, width): + """Choose each coordinate bit from two exact conditional norms.""" + n, d = paths[0].n, 1 << paths[0].n + initial = c.energy(coefficients, inner, width) + c.require(initial > 0, "Positive residual norm") + current = list(coefficients) + output, inputs = [], [] + partial_cache = {} + + def score(x, y, remaining): + key = tuple(x), tuple(y) + if key not in partial_cache: + partial_cache[key] = [[partial_inner(a, b, x, y) for b in paths] for a in paths] + partial = partial_cache[key] + value = sum((c.conjugate(a)*b*partial[i][j]*c.power(inner[i][j], remaining) + for i, a in enumerate(current) for j, b in enumerate(current)), c.G(0)) + c.require(value.imag == 0 and value.real >= 0, "Conditional squared norm") + return value.real + + for remaining in range(width-1, -1, -1): + x, y = [], [] + parent = d*c.energy(current, inner, remaining+1) + for coordinate in (x, y): + for _ in range(n): + children = [] + for bit in (0, 1): + coordinate.append(bit) + children.append(score(x, y, remaining)) + coordinate.pop() + c.require(sum(children) == parent, "Conditional norm split") + bit = int(children[1] > children[0]) + coordinate.append(bit) + parent = children[bit] + c.require(parent > 0, "Conditional witness vanished") + a, b = sum(bit << j for j, bit in enumerate(x)), sum(bit << j for j, bit in enumerate(y)) + output.append(a) + inputs.append(b) + current = [coefficient*path.entry(a, b) for coefficient, path in zip(current, paths)] + value = sum(current, c.G(0)) + c.require(c.norm2(value)*d**width >= initial, "Compact entry lower bound") + return {"width": width, "output_tuple": output, "input_tuple": inputs, "discrepancy": str(value)} + + +def analyze(n, coefficients, paths, inner): + polynomial = c.cutoff_polynomial(n) + mass = sum(c.norm2(a) for a in coefficients) + norms = c.bucket_energies(c.trace_buckets(coefficients, inner), 8*n+4) + c.require(sum(b*v for b, v in zip(polynomial[1:], norms)) == mass, "Compact trace interpolation") + c.require(max(norms) >= Q(75, 76)*mass, "Improved stable separation") + c.require(any(norms[f-1] for f in decision_widths(n)), "Reduced width criterion") + width = 1+max(range(len(norms)), key=norms.__getitem__) + return {"support": len(paths), "coefficient_norm_squared": str(mass), + "normalized_squared_norms": [str(x) for x in norms], + "witness": entry_witness(coefficients, paths, inner, width)} + + +def certify(problem): + entries = residuals(problem) + n = problem["axes"] + result = {"schema": "clifford-tensor-gram/native-v1", "axes": n, + "problem_sha256": hashlib.sha256(json.dumps(problem, sort_keys=True, separators=(",", ":")).encode()).hexdigest(), + "cutoff": 8*n+4, "decision_widths": decision_widths(n), + "equivalent_at_all_positive_widths": not entries, "nonzero_endpoint_entries": len(entries)} + if entries: + output, input_role, coefficients, paths, inner = entries[0] + result["failure"] = {"output_role": output, "input_role": input_role, + **analyze(n, coefficients, paths, inner)} + return result + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("problem", type=Path) + args = parser.parse_args() + print(json.dumps(certify(json.loads(args.problem.read_text())), indent=2, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/examples/native-64.certificate.json b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/examples/native-64.certificate.json new file mode 100644 index 0000000000..e2a64e17cc --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/examples/native-64.certificate.json @@ -0,0 +1,552 @@ +{ + "axes": 64, + "cutoff": 516, + "decision_widths": [ + 509, + 510, + 511, + 512, + 513, + 514, + 515, + 516 + ], + "equivalent_at_all_positive_widths": false, + "failure": { + "coefficient_norm_squared": "1", + "input_role": 0, + "normalized_squared_norms": [ + "1", + "1", + "1", + "1", + "1", + "1", + "1", + "1", + "1", + "1", + "1", + "1", + 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No source evaluator is imported. +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +""" +from collections import Counter +from fractions import Fraction as Q +from functools import lru_cache +import gzip +import hashlib +import json +from pathlib import Path + +from check_witness import need +from quadratic import inverse_circuit, rank + +HERE = Path(__file__).resolve().parent +N, D, PERSISTENT, OWNED = 9, 512, 632, 632 + + +def read_inputs(): + manifest = json.loads((HERE / "provider/SOURCES.json").read_bytes()) + objects = {} + for item in manifest["inputs"]: + raw = (HERE / "provider" / item["file"]).read_bytes() + need(hashlib.sha256(raw).hexdigest() == item["sha256"], "Provider source bytes: " + item["file"]) + payload = gzip.decompress(raw) if item["file"].endswith(".gz") else raw + objects[item["name"]] = ([json.loads(line) for line in payload.splitlines()] + if ".jsonl" in item["file"] else json.loads(payload)) + return manifest, objects + + +def transpose(rows): + return [sum(((row >> j) & 1) << k for k, row in enumerate(rows)) for j in range(N)] + + +def inverse(rows): + work = [v | (1 << (N+j)) for j, v in enumerate(rows)] + for j in range(N): + pivot = next((k for k in range(j, N) if work[k] >> j & 1), None) + need(pivot is not None, "Invertible native address map") + work[j], work[pivot] = work[pivot], work[j] + for k in range(N): + if k != j and work[k] >> j & 1: + work[k] ^= work[j] + return [v >> N for v in work] + + +def native_map(columns): + rows = transpose(columns) + inverse_columns = transpose(inverse(rows)) + quadratic = [(1 << j) ^ sum(((a & b).bit_count() % 2) << k + for k, b in enumerate(inverse_columns)) + for j, a in enumerate(inverse_columns)] + return [["P", rows], ["D", quadratic, [(quadratic[j] >> j) & 1 for j in range(N)]]] + + +def conjugate(circuit): + out = [] + for gate in circuit: + if gate[0] == "D": + out.append(["D", gate[1], [(-a) % 4 for a in gate[2]]]) + elif gate[0] in ("C", "phase"): + out.append(list(gate[:-1]) + [-gate[-1]]) + else: + out.append(gate) + return out + + +def normalizer(rec): + need(set(rec) == {"matrix_rows", "quadratic_rows", "linear_Z4", "offset", "phase"}, + "Complete monomial recipe") + need(type(rec["phase"]) is int and 0 <= rec["phase"] < 4, "Canonical native phase") + return [["D", rec["quadratic_rows"], rec["linear_Z4"]], + ["P", rec["matrix_rows"]], ["X", rec["offset"]], ["phase", rec["phase"]]] + + +def recipe(rec): + need(set(rec) == {"left", "right", "rank"}, "Complete paid recipe") + r = rec["rank"] + need(type(r) is int and 0 <= r <= N, "Recipe rank") + if not r: + need(rec["right"] is None, "Rank-zero recipe shape") + return normalizer(rec["left"]) + return normalizer(rec["right"]) + [["C", 1 << j, 1] for j in range(r)] + normalizer(rec["left"]) + + +class Provider: + def __init__(self, word): + self.word = word + self.c = word["canonical"] + c = self.c + need(c["h"] == N and c["v"] == 112 and len(c["start"]) == len(c["final"]) == PERSISTENT, + "Complete selected local boundary") + need(set(word["programs"]) == {"forward", "backward"}, "Both provider directions") + need(all(len(u) <= N and all(type(x) is int and 0 < x < D for x in u) + and rank(u) == len(u) for u in c["frames"]), "Independent native frame bases") + self.maps = {row["op"]: native_map(row["G_columns"]) for row in c["warps"]} + need(set(self.maps) == set(range(1, 73)) and len(c["warps"]) == 72, "All 72 native maps") + + @lru_cache(None) + def frame(self, index): + basis = self.c["frames"][index] + r = len(basis) + if not r: + return [] + if r == N: + return [["C", 1 << j, 1] for j in range(N)] + extended = [] + for v in basis + [1 << j for j in range(N)]: + if rank(extended + [v]) > len(extended): + extended.append(v) + change = native_map(extended) + return inverse_circuit(N, change) + [["C", 1 << j, 1] for j in range(r)] + change + + def edge(self, a, b, direction): + circuit = inverse_circuit(N, self.frame(a)) + self.frame(b) + return conjugate(circuit) if direction == "backward" else circuit + + def warp(self, signed, a, b, direction): + middle = self.maps[abs(signed)] + if signed < 0: + middle = inverse_circuit(N, middle) + circuit = inverse_circuit(N, self.frame(a)) + middle + self.frame(b) + return conjugate(circuit) if direction == "backward" else circuit + + def old_frame(self, role, entrance): + if role >= 224: + return self.frame(self.c["start" if entrance else "final"][role]) + if entrance: + return [["C", self.c["ports"][role], 1]] if role < 112 else [] + return self.frame(1) if role < 112 else [["C", self.c["ports"][role-112], -1]] + self.frame(1) + + def audit_word(self, direction): + """Check every event, frame contact, owned lifetime and paid charge.""" + c, program = self.c, self.word["programs"][direction] + current = list(c["start"]) + [None] + live, paid, counts, adapters, pairs, warps = False, Counter(), Counter(), {}, {}, set() + contacts = {r: [] for r in range(224)} + for j, event in enumerate(program): + kind = event[0] + counts[kind] += 1 + if kind in ("climb", "center"): + if kind == "climb": + _, _, target, a, b, r = event + need(0 <= target < PERSISTENT and not live, "Persistent climb at a closed owned cut") + need(len(c["frames"][b]) > len(c["frames"][a]), "Ascending persistent edge") + else: + _, target, a, b, r = event + need(target == 0 and live, "Live owned center") + target = OWNED + u, v = c["frames"][a], c["frames"][b] + need(current[target] == a and r == abs(len(u)-len(v)) > 0 + and rank(u+v) == max(len(u), len(v)), "Chronological nested paid edge") + current[target] = b + if target < 224: + contacts[target].append(j) + paid[r] += 1 + pairs[a, b] = r + elif kind == "warp": + _, register, signed, a, b = event + target = role(register) + if target < 224: + contacts[target].append(j) + need(current[target] == a and abs(signed) in self.maps, "Chronological signed warp") + rows = transpose(next(row["G_columns"] for row in c["warps"] if row["op"] == abs(signed))) + if signed < 0: + rows = inverse(rows) + mapped = [sum(((v & row).bit_count() % 2) << k for k, row in enumerate(rows)) + for v in c["frames"][a]] + need(rank(mapped+c["frames"][b]) == len(mapped) == len(c["frames"][b]), + "Actual signed warp transports its source subspace") + current[target] = b + warps.add((signed, a, b)) + elif kind == "scalar": + gate, f = event[1:] + target = role(gate[1]) + if target < 224: + contacts[target].append(j) + op = gate[0] + if op in ("clear", "copy"): + need(target == OWNED, "Only owned storage can be overwritten") + if op == "clear": + live = False + current[target] = f + continue + need(current[target] == f, "Scalar receiver frame") + if op in ("add", "copy"): + source = role(gate[2]) + if source < 224: + contacts[source].append(j) + need(source != target and current[source] == f, "Scalar source frame") + need(source != OWNED or live, "Owned source is initialized") + if op == "copy": + need(not live, "Copy starts an owned lifetime") + live = True + else: + q = Q(gate[3], gate[4]) + need(q and q.denominator & (q.denominator-1) == 0, "Nonzero dyadic shear") + if target == OWNED: + live = True + else: + need(op == "scale", "Known scalar operation") + q = Q(gate[2], gate[3]) + a = abs(q.numerator) + need(a and a & (a-1) == 0 and q.denominator & (q.denominator-1) == 0, + "Invertible dyadic scale") + elif kind == "adapter": + _, side, target, f = event + need(0 <= target < 224 and side in ("old_to_new", "new_to_old"), "Main adapter domain") + entrance = side == "old_to_new" + need(f == c["start" if entrance else "final"][target], "Exact main adapter boundary") + need(current[target] == f or self.old_frame(target, entrance) == self.frame(f), + "A moved adapter must be exactly the identity") + need((side, target) not in adapters, "No repeated main adapter") + adapters[side, target] = j + else: + need(kind == "phase", "Known provider event") + need(not live and current[:PERSISTENT] == c["final"], "Complete final frame and owned return") + need(set(adapters) == {(side, r) for side in ("old_to_new", "new_to_old") for r in range(224)}, + "All 448 main adapter events") + for (side, target), position in adapters.items(): + entrance = side == "old_to_new" + f = c["start" if entrance else "final"][target] + if self.old_frame(target, entrance) != self.frame(f): + need(all(position < j if entrance else j < position for j in contacts[target]), + "Nonidentity adapters surround every use of their role") + need(dict(paid) == {int(k): v for k, v in c["local_profile"].items()}, "Complete paid profile") + return dict(events=dict(counts), paid=dict(sorted(paid.items())), pairs=pairs, warps=warps) + + def problem(self, direction): + """Expand every physical event and keep all 633 input and return roles.""" + bank = {} + + def put(name, circuit): + if not circuit: + return None + oriented = conjugate(circuit) if direction == "backward" else circuit + need(name not in bank or bank[name] == oriented, "One circuit per symbol") + bank[name] = oriented + return name + + def frame(index): + return put("frame_" + str(index), self.frame(index)) + + def old(register, entrance): + circuit = self.old_frame(register, entrance) + index = self.c["start" if entrance else "final"][register] + if circuit == self.frame(index): + return frame(index) + return put(("entrance_" if entrance else "exit_") + str(register), circuit) + + def apply(out, target, symbol, inverse=False): + if symbol is not None: + out.append(dict(op="apply", dst=target, symbol=symbol, inverse=inverse)) + + program = [] + offsets = [] + for event in self.word["programs"][direction]: + offsets.append(len(program)) + kind = event[0] + if kind in ("climb", "center", "warp"): + if kind == "climb": + target, a, b = event[2:5] + elif kind == "center": + target, a, b = OWNED, event[2], event[3] + else: + target, signed, a, b = role(event[1]), *event[2:] + apply(program, target, frame(a), True) + if kind == "warp": + apply(program, target, put("warp_" + str(abs(signed)), self.maps[abs(signed)]), signed < 0) + apply(program, target, frame(b)) + elif kind == "adapter": + _, side, target, f = event + if side == "old_to_new": + apply(program, target, old(target, True), True) + apply(program, target, frame(f)) + else: + apply(program, target, frame(f), True) + apply(program, target, old(target, False)) + elif kind == "scalar": + gate = event[1] + target, op = role(gate[1]), gate[0] + if op in ("clear", "copy"): + program.append(dict(op="scale", dst=target, coefficient="0")) + if op in ("copy", "add"): + program.append(dict(op="add", dst=target, src=role(gate[2]), + coefficient=str(Q(1) if op == "copy" else Q(gate[3], gate[4])))) + elif op == "scale": + program.append(dict(op="scale", dst=target, coefficient=str(Q(gate[2], gate[3])))) + else: + need(kind == "phase", "Known physical program marker") + offsets.append(len(program)) + reference = [] + for register in range(PERSISTENT): + apply(reference, register, old(register, True), True) + for j in range(112): + source, target, sign = (112+j, j, -1) if direction == "backward" else (j, 112+j, 1) + reference.append(dict(op="add", dst=target, src=source, coefficient=str(sign))) + for register in range(PERSISTENT): + apply(reference, register, old(register, False)) + reference.append(dict(op="scale", dst=OWNED, coefficient="0")) + return dict(axes=N, roles=PERSISTENT+1, operators=bank, program=program, reference=reference), offsets + + +def role(register): + need(type(register) is list and len(register) == 2, "Register syntax") + tag, index = register + need(type(index) is int and ((tag == "L" and 0 <= index < PERSISTENT) or (tag == "C" and index == 0)), + "Register domain") + return index if tag == "L" else OWNED + + +def add(target, source, coefficient=Q(1)): + for key, value in tuple(source.items()): + value = target.get(key, Q(0)) + coefficient*value + if value: + target[key] = value + else: + target.pop(key, None) + + +def append_letter(word, letter, right=False): + if right: + return word[:-1] if word and word[-1] == -letter else word + (letter,) + return word[1:] if word and word[0] == -letter else (letter,) + word + + +def interval(program, first, second, register, transpose_row=False): + """Compute one full row or column of the logical interval matrix.""" + rows = [{} for _ in range(PERSISTENT+1)] + rows[register][()] = Q(1) + events = program[first+1:second] + for event in reversed(events) if transpose_row else events: + kind = event[0] + if kind == "warp": + target, signed = role(event[1]), event[2] + rows[target] = {append_letter(w, signed, transpose_row): q for w, q in rows[target].items()} + elif kind == "scalar": + gate = event[1] + target, op = role(gate[1]), gate[0] + if op == "clear": + rows[target] = {} + elif op == "copy": + source = role(gate[2]) + if transpose_row: + add(rows[source], rows[target]) + rows[target] = {} + else: + rows[target] = rows[source].copy() + elif op == "add": + source, q = role(gate[2]), Q(gate[3], gate[4]) + add(rows[source], rows[target], q) if transpose_row else add(rows[target], rows[source], q) + else: + need(op == "scale", "Known interval scalar") + q = Q(gate[2], gate[3]) + rows[target] = {w: q*v for w, v in rows[target].items()} + return rows[:PERSISTENT] + + +def fusion_pairs(program): + previous, out = {}, [] + for j, event in enumerate(program): + if event[0] != "climb": + continue + target = event[2] + for k, earlier in previous.get(target, []): + out.append((k, j, target, earlier[3], earlier[4], event[3], event[4])) + previous.setdefault(target, []).append((j, event)) + return out + + +def contact_witness(program, pair): + first, second, target, a, b, c, d = pair + for transposed in (False, True): + rows = interval(program, first, second, target, transposed) + for other, entry in enumerate(rows): + if other != target and len(entry) == 1: + word, coefficient = next(iter(entry.items())) + return dict(first=first, second=second, role=target, frames=[a, b, c, d], + ranks=[program[first][5], program[second][5]], + output=target if transposed else other, input=other if transposed else target, + coefficient=str(coefficient), word=list(word)) + raise ValueError("No single-term contact certificate for " + str(pair)) + + +def complete_endpoint(problem, instructions): + """Expand all independent inputs together. Coefficients remain rational.""" + symbols = {name: j+1 for j, name in enumerate(problem["operators"])} + rows = [{(j, ()): Q(1)} for j in range(problem["roles"])] + total = peak_total = problem["roles"] + peak_row = 1 + for instruction in instructions: + target, op = instruction["dst"], instruction["op"] + total -= len(rows[target]) + if op == "apply": + signed = symbols[instruction["symbol"]] * (-1 if instruction.get("inverse", False) else 1) + rows[target] = {(entry, append_letter(word, signed)): q for (entry, word), q in rows[target].items()} + elif op == "add": + add(rows[target], rows[instruction["src"]], Q(instruction["coefficient"])) + else: + need(op == "scale", "Known complete program instruction") + q = Q(instruction["coefficient"]) + rows[target] = {key: q*value for key, value in rows[target].items()} if q else {} + total += len(rows[target]) + peak_total, peak_row = max(peak_total, total), max(peak_row, len(rows[target])) + return rows, dict(peak_total_terms=peak_total, peak_row_terms=peak_row, final_terms=total) diff --git a/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/provider/FUSIONS.json.gz b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/provider/FUSIONS.json.gz new file mode 100644 index 0000000000..895c0d4c4a Binary files /dev/null and b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/provider/FUSIONS.json.gz differ diff --git a/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/provider/HELPERS.json.gz b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/provider/HELPERS.json.gz new file mode 100644 index 0000000000..0910f74138 Binary files /dev/null and b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/provider/HELPERS.json.gz 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diff --git a/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/provider/NOTICE.md b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/provider/NOTICE.md new file mode 100644 index 0000000000..50ee0013c3 --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/provider/NOTICE.md @@ -0,0 +1,55 @@ +# Provider sources and attribution + +New material: Ali Romman, with substantial OpenAI Codex assistance in the +proof, implementation, checks and publication. Apache-2.0. The checks do not +constitute independent human review or a proof-kernel verification. + +The source checkpoint is canonical main +`1ec1119972c9aefe42525172d07b332fcff81cb4`. `SOURCES.json` records exact +source paths, Git objects and SHA-256 values for the copied data. + +- **Cao Yifan / intqwq** supplies the final + [PR #4610](https://github.com/CrocSwap/integer-mult-bounds/pull/4610) + native word and phase data. His + [construction proof](https://github.com/CrocSwap/integer-mult-bounds/blob/1ec1119972c9aefe42525172d07b332fcff81cb4/research/kappa-round3-warp-20261022/PROOF.md) + records the changed construction and its OpenAI assistance. `WORD.json.gz` + and `PHASES.json.gz` are byte-exact copies of that selected source. +- **Chris R / Clear1nsight** supplies the + [PR #5241](https://github.com/CrocSwap/integer-mult-bounds/pull/5241) + independent admission and paid catalogue. `PAID.jsonl.gz` is a byte-exact + copy. The [admission proof](https://github.com/CrocSwap/integer-mult-bounds/blob/1ec1119972c9aefe42525172d07b332fcff81cb4/research/final4610-independent-admission/PROOF.md) + already contains a quantified free-group lift. The new work does not claim + priority for that argument. The prior source uses substantial OpenAI + Codex assistance and retains Apache-2.0. +- **Cinna Davis / 1337isnot1337** supplies the joint-helper, native warp, + query-thinned controller and preceding construction chain. `HELPERS.json.gz` + retains the recipes from the + [joint-helper source](https://github.com/CrocSwap/integer-mult-bounds/blob/1ec1119972c9aefe42525172d07b332fcff81cb4/research/joint-helper-lattice/PROOF.md). + **zxv**, **Jacob Alan Sussman** and **Dugongue** retain credit for productive + helpers, mixed-target recursion and frame/physical interfaces. See the + [selected contributor map](https://github.com/CrocSwap/integer-mult-bounds/blob/1ec1119972c9aefe42525172d07b332fcff81cb4/docs/research/community-native4610-contributors.md). +- **Rohan Arun**, **Jeremy Kothe** and the full native lineage supply the + retained exact Clifford kernel. **Tekalign / tekuuu** retains it in the + source package. The byte-exact kernel, scalar layer and full lineage + notice remain in `../vendor/`. The scalar layer is from **zxv**. +- **icekylinx** supplies the earlier phase-lowering source, with Codex + assistance. **DreamingOfClouds** supplies the wrapper source, with Claude + Opus 5.5 assistance; that source credits **chafreaky** for the residual + wrapper construction. Cinna Davis adds native warp support. The + [phase source](https://github.com/CrocSwap/integer-mult-bounds/blob/1ec1119972c9aefe42525172d07b332fcff81cb4/research/t74-native-fast/vendor/native/new/code/borrow/bw_phases.py) + gives the exact main-adapter formula used here. The + [wrapper source](https://github.com/CrocSwap/integer-mult-bounds/blob/1ec1119972c9aefe42525172d07b332fcff81cb4/research/t74-native-fast/vendor/native/new/code/borrow/bw_adapters.py) + retains the source notice and predecessor credit. + +The [PR #5243 handoff](https://github.com/CrocSwap/integer-mult-bounds/discussions/1166#discussioncomment-19147021) +motivates the initial paid-pair test. The separate +[PR #5393](https://github.com/CrocSwap/integer-mult-bounds/pull/5393) concerns +zero-row deletion and single-field reachability on a frozen eight-relation +provider. It is related work, not an input to this proof or an additional gain. + +The source construction, proposed recipe compiler, new quadratic-sum checker, +complete word interpreters and literal witness checker have different roles. +The Gaussian scalar layer is shared. The proof and implementation are not +independent of all earlier source definitions. No general stabilizer-method +priority is claimed; the classical code and quadratic-form work is credited +in `../ADVANCES.md`. diff --git a/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/provider/PAID.jsonl.gz b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/provider/PAID.jsonl.gz new file mode 100644 index 0000000000..73fa3ced93 Binary files /dev/null and b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/provider/PAID.jsonl.gz differ diff --git a/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/provider/PHASES.json.gz b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/provider/PHASES.json.gz new file mode 100644 index 0000000000..ac77b78547 Binary files /dev/null and b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/provider/PHASES.json.gz differ diff --git a/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/provider/RESEARCH-NOTES.md b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/provider/RESEARCH-NOTES.md new file mode 100644 index 0000000000..83b4901e17 --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/provider/RESEARCH-NOTES.md @@ -0,0 +1,97 @@ +# Provider experiment record + +The user requested an application of the new verifier to a complete current +provider, with a real kappa gain or a useful obstruction as the target. + +## Source and decision + +Canonical main was refreshed to +`1ec1119972c9aefe42525172d07b332fcff81cb4`, priority revision 7. The selected +record points to the final PR4610 word and PR5241 admission. The selected +value is 0.0030217758. The older verifier proof inputs remain pinned to their +original base. This application uses a separate current-source manifest. + +The first live overlap check covered 347 open PRs and 4,681 Discussion +records, with complete remote pagination. Local notes were sparse. The +PR5243 handoff asks for a physical H1+H1->H2 pair. PR5393 proves a different +zero-row result on a frozen eight-relation provider. The new scope is the +complete selected local provider and literal early/late fusion on one +persistent role. The first test uses adjacent rank-one climbs. No other +chat's work is changed. + +A second live check at 22:28 UTC on 2026-10-23 covered 350 open PRs and +4,684 Discussion records, with complete remote pagination. The terms were +`pair fusion`, `paid climbs`, `same persistent role`, `30328` and +`clifford-tensor-gram`. No competing claim for this exact provider audit was +found. Local coverage was 16 of 7,269 note paths; this check is not a full +historical novelty certificate. + +## Experiments and corrections + +1. The source has 21,449 events in each direction, 632 persistent roles and + one owned role. The 5,710 paid class records cover 6,596 instances. Only + checking a single native warp would not cover this boundary. +2. The first importer required each adapter marker's frame to be the current + frame. This rejected 82 source exit markers. Source inspection showed that + these adapters are identities. The importer now proves identity for a + moved marker. It still rejects a nonidentity adapter at a wrong frame. +3. The first owned-lifetime tracker marked COPY but not ADD into a cleared + owned register as live. The backward source accumulates its center by + ADD. The tracker was corrected before any complete-provider claim. +4. The native inverse circuit returns tuple gates. The first conjugation + helper combined a tuple with a list. This was a representation error, + not a mathematical failure. The helper now makes the new gate list + explicitly. Both orientations are replayed. +5. All 5,710 paid recipes then passed the new phase-exact Gram test. The + rank-one normalized traces were zero or `(1+i)/2^j` and its conjugate, + with j from 1 to 4. The proof uses the more general checked bounds + `Re(tau)<=1/2` and `|tau|^2<=1/2`. +6. The initial fusion scan required a common middle frame. It found 1,341 + pairs per direction and a single-term off-diagonal contact for every + pair. The two-sided cut formula removed that unnecessary restriction. + The second census covers all 1,363 adjacent rank-one pairs per direction, + including 22 with an intervening change of middle frame. It excludes + both endpoint placements for each pair: 5,452 replacements in total. + The same proof then applies to all 2,658 adjacent pairs at all ranks. + A final extension removes adjacency as well: all 7,582 pairs on one + persistent role per direction have a certificate. The final result + excludes 30,328 endpoint placements. Each extension changes the search + domain explicitly; it does not reuse a smaller-domain receipt as proof. +7. The complete physical programs pass the existing compact verifier. A + separate sparse expansion measures peak total support 22,331 forward + and 12,930 backward. Support growth is manageable for this source. No + general polynomial support bound follows. +8. The proof is stronger than a width-one rejection: each saved contact + defect has normalized squared norm at least q^2 at every positive + width. The full-provider norm need not have that bound, because its + prefix and suffix can be nonunitary. Invertibility transfers nonzero + defect, not a condition-number estimate. +9. The final proof audit checks the positions of all 224 nonidentity main + adapters in each direction. Each entrance precedes all uses of its role; + each exit follows all uses. This check is part of the importer. It makes + the interval's logical-frame interpretation explicit. All receipts keep + the same mathematical values. + A separate negative check moved role 112's nonidentity exit adapter from + event 15,723 to event 14,298, before its last scalar contact. The audit + rejected it with `Nonidentity adapters surround every use of their role`. +10. The first hosted replay on Linux / CPython 3.12.15 passed the four earlier + checks, all native recipe classes and both complete provider endpoints. + Its 240-second provider limit then expired during the remaining checks. + No mathematical failure was reported. The manifest now assigns 90 seconds + to each earlier check and 420 seconds to each provider check. The total + stays 1,200 seconds. Source code, proof and scientific receipts are + unchanged by this budget correction. + +No promising fusion survived the exact endpoint test. The source remains +unchanged. The hypothetical invoice delta is not an achieved saving, so a +new compiler or outer arithmetic run is not warranted by this experiment. + +## Verification record + +`RESULT.json` contains the deterministic complete result. `FUSIONS.json.gz` +contains every contact certificate. `WITNESSES.json` contains full physical +program counterexamples. The same commands run in normal and optimized +Python. The repository replay manifest includes both modes. Final export, +committed-byte and publication results are recorded in the public handoff. + +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. diff --git a/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/provider/RESULT.json b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/provider/RESULT.json new file mode 100644 index 0000000000..0e471c979c --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/provider/RESULT.json @@ -0,0 +1 @@ +{"achieved_paid_delta":{},"admission_head":"13efb5fc5f3b7c14ec2cfa181dd9eb6480972cf2","complete_local_provider":{"backward":{"certificate":{"axes":9,"cutoff":76,"decision_widths":[69,70,71,72,73,74,75,76],"equivalent_at_all_positive_widths":true,"nonzero_endpoint_entries":0,"problem_sha256":"94d24c4876b09ca464c6f3bed1b14f59219dc7ffc3360b7a8a772b14c6b8a2cc","schema":"clifford-tensor-gram/native-v1"},"events":{"adapter":448,"center":8,"climb":3290,"phase":10,"scalar":17453,"warp":240},"instructions":24819,"native_symbols":1297,"paid":{"1":2201,"2":412,"3":510,"4":127,"5":40,"8":8},"support":{"final_terms":744,"peak_row_terms":148,"peak_total_terms":12930}},"forward":{"certificate":{"axes":9,"cutoff":76,"decision_widths":[69,70,71,72,73,74,75,76],"equivalent_at_all_positive_widths":true,"nonzero_endpoint_entries":0,"problem_sha256":"d141a880691f5f0fb79266b5e8a990fa59b399d3f63f3458b7a8582446ecb433","schema":"clifford-tensor-gram/native-v1"},"events":{"adapter":448,"center":8,"climb":3290,"phase":10,"scalar":17453,"warp":240},"instructions":24827,"native_symbols":1297,"paid":{"1":2201,"2":412,"3":510,"4":127,"5":40,"8":8},"support":{"final_terms":744,"peak_row_terms":156,"peak_total_terms":22331}}},"controls":[{"name":"missing_paid_class","rejected":"All oriented paid classes, without gaps"},{"name":"paid_absolute_phase","rejected":"Exact native Gram equality with absolute phase"},{"name":"borrowed_erasure","rejected":"Only owned storage can be overwritten"},{"name":"live_owned_cut","rejected":"Persistent climb at a closed owned cut"},{"name":"missing_contact_is_not_a_certificate","rejected":"No single-term contact certificate for (-1, 0, 0, 0, 2, 2, 3)"}],"full_program_basis_witnesses":12,"fusion":{"contact_types":{"backward_column":6632,"backward_row":950,"forward_column":6640,"forward_row":942},"normalized_squared_cut_defect_lower_bound":"coefficient^2","pairs_by_direction":{"backward":7582,"forward":7582},"rank_pairs":{"[1, 1]":8132,"[1, 2]":1220,"[1, 3]":1098,"[1, 4]":542,"[1, 5]":64,"[2, 1]":1210,"[2, 2]":274,"[2, 3]":150,"[2, 4]":30,"[2, 5]":24,"[3, 1]":1156,"[3, 2]":234,"[3, 3]":476,"[3, 4]":2,"[4, 1]":330,"[4, 2]":70,"[5, 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diff --git a/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/provider/WORD.json.gz b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/provider/WORD.json.gz new file mode 100644 index 0000000000..46d929df83 Binary files /dev/null and b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/provider/WORD.json.gz differ diff --git a/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/provider/generate_adapters.py b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/provider/generate_adapters.py new file mode 100644 index 0000000000..b256bc0ca0 --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/provider/generate_adapters.py @@ -0,0 +1,47 @@ +"""Propose main adapter recipes with the frozen source compiler. + +The verifier checks these data with quadratic sums. It does not run this file. +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +""" +import json +from pathlib import Path +import sys + +PACKAGE = Path(__file__).resolve().parent.parent +sys.path.insert(0, str(PACKAGE)) +sys.path.insert(0, str(PACKAGE / "vendor")) +import clifford_exact as source +import provider + + +def generate(): + _, data = provider.read_inputs() + model = provider.Provider(data["word"]) + rows = [] + for entrance in (True, False): + for role in range(224): + f = model.c["start" if entrance else "final"][role] + old = model.old_frame(role, entrance) + circuit = provider.inverse_circuit(9, old) + model.frame(f) + # Tableau generation is part of proposal generation only. + op = source.ident(9) + for gate in circuit: + kind = gate[0] + if kind == "P": + part = source.perm(9, tuple(gate[1])) + elif kind == "D": + part = source.diag(9, tuple(gate[1]), tuple(gate[2])) + else: + provider.need(kind == "C", "Adapter generator gate") + part = source.cgate(9, gate[1], gate[2]) + op = op.then(part) + recipe, _ = source.lower_child(op) + provider.need(recipe["rank"] == 0, "Proposed main adapter is monomial") + rows.append(dict(entrance=entrance, role=role, frame=f, recipe=recipe)) + return rows + + +if __name__ == "__main__": + target = Path(__file__).resolve().parent / "MAIN-ADAPTERS.json" + target.write_text(json.dumps(generate(), sort_keys=True, separators=(",", ":")) + "\n") + print("PROPOSED_448_MAIN_ADAPTERS_REQUIRES_GRAM_CHECK") diff --git a/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/quadratic.py b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/quadratic.py new file mode 100644 index 0000000000..a57ba96a01 --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/quadratic.py @@ -0,0 +1,256 @@ +"""Exact sums of native Clifford paths, with no state vector. + +The proof and cost bounds are in ADVANCES.md. Binary affine forms use bit +zero for the constant and bit j+1 for variable j. All phases are retained. +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +""" +from itertools import combinations +from pathlib import Path +import sys + +sys.path.insert(0, str(Path(__file__).resolve().parent / "vendor")) +from fields import Gaussian as G + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def bits(mask): + while mask: + low = mask & -mask + yield low.bit_length()-1 + mask ^= low + + +def parity_sum(values): + out = 0 + for value in values: + out ^= value + return out + + +class Phase: + """A constant plus linear terms and even quadratic terms modulo four.""" + + def __init__(self, variables): + self.constant = 0 + self.linear = [0]*variables + self.cross = set() + + def toggle(self, i, j): + if i == j: + self.linear[i] = (self.linear[i]+2) % 4 + else: + term = tuple(sorted((i, j))) + self.cross.symmetric_difference_update((term,)) + + def add_parity(self, mask, coefficient): + constant = mask & 1 + variables = list(bits(mask >> 1)) + self.constant = (self.constant+coefficient*constant) % 4 + for i in variables: + self.linear[i] = (self.linear[i]+coefficient*(1-2*constant)) % 4 + if coefficient % 2: + self.cross.symmetric_difference_update(combinations(variables, 2)) + + def add_product(self, left, right): + """Add twice the product of two binary affine forms.""" + if left & 1: + self.add_parity(right, 2) + if right & 1: + self.add_parity(left ^ (left & 1), 2) + for i in bits(left >> 1): + for j in bits(right >> 1): + self.toggle(i, j) + + def substitute(self, mapping, variables): + out = Phase(variables) + out.constant = self.constant + for i, coefficient in enumerate(self.linear): + out.add_parity(mapping[i], coefficient) + for i, j in self.cross: + out.add_product(mapping[i], mapping[j]) + return out + + def restrict(self, equations): + pivots = {} + for equation in equations: + while equation > 1: + pivot = equation.bit_length()-1 + if pivot not in pivots: + pivots[pivot] = equation + break + equation ^= pivots[pivot] + if equation == 1: + return None + mapping, free = [], 0 + for j in range(1, len(self.linear)+1): + if j in pivots: + equation = pivots[j] ^ (1 << j) + value = (equation & 1) ^ parity_sum(mapping[k] for k in bits(equation >> 1)) + else: + free += 1 + value = 1 << free + mapping.append(value) + return self.substitute(mapping, free) + + def drop(self, j): + mapping = [0 if k == j else 1 << (k+1-(k > j)) for k in range(len(self.linear))] + return self.substitute(mapping, len(mapping)-1), mapping + + +def gauss_sum(phase, equations=()): + """Sum i**phase over all solutions of the binary equations.""" + phase = phase.restrict(equations) + if phase is None: + return G(0) + factor = G(1) + units = (G(1), G("i"), G(-1), G("-i")) + while phase.linear: + j = next((j for j, a in enumerate(phase.linear) if a % 2), None) + if j is not None: + a = phase.linear[j] + neighbors = [u if v == j else v for u, v in phase.cross if j in (u, v)] + phase, mapping = phase.drop(j) + phase.add_parity(parity_sum(mapping[k] for k in neighbors), -a) + factor = factor*(1+units[a]) + elif phase.cross: + j = min(phase.cross)[0] + constant = phase.linear[j]//2 + neighbors = [u if v == j else v for u, v in phase.cross if j in (u, v)] + phase, mapping = phase.drop(j) + equation = constant ^ parity_sum(mapping[k] for k in neighbors) + phase = phase.restrict((equation,)) + if phase is None: + return G(0) + factor = factor*2 + else: + if any(phase.linear): + return G(0) + factor = factor*(1 << len(phase.linear)) + phase.linear = [] + return factor*units[phase.constant] + + +def rank(rows): + pivots = {} + for row in rows: + while row: + j = row.bit_length()-1 + if j not in pivots: + pivots[j] = row + break + row ^= pivots[j] + return len(pivots) + + +class Paths: + """Build a quadratic path sum from the frozen native gate grammar.""" + + def __init__(self, n, circuit): + need(type(n) is int and n >= 0, "Nonnegative axis count") + self.n = n + self.phase = Phase(n) + self.inputs = [1 << (j+1) for j in range(n)] + self.outputs = self.inputs.copy() + self.factor = G(1) + limit = 1 << n + + def mask(x): + return type(x) is int and 0 <= x < limit + + for gate in circuit: + need(type(gate) in (tuple, list) and bool(gate), "Native gate") + kind = gate[0] + if kind == "P": + need(len(gate) == 2 and len(gate[1]) == n and all(mask(x) for x in gate[1]) + and rank(gate[1]) == n, "Invertible native permutation") + self.outputs = [parity_sum(self.outputs[j] for j in bits(row)) for row in gate[1]] + elif kind == "X": + need(len(gate) == 2 and mask(gate[1]), "Native translation") + self.outputs = [x ^ ((gate[1] >> j) & 1) for j, x in enumerate(self.outputs)] + elif kind == "D": + need(len(gate) == 3 and len(gate[1]) == len(gate[2]) == n, "Native diagonal shape") + rows, alpha = gate[1:] + need(all(mask(x) for x in rows) and all(type(a) is int and 0 <= a < 4 for a in alpha), + "Native diagonal entries") + need(all((rows[i] >> j) & 1 == (rows[j] >> i) & 1 for i in range(n) for j in range(n)) + and all(alpha[j] % 2 == (rows[j] >> j) & 1 for j in range(n)), "Native diagonal parity") + for j, a in enumerate(alpha): + self.phase.add_parity(self.outputs[j], a) + for i, row in enumerate(rows): + for j in bits(row >> (i+1)): + self.phase.add_product(self.outputs[i], self.outputs[j+i+1]) + elif kind == "C": + need(len(gate) == 3 and mask(gate[1]) and type(gate[2]) is int and gate[2] in (-1, 1), + "Native C gate") + q, sign = gate[1:] + self.phase.linear.append((-sign) % 4) + variable = 1 << len(self.phase.linear) + self.outputs = [x ^ (variable if q >> j & 1 else 0) for j, x in enumerate(self.outputs)] + self.factor = self.factor*G.pair(1, sign)/2 + elif kind == "phase": + need(len(gate) == 2 and type(gate[1]) is int, "Native global phase") + self.phase.constant = (self.phase.constant+gate[1]) % 4 + else: + raise ValueError("Unknown native gate") + + def entry(self, output, input_index): + need(type(output) is int and type(input_index) is int and + 0 <= output < 1 << self.n and 0 <= input_index < 1 << self.n, "Base coordinate") + equations = [x ^ ((input_index >> j) & 1) for j, x in enumerate(self.inputs)] + equations += [x ^ ((output >> j) & 1) for j, x in enumerate(self.outputs)] + return self.factor*gauss_sum(self.phase, equations) + + def trace(self): + return self.factor*gauss_sum(self.phase, [x ^ y for x, y in zip(self.inputs, self.outputs)]) + + +def partial_inner(left, right, output_prefix=(), input_prefix=()): + """Sum conjugate(left[x,y])*right[x,y] over the unspecified bits.""" + need(left.n == right.n, "Common axis count") + n = left.n + need(len(output_prefix) <= n and len(input_prefix) <= n and + all(type(b) is int and b in (0, 1) for b in (*output_prefix, *input_prefix)), "Coordinate prefix") + a, b = len(left.phase.linear), len(right.phase.linear) + phase = Phase(a+b) + phase.constant = (-left.phase.constant+right.phase.constant) % 4 + phase.linear = [(-x) % 4 for x in left.phase.linear]+right.phase.linear + phase.cross = left.phase.cross | {(i+a, j+a) for i, j in right.phase.cross} + + def shift(mask): + return (mask & 1) | ((mask >> 1) << (a+1)) + + equations = [x ^ shift(y) for x, y in zip(left.inputs, right.inputs)] + equations += [x ^ shift(y) for x, y in zip(left.outputs, right.outputs)] + equations += [left.outputs[j] ^ x for j, x in enumerate(output_prefix)] + equations += [left.inputs[j] ^ x for j, x in enumerate(input_prefix)] + factor = G.pair(left.factor.real, -left.factor.imag)*right.factor + return factor*gauss_sum(phase, equations) + + +def inverse_circuit(n, circuit): + """Invert a circuit after Paths has checked its gate data.""" + out = [] + for gate in reversed(circuit): + kind = gate[0] + if kind == "P": + rows = [x | (1 << (n+j)) for j, x in enumerate(gate[1])] + for j in range(n): + k = next(k for k in range(j, n) if rows[k] >> j & 1) + rows[j], rows[k] = rows[k], rows[j] + for k in range(n): + if k != j and rows[k] >> j & 1: + rows[k] ^= rows[j] + out.append((kind, tuple(x >> n for x in rows))) + elif kind == "D": + out.append((kind, gate[1], tuple((-a) % 4 for a in gate[2]))) + elif kind == "C": + out.append((kind, gate[1], -gate[2])) + elif kind == "phase": + out.append((kind, -gate[1])) + else: + out.append(gate) + return out diff --git a/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/vendor/NATIVE-LINEAGE-NOTICE b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/vendor/NATIVE-LINEAGE-NOTICE new file mode 100644 index 0000000000..380e979f0e --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/vendor/NATIVE-LINEAGE-NOTICE @@ -0,0 +1,14 @@ +Anticipatory dirty borrowing: PR2226 (Cinna Davis / 1337isnot1337, with substantial OpenAI Codex assistance) is credited first. Its alias rule, changed-reference K_G handoffs, initial compensation and exact free-operator replay (vendored under new/code/borrow/vendor, see new/code/borrow/NOTICE-PR2226.md) are applied here to the T74 pivot-566+554 words; the native lowering, window-exact owner fill and independent audit of the borrow words are new in this package. Bootstrap carried-cutoff repair: PR1956 (Josie Elliston); Lemma G label/adapter checks and X/Y/Z mutants: PR1964 (thakrarsagar), extended here with borrow warp/zero-buffer controls. + +New research prepared by Rohan Arun with substantial OpenAI Codex assistance. Apache-2.0. Parent words and build recipe method derive from Jeremy Kothe PR1274 and Rohan Arun PR1218, with lineage credited in README.md. All inherited mathematical qualifications are retained. +Additional pivot555 and567 composition by Rohan Arun with substantial OpenAI Codex assistance. + +T74 exact-fill owner construction by Rohan Arun with substantial OpenAI Codex assistance. + +PR1377 grid refinement credited to Jeremy Kothe. Outer witness refinement by Rohan Arun with OpenAI Codex assistance; construction unchanged. + +Pivot-566 kernel, words, edits, rebuild.py and rebind.py: PR1625 (mdumitrean). Endpoint/outer-witness stacking, fine_cache.py and oracle stage by jeremykothe2 with oh-my-pi assistance. + +The preceding paragraphs are inherited source notices, not attribution of this derivative. +This joint twelve-source construction, generator, independent replay, hosting composition and package: Tekalign (@tekuuu), with substantial OpenAI Codex assistance. No independent human review claimed. +Credits: Cinna Davis/PR2226 anticipatory dirty borrowing; Tekalign/PR2436 four lifted targets; Jeremy Kothe/PR2462,2588,2673 source pipeline, source-label swap and order/fill; zxv/PR2530 eight aliases; Mason Hale/PR2696 concentrated source-partner assignment and independent local interpreter; Philippe Van Velzen/PR2559,2679 evacuation, six pre-life hosts and refit/alias; themilkman216/PR2621 priority order; Marius-Paul Dumitrean/PR2733 independent concentrated/pre-life composition; Vlado Vojdanovski/PR2322 generator utilities. PR2720's fixed-old-path cut obstruction motivates the changed premise. The retained owner/native/bit/modern outer lineage and their notices remain in the pinned source. New work Apache-2.0. diff --git a/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/vendor/clifford_exact.py b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/vendor/clifford_exact.py new file mode 100644 index 0000000000..166841a037 --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/vendor/clifford_exact.py @@ -0,0 +1,149 @@ +"""Small exact Gaussian-dyadic Clifford compiler, independent of gx internals. +Paulis use i^p X^x Z^z. State vectors use integer Gaussian numerators / 2^d. +The tableau is supplemented by a literal circuit, so global phases are kept. +""" +from dataclasses import dataclass + +def parity(x):return x.bit_count()&1 +def rank(rows): + p={} + for x in rows: + while x: + b=x.bit_length()-1 + if b not in p:p[b]=x;break + x^=p[b] + return len(p) +def transpose(rows,n):return tuple(sum(((rows[j]>>i)&1)<>j&1);a[j],a[k]=a[k],a[j] + for i in range(n): + if i!=j and a[i]>>j&1:a[i]^=a[j] + assert [r&((1<>n for r in a) +def basis_extend(cols,n): + out=[] + for x in list(cols)+[1<len(out):out.append(x) + assert len(out)==n + return tuple(out) +def nullspace(rows,n): + a=list(rows);p=[];k=0 + for j in range(n): + t=next((i for i in range(k,len(a)) if a[i]>>j&1),None) + if t is None:continue + a[t],a[k]=a[k],a[t] + for i in range(len(a)): + if i!=k and a[i]>>j&1:a[i]^=a[k] + p.append(j);k+=1 + return tuple((1<>j)&1)<>i&1:out=pmul(out,T[i]) + for i in range(n): + if z>>i&1:out=pmul(out,T[n+i]) + return out +def compose(A,B):return tuple(apply(A,p) for p in B) +def inverse(T): + n=len(T)//2;cols=[x|(z<>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4)) + return tuple(out) +def qvalue(Q,alpha,x,n): + return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4 +def mul_i(a,p): + x,y=a;p%=4 + return [(x,y),(-y,x),(-x,-y),(y,-x)][p] +@dataclass +class Op: + n:int + tab:tuple + circuit:list + def then(self,b): + assert self.n==b.n + return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit) + def adjoint(self): + circ=[] + for e in reversed(self.circuit): + if e[0]=='P':circ.append(('P',inv(e[1],self.n))) + elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2]))) + elif e[0]=='C':circ.append(('C',e[1],-e[2])) + elif e[0]=='phase':circ.append(('phase',(-e[1])%4)) + else:circ.append(e) + return Op(self.n,inverse(self.tab),circ) + def zero_state(self,basis=0): + N=1<>i)&1 for i in range(n)) + assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n)) + return Op(n,tuple([(1<>i&1 else 0,1<>i&1 else 0) for i in range(n)]),[('C',q,sgn)]) +def xgate(n,b):return Op(n,tuple([(1<>i)&1)) for i in range(n)]),[('X',b)]) +def fourier(n,axes=None): + out=ident(n) + for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<len(selected):picks.append(j);selected.append(x) + assert len(picks)==r and all(x>>r==0 for x in Bcols) + Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1<= 0 else "")+str(self.imag)+"i" + + __repr__ = __str__ + + +def scalars(problem): + p = problem.get("field", "Q") + if p == "Q": + return Fraction + if p == "Qi": + return Gaussian + if type(p) is not int: + raise ValueError("field must be Q, Qi or a prime at most 2^31-1") + return prime_scalars(p) + + +@lru_cache(maxsize=32) +def prime_scalars(p): + if not 2 <= p <= 2**31-1 or any(p % d == 0 for d in range(2, isqrt(p)+1)): + raise ValueError("field must be Q, Qi or a prime at most 2^31-1") + + class Prime: + def __init__(self, x=0): + if isinstance(x, Prime): + self.value = x.value + else: + q = Fraction(x) + self.value = q.numerator*pow(q.denominator, -1, p) % p + + def __add__(self, other): + return Prime(self.value+Prime(other).value) + + __radd__ = __add__ + + def __mul__(self, other): + return Prime(self.value*Prime(other).value) + + __rmul__ = __mul__ + + def __neg__(self): + return Prime(-self.value) + + def __sub__(self, other): + return self+-Prime(other) + + def __rsub__(self, other): + return Prime(other)+-self + + def __truediv__(self, other): + return Prime(self.value*pow(Prime(other).value, -1, p)) + + def __rtruediv__(self, other): + return Prime(other)/self + + def __eq__(self, other): + return self.value == Prime(other).value + + def __bool__(self): + return bool(self.value) + + def __str__(self): + return str(self.value) + + __repr__ = __str__ + + return Prime diff --git a/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/verify.py b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/verify.py new file mode 100644 index 0000000000..ff3365a66c --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/verify.py @@ -0,0 +1,351 @@ +"""Check the trace proof, native source and literal tensor failures. + +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +""" +import argparse +from collections import Counter, deque +from fractions import Fraction as Q +import hashlib +import json +from pathlib import Path +import random +import sys + +HERE = Path(__file__).resolve().parent + + +def need(condition, message): + if not condition: + raise ValueError(message) + + +def source_integrity(): + sources = json.loads((HERE / "SOURCES.json").read_text()) + pairs = {"fields.py": "research/universal-dirty-certificates/fields.py", + "clifford_exact.py": "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py"} + for local, original in pairs.items(): + record = next(item for item in sources["files"] if item["path"] == original) + need(hashlib.sha256((HERE / "vendor" / local).read_bytes()).hexdigest() == record["sha256"], "Frozen source: "+local) + + +source_integrity() +sys.path.insert(0, str(HERE)) +sys.path.insert(0, str(HERE / "vendor")) +import certify as c +import check_witness as independent +import clifford_exact as native +G = c.G + + +def source_matrix(op): + columns = [] + for j in range(1 << op.n): + values, exponent = op.zero_state(j) + columns.append([G.pair(Q(a, 1 << exponent), Q(b, 1 << exponent)) for a, b in values]) + return tuple(tuple(column[i] for column in columns) for i in range(1 << op.n)) + + +def example(operators, program, reference=(), axes=1, roles=3): + return {"axes": axes, "roles": roles, "operators": {name: [[str(x) for x in row] for row in a] for name, a in operators.items()}, + "program": list(program), "reference": list(reference)} + + +def group_one_axis(): + generators = [native.cgate(1, 1), native.diag(1, (1,))] + bank = {c.key(c.identity(2)): (c.identity(2), native.ident(1))} + queue = deque(bank.values()) + edges = 0 + while queue: + a, op = queue.popleft() + for generator in generators: + product = c.multiply(source_matrix(generator), a) + label = c.key(product) + edges += 1 + if label not in bank: + following = product, op.then(generator) + bank[label] = following + queue.append(following) + need(len(bank) == 96 and edges == 192, "Complete group closure") + for a, op in bank.values(): + need(a == source_matrix(op), "Literal native word phase") + c.validate_operator(a, 1) + return [a for a, _ in bank.values()] + + +def kron(a, b): + return tuple(tuple(x*y for x in row_a for y in row_b) for row_a in a for row_b in b) + + +def dense_tensor_norm(terms, width): + d = len(terms[0][1])**width + out = [[G(0) for _ in range(d)] for _ in range(d)] + for coefficient, a in terms: + tensor = ((G(1),),) + for _ in range(width): + tensor = kron(tensor, a) + for i in range(d): + for j in range(d): + out[i][j] = out[i][j]+coefficient*tensor[i][j] + return sum(c.norm2(z) for row in out for z in row)/d + + +def dense_program(problem, instructions, width): + d, r = (1 << problem["axes"])**width, problem["roles"] + count = d*r + rows = [[[G(int(i == role*d+j)) for i in range(count)] for j in range(d)] for role in range(r)] + lifted = {} + for name, encoded in problem["operators"].items(): + a = tuple(tuple(G(x) for x in row) for row in encoded) + tensor = ((G(1),),) + for _ in range(width): + tensor = kron(tensor, a) + lifted[name, False], lifted[name, True] = tensor, independent.star(tensor) + for op in instructions: + kind, dst = op["op"], op["dst"] + src = op.get("src", dst) + if kind == "swap": + rows[dst], rows[src] = rows[src], rows[dst] + elif kind == "scale": + rows[dst] = [[G(op["coefficient"])*x for x in row] for row in rows[dst]] + else: + image = rows[src] + if kind in ("apply", "query"): + a = lifted[op["symbol"], op.get("inverse", False)] + image = [[sum((a[j][k]*rows[src][k][i] for k in range(d)), G(0)) for i in range(count)] for j in range(d)] + if kind == "apply": + rows[dst] = image + else: + rows[dst] = [[x+G(op.get("coefficient", 1))*y for x, y in zip(a, b)] for a, b in zip(rows[dst], image)] + return rows + + +def independent_residual(problem): + bank = independent.matrices(problem) + d, r = 1 << problem["axes"], problem["roles"] + result = {} + for input_role in range(r): + left = independent.word_endpoint(problem, problem["program"], input_role) + right = independent.word_endpoint(problem, problem["reference"], input_role) + for output in range(r): + row = {} + for sign, words in [(1, left[output]), (-1, right[output])]: + for word, coefficient in words.items(): + a = independent.evaluate_word(word, bank, d) + c.accumulate(row, (output, input_role, c.key(a)), coefficient*sign) + result.update(row) + return result + + +def verify(write=False): + rng = random.Random(20261023) + group = group_one_axis() + C, S = source_matrix(native.cgate(1, 1)), source_matrix(native.diag(1, (1,))) + H, I = source_matrix(native.hadamard(1, [0])), c.identity(2) + phase_i = tuple(tuple(G("i")*z for z in row) for row in I) + need(c.multiply(H, H) == phase_i, "Source Hadamard phase") + operators = {"C": C, "S": S, "H": H, "iI": phase_i} + zero_axis = example({str(k): ((c.power(G("i"), k),),) for k in range(4)}, + [{"op": "query", "src": 0, "dst": 1, "symbol": str(k), "coefficient": "1/4"} + for k in range(4)], axes=0, roles=2) + zero_certificate = c.certify(zero_axis) + need(not zero_certificate["equivalent_at_all_positive_widths"], "Zero-axis scalar group") + need(zero_certificate["failure"]["normalized_squared_norms"] == ["0", "0", "0", "1"], "Zero-axis scalar group") + independent.check(zero_axis, zero_certificate) + need(c.certify(example({}, [], axes=0, roles=1))["equivalent_at_all_positive_widths"], "Empty zero-axis program") + polynomial_values = 0 + for n in range(13): + polynomial = c.cutoff_polynomial(n) + need(len(polynomial) == 8*n+5 and polynomial[0] == 0 and sum(polynomial) == 1, "Polynomial endpoints") + need(sum(abs(b) for b in polynomial) < Q(8, 7), "Coefficient norm") + need(sum(b for b in polynomial if b > 0) < Q(15, 14), "Positive coefficient mass") + alphabet = [G(0)] + [c.power(G("i"), k)*c.power(G("1+1i"), d)/(1 << n) for d in range(2*n+1) for k in range(4)] + for z in alphabet: + value = G(0) + for b in reversed(polynomial): + value = value*z+b + need(value == int(z == 1), "Trace-filter value") + polynomial_values += 1 + source_columns = 192 + native_fixtures = [] + for n in range(1, 5): + for q in range(1, 1 << n): + for sign in (-1, 1): + a = source_matrix(native.cgate(n, q, sign)) + first, second = G.pair(Q(1, 2), Q(sign, 2)), G.pair(Q(1, 2), Q(-sign, 2)) + expected = tuple(tuple(first if i == j else second if i == (j ^ q) else G(0) for j in range(1 << n)) for i in range(1 << n)) + need(a == expected, "Source C column formula") + c.validate_operator(a, n) + source_columns += 1 << n + if n <= 3: + native_fixtures.append((n, a)) + for sign in (-1, 1): + op = native.cgate(9, 173, sign) + for j in range(512): + values, den = op.zero_state(j) + expected = [(0, 0)]*512 + expected[j], expected[j ^ 173] = (1, sign), (1, -sign) + need(den == 1 and values == expected, "Nine-axis source column") + source_columns += 1 + entangling_trace_cases = 0 + for n in (2, 3): + for _ in range(24): + op = native.ident(n) + for _ in range(4): + source_axis, target_axis = rng.sample(range(n), 2) + rows = [1 << j for j in range(n)] + rows[target_axis] ^= 1 << source_axis + phase_rows = tuple(1 << j if j == target_axis else 0 for j in range(n)) + op = op.then(native.cgate(n, rng.randrange(1, 1 << n), rng.choice([-1, 1]))) + op = op.then(native.diag(n, phase_rows)).then(native.perm(n, rows)) + a = source_matrix(op) + need(tuple(c.validate_operator(a, n)) == op.tab, "Entangling source tableau") + trace = sum((a[j][j] for j in range(1 << n)), G(0)) + fixed_sum = 0 + for x in range(1 << n): + for z in range(1 << n): + phase = (x & z).bit_count() % 4 + u, v, p = native.apply(op.tab, (x, z, phase)) + if (u, v) == (x, z): + need((p-phase) % 4 in (0, 2), "Hermitian Pauli sign") + fixed_sum += 1 if p == phase else -1 + need(c.norm2(trace) == fixed_sum, "Pauli conjugation trace identity") + alphabet = [G(0)] + [c.power(G("i"), k)*c.power(G("1+1i"), d) for d in range(2*n+1) for k in range(4)] + need(trace in alphabet, "Entangling trace alphabet") + native_fixtures.append((n, a)) + source_columns += 1 << n + entangling_trace_cases += 1 + dense_norm_cases = 0 + for n in (1, 2): + pool = group if n == 1 else list({c.key(a): a for k, a in native_fixtures if k == n}.values()) + for _ in range(12): + selected = rng.sample(pool, 4) + terms = [(G(rng.choice([-2, -1, "i", "1/2", "1/2-1/2i"])), a) for a in selected] + inner = c.gram(selected) + for width in range(1, 4 if n == 1 else 3): + need(c.energy([x for x, _ in terms], inner, width) == dense_tensor_norm(terms, width), "Independent dense norm") + dense_norm_cases += 1 + result = c.analyze(n, terms) + w = result["witness"] + need(c.tensor_entry([x for x, _ in terms], selected, w["output_tuple"], w["input_tuple"]) == G(w["discrepancy"]) != 0, "Tensor entry") + differential_cases = literal_witnesses = full_column_cases = 0 + for trial in range(72): + instructions = [] + for _ in range(8): + kind = rng.choice(["add", "query", "apply", "scale", "swap"]) + op = {"op": kind, "dst": rng.randrange(3)} + if kind in ("add", "query", "swap"): + op["src"] = rng.randrange(3) + if kind in ("query", "apply"): + op.update(symbol=rng.choice(list(operators)), inverse=bool(rng.randrange(2))) + if kind in ("add", "query", "scale"): + op["coefficient"] = rng.choice([-1, 0, 1, "1/2", "i"]) + instructions.append(op) + problem = example(operators, instructions, instructions if trial % 3 == 0 else []) + _, differences = c.compile_difference(problem) + observed = {(o, i, c.key(a)): x for o, i, terms in differences for x, a in terms} + need(observed == independent_residual(problem), "Signed-word complete endpoint") + differential_cases += 1 + if trial < 12: + for width in (1, 2): + left = dense_program(problem, problem["program"], width) + right = dense_program(problem, problem["reference"], width) + lookup = {(o, i): terms for o, i, terms in differences} + d = 2**width + for o in range(3): + for i in range(3): + terms = lookup.get((o, i), []) + for x in range(d): + for y in range(d): + xt = [(x >> k) & 1 for k in reversed(range(width))] + yt = [(y >> k) & 1 for k in reversed(range(width))] + value = c.tensor_entry([a for a, _ in terms], [b for _, b in terms], xt, yt) + need(value == left[o][x][i*d+y]-right[o][x][i*d+y], "Full tensor program column") + full_column_cases += 1 + if trial < 24: + certificate = c.certify(problem) + if not certificate["equivalent_at_all_positive_widths"]: + independent.check(problem, certificate) + literal_witnesses += 1 + positive = example(operators, [{"op": "apply", "dst": 1, "symbol": "H"}]*2, + [{"op": "apply", "dst": 1, "symbol": "iI"}]) + need(c.certify(positive)["equivalent_at_all_positive_widths"], "Native relation") + phase_trap = example(operators, positive["program"], [{"op": "scale", "dst": 1, "coefficient": "i"}]) + phase_certificate = c.certify(phase_trap) + need(phase_certificate["failure"]["first_nonzero_width"] == 2, "Phase outside tensor") + independent.check(phase_trap, phase_certificate) + reynolds = example({str(i): a for i, a in enumerate(group)}, + [{"op": "query", "src": 0, "dst": 1, "symbol": str(i), "coefficient": "1/96"} for i in range(96)], roles=2) + reynolds_certificate = c.certify(reynolds) + norms = reynolds_certificate["failure"]["normalized_squared_norms"] + need(norms == ["0"]*7+["15/256", "0", "0", "0", "155/4096"], "Reynolds norm sequence") + independent.check(reynolds, reynolds_certificate) + need(independent.discrepancy(reynolds, 1, 0, [0]*8, [0]*8) == G("5/24"), "Reynolds entry") + for f, expected in enumerate(norms, 1): + rank = sum((c.power(sum((a[i][i] for i in range(2)), G(0)), f) for a in group), G(0))/96 + need(rank.imag == 0 and rank.real.denominator == 1 and rank/(2**f) == G(expected), "Projector rank") + controls = [] + def reject(label, function): + try: + function() + except (ValueError, KeyError, TypeError, ZeroDivisionError): + controls.append(label) + return + raise ValueError("Accepted control: "+label) + bad = json.loads(json.dumps(reynolds_certificate)) + bad["failure"]["witness"]["discrepancy"] = "0" + reject("wrong witness value", lambda: independent.check(reynolds, bad)) + bad_width = json.loads(json.dumps(reynolds_certificate)) + bad_width["failure"]["witness"]["width"] = 7 + reject("wrong witness width", lambda: independent.check(reynolds, bad_width)) + for field, value in [("schema", "other"), ("problem_sha256", "0"*64), ("axes", 2), ("cutoff", 13)]: + altered = json.loads(json.dumps(reynolds_certificate)) + altered[field] = value + reject("wrong certificate "+field, lambda altered=altered: independent.check(reynolds, altered)) + for label, matrix in [("nonunitary", [[2, 0], [0, 2]]), ("continuous rational phase", [["3/5+4/5i", 0], [0, "3/5+4/5i"]]), + ("wrong shape", [[1]]), ("floating scalar", [[1.0, 0], [0, 1]])]: + invalid = example({"C": C}, []) + invalid["operators"]["C"] = matrix + reject(label, lambda invalid=invalid: c.certify(invalid)) + toffoli = [[int(i == (j ^ (4 if j & 3 == 3 else 0))) for j in range(8)] for i in range(8)] + invalid = {"axes": 3, "roles": 1, "operators": {"T": toffoli}, "program": [], "reference": []} + reject("non-Clifford dyadic unitary", lambda: c.certify(invalid)) + for op in [{"op": "apply", "dst": 3, "symbol": "C"}, {"op": "apply", "dst": 0, "symbol": "missing"}, + {"op": "apply", "dst": 0, "symbol": "C", "inverse": 1}, {"op": "add", "src": 0, "dst": 1, "coefficient": 0.5}, + {"op": "query", "dst": 0, "symbol": "C"}, {"op": "apply", "dst": 0, "symbol": "C", "phase": 0}]: + reject("invalid instruction "+str(len(controls)), lambda op=op: c.certify(example(operators, [op]))) + helper = example(operators, [{"op": "query", "src": 0, "dst": 2, "symbol": "C"}]) + helper_certificate = c.certify(helper) + need(helper_certificate["failure"]["output_role"] == 2, "Dirty helper return") + independent.check(helper, helper_certificate) + controls.append("omitted helper return detected") + order = example(operators, [{"op": "apply", "dst": 0, "symbol": "C"}, {"op": "apply", "dst": 0, "symbol": "S"}], + [{"op": "apply", "dst": 0, "symbol": "S"}, {"op": "apply", "dst": 0, "symbol": "C"}]) + independent.check(order, c.certify(order)) + controls += ["noncommuting order detected", "phase outside tensor detected"] + receipt = {"status": "PASS_CLIFFORD_TENSOR_GRAM_NO_NEW_KAPPA", "cutoff": "8n+4", "separation": "14/15", + "one_axis_group_order": 96, "closure_edges": 192, + "trace_histogram": dict(sorted(Counter(str(sum((a[i][i] for i in range(2)), G(0))) for a in group).items())), + "polynomial_values": polynomial_values, "native_source_columns": source_columns, + "entangling_trace_cases": entangling_trace_cases, + "dense_norm_cases": dense_norm_cases, "complete_endpoint_comparisons": differential_cases, + "full_tensor_programs": full_column_cases, "random_literal_witnesses": literal_witnesses, + "zero_axis_cases": 2, + "reynolds": reynolds_certificate["failure"], "controls": controls} + files = {"RESULT.json": receipt, "examples/native-relation.json": positive, "examples/phase-trap.json": phase_trap, + "examples/phase-trap.certificate.json": phase_certificate, "examples/reynolds.json": reynolds, + "examples/reynolds.certificate.json": reynolds_certificate} + for name, data in files.items(): + path = HERE / name + if write: + path.parent.mkdir(parents=True, exist_ok=True) + path.write_text(json.dumps(data, indent=2, sort_keys=True)+"\n", encoding="utf-8") + else: + need(json.loads(path.read_text()) == data, "Committed result mismatch: "+name) + print(receipt["status"]) + return receipt + + +if __name__ == "__main__": + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--write", action="store_true", help="Regenerate the receipt and examples") + verify(parser.parse_args().write) diff --git a/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/verify_advances.py b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/verify_advances.py new file mode 100644 index 0000000000..22437672d9 --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/verify_advances.py @@ -0,0 +1,288 @@ +"""Replay the width refinements and compact native computation. + +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +""" +import argparse +from collections import deque +from fractions import Fraction as Q +import hashlib +import json +from pathlib import Path +import random +import sys + +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE)) +import verify as v +import compact as compact +import quadratic as q + + +def saved(name, data, write): + path = HERE / name + encoded = json.dumps(data, indent=2, sort_keys=True)+"\n" + if write: + path.write_text(encoded, encoding="utf-8") + else: + v.need(path.read_text(encoding="utf-8") == encoded, "Committed advance receipt: "+name) + + +def modular_inverse(matrix, p): + n = len(matrix) + rows = [row[:] + [int(i == j) for j in range(n)] for i, row in enumerate(matrix)] + for j in range(n): + k = next(k for k in range(j, n) if rows[k][j]) + rows[k], rows[j] = rows[j], rows[k] + scale = pow(rows[j][j], -1, p) + rows[j] = [x*scale % p for x in rows[j]] + for k in range(n): + if k != j: + scale = rows[k][j] + rows[k] = [(x-scale*y) % p for x, y in zip(rows[k], rows[j])] + return [row[n:] for row in rows] + + +def one_axis_certificate(group, write): + p, root = 65537, 256 + v.need(all(p % d for d in range(2, 257)) and root*root % p == p-1, "Prime field") + inner = v.c.gram(group) + + def reduce(z): + def part(x): + return x.numerator*pow(x.denominator, -1, p) + return (part(z.real)+root*part(z.imag)) % p + + matrix = [[sum(pow(reduce(z), f, p) for f in range(5, 9)) % p for z in row] for row in inner] + digest = hashlib.sha256(json.dumps([[[str(z) for z in row] for row in a] for a in group]).encode()).hexdigest() + path = HERE / "ONE-AXIS-RANK.json" + if write: + inverse = modular_inverse(matrix, p) + else: + inverse = json.loads(path.read_text())["inverse"] + v.need(type(inverse) is list and len(inverse) == 96 and all(type(row) is list and len(row) == 96 and + all(type(x) is int and 0 <= x < p for x in row) for row in inverse), "Modular inverse shape") + for i, row in enumerate(matrix): + for j, column in enumerate(zip(*inverse)): + v.need(sum(x*y for x, y in zip(row, column)) % p == int(i == j), "One-axis inverse product") + certificate = {"prime": p, "image_of_i": root, "widths": [5, 6, 7, 8], + "group_sha256": digest, "rank": 96, "inverse": inverse} + saved("ONE-AXIS-RANK.json", certificate, write) + return {key: value for key, value in certificate.items() if key != "inverse"} + + +def check_forms(rng): + count = 0 + units = (q.G(1), q.G("i"), q.G(-1), q.G("-i")) + for m in range(8): + for _ in range(80): + phase = q.Phase(m) + phase.constant = rng.randrange(4) + phase.linear = [rng.randrange(4) for _ in range(m)] + phase.cross = {(i, j) for i in range(m) for j in range(i+1, m) if rng.randrange(2)} + equations = [rng.randrange(1 << (m+1)) for _ in range(rng.randrange(m+1))] + expected = q.G(0) + for x in range(1 << m): + if any((e & 1) ^ (((e >> 1) & x).bit_count() % 2) for e in equations): + continue + exponent = phase.constant+sum(a*((x >> i) & 1) for i, a in enumerate(phase.linear)) + exponent += 2*sum(((x >> i) & 1)*((x >> j) & 1) for i, j in phase.cross) + expected = expected+units[exponent % 4] + v.need(q.gauss_sum(phase, equations) == expected, "Exhaustive constrained quadratic sum") + count += 1 + return count + + +def native_words(): + bank = {v.c.key(v.c.identity(2)): v.native.ident(1)} + queue = deque(bank.values()) + generators = (v.native.cgate(1, 1), v.native.diag(1, (1,))) + while queue: + op = queue.popleft() + for generator in generators: + new = op.then(generator) + label = v.c.key(v.source_matrix(new)) + if label not in bank: + bank[label] = new + queue.append(new) + v.need(len(bank) == 96, "Native word group closure") + return list(bank.values()) + + +def check_native(rng): + words = native_words() + for n in (2, 3): + for _ in range(16): + op = v.native.ident(n) + for _ in range(8): + raw = [rng.randrange(1 << n) for _ in range(n)] + rows = [sum(((raw[min(i, j)] >> max(i, j)) & 1) << j for j in range(n)) for i in range(n)] + alpha = [((rows[i] >> i) & 1)+2*rng.randrange(2) for i in range(n)] + source, target = rng.sample(range(n), 2) + permutation = [1 << j for j in range(n)] + permutation[target] ^= 1 << source + op = op.then(v.native.diag(n, rows, alpha)).then(v.native.perm(n, permutation)) + op = op.then(v.native.cgate(n, rng.randrange(1 << n), rng.choice((-1, 1)))) + op = op.then(v.native.xgate(n, rng.randrange(1 << n))) + words.append(op) + entries, traces, partials = 0, 0, 0 + for op in words: + matrix = v.source_matrix(op) + paths = q.Paths(op.n, op.circuit) + inverse = q.Paths(op.n, q.inverse_circuit(op.n, op.circuit)) + star = v.c.adjoint(matrix) + d = 1 << op.n + v.need(paths.trace() == sum((matrix[j][j] for j in range(d)), q.G(0)), "Native trace phase") + traces += 1 + for x in range(d): + for y in range(d): + v.need(paths.entry(x, y) == matrix[x][y] and inverse.entry(x, y) == star[x][y], "Native entry phase") + entries += 2 + for k in range(op.n+1): + xp = [rng.randrange(2) for _ in range(k)] + yp = [rng.randrange(2) for _ in range(op.n-k)] + expected = sum((v.c.conjugate(matrix[x][y])*star[x][y] + for x in range(d) for y in range(d) + if all(((x >> j) & 1) == bit for j, bit in enumerate(xp)) and + all(((y >> j) & 1) == bit for j, bit in enumerate(yp))), q.G(0)) + v.need(q.partial_inner(paths, inverse, xp, yp) == expected, "Native partial inner product") + partials += 1 + return {"native_words": len(words), "native_entries": entries, "native_traces": traces, + "partial_inner_products": partials} + + +def check_programs(rng): + count, witnesses, relations = 0, 0, 0 + for n in range(3): + ops = {"I": v.native.ident(n), "iI": v.native.Op(n, v.native.identity(n), [("phase", 1)])} + if n: + ops.update(C=v.native.cgate(n, (1 << n)-1), H=v.native.hadamard(n, range(n)), + S=v.native.diag(n, tuple(1 << j for j in range(n)))) + for _ in range(16): + program = [] + for _ in range(8): + kind = rng.choice(("query", "apply", "add", "scale", "swap")) + instruction = {"op": kind, "dst": rng.randrange(3)} + if kind in ("query", "add", "swap"): + instruction["src"] = rng.randrange(3) + if kind in ("query", "apply"): + instruction.update(symbol=rng.choice(list(ops)), inverse=bool(rng.randrange(2))) + if kind in ("scale", "query", "add"): + instruction["coefficient"] = rng.choice(("1", "-1", "i", "1/2")) + program.append(instruction) + problem = {"axes": n, "roles": 3, "operators": {s: o.circuit for s, o in ops.items()}, + "program": program, "reference": []} + dense = v.example({s: v.source_matrix(o) for s, o in ops.items()}, program, axes=n) + _, expected_entries = v.c.compile_difference(dense) + expected = {(output, source): {v.c.key(a): coefficient for coefficient, a in terms} + for output, source, terms in expected_entries} + actual = {} + for output, source, coefficients, paths, _ in compact.residuals(problem): + matrices = [tuple(tuple(path.entry(x, y) for y in range(1 << n)) for x in range(1 << n)) for path in paths] + actual[output, source] = {v.c.key(a): coefficient for coefficient, a in zip(coefficients, matrices)} + v.need(actual == expected, "Compact complete endpoint") + certificate = compact.certify(problem) + v.need(certificate["equivalent_at_all_positive_widths"] == (not expected), "Compact decision") + if "failure" in certificate: + f = certificate["failure"] + w = f["witness"] + value = v.independent.discrepancy(dense, f["output_role"], f["input_role"], w["output_tuple"], w["input_tuple"]) + v.need(value != 0 and str(value) == w["discrepancy"], "Compact literal witness") + witnesses += 1 + count += 1 + for n in (1, 2, 3): + ops = {"C": v.native.cgate(n, (1 << n)-1), "H": v.native.hadamard(n, range(n)), + "phase": v.native.Op(n, v.native.identity(n), [("phase", n)])} + cases = [([{"op": "apply", "dst": 2, "symbol": "C"}]*4, []), + ([{"op": "apply", "dst": 1, "symbol": "H"}]*2, + [{"op": "apply", "dst": 1, "symbol": "phase"}]), + ([{"op": "apply", "dst": 0, "symbol": "C"}, + {"op": "apply", "dst": 0, "symbol": "C", "inverse": True}], [])] + for program, reference in cases: + problem = {"axes": n, "roles": 3, "operators": {s: o.circuit for s, o in ops.items()}, + "program": program, "reference": reference} + dense = v.example({s: v.source_matrix(o) for s, o in ops.items()}, program, reference, axes=n) + v.need(compact.certify(problem)["equivalent_at_all_positive_widths"] and + v.c.certify(dense)["equivalent_at_all_positive_widths"], "Compact exact native relation") + relations += 1 + phase_trap = {"axes": 1, "roles": 1, "operators": {"iI": [("phase", 1)]}, + "program": [{"op": "apply", "dst": 0, "symbol": "iI"}], + "reference": [{"op": "scale", "dst": 0, "coefficient": "i"}]} + norms = compact.certify(phase_trap)["failure"]["normalized_squared_norms"] + v.need(norms[0] == "0" and Q(norms[1]) > 0, "Compact phase stays inside tensor") + return {"complete_programs": count, "literal_witnesses": witnesses, "exact_native_relations": relations, + "scalar_phase_traps": 1} + + +def verify(write=False): + rng = random.Random(5376) + code = {q.parity_sum(row for j, row in enumerate((255, 240, 204, 170)) if mask >> j & 1) for mask in range(16)} + v.need(len(code) == 16 and all(x.bit_count() % 4 == 0 for x in code), "Doubly even code") + for y in range(256): + v.need(sum((-1)**((x & y).bit_count() % 2) for x in code) == 16*int(y in code), "Code Fourier invariant") + h = v.source_matrix(v.native.hadamard(1, [0])) + v.need(h == ((q.G("1/2+1/2i"), q.G("1/2+1/2i")), + (q.G("1/2+1/2i"), q.G("-1/2-1/2i"))) and v.c.power(h[0][0], 8) == q.G("1/16"), + "Eight-copy native phase") + previous = None + for n in range(65): + polynomial = v.c.cutoff_polynomial(n) + norm = sum(abs(x) for x in polynomial) + v.need(norm <= Q(77, 75) and sum(x for x in polynomial if x > 0) <= Q(76, 75), "Improved filter bound") + descending = list(reversed(polynomial[1::4])) + v.need(all((x > 0) == ((-1)**(j*(j+3)//2) == 1) for j, x in enumerate(descending)), "Filter coefficient signs") + if n >= 2: + v.need(norm < previous, "Filter norm decreases") + previous = norm + forms = check_forms(rng) + rank_certificate = one_axis_certificate(v.group_one_axis(), write) + native = check_native(rng) + programs = check_programs(rng) + large = [] + for n in (64, 65): + h = v.native.hadamard(n, range(n)) + operators = {"H": h.circuit, "iI": [("phase", 1)]} + if n == 64: + program = [{"op": "query", "src": 0, "dst": 1, "symbol": "H"}] + reference = [] + else: + program = [{"op": "apply", "dst": 0, "symbol": "H"}]*2 + reference = [{"op": "apply", "dst": 0, "symbol": "iI"}] + problem = {"axes": n, "roles": 2, "operators": operators, "program": program, "reference": reference} + certificate = compact.certify(problem) + v.need(certificate["equivalent_at_all_positive_widths"] == (n == 65), "Large native decision") + if n == 64: + v.need(certificate["failure"]["witness"] == {"width": 1, "output_tuple": [0], "input_tuple": [0], + "discrepancy": "1/4294967296"}, "Large literal Hadamard entry") + saved(f"examples/native-{n}.json", problem, write) + saved(f"examples/native-{n}.certificate.json", certificate, write) + large.append({"axes": n, "base_dimension": str(1 << n), "equivalent": n == 65}) + controls = [] + for label, function in [ + ("singular permutation", lambda: q.Paths(2, [("P", [1, 1])])), + ("diagonal parity", lambda: q.Paths(1, [("D", [1], [0])])), + ("asymmetric diagonal", lambda: q.Paths(2, [("D", [2, 0], [0, 0])])), + ("wrong C sign", lambda: q.Paths(1, [("C", 1, 0)])), + ("unknown gate", lambda: q.Paths(1, [("H", 0)])), + ("coordinate out of range", lambda: q.Paths(1, []).entry(2, 0)), + ("invalid prefix", lambda: q.partial_inner(q.Paths(1, []), q.Paths(1, []), [2])), + ("negative axes", lambda: q.Paths(-1, [])), + ]: + try: + function() + except ValueError: + controls.append(label) + else: + raise ValueError("Accepted control: "+label) + receipt = {"status": "PASS_CLIFFORD_ADVANCES_NO_NEW_KAPPA", "general_test_widths": "8n-3 through 8n+4 for n>=2", + "stable_separation": "75/76", "filter_axis_counts": 65, "code_fourier_values": 256, + "one_axis": rank_certificate, "exhaustive_quadratic_forms": forms, + **native, **programs, "large_native_programs": large, "controls": controls} + saved("ADVANCES-RESULT.json", receipt, write) + print(receipt["status"]) + return receipt + + +if __name__ == "__main__": + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--write", action="store_true", help="Regenerate the advance receipts") + verify(parser.parse_args().write) diff --git a/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/verify_provider.py b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/verify_provider.py new file mode 100644 index 0000000000..6a63161f9d --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/clifford-tensor-gram/verify_provider.py @@ -0,0 +1,310 @@ +"""Check the complete selected provider and the fixed pair-fusion domain. + +Use --write to save receipts. Normal replay does not change package files. +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +""" +from collections import Counter +from copy import deepcopy +from fractions import Fraction as Q +import gzip +import hashlib +import json +from pathlib import Path +import sys + +sys.path.insert(0, str(Path(__file__).resolve().parent)) +import compact +import certify as c +import provider as p +from check_witness import word_endpoint +from quadratic import Paths, partial_inner, inverse_circuit +from verify import source_integrity + +HERE = Path(__file__).resolve().parent + + +def canonical(value): + return (json.dumps(value, sort_keys=True, separators=(",", ":")) + "\n").encode() + + +def saved(name, value, write): + raw = canonical(value) + path = HERE / "provider" / name + if write: + path.write_bytes(gzip.compress(raw, mtime=0) if name.endswith(".gz") else raw) + else: + expected = path.read_bytes() + if name.endswith(".gz"): + expected = gzip.decompress(expected) + p.need(expected == raw, "Provider receipt differs: " + name) + return hashlib.sha256(raw).hexdigest() + + +def equal(left, right): + a, b = Paths(p.N, left), Paths(p.N, right) + value = partial_inner(a, b) / p.D + p.need(value == 1, "Exact native Gram equality with absolute phase") + return a + + +def check_catalogue(model, data, audits): + expected = {(a, b, direction): rank for direction, audit in audits.items() + for (a, b), rank in audit["pairs"].items()} + header, *records = data["paid"] + raw = gzip.decompress((HERE / "provider/WORD.json.gz").read_bytes()) + p.need(header["word_payload_sha256"] == hashlib.sha256(raw).hexdigest() + and not header["partial"], "Complete catalogue bound to the exact word") + seen, traces = set(), {} + for row in records: + a, b, direction = row["input"], row["output"], row["direction"] + key = a, b, direction + p.need(key in expected and key not in seen and row["rank"] == row["recipe"]["rank"] == expected[key], + "Unique actual paid class and rank") + actual = equal(model.edge(a, b, direction), p.recipe(row["recipe"])) + traces[key] = actual.trace() / p.D + seen.add(key) + p.need(seen == set(expected) and len(seen) == header["expected_complete_oriented_classes"], + "All oriented paid classes, without gaps") + + warp_records = {(row["operator"], row["input"], row["output"]): row + for row in data["phases"]["actual_warp_classes"]} + p.need(len(warp_records) == len(data["phases"]["actual_warp_classes"]), "No duplicate warp classes") + for direction, audit in audits.items(): + p.need(set(warp_records) == audit["warps"], "All actual native warp classes") + for (signed, a, b), row in warp_records.items(): + rec = row["recipes"][direction] + p.need(rec["rank"] == 0, "Every warp is a monomial") + equal(model.warp(signed, a, b, direction), p.recipe(rec)) + + helpers = {} + for row in data["helpers"]["new_physical_edges_and_boundaries"]: + helpers[row["old"], row["new"]] = row + for row in data["phases"]["changed_helper_boundaries"]: + helpers[row["input"], row["output"]] = row + actual_helpers = Counter(zip(model.c["start"][224:], model.c["final"][224:])) + helper_profile = Counter() + for (a, b), count in sorted(actual_helpers.items()): + u, v = model.c["frames"][a], model.c["frames"][b] + r = len(v)-len(u) + p.need(r > 0 and p.rank(u+v) == len(v), "Strict productive helper boundary") + helper_profile[r] += count + for direction in ("forward", "backward"): + rec = helpers[a, b]["recipes"][direction] + p.need(rec["rank"] == r, "Complete helper recipe rank") + equal(model.edge(a, b, direction), p.recipe(rec)) + + adapters = json.loads((HERE / "provider/MAIN-ADAPTERS.json").read_bytes()) + adapter_seen = set() + for row in adapters: + entrance, register, f = row["entrance"], row["role"], row["frame"] + p.need(type(entrance) is bool and type(register) is int and 0 <= register < 224, + "Main adapter label") + key = entrance, register + p.need(key not in adapter_seen and f == model.c["start" if entrance else "final"][register], + "Exact complete adapter boundary") + p.need(row["recipe"]["rank"] == 0, "Main adapter is a monomial") + target = inverse_circuit(p.N, model.old_frame(register, entrance)) + model.frame(f) + decoded = p.recipe(row["recipe"]) + for direction in ("forward", "backward"): + equal(target if direction == "forward" else p.conjugate(target), + decoded if direction == "forward" else p.conjugate(decoded)) + adapter_seen.add(key) + p.need(adapter_seen == {(side, r) for side in (False, True) for r in range(224)}, + "All main adapters in both orientations") + return traces, dict(paid_oriented_classes=len(seen), warp_oriented_classes=2*len(warp_records), + helper_oriented_classes=2*len(actual_helpers), helper_roles=sum(actual_helpers.values()), + helper_profile=dict(sorted(helper_profile.items())), + main_adapter_oriented_classes=2*len(adapter_seen)) + + +def fusion_census(model, traces): + evidence, trace_counts, kinds, ranks = {}, Counter(), Counter(), Counter() + for direction, program in model.word["programs"].items(): + rows = [] + for pair in p.fusion_pairs(program): + row = p.contact_witness(program, pair) + a, b, c0, d = row["frames"] + for name, key in (("late_trace", (a, b, direction)), ("early_trace", (c0, d, direction))): + tau = traces[key] + # f=1: Re(tau)<=1/2. f>=2: |tau|^f<=1/2. + p.need(tau.real <= Q(1, 2) and c.norm2(tau) <= Q(1, 2), "Uniform noncentral trace bound") + row[name] = str(tau) + trace_counts[str(tau)] += 1 + p.need(Q(row["coefficient"]) != 0, "Nonzero contact coefficient") + kinds[direction + ("_row" if row["output"] == row["role"] else "_column")] += 1 + ranks[str(row["ranks"])] += 1 + rows.append(row) + evidence[direction] = rows + minimum = min(Q(row["coefficient"])**2 for rows in evidence.values() for row in rows) + return evidence, dict(trace_counts=dict(sorted(trace_counts.items())), contact_types=dict(sorted(kinds.items())), + rank_pairs=dict(sorted(ranks.items())), uniform_squared_cut_block_lower_bound=str(minimum), + pairs_by_direction={d: len(rows) for d, rows in evidence.items()}, + rejected_fusions=2*sum(map(len, evidence.values())), + width_domain="every positive integer", + normalized_squared_cut_defect_lower_bound="coefficient^2") + + +def check_contact_certificates(model, evidence): + """Check coverage by role lists, then use the older input-column engine.""" + count = 0 + for direction, certificates in evidence.items(): + events = model.word["programs"][direction] + expected = set() + for register in range(p.PERSISTENT): + climbs = [(j, event) for j, event in enumerate(events) + if event[0] == "climb" and event[2] == register] + expected.update((a, b) for j, (a, _) in enumerate(climbs) for b, _ in climbs[j+1:]) + p.need(len(certificates) == len(expected) and {(r["first"], r["second"]) for r in certificates} == expected, + "Independent complete same-role pair census") + skeleton = [] + for event in events: + instructions = [] + if event[0] == "warp": + instructions.append(dict(op="apply", dst=p.role(event[1]), symbol=str(abs(event[2])), inverse=event[2] < 0)) + elif event[0] == "scalar": + gate = event[1] + target, op = p.role(gate[1]), gate[0] + if op in ("clear", "copy"): + instructions.append(dict(op="scale", dst=target, coefficient="0")) + if op in ("copy", "add"): + instructions.append(dict(op="add", src=p.role(gate[2]), dst=target, + coefficient=str(Q(1) if op == "copy" else Q(gate[3], gate[4])))) + elif op == "scale": + instructions.append(dict(op="scale", dst=target, coefficient=str(Q(gate[2], gate[3])))) + skeleton.append(instructions) + interface = dict(roles=p.PERSISTENT+1, operators={str(j): None for j in range(1, 73)}) + for row in certificates: + program = [instruction for event in skeleton[row["first"]+1:row["second"]] for instruction in event] + result = word_endpoint(interface, program, row["input"])[row["output"]] + word = tuple((str(abs(signed)), signed < 0) for signed in row["word"]) + p.need(result == {word: c.G(row["coefficient"])}, "Separate complete contact coefficient replay") + count += 1 + return count + + +def fused_program(problem, offsets, pair, early): + first, second, *_ = pair + program = problem["program"] + merged = program[offsets[first]:offsets[first+1]] + program[offsets[second]:offsets[second+1]] + return (program[:offsets[first]] + (merged if early else []) + + program[offsets[first+1]:offsets[second]] + ([] if early else merged) + + program[offsets[second+1]:]) + + +def full_witness(problem, program, reference): + """Find a width-one basis witness, then check a separate input-column replay.""" + actual, _ = p.complete_endpoint(problem, program) + names = list(problem["operators"]) + bank = compact.validate(problem) + for output, (left, right) in enumerate(zip(actual, reference)): + difference = left.copy() + p.add(difference, right, Q(-1)) + for entry in sorted({key[0] for key in difference}): + terms = [(word, q) for (source, word), q in difference.items() if source == entry] + circuits = [[gate for signed in reversed(word) + for gate in bank[names[abs(signed)-1], signed < 0]] for word, q in terms] + coefficients, paths, inner = compact.merge_terms([c.G(q) for word, q in terms], + [Paths(p.N, circuit) for circuit in circuits]) + if not coefficients or c.energy(coefficients, inner, 1) == 0: + continue + witness = compact.entry_witness(coefficients, paths, inner, 1) + literal = word_endpoint(problem, program, entry)[output] + wanted = word_endpoint(problem, problem["reference"], entry)[output] + from check_witness import add_term + for word, q in wanted.items(): + add_term(literal, word, -q) + # Independent source amplitude evaluator; no Gram or path sum. + sys.path.insert(0, str(HERE / "vendor")) + import clifford_exact as source + value = c.G(0) + for word, q in literal.items(): + circuit = [gate for letter in reversed(word) for gate in bank[letter]] + vector, denominator = source.Op(p.N, source.identity(p.N), circuit).zero_state(witness["input_tuple"][0]) + real, imag = vector[witness["output_tuple"][0]] + value += q*c.G.pair(Q(real, 1 << denominator), Q(imag, 1 << denominator)) + p.need(value != 0 and str(value) == witness["discrepancy"], "Independent complete-provider basis witness") + return dict(output_role=output, input_role=entry, **witness, + normalized_squared_norm=str(c.energy(coefficients, inner, 1)), + mutated_program_sha256=hashlib.sha256(canonical(program)).hexdigest()) + raise ValueError("No width-one full-program witness") + + +def rejection(name, action): + try: + action() + except (ValueError, KeyError) as error: + return dict(name=name, rejected=str(error)) + raise ValueError("Accepted negative control: " + name) + + +def verify(write=False): + source_integrity() + manifest, data = p.read_inputs() + model = p.Provider(data["word"]) + audits = {d: model.audit_word(d) for d in ("forward", "backward")} + traces, native = check_catalogue(model, data, audits) + print("PASS_ALL_PROVIDER_NATIVE_CLASSES", native, flush=True) + results, witnesses = {}, [] + for direction in ("forward", "backward"): + problem, offsets = model.problem(direction) + actual, support = p.complete_endpoint(problem, problem["program"]) + reference, _ = p.complete_endpoint(problem, problem["reference"]) + p.need(actual == reference, "Complete sparse physical endpoint") + certificate = compact.certify(problem) + p.need(certificate["equivalent_at_all_positive_widths"], "Complete compact provider certificate") + p.need(not actual[p.OWNED], "Arbitrary owned input is erased at return") + results[direction] = dict(certificate=certificate, support=support, instructions=len(problem["program"]), + native_symbols=len(problem["operators"]), events=audits[direction]["events"], + paid=audits[direction]["paid"]) + pairs = p.fusion_pairs(model.word["programs"][direction]) + selected = [min(pairs, key=lambda row: (row[1]-row[0], row)), + min((row for row in pairs if row[4] != row[5]), key=lambda row: (row[1]-row[0], row))] + events = model.word["programs"][direction] + selected.append(min((row for row in pairs if max(events[row[0]][5], events[row[1]][5]) > 1 + and any(event[0] == "climb" and event[2] == row[2] + for event in events[row[0]+1:row[1]])), + key=lambda row: (row[1]-row[0], row))) + for pair in selected: + for early in (True, False): + witness = full_witness(problem, fused_program(problem, offsets, pair, early), reference) + witnesses.append(dict(direction=direction, placement="early" if early else "late", + pair=list(pair), **witness)) + print("PASS_COMPLETE_PROVIDER", direction, support, flush=True) + fusions, fusion_result = fusion_census(model, traces) + fusion_result["separate_contact_replays"] = check_contact_certificates(model, fusions) + controls = [] + bad = deepcopy(data) + bad["paid"] = bad["paid"][:-1] + controls.append(rejection("missing_paid_class", lambda: check_catalogue(model, bad, audits))) + first = data["paid"][1] + wrong = deepcopy(first["recipe"]) + wrong["left"]["phase"] = (wrong["left"]["phase"]+1) % 4 + controls.append(rejection("paid_absolute_phase", lambda: equal(model.edge(first["input"], first["output"], first["direction"]), p.recipe(wrong)))) + broken = deepcopy(data["word"]) + broken["programs"]["forward"].insert(0, ["scalar", ["clear", ["L", 224]], broken["canonical"]["start"][224]]) + controls.append(rejection("borrowed_erasure", lambda: p.Provider(broken).audit_word("forward"))) + broken_live = deepcopy(data["word"]) + prog = broken_live["programs"]["backward"] + at = next(j for j, event in enumerate(prog) if event[0] == "center") + prog.insert(at, next(event for event in prog if event[0] == "climb")) + controls.append(rejection("live_owned_cut", lambda: p.Provider(broken_live).audit_word("backward"))) + # A block with no contact can permit fusion. The exclusion needs its contact witness. + p.need(all(not row for j, row in enumerate(p.interval([], -1, 0, 0)) if j != 0), "Identity interval positive control") + controls.append(rejection("missing_contact_is_not_a_certificate", lambda: p.contact_witness([], (-1, 0, 0, 0, 2, 2, 3)))) + evidence_sha = saved("FUSIONS.json.gz", fusions, write) + witness_sha = saved("WITNESSES.json", witnesses, write) + result = dict(status="PASS_COMPLETE_PR4610_PROVIDER_AND_30328_FUSION_OBSTRUCTIONS", source_main=manifest["base_commit"], + provider_head=manifest["provider_head"], admission_head=manifest["admission_head"], + complete_local_provider=results, native=native, fusion=fusion_result, + fusion_payload_sha256=evidence_sha, witness_payload_sha256=witness_sha, + full_program_basis_witnesses=len(witnesses), controls=controls, + new_kappa=False, achieved_paid_delta={}, + limits="Fixed early/late fusion of any two persistent paid climbs on one role; no changed contacts, coupled fusions, new controller or physical/outer admission.") + saved("RESULT.json", result, write) + print(result["status"], flush=True) + return result + + +if __name__ == "__main__": + p.need(sys.argv[1:] in ([], ["--write"]), "Use --write or no argument") + verify("--write" in sys.argv) diff --git a/research/coupled-provider-independent-audit/capsule/clifford-repository/research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py new file mode 100644 index 0000000000..166841a037 --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/clifford-repository/research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py @@ -0,0 +1,149 @@ +"""Small exact Gaussian-dyadic Clifford compiler, independent of gx internals. +Paulis use i^p X^x Z^z. State vectors use integer Gaussian numerators / 2^d. +The tableau is supplemented by a literal circuit, so global phases are kept. +""" +from dataclasses import dataclass + +def parity(x):return x.bit_count()&1 +def rank(rows): + p={} + for x in rows: + while x: + b=x.bit_length()-1 + if b not in p:p[b]=x;break + x^=p[b] + return len(p) +def transpose(rows,n):return tuple(sum(((rows[j]>>i)&1)<>j&1);a[j],a[k]=a[k],a[j] + for i in range(n): + if i!=j and a[i]>>j&1:a[i]^=a[j] + assert [r&((1<>n for r in a) +def basis_extend(cols,n): + out=[] + for x in list(cols)+[1<len(out):out.append(x) + assert len(out)==n + return tuple(out) +def nullspace(rows,n): + a=list(rows);p=[];k=0 + for j in range(n): + t=next((i for i in range(k,len(a)) if a[i]>>j&1),None) + if t is None:continue + a[t],a[k]=a[k],a[t] + for i in range(len(a)): + if i!=k and a[i]>>j&1:a[i]^=a[k] + p.append(j);k+=1 + return tuple((1<>j)&1)<>i&1:out=pmul(out,T[i]) + for i in range(n): + if z>>i&1:out=pmul(out,T[n+i]) + return out +def compose(A,B):return tuple(apply(A,p) for p in B) +def inverse(T): + n=len(T)//2;cols=[x|(z<>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4)) + return tuple(out) +def qvalue(Q,alpha,x,n): + return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4 +def mul_i(a,p): + x,y=a;p%=4 + return [(x,y),(-y,x),(-x,-y),(y,-x)][p] +@dataclass +class Op: + n:int + tab:tuple + circuit:list + def then(self,b): + assert self.n==b.n + return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit) + def adjoint(self): + circ=[] + for e in reversed(self.circuit): + if e[0]=='P':circ.append(('P',inv(e[1],self.n))) + elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2]))) + elif e[0]=='C':circ.append(('C',e[1],-e[2])) + elif e[0]=='phase':circ.append(('phase',(-e[1])%4)) + else:circ.append(e) + return Op(self.n,inverse(self.tab),circ) + def zero_state(self,basis=0): + N=1<>i)&1 for i in range(n)) + assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n)) + return Op(n,tuple([(1<>i&1 else 0,1<>i&1 else 0) for i in range(n)]),[('C',q,sgn)]) +def xgate(n,b):return Op(n,tuple([(1<>i)&1)) for i in range(n)]),[('X',b)]) +def fourier(n,axes=None): + out=ident(n) + for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<len(selected):picks.append(j);selected.append(x) + assert len(picks)==r and all(x>>r==0 for x in Bcols) + Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1<= 0 else "")+str(self.imag)+"i" + + __repr__ = __str__ + + +def scalars(problem): + p = problem.get("field", "Q") + if p == "Q": + return Fraction + if p == "Qi": + return Gaussian + if type(p) is not int: + raise ValueError("field must be Q, Qi or a prime at most 2^31-1") + return prime_scalars(p) + + +@lru_cache(maxsize=32) +def prime_scalars(p): + if not 2 <= p <= 2**31-1 or any(p % d == 0 for d in range(2, isqrt(p)+1)): + raise ValueError("field must be Q, Qi or a prime at most 2^31-1") + + class Prime: + def __init__(self, x=0): + if isinstance(x, Prime): + self.value = x.value + else: + q = Fraction(x) + self.value = q.numerator*pow(q.denominator, -1, p) % p + + def __add__(self, other): + return Prime(self.value+Prime(other).value) + + __radd__ = __add__ + + def __mul__(self, other): + return Prime(self.value*Prime(other).value) + + __rmul__ = __mul__ + + def __neg__(self): + return Prime(-self.value) + + def __sub__(self, other): + return self+-Prime(other) + + def __rsub__(self, other): + return Prime(other)+-self + + def __truediv__(self, other): + return Prime(self.value*pow(Prime(other).value, -1, p)) + + def __rtruediv__(self, other): + return Prime(other)/self + + def __eq__(self, other): + return self.value == Prime(other).value + + def __bool__(self): + return bool(self.value) + + def __str__(self): + return str(self.value) + + __repr__ = __str__ + + return Prime diff --git a/research/coupled-provider-independent-audit/capsule/repository/research/coded-native-caller/NORMALIZERS.json b/research/coupled-provider-independent-audit/capsule/repository/research/coded-native-caller/NORMALIZERS.json new file mode 100644 index 0000000000..bca92c222c --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/repository/research/coded-native-caller/NORMALIZERS.json @@ -0,0 +1,126 @@ +{ + "clifford_sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962", + "code_sha256": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0", + "finite_checks": {"absolute_phase_mutations_rejected":112,"exact_endpoint_factor_identities":896,"gaussian_free_compiled_wrappers":896,"monomial_wrappers":896,"omitted_phase_rejections":112,"ports":112,"scalar_basis_recodings":224,"weight_congruence_addresses":57344}, + "local_gauge_bill": 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+ ], + "recoding_bill": {"forward_prefix_component_l1_upper":57,"forward_update_coefficient":"-1/4","inverse_output_prefix_component_l1_upper":"69/13","inverse_prefix_component_l1_upper":56,"inverse_update_coefficient":"-1/52","monomial_field_maps":224,"output_scaled_adds":448,"owned_fields":8,"owned_initial_clears":8,"owned_terminal_clears":8,"signed_mode_adds":448}, + "schema": "coded-native-real-normalizers/1", + "scope": "Exact physical central ABI and local gauges; not full-controller or multiplication admission.", + "source_payload_sha256": "cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd", + "status": "PASS_CODED_NATIVE_REAL_NORMALIZERS" +} diff --git a/research/coupled-provider-independent-audit/capsule/repository/research/coded-native-caller/PHYSICAL.md b/research/coupled-provider-independent-audit/capsule/repository/research/coded-native-caller/PHYSICAL.md new file mode 100644 index 0000000000..da8837ba67 --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/repository/research/coded-native-caller/PHYSICAL.md @@ -0,0 +1,71 @@ +# Real physical normalizers for the coded producer + +This is local constructive research on canonical/pr4929, not a completed supplier or exponent claim. Source code and Gaussian conventions retain the original authors' credit. + +Let n=9 and let q be any of the source's 112 port vectors (weight 3 or 7). Let e0=1. Construct an orthogonal binary matrix G taking e0 to q. If q_0=0, use the orthogonal transvection T_(e0+q). If q_0=1, select j>0 with q_j=0 and use T_(ej+q) T_(e0+ej). Here T_v(x)=x+(v dot x)v; both v have even weight, hence T_v is orthogonal. Such j exists because q is not the all-ones vector. + +For row j of G put z_j=(wt(row_j G)-1)/2 modulo 2. Define K=Z_z P_G. It is a real signed permutation. The full Gaussian R has entries alpha*(-i)^wt(x+y), with alpha=(1+i)^9/2^9. Orthogonality gives + +wt(G^-1 d)-wt(d) = 2 z dot d (mod 4). + +Indeed the degree-two coefficients vanish modulo four because distinct columns of G^-1 have even dot product; the linear coefficient is the weight of that column minus one. Therefore K R K^-1=R exactly, including absolute phase. K also maps the central line to span(q), and its orthogonal complement to q-perp, at the canonical-frame Lagrangian level. All these statements tensor to every positive digit-column count. + +Let Q be the central C gate, D the product of the other eight C gates, so R=DQ. Let E_i and S_i be the actual retained entrance-line and exit-hyperplane frame operators. With the operator convention that rightmost applies first, use + +input X: E_i K_i Q^-1 +input Y: K_i +output X: K_i^-1 +output Y: D K_i^-1 S_i^-1. + +All four wrappers are monomial. Their Lagrangian incidences prove this for every port, and the scratch verifier checks exact tableaus and absolute phases at every one of the 112 source ports. With A from PR4929, define C_ij= A_ij K_i^-1 K_j. Then the full main endpoint is + +F = diag(D,D) [[I,0],[C Q^-1,I]]. + +C is a physically implementable fixed owner recoding: apply K_i to each owner, apply A among the owners at common physical coordinates, and apply K_i^-1. Its inverse uses A^-1=(A+12I)/13. Since each K_i is real orthogonal and A is real symmetric, C^T=C. Since K_i commutes with R, C commutes with R. The polynomial C^2+12C-13I=0 follows by similarity. The 408 independent helper jobs and every paid Gaussian child are unchanged. + +For the actual raw inverse transpose, F^-T=diag(D^-1,D^-1) [[I,-Q^-1 C],[0,I]], since Q,D are symmetric. Multiply both outputs by D^2, then conjugate the physical X bank by Q^2 (input Q^-2 and output Q^2). These are explicit monomial powers. The result is + +B = diag(D,D) [[I,-Q C],[0,I]]. + +The old source convention using Y-only Q^2 conjugation cannot simply be copied for noncommuting C. The X-only convention above is exact. + +For a prior code B0 commuting with the current D, set G(B0)=diag(B0,Q^-1 B0 Q). The following two constructive local identities hold without requiring C and Q to commute: + +(post X C) F (pre Y C) = G(C B0) F_standard G(B0)^-1, +(post X C^-1) B (pre Y C^-1) = G(C^-1 B0) B_standard G(B0)^-1. + +They use [C,DQ]=0 and [B0,D]=0. Every additional operation on the left is physically cheap fixed recoding. For disjoint fresh blocks, codes from earlier stages commute with the current D. These identities do not yet settle interstage ADD/IDLE compatibility, terminal gauges, productive jobs, or the complete moment. + +## Literal recoding and complete local bill + +The source code has an exact factorization A=I-MM^T/4 with M a 112-by-8 matrix having entries 0,+1,-1 and M^T M=56I. Each mode column has 56 nonzero entries, and each owner row has four. The mode columns are emitted in NORMALIZERS.json and all 12,544 entries are checked against the pinned CODE.json. This factorization is used here as a constructive scalar program, without relying on any common physical address chart for separate Gaussian mode transformations. + +To execute A on arbitrary independent owner fields x, allocate eight owned zero fields t. Compute t=M^T x with 448 signed ADDs; update x-=M t/4 with 448 scaled ADDs; clear the eight owned temporaries. Reading x is finished before any x is updated. Hence no input field is overwritten before its last source read. For A^-1 use the same program with coefficient -1/52, since A^-1=I-MM^T/52. Both are exact rational linear programs. The helper fields of the native producer are never used as scratch, copied as free credit, or erased. + +Conjugating this scalar program by the 112 K_i and their inverses implements C or C^-1. This pays 224 monomial field maps, 896 scalar ADDs and 16 owned CLEARs per recoding, with eight owned fields reusable sequentially. The two additional recodings in either local gauge identity therefore cost at most 448 monomial maps, 1,792 scalar ADDs and 32 CLEARs, with no recursive Gaussian child. The four actual port normalizers contribute 448 monomial maps per native invocation. The displayed backward conversion contributes at most 448 further monomial maps (112 input X powers, 112 output X powers and 224 output D-squares); fusing maps can reduce this upper bound but is not assumed. + +These are field-level operation counts. A lifted K_i is an explicit binary map on nine f-bit address blocks together with signs given by block parity. Its constants, indexed movement and phase passes use the retained native monomial implementation. It is therefore a fixed finite O(V polylog p) nonrecursive operation under that caller's precision/address ABI, not a zero-work instruction. Each fixed rational ADD is likewise charged at its actual scalar precision. In particular the inverse denominator 52 must be implemented and rounded; no free exact real-division oracle is assumed. This lemma makes no independent TM tariff or outer-budget claim. + +The maximum exact component-l1 prefix bound for the scalar A program, including its temporaries, is 57. For A^-1 it is 56 (the output-only bound is 69/13). Signed monomial maps preserve component magnitude. A fixed local sequence has a fixed suffix bound obtained by multiplying elementary bounds 1+|coefficient|; owned CLEAR has bound one. This gives a finite bound for local rounding propagation. The number of local uses, compiler precision and complete outer error allocation still belong to the caller theorem. + +The normalized producer still has its exact PR4929 paid profile + + {1:2201, 2:412, 3:510, 4:127, 5:40} + +and independent helper profile + + {4:28, 7:7, 8:47, 9:326}. + +No productive main ranks are asserted merely from the coupled central ABI. Those depend on the completed caller, its initial/final gauges and every paid correction. + +## Universal scope and reproducible evidence + +PR4929 supplies the arbitrary-input logical identity over Q[FreeGroup72] for its emitted center-free word with ground-chart helper pre-compensation. Its normalized main endpoint is L(A), its raw dual is L(A)^-T, and every one of the 408 helper endpoints is autonomous. This proof is an inherited premise with exact source pins, not a consequence of this normalizer checker. The present wrappers and owner recodings act exclusively on the 224 main fields; new scratch is explicitly owned. Thus the helper block remains autonomous and its independent inputs, requested transforms and paid profile remain unchanged. + +For every f>=1, assign the shared native letters their actual consistent invertible lifted operators. Evaluation of the source free-group algebra is a homomorphism and gives the source logical identity. Independently lift each K_i as its f-fold tensor product, retaining spectator coordinates; its signed-permutation word, the two direct frame identities and its commutation with R lift by operator composition. In every compiled monomial word, P and X act columnwise on the f-bit blocks, D sums its Z4 polynomial over the f columns, and a one-column scalar phase i^gamma becomes i^(f*gamma). Reusing the one-column global phase unchanged would be incorrect. Finally form the owner matrix C_f with entries A_ij K_i,f^-1 K_j,f. One does not tensor the whole 224-by-224 owner matrix and does not assert that tensor powers preserve sums. Instead the finite scalar owner program is evaluated directly in the algebra of these lifted address operators. This proves the central ABI and local gauge identities at every positive width. + +Run `python3 -I -B research/coded-native-caller/normalizers.py` or its optimized `-O` form. The checker authenticates the decompressed actual native payload, CODE.json and retained Clifford source before executing the latter. It verifies all 112 real signed normalizers, 57,344 explicit weight-congruence addresses, 896 forward/backward monomial wrappers and eight exact frame/block identities per port, including absolute phase. Each emitted wrapper is separately lowered to a literal P/D/X/phase-only word and checked against its defining expression by exact tableau and absolute-phase state. No C gate remains in an emitted wrapper. The independent incoming-column and outgoing-row identities imply all 5,824 nonzero off-diagonal code blocks, without sampling those pairs. It also executes the eight-mode recoding on all 112 arbitrary-input basis columns in both directions. Omitting the essential signed phase is rejected at every affected port. The default command compares a regenerated mathematical receipt and performs no writes; `--write` is the explicit authoring path. + +Source pins: canonical main 624de9dc66858af0945e5f8a0942488d62280d43, `research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz`, decompressed SHA-256 cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd; PR4929 head 361f5d4100640177d6a983dd2f336021c75bfd5e, `research/native-center-free-code/CODE.json`, SHA-256 8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0; canonical `research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py`, SHA-256 2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962. Gzip container bytes are not substituted for decompressed source identity. + +Credit Dugongue's PR4929 for the coded producer and stable code; Cinna Davis's PR4694/4698 and the original cache/helper construction; Cao Yifan's PR4610 native word; the retained zxv, Jacob Alan Sussman, Cinna Davis and Clifford/native/compiler lineage. The exact canonical-frame implementation and phase conventions are retained source material. The constructive real centralizing normalizers, their explicit lifted words, X-only raw-dual convention and costed local code gauges are the additions here. New work is Apache-2.0 and has substantial OpenAI Codex assistance; no formal-kernel or independent human acceptance is asserted. diff --git a/research/coupled-provider-independent-audit/capsule/repository/research/coded-native-caller/clifford_exact.py b/research/coupled-provider-independent-audit/capsule/repository/research/coded-native-caller/clifford_exact.py new file mode 100644 index 0000000000..166841a037 --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/repository/research/coded-native-caller/clifford_exact.py @@ -0,0 +1,149 @@ +"""Small exact Gaussian-dyadic Clifford compiler, independent of gx internals. +Paulis use i^p X^x Z^z. State vectors use integer Gaussian numerators / 2^d. +The tableau is supplemented by a literal circuit, so global phases are kept. +""" +from dataclasses import dataclass + +def parity(x):return x.bit_count()&1 +def rank(rows): + p={} + for x in rows: + while x: + b=x.bit_length()-1 + if b not in p:p[b]=x;break + x^=p[b] + return len(p) +def transpose(rows,n):return tuple(sum(((rows[j]>>i)&1)<>j&1);a[j],a[k]=a[k],a[j] + for i in range(n): + if i!=j and a[i]>>j&1:a[i]^=a[j] + assert [r&((1<>n for r in a) +def basis_extend(cols,n): + out=[] + for x in list(cols)+[1<len(out):out.append(x) + assert len(out)==n + return tuple(out) +def nullspace(rows,n): + a=list(rows);p=[];k=0 + for j in range(n): + t=next((i for i in range(k,len(a)) if a[i]>>j&1),None) + if t is None:continue + a[t],a[k]=a[k],a[t] + for i in range(len(a)): + if i!=k and a[i]>>j&1:a[i]^=a[k] + p.append(j);k+=1 + return tuple((1<>j)&1)<>i&1:out=pmul(out,T[i]) + for i in range(n): + if z>>i&1:out=pmul(out,T[n+i]) + return out +def compose(A,B):return tuple(apply(A,p) for p in B) +def inverse(T): + n=len(T)//2;cols=[x|(z<>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4)) + return tuple(out) +def qvalue(Q,alpha,x,n): + return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4 +def mul_i(a,p): + x,y=a;p%=4 + return [(x,y),(-y,x),(-x,-y),(y,-x)][p] +@dataclass +class Op: + n:int + tab:tuple + circuit:list + def then(self,b): + assert self.n==b.n + return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit) + def adjoint(self): + circ=[] + for e in reversed(self.circuit): + if e[0]=='P':circ.append(('P',inv(e[1],self.n))) + elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2]))) + elif e[0]=='C':circ.append(('C',e[1],-e[2])) + elif e[0]=='phase':circ.append(('phase',(-e[1])%4)) + else:circ.append(e) + return Op(self.n,inverse(self.tab),circ) + def zero_state(self,basis=0): + N=1<>i)&1 for i in range(n)) + assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n)) + return Op(n,tuple([(1<>i&1 else 0,1<>i&1 else 0) for i in range(n)]),[('C',q,sgn)]) +def xgate(n,b):return Op(n,tuple([(1<>i)&1)) for i in range(n)]),[('X',b)]) +def fourier(n,axes=None): + out=ident(n) + for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<len(selected):picks.append(j);selected.append(x) + assert len(picks)==r and all(x>>r==0 for x in Bcols) + Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1< (X,Y+X,H)`. Physical entrance and exit charts remain exactly those of the frozen source. + +There is a completely emitted constant dyadic pre-compensation, followed by the source word with every center Gaussian operation replaced by an owned CLEAR, whose exact normalized endpoint is + +`X' = X; Y' = Y + A X; H' = H`. + +All 632 persistent inputs are arbitrary and independent; no helper is initialized, discarded, identified or counted twice. The literal backward construction has exact normalized endpoint + +`X' = X - A^T Y; Y' = Y; H' = H`, + +the raw inverse transpose of the forward endpoint. The paid profile in both directions is + +`{1:2201, 2:412, 3:510, 4:127, 5:40}`. + +The helper profile stays `{4:28,7:7,8:47,9:326}`. Relative to the source, exactly eight rank-eight children are removed and no Gaussian child is added. The pre-compensation adds 6,596 scalar ADDs with a retained scalar allowance of 32,652 primitives; all numerator magnitudes and denominators are at most 4. These finite scalar operations do not establish a better recursive exponent on their own. + +## Constructive proof + +Delete all eight center calls by replacing each with CLEAR of the owned center field in the call's destination chart. Zero has every chart, so this is a valid erasure of owned scratch, not a borrowed input overwrite. Retain every other physical instruction and every endpoint chart. + +The exact sparse replay over the rational free group algebra on the 72 native symbols gives + +`M_0 = I + S + E_X + E_H`. + +Here S is the original transfer X to Y. Both error blocks land only in Y. E_X reads X; E_H reads only 106 particular helpers, each with a ground entrance and full-frame exit. Every helper and every X output remains autonomous. All error terms have EMPTY native word: the errors are ordinary constant dyadic matrices, not uncomputed address-operator oracles. The 12,532 nonzero entries split into 5,936 in E_X and 6,596 in E_H. + +Every pairwise product of S, E_X and E_H is zero, because all three maps land in Y and none reads Y. Before executing the center-cleared word, apply `I-E_H`. Every required source and target is in the actual ground chart: the targets are Y and the sources are those 106 ground-ended helpers. The operation is the explicit list of 6,596 dyadic ADDs. + +Consequently + +`M_0 (I-E_H) = I+S+E_X`. + +Thus `A=I+E_X` on the 112 main port indices gives the claimed offer, with no helper contamination. Scalar operations in one common address chart have their exact owner-space action, so this is a physical fixed-template pre-compensation and not an abstract change of logical coordinates. + +For the backward direction, the separately emitted center-cleared source word is verified to equal `I-S^T-E_X^T-E_H^T`, with the source's distinct inverse-transpose native letters. Prepend `I+E_H^T`, again using only actual ground-chart fields. The product is `I-S^T-E_X^T`. The verifier compares all 632 independent rows in both orientations. The owned center field is empty at termination. + +## Explicit code, inverse and conditioning + +The same exact entries satisfy + +`E_X^T = E_X, E_X^2 = -14 E_X, tr(E_X) = -112`. + +Set `P=-E_X/14`. It is a real symmetric idempotent of trace 8, hence an orthogonal projection of rank 8. Therefore + +`A=I-14P`, + +with eigenvalue -13 on the eight-dimensional image of P and eigenvalue +1 on its 104-dimensional kernel. In particular + +`A^-1 = I + E_X/13`, + +and its Euclidean condition number is exactly 13. The complete main shear is I+N_A with N_A^2=0 and ||N_A||_2=13; both it and its inverse have norm at most 14, so its condition number is at most 196. Helpers are an independent identity block, and the physical boundary charts are unitary, so this same bound applies to the complete physical coded offer. Its inverse uses I-N_A and needs no 1/13 arithmetic; 1/13 appears only when separately inverting the main code A. Every diagonal entry of A is zero; its 5,824 nonzero off-diagonal entries are ±1/2. The exact checker verifies the degree-two polynomial entry by entry over rational arithmetic, so the spectrum and inverse are universal consequences of that identity rather than numerical eigenvalue observations. + +The coefficient 1/13 is part of the mathematical inverse formula. This deliverable does not call it a free dyadic SCALE, assume a division oracle, or insert A^-1 across different physical address charts without paying for the resulting adapters. + +## Arbitrary fiber widths + +The replay identities hold over Q[FreeGroup72]. Every consistently shared invertible assignment of the 72 native operators defines an evaluation homomorphism. Hence the logical word identity holds at every positive column multiplicity under the retained source native implementation. It does not rely on one-column matrix testing, erasure of central phases or tensor powers preserving sums. + +Every physical frame, native monomial and Gaussian child is retained from the authenticated source, except the eight deleted owned-center calls. The new instructions are only constant dyadic scalar operations at an explicitly common ground chart. No fresh nonmonomial address implementation is introduced. + +The exact observed maximum prefix coefficient ℓ1 norms are 457 forward and 258 backward, checked on the fixed free-symbol words. Unitary evaluation bounds intermediate exact states and perturbations at the initial input in the maximum-over-fields Euclidean fiber norm by fixed constants independent of fiber width. For discrepancies inserted at later sites, use a separate suffix bound: assign each scalar ADD or SCALE of coefficient c the bound 1+|c|, and every unitary Gaussian/monomial, owned CLEAR or owned COPY the bound 1. The product of these elementary bounds over the finite word bounds every suffix. Thus the sum of local error magnitudes times this fixed product bounds propagated rounding error; no prefix norm is substituted for a suffix norm. Entrywise infinity-norm statements require the appropriate square-root fiber-volume conversion. There is no precision-dependent epsilon and no recursive border-precision claim. + +## Integration boundary + +The old source wrapper's port-dependent entrance lines and exit hyperplanes remain. A is a constant matrix in the stated normalized logical coordinates. It must not be silently treated as a constant free recoding in every physical main chart or in a different standardized central-Q ABI. Its nonzero off-diagonal entries connect distinct entrance-line charts. A useful next step is an actual coded caller or a paid simultaneous adapter that exploits the eight-mode structure, together with complete moment, raw-dual, compiler, finite precision and outer recovery budgets. This document supplies the exact producer and its bill, not those missing consumers. + +## Predecessor overlap and credit + +Cinna Davis's PR #4694, head `2add42d1edf14a263abe90a3bcde67fc1ba30768`, already emits a center-free kernel with paid profile minus eight rank-eight calls, records its coupled cache ABI, constructs its raw dual, and proves that its 106 observed helpers start at the empty chart. The source CACHE.md was read directly. None of center deletion, the cold-helper observation or the abstract block Schur elimination is claimed here as new. PR #4698, scientific head `9079ab66ba9a1717df478a08eb957c20d84d3e61`, already emits a dyadic helper basis of 379 gates in each direction reducing observations to eight helpers, and a conditional consumer. The present deliberately dense 6,596-ADD pre-compensation is easier to audit, not a claim to a better basis count. Its changed sufficient result is the actual fixed-template helper-independent coded offer, explicit A entries, exact eight-mode spectrum/inverse/conditioning, and unchanged independent helper ABI. + + +Cao Yifan / intqwq supplies the joint-helper/native-map round-three word at canonical `research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz`, commit `624de9dc66858af0945e5f8a0942488d62280d43`. Its predecessor and refreshed public lineage includes PR #4610; the exact source package and bytes, rather than an older PR headline, bind this result. Cinna Davis, the PR #4470 native/helper/controller lineage, Dugongue's exact native and complementary-provider work, DaysSky, Nick Petalas, Ryanson Jonathan, Jacob Alan Sussman, zxv and the retained scalar, Clifford, precision, compiler and outer contributors retain predecessor credit. The common-chart pre-compensation and exact eight-mode code are the present construction. Local MathProof's Schur block elimination and low-rank composition notes motivated the representation; their source-only inspection is not a fresh Lean/kernel audit or a claim of priority for elementary projection algebra. diff --git a/research/coupled-provider-independent-audit/capsule/repository/research/native-center-free-code/SOURCE-WORD.json.gz b/research/coupled-provider-independent-audit/capsule/repository/research/native-center-free-code/SOURCE-WORD.json.gz new file mode 100644 index 0000000000..46d929df83 Binary files /dev/null and b/research/coupled-provider-independent-audit/capsule/repository/research/native-center-free-code/SOURCE-WORD.json.gz differ diff --git a/research/coupled-provider-independent-audit/capsule/repository/research/native-rank8-helper-provider/ATTRIBUTION.md b/research/coupled-provider-independent-audit/capsule/repository/research/native-rank8-helper-provider/ATTRIBUTION.md new file mode 100644 index 0000000000..efe3acb566 --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/repository/research/native-rank8-helper-provider/ATTRIBUTION.md @@ -0,0 +1,50 @@ +# Predecessors and exact scope + +Ali Romman's [PR5383](https://github.com/CrocSwap/integer-mult-bounds/pull/5383), +head `4bd6efa51a495a7c7b7754915cf0244e7e60969e`, supplies the exact eight +cached-center candidate rows and sites. Its WITNESS is retained verbatim as +package-local candidate data. The byte hash is checked, and all used +relations, chronology and zero-call claims are independently recomputed from +the pinned main native source. The PR head is provenance, not a required Git +object or an assumed accepted theorem. We do not claim priority for the +cached-center relation or for center deletion. + +Cao Yifan / intqwq supplies `kappa-round3-warp-20261022`'s canonical native +helper/map/contact source and the PR4610 lineage. Its exact payload is +retained by main's `native-center-free-code/SOURCE-WORD.json.gz`. +Dugongue / mdumitrean supplies [PR4929](https://github.com/CrocSwap/integer-mult-bounds/pull/4929)'s +center-free code, eight-mode factorization, source construction and analytic +interpretation. Cinna Davis / 1337isnot1337 supplies the +[PR4694](https://github.com/CrocSwap/integer-mult-bounds/pull/4694) retained-center +interface, [PR4698](https://github.com/CrocSwap/integer-mult-bounds/pull/4698) +common-chart helper basis and conditional consumer, and +[PR4470](https://github.com/CrocSwap/integer-mult-bounds/pull/4470) controller. +A retained cache or eight-dimensional defect is not newly discovered here. + +The pinned `coded-native-caller` supplies the physical main normalizers, +corrected conjugated backward convention, compiled wrapper recipes, contact +matrix M, and exact Clifford evaluator. Its Clifford source traces through +`t74-native-fast/vendor/native/new/code/borrow/vendor/clifford`; retain zxv's +native/productive/compiler work and the original license. Retain Jacob Alan +Sussman's mixed-target recursion, Ryanson Jonathan's controller checks, +Dugongue's transported-frame lemma and the cumulative helper/native lineage +identified by the predecessor packages. The exact shared bytes are pinned in +SOURCES.json rather than duplicated under new authorship. + +Within this continuation, coordinated OpenAI Codex agents constructed the +unrestricted retained-cache source, independently replayed all 641 columns, +derived the dual retraction and physical rank-eight normalization, and +reviewed the basis costs. This package combines that work into one fresh +registered replay with an explicit all-owner boundary recipe, verbatim +candidate provenance, local bill and every-positive-width proof. New work is +the fully owned **coupled** provider with all 632 originals preserved and all +nine owned outputs cleared. It is not a caller, an autonomous H8 donor, an +exponent improvement, a formal-kernel proof or independent human review. + +The broader investigation and priority/overlap checkpoints remain in the +campaign's [Discussion4930](https://github.com/CrocSwap/integer-mult-bounds/discussions/4930) +and TASK.json. This package preserves the same frozen native payload while +binding its publication task metadata to main at +`1ec1119972c9aefe42525172d07b332fcff81cb4`. It does not claim an exhaustive +novelty search or alter the selected result. Prepared for Dillon with +substantial OpenAI Codex assistance. Apache-2.0. diff --git a/research/coupled-provider-independent-audit/capsule/repository/research/native-rank8-helper-provider/PROOF.md b/research/coupled-provider-independent-audit/capsule/repository/research/native-rank8-helper-provider/PROOF.md new file mode 100644 index 0000000000..5cbfc4fd02 --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/repository/research/native-rank8-helper-provider/PROOF.md @@ -0,0 +1,236 @@ +# A source-bound backward provider with eight coupled rank-eight outputs + +The construction has 632 arbitrary original inputs and nine arbitrary owned +inputs. Its paid native profile is +`{1:2193,2:412,3:510,4:127,5:40}`. It returns 400 unchanged native helper jobs +and a coupled block on the 224 main and eight remaining helper owners: + +\[ + X=Dx-Ry+RW h,\qquad Y=Dy,\qquad H=D(h-Zy). \tag{1} +\] + +Here `R=DQ` is the full native rank-nine Gaussian, `D` acts on the eight +noncentral axes, and `Q` acts on the central axis. The eight `H` outputs remain +coupled; they are **not eight autonomous H8 targets**. No complete caller or +new multiplication exponent follows. All nine owned outputs are zero. + +## 1. Exact source and the changed word + +`SOURCES.json` pins the main-branch source, code, normalizers and Clifford +compiler. The native source's decompressed SHA256 is +`cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd`. +`WITNESS.json` retains Ali Romman's PR5383 candidate verbatim, with SHA256 +`24599011da06325e1012619b2b84a4dd3aceb90ab42d3caaf6414879e7d16591`. +It supplies candidate sites and rational rows; it is not a proof oracle or a +pending Git-object dependency. Every used identity is checked again against +the pinned main source. + +For witness row `i`, after the indicated original `cached_event`, CLEAR owned +`C[i+1]` and COPY the indicated persistent row into it at its actual chart. +Every cache precedes every removed center. At the original center event, +replace the H8 call by CLEAR `C0`, then COPY `C[i+1]` into `C0` at that same +rank-eight chart. At the indicated later H1 call, replace the call by a +`zero_retag`: this is physical identity on the **exactly zero** field, with +its bookkeeping chart changed to the old call's output chart. All other +instructions, including inherited physical metadata, remain unchanged. +`WORD.json.gz` emits the complete resulting backward native word; the verifier +regenerates it from the canonical source and compares its parsed content. + +The replay begins with one independent formal column per field, including +all nine owned fields. It tracks exact rational coefficients in the free +group on the source's native warp symbols, their inverses, and actual chart +tags. Every ordinary operation is checked at its true chart. COPY fills only +owned zero; CLEAR acts only on owned fields. Before each of the eight retags, +every one of the 641 input coefficients is zero. All initial owned dirt is +cleared before use and is absent from every endpoint. + +The source's ten `phase` records are named stage annotations, not scalar +Clifford phase gates; its 448 `adapter` records retain the predecessor's +physical entrance/exit bindings (there are no `residual_adapter` records in +this backward word). As in the pinned predecessor normalized-row semantics, +these do not update formal rows. They are preserved in the emitted word, +not deleted or priced away. Their physical interpretation and native cost +are inherited; this package separately verifies every new physical boundary +identity including absolute phase. + +The same interpreter replays the original source, obtaining its full +632-row normalized backward endpoint `(x-y,y,h)` and clean original temporary. +It separately replays center deletion to derive the native coupling below. +The changed word has eight fewer H8 and eight fewer H1 calls than the original +source, with no additional Gaussian call. It has 16 extra COPYs and 16 extra +CLEARs. This is a changed source construction, not a constraint such as +`Delta h=0` on otherwise independent inputs. + +## 2. Source-derived coupling and an ordinary helper basis + +Use the inherited 112-by-8 matrix `M`, stored transposed as `mode_columns`. +The verifier checks all entries of + +\[ + M^T M=56I_8,\qquad A=I-MM^T/4. +\] + +Fresh replay of the center-deleted source gives + +\[ + X=x-A^Ty,\qquad Y=y,\qquad H=h-B^TM^Ty. +\] + +The verifier derives every entry of `B` by projecting the actual 408-by-112 +helper-to-Y coefficient matrix onto `M/56`; it then checks the entire +factorization and all 632 endpoints. The eight candidate rows `Delta` satisfy +`Delta B^T = S`, an exactly checked signed permutation. Put `E=S^-1 Delta`. +Thus `E B^T=I8`. Fresh original-prefix replay also binds the candidate cache +rows, their chronology and their actual rank-eight charts. + +In these coordinates the changed word has normalized endpoint + +\[ + X=x-y+(M/4)Eh,\quad Y=y,\quad H=(I-B^TE)h, \tag{2} +\] + +and its canonical mode-`k` cache is + +\[ + f_i(E_kh-M_k^Ty),\qquad f_i=\texttt{zero_factor}_i\,S_{ik}. \tag{3} +\] + +The registered check composes all changed endpoint rows with the following +basis, rather than accepting (2) or (3) from a saved endpoint registry. + +The union of supports of `B` and `E` comprises 122 actual cold H9 owners: each +has ground entrance chart and full-R exit chart. Choose the eight original +mode owners `[224,225,227,229,240,241,256,257]`. Define `L` on these 122 owners: +its mode columns are `B^T`; its other columns are `(I-B^TE)e_j`. Exact +Gauss-Jordan reduction constructs `L^-1` and verifies both inverse products, +`EL` selecting precisely the eight mode coordinates, and `L^-1B^T` embedding +precisely those coordinates. Every coefficient is dyadic. The emitted +`input_basis_program` and `output_basis_program` execute these two maps in +place, without extra owned basis storage. + +Both bases mix only fields sharing the appropriate physical chart, so scalar +owner operations implement them ordinarily. After entrance `L` and exit +`L^-1`, every one of the 632 persistent rows is checked: the eight selected +helper rows are zero, the other 400 helper rows are unchanged, `Y=y`, and +`X=x-y+(M/4)h_mode`. Each cache is exactly +`f_i(h_mode,k-M_k^T y)`. Thus the cache fills a vacated original direction; +it supplies no additional productive input or job credit. + +## 3. Literal physical boundary maps and ownership + +Backward frames use complex conjugation of the native frames, as in the +pinned source convention; they are not silently replaced by adjoints. Let +`Kp` be the 112 inherited main normalizers. For each actual cache frame `F8`, +the verifier constructs an orthogonal, phase-correct monomial `Km` from its +unique missing odd noncharacteristic line, and compiles a monomial `N` with + +\[ + N\overline{F8}K_m=D,\qquad K_mR=RK_m. +\] + +`PROVIDER.json` contains all eight literal `Km` and `N` words, signed tableaux +and nonzero zero-column phase anchors. The compiler's output is checked +explicitly even under Python `-O`. All `Kp` commute with `R`, including +absolute phase. Every boundary word contains only monomial gates. + +Apply `2Km` to the eight original mode inputs before `L`. At the exit, apply +`N/(2f_i)` to each cache. Use the inherited **fused compiled** backward main +input/output wrappers. The verifier checks 336 main diagonal/shear blocks, +896 nonzero main/helper coupling blocks and eight helper diagonal blocks, +for 1,240 exact physical equations. Comparison includes the signed tableau +and exact zero-state vector, so an undetected global phase is impossible +within this Clifford model. These equations yield (1), with + +\[ + W=\operatorname{diag}(K_p^{-1})M\operatorname{diag}(K_m)/2, + \quad + Z=\operatorname{diag}(K_m^{-1})M^T\operatorname{diag}(K_p)/2. +\] + +The main code is the predecessor's `C=diag(Kp^-1) A diag(Kp)`. Exact word +cancellation and the scalar factorization give +`ZW=14I8`, `WZ=I-C`; `W` and `Z` intertwine `R` on their respective banks. +No commutation with `D` or `Q` is assumed. These are finite ordinary code +maps with exterior scalar coefficients, not additional Gaussian calls. + +After normalization, SWAP each cache's **whole physical field and chart tag** +with its identically zero original mode output. The original owner now holds +the normalized coupled output; the owned slot holds zero and can be CLEARed. +There is no persistent erasure and no attempted free chart conversion of a +nonzero field. `C0` is already zero, so all nine owned outputs are zero. +Ordering the coupled input/output banks as `(y,h,x)` makes (1) triangular +with invertible diagonal `D`. Together with the 400 unchanged native jobs, +this proves preservation of all 632 original input directions. It does not +emit an inverse schedule or establish a same-cost inverse/transpose. + +## 4. Exact local bill + +Relative to the original raw backward source, the selected schedule adds: + +| Ordinary operation | Added field operations | +| --- | ---: | +| ADD | 1,644 | +| SCALE | 40 | +| COPY | 16 | +| CLEAR | 24 | +| Whole-field SWAP, with chart tag | 8 | +| Monomial field map | 464 | + +Each basis direction uses 822 ADD and 12 SCALE: its three elimination swaps +are expanded into three ADDs and one SCALE each. Eight input scalings and +eight cache scalings give the remaining 16 SCALEs. The source rewrite adds +16 COPY and 16 CLEAR; final cache consumption adds eight CLEAR. The 464 +monomial maps are 448 fused inherited main standardizers, eight `Km` and +eight `N`. This counts the newly installed boundary schedule; all unchanged +source warp/phase/adapter traffic and native child implementations remain in +the emitted word and retain their inherited costs. In particular, this table +does not assert that a field monomial map is zero machine work. + +The original source has 16,273 ADD, 1,164 SCALE and 16 CLEAR. Including the +new boundary scalars, the schedule therefore has 17,917 ADD, 1,204 SCALE, +16 COPY, 40 CLEAR and eight whole-field SWAP, plus the explicitly described +monomial boundary maps and inherited native operations. Nine owned fields +suffice: the original center temporary and eight retained caches. Their +initial values are arbitrary; their final values are zero. The autonomous +helper profile is `{4:28,7:7,8:47,9:318}`. The physical implementations of +those unchanged native helper jobs are inherited from the pinned source; +scalar identity rows alone are not a new proof of those implementations. + +For an explicit local stability bound, use the maximum of field Euclidean +norms. ADD by `a` has norm at most `1+|a|`, SCALE has norm at most +`max(1,|a|)`, and unitary Gaussian/monomial maps, COPY, CLEAR and SWAP have +norm at most one. The verifier sums upward-rounded base-two logarithms for +every scalar operation in this finite schedule, obtaining **18,996**. Hence +every suffix amplifies an injected field error by at most `2^18996`; at most +`m` injections of norm `epsilon` give the conservative bound +`m*2^18996*epsilon`. All dyadic constants and word lengths are fixed. This +establishes local bounded amplification, not a complete coordinate rounding, +tape movement, recursive precision or outer multiplier budget. + +## 5. Every positive fiber width and verification boundary + +A free-group identity evaluates in any assignment of invertible native warp +operators. Therefore the exact rational row equalities and zero-retag +premises hold uniformly when native operations act on any positive fiber +width `f`. The scalar owner coefficients and scalar `L/L^-1` programs stay +outside the tensor product; in particular `ZW=14I`, not `14^f I`. Each +compiled monomial word uses the inherited prescription: `P` and `X` act +columnwise, `D` sums its Z4 polynomial over the columns, and a `phase` gate +contributes its phase once per column. Each address-operator identity is lifted +columnwise; an absolute phase `i^gamma` lifts to `i^(f gamma)`, rather than +being confused with an exterior scalar sign. Exact one-column operator +identities, word cancellation and rational matrix identities then prove the +same physical boundary composition for every `f`. The inherited native +uniform implementation hypotheses remain inherited. + +The registered verifier performs complete 641-column native row replay, +exact scalar endpoint composition, and the 1,240 physical boundary checks. +It does not claim a separately flattened 641-column physical-matrix replay, +a formal-kernel proof, independent human approval, hosted CI, or a complete +caller. It rejects a nonzero zero-retag, a single changed basis ADD +coefficient, a changed saved-cache coefficient and a phase-only error with +the correct tableau. Normal and optimized runs use explicit checks for the +new claims. 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+ "paid": { + "1": 2193, + "2": 412, + "3": 510, + "4": 127, + "5": 40 + }, + "autonomous_native_helpers": { + "4": 28, + "7": 7, + "8": 47, + "9": 318 + }, + "owned_fields": { + "count": 9, + "initial_values": "arbitrary", + "final_values": "zero", + "productive_credit": 0 + }, + "added_ordinary_work_vs_original_raw_source": { + "ADD": 1644, + "SCALE": 40, + "COPY": 16, + "CLEAR": 24, + "whole_field_SWAP": 8, + "monomial_field_maps": 464, + "monomial_breakdown": { + "fused_inherited_main_standardizers": 448, + "mode_inputs": 8, + "cache_outputs": 8 + } + }, + "local_error_amplification_power2_bound": 18996, + "source_original_scalar_counts": { + "add": 16273, + "clear": 16, + "scale": 1164 + }, + "source_changed_scalar_counts": { + "add": 16273, + "clear": 32, + "copy": 16, + "scale": 1164 + }, + "physical_phase_bindings": { + "main_diagonal_and_shear": 336, + "two_coupling_directions": 896, + "helper_diagonal": 8 + }, + "exact_zero_retags": [ + [ + 15608, + 92, + 254, + 1 + ], + [ + 15894, + 9, + 624, + 1 + ], + [ + 15900, + 11, + 621, + 1 + ], + [ + 17269, + 240, + 280, + 1 + ], + [ + 17280, + 81, + 619, + 1 + ], + [ + 17288, + 57, + 274, + 1 + ], + [ + 17604, + 288, + 281, + 1 + ], + [ + 17746, + 224, + 279, + 1 + ] + ], + "formula": { + "X": "D x - R y + R W h", + "Y": "D y", + "H": "D (h - Z y)", + "W": "diag(K_port^-1) M diag(K_mode)/2", + "Z": "diag(K_mode^-1) M^T diag(K_port)/2" + }, + "failure_controls": [ + "nonzero zero-retag rejected", + "one altered basis ADD coefficient rejected", + "same-tableau phase-only cache error rejected", + "one altered saved-cache coefficient rejected" + ], + "scope": "Changed coupled backward provider. No autonomous credit for eight coupled outputs; no completed caller, inverse/transpose implementation, new kappa or selected-result change." +} diff --git a/research/coupled-provider-independent-audit/capsule/repository/research/native-rank8-helper-provider/README.md b/research/coupled-provider-independent-audit/capsule/repository/research/native-rank8-helper-provider/README.md new file mode 100644 index 0000000000..92d0d7e523 --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/repository/research/native-rank8-helper-provider/README.md @@ -0,0 +1,83 @@ +# Eight coupled helper outputs from the retained-center native word + +This package constructs and replays an exact changed backward native provider +on all 632 original owners. It replaces eight rank-eight center calls by +retained earlier same-frame caches; eight later H1 inputs become identically +zero and their calls disappear. The resulting paid profile is +`{1:2193,2:412,3:510,4:127,5:40}`: the center-free profile minus eight H1 calls. + +After explicit ordinary basis and boundary operations, the coupled outputs are + +```text +X = D x - R y + R W h +Y = D y +H = D(h - Z y) +``` + +Here `R=DQ`, `D` is the native rank-eight Gaussian, `ZW=14I8`, and `WZ=I-C` +for the existing physical code `C`. The 400 other original helpers retain +their native jobs, with profile `{4:28,7:7,8:47,9:318}`. All nine owned fields +start arbitrary and finish zero. **The eight H outputs remain coupled; no +new autonomous Gaussian targets, complete caller or improved κ are claimed.** + +[PROOF.md](PROOF.md) gives the every-positive-width argument, ownership rule, +exact local bill and precision boundary. [WORD.json.gz](WORD.json.gz) is the +complete changed native word. [PROVIDER.json](PROVIDER.json) is its ordered +boundary recipe, including explicit dyadic basis programs and phase-bound +monomial words; its references to the pinned source main normalizers are part +of that recipe. The verifier recomputes the word and recipe from authenticated +main inputs, with no scratch paths or network access. + +The new schedule adds 1,644 ADD, 40 SCALE, 16 COPY, 24 CLEAR, eight physical +SWAPs and 464 monomial maps relative to the original raw source. The 464 maps +include 448 fused inherited main wrappers. Unchanged native internal traffic +and implementations remain inherited. These are ordinary work, not free +machine operations. Nine owned fields suffice without basis scratch storage. + +## Reproduce + +From the repository root, using only Python 3.12 and its standard library: + +```sh +python3.12 -B scripts/research_package.py --package research/native-rank8-helper-provider +python3.12 -I -Werror -B research/native-rank8-helper-provider/verify.py +python3.12 -I -Werror -O -B research/native-rank8-helper-provider/verify.py +``` + +The registered normal and optimized commands check all 641 native input +columns, every original endpoint, all nine owned outputs and 1,240 physical +phase bindings. Mutation controls reject a changed basis ADD coefficient, a +changed cache coefficient, nonzero zero-retag input and a same-tableau phase +error. A direct run takes about 13 seconds on the preparation machine; the +registered pair is bounded separately in [VERIFY.json](VERIFY.json). +`--emit` regenerates only the package-local `PROVIDER.json`; normal replay is +read-only. Frozen scientific source inputs are never regenerated or modified. + +[WITNESS.json](WITNESS.json) retains Ali Romman's PR5383 candidate verbatim, +from head `4bd6efa51a495a7c7b7754915cf0244e7e60969e`, SHA256 +`24599011da06325e1012619b2b84a4dd3aceb90ab42d3caaf6414879e7d16591`. +The candidate is package-local data; every used relation is reproved against +main's native source. No pending PR Git object is required. The phase engine, +existing code and native implementation retain their predecessor proof +boundaries; this is author-side exact replay, not formal or human acceptance. + +## Open next questions + +The complete structured obligations are in [TASK.json](TASK.json). A caller +must close the 224 main and eight coupled helper outputs while retaining the +400 autonomous helpers per call, price all additional children and ordinary +work, then prove its final Gaussian ranks, chronology, finite precision and +outer budget. Begin with one fully owned caller identity; a field becoming +available at rank eight is insufficient for autonomous target credit. The +selected frontier is unchanged. + +## Credit + +Ali Romman supplies PR5383's exact cached-center relations. Cao Yifan supplies +the native round-three helper/map word; Dugongue supplies the center-free code +and its factorization; Cinna Davis supplies the earlier retained-center, +helper-basis and controller work. Retain zxv's Clifford/native/compiler work, +Jacob Alan Sussman's recursion, Ryanson Jonathan's controller checks, and the +full source lineage. See [ATTRIBUTION.md](ATTRIBUTION.md). Prepared for Dillon +with substantial OpenAI Codex assistance from coordinated construction, +mechanism and review agents. Apache-2.0. diff --git a/research/coupled-provider-independent-audit/capsule/repository/research/native-rank8-helper-provider/SOURCES.json b/research/coupled-provider-independent-audit/capsule/repository/research/native-rank8-helper-provider/SOURCES.json new file mode 100644 index 0000000000..dd77397ca5 --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/repository/research/native-rank8-helper-provider/SOURCES.json @@ -0,0 +1,54 @@ +{ + "schema_version": 1, + "base_commit": "1ec1119972c9aefe42525172d07b332fcff81cb4", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "b288ae44032fd84dd5564243422836cbcd29835e", + "sha256": "f9ed52bb642cd1e1486cf2743557ac5fa23cf1514a3277d786a644e39a565038" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602", + "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72" + }, + { + "path": "research/coded-native-caller/NORMALIZERS.json", + "usage": "input", + "git_blob": "bca92c222c395d3d75c047fbb678f3cd0947c60f", + "sha256": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da" + }, + { + "path": "research/coded-native-caller/PHYSICAL.md", + "usage": "input", + "git_blob": "da8837ba67423ef08ef1afb8e8297a8032aafe9f", + "sha256": "4321b159ff8d3fe705419adaaa1beef75606e869e34341bda553f17d598a6078" + }, + { + "path": "research/coded-native-caller/clifford_exact.py", + "usage": "input", + "git_blob": "166841a037f069249f6f7f6dedb89248812f59e2", + "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962" + }, + { + "path": "research/native-center-free-code/CODE.json", + "usage": "input", + "git_blob": "03170f4a31f7a8a3db7228f1cd5a6fdcb32720ae", + "sha256": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0" + }, + { + "path": "research/native-center-free-code/CODED-PROOF.md", + "usage": "input", + "git_blob": "1f28d33884ec99b34f8366d022d8f7b9b7653ae2", + "sha256": "acd904af677718da8cdaf81d205d29866a6855efd393047e7128320a46753b01" + }, + { + "path": "research/native-center-free-code/SOURCE-WORD.json.gz", + "usage": "input", + "git_blob": "46d929df83817b85a5387bcdb9745e0627d6366e", + "sha256": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05" + } + ] +} diff --git a/research/coupled-provider-independent-audit/capsule/repository/research/native-rank8-helper-provider/TASK.json b/research/coupled-provider-independent-audit/capsule/repository/research/native-rank8-helper-provider/TASK.json new file mode 100644 index 0000000000..e82da0445c --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/repository/research/native-rank8-helper-provider/TASK.json @@ -0,0 +1,88 @@ +{ + "schema_version": 1, + "task_id": "centre-path-sharing", + "priority_revision": 7, + "base_commit": "1ec1119972c9aefe42525172d07b332fcff81cb4", + "original_card": { + "id": "centre-path-sharing", + "question": "Can the 64-per-call centre path (eight rank-8 COPY/ERASE totals through the private temporary) be shared across calls or shrunk?", + "starting_points": [ + "docs/research/research-family-status.md", + "research/complex-local-word-ceiling/README.md", + "research/split-centres-global/proofs/PR386-BIT-GEOMETRY.txt", + "certificates/selected-result.json" + ], + "methods": [ + "Derive a fully charged favorable relaxation for sharing one centre path across k calls, including restoration, hosting and precision.", + "Prove a lower bound on copied information per call for the selected decoder contract." + ], + "acceptance_gate": "Show the changed centre charge and copy profile per call with every added restoration or hosting cost charged, and its ceiling via ceiling.ceiling(centre=...). A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "research/complex-local-word-ceiling/verify.py" + ], + "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING", + "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.", + "scope": "Positive control and planning budget only; this is not a new construction or full cold replay." + }, + "first_experiment": "Write the per-call centre charge and copy children for sharing across k = 2 calls, charge the sharing overhead, and screen it; stop this route if even the ideal sharing gains under 10%. Ideal budgets: free 2.80x, shared by two 1.90x (levers.py).", + "bottleneck_link": "The centre path consumes 64 of about 99.6 unpaid coordinates per call, i.e. about 64% of the raw deficit.", + "allowed_variations": [ + "One sharing pattern across a fixed number of calls.", + "One reduced copied-total contract for the existing decoder.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "scope_change_triggers": [ + "Removing copies without a replacement contract for the decoder's copied totals.", + "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts." + ], + "overlap_terms": [ + "centre path", + "copied totals", + "private temporary", + "shared centre", + "batching" + ] + }, + "scope_status": "refined", + "actual_scope": "Emit a source-bound backward provider using retained center caches and an invertible cold-helper basis, with eight coupled rank-eight helper outputs, all 632 original owners retained and all 9 owned outputs zero.", + "scope_change_reason": "The user explicitly authorized ambitious changed-source research and removed the hour limit. This focused result replaces the copied-center path using source-proved early observations, while preserving every original direction; it does not claim an autonomous supplier or complete caller.", + "bottleneck_link": "Deletes all eight native H8 center calls and eight later H1 calls. The new bottleneck is closing eight main/helper couplings under a paid, fully owned caller rather than treating them as autonomous H8 targets.", + "budget_minutes": null, + "stop_rule": "Freeze this focused provider once original/changed all-owner replay, explicit ordinary basis programs, exact physical boundaries, owned cleanup, operation counts and every-positive-width proof pass. Further caller work is separate and must close all original outputs before admitting target credit.", + "outcome": "partial", + "evidence": "Registered Python3.12 normal and optimized replay derives B from main source, reproves the verbatim Ali candidate, checks 641 native input columns and 1240 exact physical phase bindings, executes both 122-owner basis programs, clears all 9 owned outputs and rejects coefficient/phase/zero-retag mutations.", + "author": "Dillon / dillona", + "ai_assistance": "Substantial OpenAI Codex assistance from coordinated construction, mechanism, packaging and independent author-side review agents; no independent human or kernel acceptance claimed.", + "open_questions": [ + { + "question": "Can a complete chronological caller close all 224 main and eight coupled helper outputs while retaining 400 autonomous native helper jobs per provider?", + "why_it_matters": "The eight D outputs depend on main inputs and earn no autonomous target credit. The paid savings alone do not imply a recursive multiplier or improved kappa.", + "first_step": "Emit one fully owned caller word using the exact W/Z physical maps; replay every original input and output, price all added Gaussian calls and keep all helper outputs.", + "blocked_by": "No accepted closure with final Gaussian ranks, complete query invoice and owner chronology is supplied by this provider package." + }, + { + "question": "What finite-precision and machine-work budget supports any successful complete caller?", + "why_it_matters": "The local finite schedule has bounded amplification and exact dyadic coefficients, but those facts do not supply recursive rounding, indexed movement or the outer multiplication recurrence.", + "first_step": "Use the emitted ordinary counts and local 2^18996 suffix amplification bound to assign coordinate precision and movement costs to the proposed complete caller.", + "blocked_by": "Depends on a complete caller and its recursion/packing contract; this package claims only the source-bound local primitive." + } + ], + "checkpoint": { + "canonical_main": "1ec1119972c9aefe42525172d07b332fcff81cb4", + "priority_revision": 7, + "selected_kappa": "0.0030217758", + "frozen_source_payload_sha256": "cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd", + "overlap": [ + "Ali Romman PR5383 retained-center candidate at 4bd6efa51a495a7c7b7754915cf0244e7e60969e", + "Cinna Davis PR4694 retained-center and PR4698 common-chart helper basis", + "Dugongue PR4929 center-free code and coded-native-caller physical normalizers", + "PR5397 scoped owned-exchange ceiling, PR5398 direct backward conjugation and independent PR5399/5400 reviews; these do not supply this unrestricted coupled-output contract." + ], + "campaign_thread": "https://github.com/CrocSwap/integer-mult-bounds/discussions/4930", + "frontier_changed": false, + "checked_at_utc": "2026-10-23T22:26:00Z" + } +} diff --git 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+] diff --git a/research/coupled-provider-independent-audit/capsule/repository/research/native-rank8-helper-provider/WORD.json.gz b/research/coupled-provider-independent-audit/capsule/repository/research/native-rank8-helper-provider/WORD.json.gz new file mode 100644 index 0000000000..f3111b47e8 Binary files /dev/null and b/research/coupled-provider-independent-audit/capsule/repository/research/native-rank8-helper-provider/WORD.json.gz differ diff --git a/research/coupled-provider-independent-audit/capsule/repository/research/native-rank8-helper-provider/verify.py b/research/coupled-provider-independent-audit/capsule/repository/research/native-rank8-helper-provider/verify.py new file mode 100644 index 0000000000..b62af49c87 --- /dev/null +++ b/research/coupled-provider-independent-audit/capsule/repository/research/native-rank8-helper-provider/verify.py @@ -0,0 +1,602 @@ +#!/usr/bin/env python3 +"""Source-bound coupled provider, exact rational rows and absolute phases. + +No scratch registry, pending Git object, network access or third-party package. +The authenticated predecessor Clifford evaluator is the only imported module. +""" +from collections import Counter +from fractions import Fraction as F +from functools import lru_cache +from hashlib import sha256 +from pathlib import Path +import argparse +import gzip +import importlib.util +import json +import sys +import time + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parent.parent +SOURCE_HASH = 'cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd' +WITNESS_HASH = '24599011da06325e1012619b2b84a4dd3aceb90ab42d3caaf6414879e7d16591' +MODE = [224, 225, 227, 229, 240, 241, 256, 257] +PAID = Counter({1: 2193, 2: 412, 3: 510, 4: 127, 5: 40}) + + +def need(condition, message): + if not condition: + raise ValueError(message) + + +def enc(row): + return [[j, str(a)] for j, a in sorted(row.items()) if a] + + +def add(target, source, factor=1): + for key, value in tuple(source.items()): + value = target.get(key, F(0)) + factor * value + if value: + target[key] = value + else: + target.pop(key, None) + + +def addr(ref): + need(ref[0] in ('L', 'C'), 'unknown field kind') + return ref[1] + (632 if ref[0] == 'C' else 0) + + +def replay(program, c, owners, snapshots=()): + """Every owner is an independent free-group column, including dirty C fields.""" + rows = [{(j, ()): F(1)} for j in range(owners)] + charts = c['start'][:] + [None] * (owners - 632) + paid, scalar = Counter(), Counter() + zeros, dirt_clears, saved = [], [], {} + for event, e in enumerate(program): + kind = e[0] + if kind == 'scalar': + op, chart = e[1:] + dst = addr(op[1]) + scalar[op[0]] += 1 + if op[0] == 'clear': + need(dst >= 632, 'persistent CLEAR forbidden') + dirt = {k: v for k, v in rows[dst].items() if k[0] >= 632} + if dirt: + dirt_clears.append((dst, dirt)) + rows[dst], charts[dst] = {}, chart + else: + need(charts[dst] == chart, 'destination chart') + if op[0] in ('copy', 'add'): + src = addr(op[2]) + need(charts[src] == chart, 'source chart') + if op[0] == 'copy': + need(dst >= 632 and not rows[dst], 'COPY must fill owned zero') + rows[dst] = dict(rows[src]) + else: + need(dst != src, 'ADD self alias') + add(rows[dst], rows[src], F(op[3], op[4])) + else: + need(op[0] == 'scale', 'unknown scalar operation') + factor = F(op[2], op[3]) + rows[dst] = {k: v * factor for k, v in rows[dst].items() if v * factor} + elif kind == 'warp': + _, ref, warp, old, new = e + dst = addr(ref) + need(charts[dst] == old, 'warp chart') + symbol = (1 if warp > 0 else -1) * (abs(warp) + 1000000) + after = {} + for (owner, word), value in rows[dst].items(): + word = word[1:] if word and word[0] == -symbol else (symbol,) + word + add(after, {(owner, word): value}) + rows[dst], charts[dst] = after, new + elif kind in ('climb', 'center'): + if kind == 'climb': + _, _, dst, old, new, rank = e + expected = len(c['frames'][new]) - len(c['frames'][old]) + else: + _, dst, old, new, rank = e + dst += 632 + expected = abs(len(c['frames'][new]) - len(c['frames'][old])) + need(charts[dst] == old and rank == expected and rank > 0, + 'paid child chart/rank') + charts[dst] = new + paid[rank] += 1 + elif kind == 'zero_retag': + _, dst, old, new = e + need(charts[dst] == old and not rows[dst], 'zero retag has nonzero input') + zeros.append([event, dst, old, new]) + charts[dst] = new + else: + # Inherited source annotations / physical boundary bindings. The + # predecessor's normalized-row convention treats these as no row + # update; they remain byte-for-byte records in the emitted word. + # New physical boundaries are checked separately below, with phase. + need(kind in ('phase', 'adapter', 'residual_adapter'), 'unknown source record') + for at, owner in snapshots: + if event == at: + saved[(at, owner)] = (charts[owner], dict(rows[owner])) + return rows, charts, paid, scalar, zeros, dirt_clears, saved + + +def scalar(row): + need(all(not word for _, word in row), 'endpoint has unreduced native word') + return {j: a for (j, _), a in row.items()} + + +def rewrite(source, witness): + centers = {r['event']: i for i, r in enumerate(witness)} + late = {r['zero_event']: i for i, r in enumerate(witness)} + caches = {r['cached_event']: i for i, r in enumerate(witness)} + need(len(centers) == len(late) == len(caches) == 8, 'distinct eight sites') + need(max(caches) < min(centers), 'caches must precede all replacements') + word = [] + for event, op in enumerate(source['programs']['backward']): + if event in centers: + i = centers[event] + frame = witness[i]['frame'] + need(op == ['center', 0, 0, frame, 8], 'center source binding') + word += [['scalar', ['clear', ['C', 0]], frame], + ['scalar', ['copy', ['C', 0], ['C', i + 1]], frame]] + elif event in late: + r = witness[late[event]] + need(op == ['climb', 'warp_retimed', r['zero_role'], r['frame'], 1, 1], + 'late H1 source binding') + word.append(['zero_retag', r['zero_role'], r['frame'], 1]) + else: + word.append(op) + if event in caches: + i = caches[event] + r = witness[i] + word += [['scalar', ['clear', ['C', i + 1]], r['frame']], + ['scalar', ['copy', ['C', i + 1], ['L', r['cached_role']]], r['frame']]] + return {'source_sha256': SOURCE_HASH, 'direction': 'backward', 'word': word} + + +def inverse(matrix): + n = len(matrix) + a, b, ops = [dict(r) for r in matrix], [{j: F(1)} for j in range(n)], [] + for j in range(n): + k = next((i for i in range(j, n) if a[i].get(j)), None) + need(k is not None, 'singular basis') + if k != j: + a[j], a[k], b[j], b[k] = a[k], a[j], b[k], b[j] + ops.append(['swap', j, k]) + factor = 1 / a[j][j] + if factor != 1: + a[j] = {k: factor * v for k, v in a[j].items()} + b[j] = {k: factor * v for k, v in b[j].items()} + ops.append(['scale', j, str(factor)]) + for i in range(n): + if i == j or not a[i].get(j): + continue + factor = -a[i][j] + add(a[i], a[j], factor) + add(b[i], b[j], factor) + ops.append(['add', i, j, str(factor)]) + need(a == [{j: F(1)} for j in range(n)], 'basis reduction') + return b, ops + + +def ordinary(ops, roles, reverse=False): + out = [] + for e in reversed(ops) if reverse else ops: + if e[0] == 'swap': + a, b = roles[e[1]], roles[e[2]] + out += [['add', a, b, '1'], ['add', b, a, '-1'], + ['add', a, b, '1'], ['scale', b, '-1']] + elif e[0] == 'scale': + v = F(e[2]) + out.append(['scale', roles[e[1]], str(1 / v if reverse else v)]) + else: + v = F(e[3]) + out.append(['add', roles[e[1]], roles[e[2]], str(-v if reverse else v)]) + return out + + +def apply_ordinary(program, rows): + rows = [dict(r) for r in rows] + for e in program: + if e[0] == 'add': + need(e[1] != e[2], 'ordinary ADD alias') + add(rows[e[1]], rows[e[2]], F(e[3])) + else: + need(e[0] == 'scale', 'ordinary operation') + rows[e[1]] = {j: a * F(e[2]) for j, a in rows[e[1]].items() if a * F(e[2])} + return rows + + +def authenticate(): + pins = json.loads((HERE / 'SOURCES.json').read_text()) + for r in pins['files']: + if r['usage'] == 'input': + need(sha256((ROOT / r['path']).read_bytes()).hexdigest() == r['sha256'], + 'changed scientific input: ' + r['path']) + raw = gzip.decompress((ROOT / 'research/native-center-free-code/SOURCE-WORD.json.gz').read_bytes()) + need(sha256(raw).hexdigest() == SOURCE_HASH, 'native payload') + need(sha256((HERE / 'WITNESS.json').read_bytes()).hexdigest() == WITNESS_HASH, + 'Ali verbatim candidate provenance') + cp = ROOT / 'research/coded-native-caller/clifford_exact.py' + spec = importlib.util.spec_from_file_location('rank8_provider_clifford', cp) + ce = importlib.util.module_from_spec(spec) + sys.modules[spec.name] = ce + spec.loader.exec_module(ce) + return json.loads(raw), json.loads((HERE / 'WITNESS.json').read_text()), ce + + +def main(emit=False): + started = time.monotonic() + source, witness, ce = authenticate() + c = source['canonical'] + normal = json.loads((ROOT / 'research/coded-native-caller/NORMALIZERS.json').read_text()) + M = normal['mode_columns'] + A = [[F(a) for a in r] for r in json.loads((ROOT / 'research/native-center-free-code/CODE.json').read_text())['A']] + need(c['start'][112:224] == [0] * 112, 'main Y inputs have ground chart') + need(len(M) == 8 and all(len(r) == 112 for r in M), 'M dimensions') + need(all(sum(M[k][i] * M[l][i] for i in range(112)) == 56 * int(k == l) + for k in range(8) for l in range(8)), 'M Gram') + need(all(A[i][j] == F(i == j) - sum(F(M[k][i] * M[k][j], 4) for k in range(8)) + for i in range(112) for j in range(112)), 'A factorization') + original = replay(source['programs']['backward'], c, 633, + [(r['cached_event'], r['cached_role']) for r in witness]) + oldrows, oldcharts, oldpaid, oldscalar = original[:4] + expected = [{(j, ()): F(1)} for j in range(632)] + for j in range(112): + expected[j][(j + 112, ())] = F(-1) + need(oldrows[:632] == expected and not oldrows[632], 'original 632-row endpoint') + need(oldcharts[:632] == c['final'], 'original exit charts') + + centerfree = [['scalar', ['clear', ['C', e[1]]], e[3]] if e[0] == 'center' else e + for e in source['programs']['backward']] + cf = replay(centerfree, c, 633) + cfrows = [scalar(r) for r in cf[0]] + need(cf[1][:632] == c['final'] and not cfrows[632], 'center-free charts/owned') + P = [[-cfrows[j + 224].get(i + 112, F(0)) for i in range(112)] for j in range(408)] + B = [[sum(P[j][i] * M[k][i] for i in range(112)) / 56 for j in range(408)] for k in range(8)] + need(all(P[j][i] == sum(B[k][j] * M[k][i] for k in range(8)) + for j in range(408) for i in range(112)), 'full native coupling factorization') + for j in range(632): + row = {j: F(1)} + if j < 112: + for i in range(112): + if A[i][j]: + row[i + 112] = -A[i][j] + elif j >= 224: + for i, a in enumerate(P[j - 224]): + if a: + row[i + 112] = -a + need(cfrows[j] == row, 'center-free complete scalar endpoint') + + delta = [{j - 224: F(a) for j, a in r['relation']} for r in witness] + coupling = [[sum(a * B[k][j] for j, a in d.items()) for k in range(8)] for d in delta] + need(all(sum(bool(a) for a in r) == 1 and set(r) <= {F(0), F(1), F(-1)} + for r in coupling), 'candidate is not a signed retraction') + perm = [next(k for k, a in enumerate(r) if a) for r in coupling] + sign = [coupling[i][perm[i]] for i in range(8)] + need(sorted(perm) == list(range(8)), 'retraction permutation') + E = [{} for _ in range(8)] + for i, k in enumerate(perm): + E[k] = {j: sign[i] * a for j, a in delta[i].items()} + row = {(j + 224, ()): F(witness[i]['zero_factor']) * a for j, a in delta[i].items()} + for j in range(112): + a = -F(witness[i]['zero_factor']) * sign[i] * M[k][j] + if a: + row[(j + 112, ())] = a + need(original[6][(witness[i]['cached_event'], witness[i]['cached_role'])] + == (witness[i]['frame'], row), 'fresh original cached row binding') + need(all(sum(a * B[l][j] for j, a in E[k].items()) == int(k == l) + for k in range(8) for l in range(8)), 'E B^T identity') + active = sorted(set(j for r in B for j, a in enumerate(r) if a) | set(j for r in E for j in r)) + roles, index = [224 + j for j in active], {j: i for i, j in enumerate(active)} + need(len(active) == 122 and all(c['start'][j] == 0 and c['final'][j] == 1 for j in roles), + 'basis requires 122 actual cold H9 owners') + J = [j - 224 for j in MODE] + L = [{} for _ in active] + for k, j in enumerate(J): + for r in active: + if B[k][r]: + L[index[r]][index[j]] = B[k][r] + for j in active: + if j in J: + continue + for r in active: + a = F(r == j) - sum(B[k][r] * E[k].get(j, F(0)) for k in range(8)) + if a: + L[index[r]][index[j]] = a + Li, ops = inverse(L) + for left, right in ((L, Li), (Li, L)): + for i, row in enumerate(left): + product = {} + for j, a in row.items(): + add(product, right[j], a) + need(product == {i: F(1)}, 'two-sided basis inverse') + for k, row in enumerate(E): + product = {} + for j, a in row.items(): + add(product, L[index[j]], a) + need(product == {index[J[k]]: F(1)}, 'E L mode selection') + need(all(sum(a * B[k][active[j]] for j, a in row.items()) == int(i == index[J[k]]) + for i, row in enumerate(Li) for k in range(8)), 'Li B mode embedding') + need(all(a.denominator & (a.denominator - 1) == 0 + for matrix in (L, Li) for row in matrix for a in row.values()), 'dyadic basis') + entrance, exitword = ordinary(ops, roles, True), ordinary(ops, roles) + identity = [{j: F(1)} for j in range(632)] + entered = apply_ordinary(entrance, identity) + def check_basis(rows): + for i, j in enumerate(roles): + need(rows[j] == {roles[k]: a for k, a in L[i].items()}, 'literal L program') + check_basis(entered) + need(apply_ordinary(exitword, entered) == identity, 'literal Li program') + need(Counter(e[0] for e in entrance) == Counter(add=822, scale=12), 'basis program bill') + need(Counter(e[0] for e in exitword) == Counter(add=822, scale=12), 'inverse program bill') + + changed = rewrite(source, witness) + frozen_word = json.loads(gzip.decompress((HERE / 'WORD.json.gz').read_bytes())) + need(changed == frozen_word, 'committed exact word differs from source rewrite') + result = replay(changed['word'], c, 641) + rawrows, charts, paid, scalars, zeros, dirt = result[:6] + need(charts[:632] == c['final'] and not rawrows[632], 'changed persistent charts/C0') + need(paid == PAID and oldpaid == paid + Counter({1: 8, 8: 8}), 'paid children') + need(scalars == oldscalar + Counter(clear=16, copy=16), 'source ordinary delta') + need(len(zeros) == 8, 'eight exact zero retags') + need(len(dirt) == 9 and {j for j, _ in dirt} == set(range(632, 641)) + and all(d == {(j, ()): F(1)} for j, d in dirt), 'all arbitrary owned dirt cleared') + need(not any(j >= 632 for row in rawrows for j, _ in row), 'owned dirt leaked') + need(sum(rawrows[j] != oldrows[j] for j in range(632)) == 218, 'changed endpoint count') + endpoint = [] + for row in rawrows: + out = {} + for j, a in scalar(row).items(): + add(out, entered[j], a) + endpoint.append(out) + endpoint = apply_ordinary(exitword, endpoint) + for j in range(632): + expected = {} if j in MODE else {j: F(1)} + if j < 112: + expected[j + 112] = F(-1) + for k in range(8): + if M[k][j]: + expected[MODE[k]] = F(M[k][j], 4) + need(endpoint[j] == expected, 'composed all-owner endpoint at ' + str(j)) + def check_cache(i, row): + r, k = witness[i], perm[i] + factor = F(r['zero_factor']) * sign[i] + expected = {MODE[k]: factor} + for j in range(112): + if M[k][j]: + expected[j + 112] = -factor * M[k][j] + need(row == expected and charts[633 + i] == r['frame'], 'composed retained cache') + for i in range(8): + check_cache(i, endpoint[633 + i]) + first_cache = dict(endpoint[633]) + + def conjugate(op): + circuit = [] + for e in op.circuit: + if e[0] == 'D': + circuit.append(('D', e[1], tuple((-x) % 4 for x in e[2]))) + elif e[0] == 'C': + circuit.append(('C', e[1], -e[2])) + elif e[0] == 'phase': + circuit.append(('phase', (-e[1]) % 4)) + else: + circuit.append(e) + return ce.Op(9, tuple((x, z, -p % 4) for x, z, p in op.tab), circuit) + + @lru_cache(None) + def frame(j, back=False): + op = ce.canonical_frame(9, c['frames'][j]) + return conjugate(op) if back else op + + def literal(word): + op = ce.ident(9) + for e in word: + if e[0] == 'P': + part = ce.perm(9, tuple(e[1])) + elif e[0] == 'D': + part = ce.diag(9, tuple(e[1]), tuple(e[2])) + elif e[0] == 'X': + part = ce.xgate(9, e[1]) + elif e[0] == 'phase': + part = ce.Op(9, ce.identity(9), [('phase', e[1])]) + else: + raise ValueError('boundary contains a Gaussian gate') + op = op.then(part) + return op + + def equal(a, b): + return a.tab == b.tab and a.zero_state() == b.zero_state() + + def rank(op): + return ce.rank([x for x, _, _ in op.tab[9:]]) + + def receipt(op): + vec, den = op.zero_state() + j = next(j for j, a in enumerate(vec) if a != (0, 0)) + return {'literal_word': op.circuit, 'signed_tableau': op.tab, + 'zero_column_anchor': {'index': j, 'gaussian_numerator': vec[j], + 'denominator_power2': den}} + + def compile_monomial(op): + need(rank(op) == 0, 'nonmonomial boundary map') + compiled, _ = ce.monomial(op) + need(equal(compiled, op) and equal(literal(compiled.circuit), op), + 'literal phase-correct monomial compilation') + return compiled + + R, D = frame(1), ce.fourier(9, range(1, 9)) + Km, N = [None] * 8, [None] * 8 + records = [None] * 8 + for i, r in enumerate(witness): + k = perm[i] + candidates = [q for q in range(1, 512) + if all(ce.parity(q & v) == 0 for v in c['frames'][r['frame']])] + need(len(candidates) == 1, 'rank-eight missing line') + q = candidates[0] + need(q.bit_count() % 2 == 1 and q != 511, 'odd noncharacteristic line') + if not q & 1: + transvections = [1 ^ q] + else: + j = next(j for j in range(1, 9) if not q >> j & 1) + transvections = [1 ^ (1 << j), (1 << j) ^ q] + cols = [] + for j in range(9): + x = 1 << j + for v in transvections: + x ^= v if ce.parity(x & v) else 0 + cols.append(x) + G = ce.transpose(cols, 9) + z = sum((((row.bit_count() - 1) // 2) & 1) << j for j, row in enumerate(G)) + K = ce.perm(9, G).then(ce.diag(9, (0,) * 9, tuple(2 * ((z >> j) & 1) for j in range(9)))) + need(equal(K.then(R), R.then(K)), 'mode K/R absolute phase') + need(all((ce.mv(ce.transpose(G, 9), x).bit_count() - x.bit_count() + - 2 * ce.parity(z & x)) % 4 == 0 for x in range(512)), 'K weight congruence') + F8 = frame(r['frame'], True) + need(rank(F8) == 8, 'actual cache rank') + Km[k] = compile_monomial(K) + N[k] = compile_monomial(K.then(F8).adjoint().then(D)) + records[k] = {'mode': k, 'owner': MODE[k], 'cache_slot': 633 + i, + 'witness_row': i, 'frame': r['frame'], 'missing_line': q, + 'cache_scalar': str(1 / (2 * F(r['zero_factor']) * sign[i])), + 'input_K': receipt(Km[k]), 'output_N': receipt(N[k])} + Kp = [literal(r['K_word']) for r in normal['ports']] + checks = Counter() + for j, port in enumerate(normal['ports']): + need(port['port'] == j and rank(Kp[j]) == 0 and equal(Kp[j].then(R), R.then(Kp[j])), + 'port K binding and R commutation') + wrappers = port['compiled_wrappers'] + BX, BY, OX, OY = [literal(wrappers[key]['word']) for key in + ('backward_input_X', 'backward_input_Y', 'backward_output_X', 'backward_output_Y')] + birth, final, finalY = frame(c['start'][j], True), frame(c['final'][j], True), frame(c['final'][112 + j], True) + need(equal(BX.then(birth.adjoint()).then(final).then(OX), D), 'X diagonal physical block') + need(equal(BY.then(finalY).then(OY), D), 'Y diagonal physical block') + need(equal(BY.then(final).then(OX), R), 'main shear physical block') + checks['main_diagonal_and_shear'] += 3 + for k in range(8): + if not M[k][j]: + continue + need(equal(Km[k].then(final).then(OX), Km[k].then(Kp[j].adjoint()).then(R)), + 'helper-to-main physical coupling') + F8 = frame(records[k]['frame'], True) + need(equal(BY.then(F8).then(N[k]), Kp[j].then(Km[k].adjoint()).then(D)), + 'main-to-helper physical coupling') + checks['two_coupling_directions'] += 2 + for k in range(8): + need(equal(Km[k].then(frame(records[k]['frame'], True)).then(N[k]), D), + 'helper diagonal physical block') + checks['helper_diagonal'] += 1 + need(dict(checks) == {'main_diagonal_and_shear': 336, 'two_coupling_directions': 896, + 'helper_diagonal': 8}, '1,240 physical bindings') + autonomous = Counter(len(c['frames'][c['final'][j]]) - len(c['frames'][c['start'][j]]) + for j in range(224, 632) if j not in MODE) + need(autonomous == Counter({4: 28, 7: 7, 8: 47, 9: 318}), '400 retained native helper jobs') + # Physical normalization precedes a complete-field SWAP, including chart tags. + for r in records: + owner, cache = r['owner'], r['cache_slot'] + need(not endpoint[owner], 'SWAP destination must be identically zero') + endpoint[owner], endpoint[cache] = endpoint[cache], endpoint[owner] + need(all(not endpoint[j] for j in range(632, 641)), 'all owned outputs clean') + + # Failure controls invoke the same predicates as the construction. + controls = [] + bad_c = dict(c) + bad_c['start'] = c['start'][:] + bad_c['start'][0] = 0 + try: + replay([['zero_retag', 0, 0, 1]], bad_c, 641) + except ValueError as e: + need(str(e) == 'zero retag has nonzero input', 'wrong rejection') + controls.append('nonzero zero-retag rejected') + need(len(controls) == 1, 'zero-retag control accepted') + corrupted = [e[:] for e in entrance] + mutated = next(e for e in corrupted if e[0] == 'add') + mutated[3] = str(F(mutated[3]) + 1) + try: + check_basis(apply_ordinary(corrupted, identity)) + except ValueError as e: + need(str(e) == 'literal L program', 'wrong basis rejection') + controls.append('one altered basis ADD coefficient rejected') + need(len(controls) == 2, 'basis coefficient mutation accepted') + badN = ce.Op(9, N[0].tab, N[0].circuit + [('phase', 1)]) + need(badN.tab == N[0].tab and not equal(Km[0].then(frame(records[0]['frame'], True)).then(badN), D), + 'phase-only error escaped') + controls.append('same-tableau phase-only cache error rejected') + wrong = dict(first_cache) + add(wrong, {MODE[perm[0]]: F(1)}) + try: + check_cache(0, wrong) + except ValueError as e: + need(str(e) == 'composed retained cache', 'wrong cache rejection') + controls.append('one altered saved-cache coefficient rejected') + need(len(controls) == 4, 'saved-cache coefficient mutation accepted') + + # An explicit, conservative local error-amplification bound for this finite + # schedule. Gaussian and monomial field maps have Euclidean norm one. + def log2_bound(a): + a, exponent = max(F(1), a), 0 + while a > 1: + a /= 2 + exponent += 1 + return exponent + amplification = 0 + for e in changed['word']: + if e[0] == 'scalar': + op = e[1] + if op[0] == 'add': + amplification += log2_bound(1 + abs(F(op[3], op[4]))) + elif op[0] == 'scale': + amplification += log2_bound(abs(F(op[2], op[3]))) + for e in entrance + exitword: + amplification += log2_bound(1 + abs(F(e[3]))) if e[0] == 'add' else log2_bound(abs(F(e[2]))) + amplification += 8 * log2_bound(F(2)) + amplification += sum(log2_bound(abs(F(r['cache_scalar']))) for r in records) + + artifact = { + 'schema_version': 1, 'source_payload_sha256': SOURCE_HASH, + 'candidate_witness_sha256': WITNESS_HASH, + 'word_payload_sha256': sha256(gzip.decompress((HERE / 'WORD.json.gz').read_bytes())).hexdigest(), + 'basis_roles': roles, 'mode_owners': MODE, + 'candidate_mode_permutation': perm, 'candidate_mode_signs': list(map(str, sign)), + 'canonical_retraction_E': [enc(row) for row in E], + 'input_basis_program': entrance, 'output_basis_program': exitword, + 'mode_boundaries': records, + 'ordered_schedule': [ + 'Main input wrappers: NORMALIZERS.ports[j].compiled_wrappers.backward_input_X/Y.', + 'On each mode owner apply input_K and scalar 2; run input_basis_program.', + 'Run every instruction of WORD.json.gz; C0..C8 initially arbitrary.', + 'Run output_basis_program on the 122 persistent common-chart helpers.', + 'For each mode apply cache_scalar and output_N to its owned cache; SWAP the whole field and chart with its zero original owner; CLEAR the owned zero.', + 'Main output wrappers: NORMALIZERS.ports[j].compiled_wrappers.backward_output_X/Y.' + ], + 'paid': dict(sorted(paid.items())), 'autonomous_native_helpers': dict(sorted(autonomous.items())), + 'owned_fields': {'count': 9, 'initial_values': 'arbitrary', 'final_values': 'zero', 'productive_credit': 0}, + 'added_ordinary_work_vs_original_raw_source': { + 'ADD': 1644, 'SCALE': 40, 'COPY': 16, 'CLEAR': 24, 'whole_field_SWAP': 8, + 'monomial_field_maps': 464, + 'monomial_breakdown': {'fused_inherited_main_standardizers': 448, 'mode_inputs': 8, 'cache_outputs': 8}}, + 'local_error_amplification_power2_bound': amplification, + 'source_original_scalar_counts': dict(sorted(oldscalar.items())), + 'source_changed_scalar_counts': dict(sorted(scalars.items())), + 'physical_phase_bindings': dict(checks), 'exact_zero_retags': zeros, + 'formula': {'X': 'D x - R y + R W h', 'Y': 'D y', 'H': 'D (h - Z y)', + 'W': 'diag(K_port^-1) M diag(K_mode)/2', + 'Z': 'diag(K_mode^-1) M^T diag(K_port)/2'}, + 'failure_controls': controls, + 'scope': 'Changed coupled backward provider. No autonomous credit for eight coupled outputs; no completed caller, inverse/transpose implementation, new kappa or selected-result change.' + } + artifact = json.loads(json.dumps(artifact)) + path = HERE / 'PROVIDER.json' + if emit: + path.write_text(json.dumps(artifact, indent=2) + '\n') + else: + need(json.loads(path.read_text()) == artifact, 'committed boundary recipe differs from replay') + print('PASS_NATIVE_RANK8_HELPER_PROVIDER ' + json.dumps({ + 'original_inputs': 632, 'arbitrary_owned_inputs': 9, 'owned_outputs_zero': 9, + 'autonomous_helpers': 400, 'coupled_helpers': 8, 'paid': dict(sorted(paid.items())), + 'phase_bindings': sum(checks.values()), 'seconds': round(time.monotonic() - started, 3)})) + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--emit', action='store_true', help='regenerate the package-local boundary recipe') + main(parser.parse_args().emit) diff --git a/research/coupled-provider-independent-audit/custody/5376/LATEST-COMMIT-CHANGE.json b/research/coupled-provider-independent-audit/custody/5376/LATEST-COMMIT-CHANGE.json new file mode 100644 index 0000000000..fc71b24f01 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/LATEST-COMMIT-CHANGE.json @@ -0,0 +1,30 @@ +{ + "old_head": "aef3c2f91a10d4c41e814ea264a9d64c9423bcb2", + "new_head": "848cdce9003262c4b6e02ec4558f302e4fae56ad", + "changed_paths": [ + "research/clifford-tensor-gram/VERIFY.json", + "research/clifford-tensor-gram/provider/RESEARCH-NOTES.md" + ], + "changed_python_paths": [], + "all_python_sources_unchanged": true, + "old_timeouts": [ + 180, + 180, + 180, + 180, + 240, + 240 + ], + "new_timeouts": [ + 90, + 90, + 90, + 90, + 420, + 420 + ], + "command_argv_unchanged": true, + "new_declared_timeout_total_seconds": 1200, + "scope": "Only metadata/source comparison. The earlier hosted timeout and later hosted success must be independently evidenced; unchanged sources do not establish successful replay here.", + "scientific_executions": 0 +} diff --git a/research/coupled-provider-independent-audit/custody/5376/NESTED-PROVIDER-INPUT-BINDINGS.json b/research/coupled-provider-independent-audit/custody/5376/NESTED-PROVIDER-INPUT-BINDINGS.json new file mode 100644 index 0000000000..9d8115bb5d --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/NESTED-PROVIDER-INPUT-BINDINGS.json @@ -0,0 +1,54 @@ +{ + "inputs": [ + { + "name": "word", + "file": "WORD.json.gz", + "source_path": "research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz", + "source_commit": "1ec1119972c9aefe42525172d07b332fcff81cb4", + "git_blob": "46d929df83817b85a5387bcdb9745e0627d6366e", + "sha256": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05", + "actual_sha256": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05", + "sha256_match": true, + "payload_sha256": "cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd", + "source_pin_matches_outer_SOURCES": true + }, + { + "name": "paid", + "file": "PAID.jsonl.gz", + "source_path": "research/final4610-independent-admission/PAID-CATALOG.jsonl.gz", + "source_commit": "1ec1119972c9aefe42525172d07b332fcff81cb4", + "git_blob": "73fa3ced93981949ad8f2432af840b787d9182c0", + "sha256": "964aa2e28057936825a67872ebe5c6b0abc3228e71a545dda6c1fc11adb983d5", + "actual_sha256": "964aa2e28057936825a67872ebe5c6b0abc3228e71a545dda6c1fc11adb983d5", + "sha256_match": true, + "payload_sha256": "dc47d96b5b651ba3446d73ac0710152f7de88547a0cb2bbd75706e691b6f0bd6", + "source_pin_matches_outer_SOURCES": true + }, + { + "name": "phases", + "file": "PHASES.json.gz", + "source_path": "research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz", + "source_commit": "1ec1119972c9aefe42525172d07b332fcff81cb4", + "git_blob": "ac77b78547d6dbf2e6bd102e1047c5b16c1bca88", + "sha256": "6eae66ed3cfa8a1533e89b9660a57276908e6646640a12f8b1e3489f4ea1354b", + "actual_sha256": "6eae66ed3cfa8a1533e89b9660a57276908e6646640a12f8b1e3489f4ea1354b", + "sha256_match": true, + "payload_sha256": "bc9de6d11fc3d5fb2141a1658785f2093ea1b735d34414ed15749df7d731b34e", + "source_pin_matches_outer_SOURCES": true + }, + { + "name": "helpers", + "file": "HELPERS.json.gz", + "source_path": "research/joint-helper-lattice/NATIVE.json.gz", + "source_commit": "1ec1119972c9aefe42525172d07b332fcff81cb4", + "git_blob": "0910f74138decf498e7fc445cc2daff4390169d6", + "sha256": "74582cce642c80f0235be7fcbce3716174666326ac6a1d46d02a62a75d7be4c6", + "actual_sha256": "74582cce642c80f0235be7fcbce3716174666326ac6a1d46d02a62a75d7be4c6", + "sha256_match": true, + "payload_sha256": "e497baacc300322b338f9e3e68d14937352bbf425aaaf5e759017c6c01e935c8", + "source_pin_matches_outer_SOURCES": true + } + ], + "all_match": true, + "scientific_executions": 0 +} diff --git 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R. Colkitt 1792780698 -0400 +committer Douglas R. Colkitt 1792780698 -0400 + +Record 91 confirmed PR merges and empty actionable queue [skip ci] diff --git a/research/coupled-provider-independent-audit/custody/5376/git-objects/848cdce9003262c4b6e02ec4558f302e4fae56ad.commit b/research/coupled-provider-independent-audit/custody/5376/git-objects/848cdce9003262c4b6e02ec4558f302e4fae56ad.commit new file mode 100644 index 0000000000..3a10165169 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/git-objects/848cdce9003262c4b6e02ec4558f302e4fae56ad.commit @@ -0,0 +1,6 @@ +tree eb1a7e9f6b14f6a651f679fbfd9dfb2c23382697 +parent aef3c2f91a10d4c41e814ea264a9d64c9423bcb2 +author Ali Romman <226877337+aliromman@users.noreply.github.com> 1792796110 -0500 +committer Ali Romman <226877337+aliromman@users.noreply.github.com> 1792796110 -0500 + +Allocate provider replay time within the fixed package budget diff --git 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b/research/coupled-provider-independent-audit/custody/5376/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/docs/research/community-native4610-contributors.md @@ -0,0 +1,13 @@ +# Contributors to the PR4610 selection + +- **Cao Yifan (@intqwq)** — [PR4610](https://github.com/CrocSwap/integer-mult-bounds/pull/4610): changed native maps, helper/contact optimization, complete paid profile and final compiler witness κ=.0030217758. +- **Chris R (@Clear1nsight)** — [PR5241](https://github.com/CrocSwap/integer-mult-bounds/pull/5241): independent source-bound phase, arbitrary-input, invoice, compiler and outer audit, including the same-assumption specialization argument. +- **Cinna Davis (@1337isnot1337)** — PR4470 and preceding joint-helper/query-thinned controller chain; the new construction builds directly on this work. +- **zxv** — productive-helper native construction, moment and compiler machinery. +- **Jacob Alan Sussman** — mixed-target recursive compilation. +- **Dugongue** — transported-frame and physical-interface foundations. +- **Mihir Srivastava, Ryanson Jonathan and Mark / Matarener** — inherited independent audits and adversarial questions recorded in the [PR4470 contributor map](community-joint4470-contributors.md). + +The [PR4359 map](community-productive4359-contributors.md), predecessor source notices and [full contributor ledger](../../CONTRIBUTORS.md) retain cumulative BIT, geometry, scalar, Clifford, precision, analytic and verification credit. Parallel audits remain attributed individually; this selection does not claim to replay every related PR. Later scalar-only compressions #5265/#5350 are not needed for this exponent. + +Maintainer acceptance by Douglas Colkitt's OpenAI assistant used substantial AI assistance. Neither this map nor a passing finite replay claims independent human review or an end-to-end Lean multiplication theorem. diff --git a/research/coupled-provider-independent-audit/custody/5376/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/final4610-independent-admission/PAID-CATALOG.jsonl.gz b/research/coupled-provider-independent-audit/custody/5376/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/final4610-independent-admission/PAID-CATALOG.jsonl.gz new file mode 100644 index 0000000000..73fa3ced93 Binary files /dev/null and b/research/coupled-provider-independent-audit/custody/5376/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/final4610-independent-admission/PAID-CATALOG.jsonl.gz differ diff --git a/research/coupled-provider-independent-audit/custody/5376/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/final4610-independent-admission/PROOF.md b/research/coupled-provider-independent-audit/custody/5376/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/final4610-independent-admission/PROOF.md new file mode 100644 index 0000000000..cc71e69b34 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/final4610-independent-admission/PROOF.md @@ -0,0 +1,73 @@ +# Conditional source-compatible admission argument + +**Complete first cold replay passed all required stages. Final committed-head replay/publication preflights remain separate gates.** This is a source-specific written argument, supported by exact finite computation. It is not a Lean theorem or an unconditional multiplier proof. + +## Statement and attribution + +Fix the canonical merged source commit `ec2780e8aeb1c88acaf5e9e470ef8c68e7fbbb6c` and final PR4610 payload SHA256 `cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd`. Assume exactly the five generic framework contracts in selected PR4470's `certificates/selected-result.json`. Under those same contracts, the complete final PR4610 construction supports `κ=15108879/5000000000=.0030217758`, exceeding selected `.00302015` by `8129/5000000000=.0000016258`. + +This is Cao Yifan's existing construction and final compiler choice. The audit's new contribution is a closed independent verification and specialization chain. The candidate differs from selected PR4470 in its complete paid profile, not merely in the decimal enclosure of the selected root. No selected record is changed. + +## 1. Finite operator semantics and complete changed coverage + +`checks/frame.py` verifies each of the 480 signed actual warp events against its exact source/target binary subspaces, using the map declared for its operator. Negative occurrences use the inverse relation. This closes a condition that formal free-warp row reduction alone cannot check; a source-bound issue4571 mutation keeps an unchanged formal cancellation but fails physical frame transport. + +`checks/native.py` independently reconstructs all 72 finite native maps, binds all 20 changed maps, and checks all 180 actual signed frame classes in both orientations. It imports no retained Clifford compiler. Each exact phase-bearing circuit is compared on every Pauli generator and an exact Gaussian-dyadic state anchor. Equal conjugation on the full Pauli generators makes the discrepancy a scalar; equality on the nonzero anchor makes that scalar one. A phase-only mutation preserving the tableau is rejected. Thus binary rank equality is never used to discard absolute phase. + +All 408 actual helper roles are grouped by their actual ordered entrance/exit bases. `checks/all_helpers.py` independently checks all 17 endpoint pairs and 34 oriented classes, with both normalizer factors, actual positive Fourier rank and exact phase. No receipt's PASS status is proof. The selected source receipt supplies candidate normalizer coefficients for unchanged classes; those coefficients are freshly checked against the final bases. The separate lineage stage reconstructs the selected PR4470 bases through its exact patches and attributes 382 source-identical helpers plus 26 changed helpers; lineage is provenance, not a substitute for the fresh phase proof. + +Every final paid pair, including owned-center descents, must likewise have a candidate circuit verified against its actual ordered bases in both orientations. The complete paid-phase stage passed on every actual pair in the first cold replay; the master continues to require it on every complete execution. A 105-new-pair receipt alone is insufficient: the final emitted word has 2,855 distinct paid pairs per orientation. Candidate recipe generation can use the pinned source compiler, but acceptance must use the separate independent Clifford checker. Its frozen catalogue is data; its mathematical correctness does not depend on trusting generation. + +`checks/helpers.py` independently follows the complete chronological word over formal rational group-ring rows. All 632 persistent inputs are arbitrary, all 408 helpers are independent, and the owned center initially has its own arbitrary symbol. Every scalar contact has its actual frame, every paid edge its actual rank, and only the owned center may be cleared or overwritten. The completed endpoint is the required main shear and identity on every helper, with the owned center zero. This is a field-level free-group identity, stronger than testing one physical numerical input. It is not permission to erase a borrowed field. + +## 2. Quantified algebraic lift, without distributing tensor power over addition + +Let `V=Q(i)^(F2^9)`. For each positive f use the fixed column-to-axis shuffle J_f and define `Lift_f(A)=J_f A^(tensor f) J_f^-1`. For every additional spectator space S, append its identity operator. This fixes the generated frame and absolute-phase convention rather than asking an unrelated 9f-dimensional canonical-basis routine to make identical choices. + +Tensor power preserves composition, identity, inverse, transpose, adjoint and entrywise conjugation. A source identity `F_V K_j F_U^-1=M` therefore lifts as a **product** identity, including its phase. A signed occurrence -j uses the true phase-bearing inverse; no native homomorphism `K_G K_H=K_GH` is assumed. A source two-sided factorization `L C_r R` lifts to its two lifted monomials and `C_(rf)` after a fixed axis shuffle. Global phases occur once per column, not once per entire lifted array. The rank-zero normalizers remain phase-bearing monomials, even when the two factors are not inverse conjugates. + +The scalar endpoint uses a different argument. The completed formal row certificate is an equality over the rational group algebra of free invertible generators, with backward generators named separately. Substitute each generator by its lifted actual invertible operator. The group-algebra evaluation is additive and multiplicative, so the *same* ADD/SCALE/copy/clear algorithm has the asserted endpoint on every vector in `V_f tensor S`, including nonseparable arrays. This is not the false assertion that `Lift_f(A+B)=Lift_f(A)+Lift_f(B)`. + +The rank histogram consequently relabels r to rf algebraically. `checks/lift.py` supplies f=2,3 phase/shuffle and two-term arbitrary-state controls, including a counterexample showing a genuine one-column relation need not survive tensor substitution. These fixtures corroborate the displayed quantified proof; they do not establish it by extrapolation or price a physical implementation. + +## 3. Specialization of the selected generic realization contract + +The selected assumptions concern a generic fixed finite template, rather than only one numerical list of charts. The source `notes/general-clifford-frames.tex` supplies two-sided monomial normal form for arbitrary nested frames; the source PR4359 and PR4416 reviews retain complete whole-job normalization, fixed-route and finite-template contracts. The final catalogue must be shown to belong to that same class, with no new primitive or stronger oracle. + +The specialization checker/proof must bind every actual borrowed climb, owned-center transport, signed warp, helper residual and scalar instruction to that class. Every actual new monomial must have an invertible binary affine address map and fixed Z4 quadratic phase, with its tensor/spectator extension. It must charge scalar decomposition, address/phase movement, storage and return, not merely label a rank zero. A constant bound on finite primitive records is not a claim of constant literal tape time at arbitrary f. The original selected physical movement/precision assumptions remain the source of those uniform tariffs. + +The detailed source-bound implication is [SPECIALIZATION.md](SPECIALIZATION.md), with executable class/decomposition/tariff checks in `checks/specialization.py`. Gaussian row elimination uses at most 72 XOR additions and eight swaps; expressing each swap as three XORs gives 96 address operations. At most nine translations, 27 unit linear phases, 36 quadratic controlled signs and three global unit phases yield 171 retained primitive records per monomial, or 342 for two adapters, within the retained 1000-record allowance. This is a record-count comparison in the selected physical tariff unit, not 1000 literal tape instructions at arbitrary f. Full dirty-control restoration, descriptor work and actual f-dependent movement retain their source charge. The new expanded template substitutes its own W,P,O,R,G,N into the selected stock/precision bounds. The ideal algebraic identities quantify over every positive f. Physical cost specialization retains the source domain: f<=p, address bound A=O(p), K/log p tending to infinity and the superpolynomial record fiber; in the actual layer f<=e<=floor(b_in^epsilon) and p=6*b_in eventually. It does not extrapolate that physical asymptotic tariff to arbitrary unrelated choices of f,p or record geometry. A claim with a new candidate-specific physical implementation premise would not prove the statement above. + +## 4. Complete productive and paid invoice + +The independent literal census first derives all local costs from actual chronological events and all helper target ranks from strict endpoints. It then independently emits and checks the p16 controller schedule and its scalar boundary programs. Its complete totals are 18 FULL calls, 15 paid thin query shears and 15 complete idle windows, plus diagonal main targets. No removed stage retains productive credit. + +The local paid profile is `{1:2201,2:412,3:510,4:127,5:40,8:8}`. The helper targets are `{4:28,7:7,8:47,9:326}`. Every one of the eight owned rank-eight center jobs remains paid without productive input credit. Complete controller totals are 64,404 paid calls, 10,928 productive fields, target rank mass 239,886, paid rank mass 239,134 and surplus 752. + +The scalar/native-route allowance is derived from actual events and boundary lengths. The fixed local routing groups count all 3,298 local paid jobs, two boundaries for 408 helpers, 240 native warp occurrences and 448 main adapters. Whole-job and normalizer movement is charged under the retained finite record tariff and physical execution contract. Controller-level scalar bounds remain finite fixed constants before input growth; none is an unbounded-cost operation declared free. + +Omitting a center, climb, query, idle, FULL or scalar normalizer changes or invalidates the independent census. These mutations test the semantics, not only a digest match. The arithmetic stage derives the paid difference against selected PR4470, verifies that the productive profile is the same, and verifies the old selected profile fails at the candidate κ. + +## 5. Charged completion, finite compiler and outer transfer + +Two independent standard-library directed interval engines recompute moments and source inequalities from the freshly derived invoice. One uses integer fixed-point atanh/log and exponential series; the other uses directed rational enclosures with a different scale and truncation. Acceptance does not inherit an author's numerical PASS flag. + +The unchanged final raw crossing lies in `(.00302177587077,.00302177587078)`. Admission uses the lower tested saving `.00302177581`, strictly above the claim `.0030217758`. At tensor power 1024 with cutoff 20, productive completion floor 21, tail offset 1/5 and reserve `10^-11`, the check proves alpha below `1-10^-11`, both paid and target-completion tails below `97/100`, and complete normalized cost + +`1/(1+1024*10^-11)+4/2^32 < 1`. + +The added target-completion bill is included. The old `10^-9` reserve fails at this tested saving and is explicitly rejected. Separation `20^64<21^63`, shifted exit capacity, the retained logarithmic majorant and initial range are checked. With outer strict gap `1/700000000000`, the sufficient integer test succeeds at j=55099, H=38,569,300,000,000,000, N=`2^H`; the preceding point on that test grid fails. No expanded uniform word is materialized and no algorithmic minimality beyond that particular sufficient grid is claimed. + +The retained ordinary BIT saving .0034 exceeds the required effective saving. Its source implementation is inherited with its selected coverage, not newly proved by a complex arithmetic test. The final parameters independently satisfy all nine outer cost rows, all 54 strict predicates and all four functional predicates. Closed uniform/epsilon endpoints, insufficient BIT and unfunded target mutations fail. The historical a/(1+a) formula is not used as a universal transfer. + +## 6. Same premises, finite envelopes and limits + +The source selected PR4470 review explicitly permits a new fixed finite scalar/route/storage/normalizer envelope and forbids reusing an old p3 numerical cap. The PR4359/4416 completed-child precision recurrence and symbolic fixed-template envelope provide the inherited form; its constants must be updated to the actual expanded template before multiplication input growth. Source-specific Gaussian conditioning, stock, prime avoidance and exact integer recovery remain in the same selected analytic/physical framework. + +Thus the conditional conclusion requires the finite source semantics, actual class membership, chronological product/completion/splitting and complete invoice verified above. It does not require inventing a new primitive for final helper charts. Conversely finite replays alone do not prove uniform physical realization, a usable practical cutoff, numerical implementation stability or the analytic integer-recovery theorem. Those are precisely the selected conditions, copied without relaxation into CLAIM.json. + +The master preauthenticates every external working file before executing a checker module and rechecks every read and final source stability. It has no historical Git-blob fallback hiding a working mutation. Canonical ancestry is checked separately, and a temporary live-file corruption must fail. Mathematical mutations recompute changed objects rather than weakening their expected hashes. A publication preflight must still establish committed bytes and source-history availability after root commits the completed package. + +## Credit and review status + +Credit Cao Yifan's PR4610, Cinna Davis's selected PR4470 and cumulative native/controller work, Dugongue's transported and physical interfaces, zxv's native/compiler lineage, Jacob Alan Sussman's mixed-target flow, the ordinary BIT contributors and all geometry, Clifford, semantic precision and outer-source authors. New independent integration/checks use substantial OpenAI Codex assistance, Apache-2.0. No independent human or formal-kernel acceptance is claimed. diff --git a/research/coupled-provider-independent-audit/custody/5376/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/joint-helper-lattice/NATIVE.json.gz b/research/coupled-provider-independent-audit/custody/5376/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/joint-helper-lattice/NATIVE.json.gz new file mode 100644 index 0000000000..0910f74138 Binary files /dev/null and b/research/coupled-provider-independent-audit/custody/5376/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/joint-helper-lattice/NATIVE.json.gz differ diff --git a/research/coupled-provider-independent-audit/custody/5376/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/joint-helper-lattice/PROOF.md b/research/coupled-provider-independent-audit/custody/5376/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/joint-helper-lattice/PROOF.md new file mode 100644 index 0000000000..e41106031d --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/joint-helper-lattice/PROOF.md @@ -0,0 +1,102 @@ +# Construction and proof obligations + +## 1. Exact predecessor and changed object + +The input is PR4447 at commit `322e0ec764aa7ef7801383feb1f656e460dd8bed`, with its credited THREE-base native word, PR4441 helper-boundary retiming, and the added three-dimensional frame at B/480. `SOURCES.json` binds all external proof inputs by Git blob and SHA-256. + +There are 632 persistent local fields: 224 main fields and 408 helpers. Each helper is an arbitrary independent input, not initialized scratch. The separate owned center is initialized and erased under the inherited native contract. None of its eight uses receives productive-input credit. + +The patch retains the scalar order and coefficients in each orientation. It retains all native warp events and every main-field boundary. It changes 38 helper entrance frames, 47 helper terminal frames, and 414 scalar contact frames. A source pin accompanies every changed boundary or contact. The two orientations retain their exact inverse-transpose scalar correspondence. + +The optional search jointly optimized both helper boundaries and every mutable scalar contact over the finite intervals of subspaces of F2^9. Fixed main and warp events bound those intervals. The largest quotient dimension was five, so its interval has 374 subspaces. The discovery model used one-hot frame choices and edge marginals, with negative whole-helper credit. Its floating-point solution is a proposal, not a certificate. The following construction and exact tests do not use its claimed optimum. + +## 2. Frame-coordinate invariant + +Let C_F be the source's exact canonical frame operator for subspace F. Interpret a field at frame F as C_F applied to its logical arbitrary value. For nested frames E contained in F, the paid transport is C_F C_E^{-1}. Its Fourier rank is dim(F)-dim(E). The implementation follows the source's `adjoint().then(...)` composition convention and lowers the operator itself, not only that rank formula. + +At each scalar operation, all participating persistent fields are first moved into its declared common frame. A scalar linear combination commutes with the common frame operator. Therefore the operation implements the unchanged logical scalar step. A native warp is run only at its original pinned input frame, and leaves the original pinned output frame. This proves the invariant by induction through the complete chronological word. + +At the end of the word, main fields have their unchanged original endpoints. Helper r has the whole residual C_{T_r} C_{S_r}^{-1}, where S_r and T_r are its new entrance and exit. Every checked S_r is a proper subspace of T_r. Its positive productive rank is dim(T_r)-dim(S_r). There is no duplicate field, discarded helper, clean-input assumption, or free temporary productive input. + +The helper normalizers are recomputed on these whole-job boundaries. Every new transport and each distinct helper boundary is lowered in both orientations with exact Clifford tableaux and absolute phases. The receipt contains 423 distinct transport/boundary pairs, including 406 newly occurring transport pairs relative to PR4447. Two retained literal interpreters check the complete 632-column endpoint. The argument is the frame-coordinate invariant; the finite replay independently checks its application to the submitted circuit. + +## 3. Complete local bill and uniform moment gain + +Write H_r for productive helpers of rank r and P_r for paid jobs of rank r. The predecessor has + + H_old = {4:26, 5:2, 7:29, 8:42, 9:309} + P_old = {1:2254, 2:514, 3:444, 4:103, 5:40, 8:8}. + +The new word has + + H_new = {4:28, 7:7, 8:47, 9:326} + P_new = {1:2237, 2:388, 3:494, 4:147, 5:36, 8:8}. + +There are 408 helpers in both words. The new paid list has 3,310 entries, 53 fewer than the predecessor. Helper rank mass increases from 3,434 to 3,471, and paid rank mass from 5,290 to 5,327. Their difference remains 1,856. In particular, the improvement is not obtained by keeping old productive credit after removing paid work. + +For 0D(1)=0 for every 0 theta^1000, + 145^(1024*TESTED) < 2^1000. + +Set kappa=0.00302015 and d=(TESTED-kappa)/7=1/1,400,000,000. The integer test + + (1,400,000,000*j + 1)^1000 < 2^j + +passes at j=45,868 and fails at j-1. Thus the retained theorem supplies the sufficient uniform rank N=2^64,215,200,000,000. This is an existence construction with explicit finite constants. The resulting word is not materialized and no practical implementation claim follows. + +The new local scalar and fixed-route bound remains below 10^7 per full call. Eighteen such calls, all 15 thin-query charges, every scalar controller and boundary operation fit the complete raw bound 10^9. The number of roles, private storage, coefficient matrices and tapes is finite for the compiled template. Their sizes affect the eventual threshold and are not claimed uniform while changing that template. + +Retain the source BIT ordinary saving 0.0034, with atom exponent 0.004. Its delayed-cover, weighted-child, row-stock and conversion conditions are rechecked through the source package. Use complex uniform saving kappa+6d, followed by b=kappa+5d, a=kappa+4d, q=kappa+3d, epsilon=1-d, beta=1-3d, r0=d/10, stop=d and layout=d. All nine outer cost rows, 54 strict predicates and four functional guards pass exactly. The old BIT cap and closed exponent gaps are explicit rejected controls. + +## 7. Status of the conclusion + +Subject to the retained all-column/native and physical-operation contracts, owned erasure, whole-job matching, finite-template compiler closure, precision and fixed-tape bounds, analytic decomposition, prime avoidance and exact recovery, this construction gives the source framework's conditional multiplication saving kappa=0.00302015. + +The submitted change establishes an exact finite native word and a fully charged conditional parameter transfer. It does not remove the inherited analytic or physical premises. It does not promote the selected frontier, certify global optimality, claim a runtime speedup, or claim independent human or proof-assistant acceptance. + +Credits: zxv's native and higher-moment/logarithmic work; Jacob Alan Sussman's finite mixed-flow theorem; Cinna Davis's prior p7 padding, query-thinned and retimed constructions; and the unchanged credited scalar, Clifford, geometry and outer-ledger sources. New material was prepared for Cinna Davis with substantial OpenAI assistance, Apache-2.0. diff --git a/research/coupled-provider-independent-audit/custody/5376/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz b/research/coupled-provider-independent-audit/custody/5376/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz new file mode 100644 index 0000000000..46d929df83 Binary files /dev/null and b/research/coupled-provider-independent-audit/custody/5376/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz differ diff --git a/research/coupled-provider-independent-audit/custody/5376/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz b/research/coupled-provider-independent-audit/custody/5376/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz new file mode 100644 index 0000000000..ac77b78547 Binary files /dev/null and b/research/coupled-provider-independent-audit/custody/5376/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz differ diff --git a/research/coupled-provider-independent-audit/custody/5376/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/kappa-round3-warp-20261022/PROOF.md b/research/coupled-provider-independent-audit/custody/5376/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/kappa-round3-warp-20261022/PROOF.md new file mode 100644 index 0000000000..97f1d19ad4 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/kappa-round3-warp-20261022/PROOF.md @@ -0,0 +1,69 @@ +# Construction and scope of the new invoice + +Let `F_U` denote the canonical nine-coordinate frame attached to an explicit +binary subspace U. A scalar contact is conjugated by the same frame at every +persistent role it touches. A paid frame change U (3^t + 5^t)/2, +P0(t) - P1(t) = 4 * (2*4^t - 3^t - 5^t) > 0. +``` + +The productive moment is identical because the helper rank census is identical, +despite 26 distinct helper operators changing their input charts. The retained +p16 controller invokes the local supplier eighteen times. Thus its complete +paid moment decreases by 72 times the bracketed expression. Every retained +query-shear, idle, diagonal and completion bill is still required. The companion +round-three whole-profile package rebuilds those terms, tensor tail/completion, +the uniform compiler and outer inequalities at the stated new kappa. + +Discovery uses a contact graph with scalar nodes and native-map edges. For the +twelve operators with extra prelude occurrences, a fixed line a must map to b +as well as the late input subspace A mapping into the next cap B. Feasibility +requires equal membership of a and b in the selected equal-dimensional source +and target subspaces. `constrained_map.py` constructs and checks the complete +invertible map on all 512 inputs. In the admitted witness all twelve prelude +operators retain their old G; the actual changes affect twenty other maps. + +The mathematical certificate trusts neither solver optimality nor floating +objective values. `regenerate.py` authenticates the exact predecessor and +reconstructs the frozen word by guarded edits. `verify_candidate.py` checks its +native identities and full invoice through two retained interpreters. +`phase_check.py` checks exact Clifford lowering, including absolute phases of +all changed data. Lean verification and numerical/outer certification are stated +with their own scoped coverage in the companion package. None alone is a +formal proof of the full integer-multiplication theorem. + +Prepared by Cao Yifan, with substantial OpenAI Codex assistance. Apache-2.0. diff --git a/research/coupled-provider-independent-audit/custody/5376/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/t74-native-fast/vendor/native/new/code/borrow/bw_adapters.py b/research/coupled-provider-independent-audit/custody/5376/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/t74-native-fast/vendor/native/new/code/borrow/bw_adapters.py new file mode 100644 index 0000000000..82beaa9c1d --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/t74-native-fast/vendor/native/new/code/borrow/bw_adapters.py @@ -0,0 +1,165 @@ +"""Paid residual wrappers for entering helpers (Lemma A): generation and independent decoding. Apache-2.0. +Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. The wrapper construction follows PR #458 +(chafreaky): a helper that starts at frame E and ends at FULL has the physical residual S_E = T_FULL T_E^-1 (apply T_E^-1 first); +S_E = L_E (C_[w] x I) R_E with R_E applied first; the wrappers R_E^-1 before the whole local invocation and L_E^-1 after its +full-frame cleanup turn the residual into the coordinate factor C_[w] x I and restore the other 9 - w coordinates identically. +usage: adapters_gk.py CANONICAL-WORD.json.gz RESIDUAL-ADAPTERS.json OUT-LEMMA-A.json +Writes the recipes (generation uses clifford_exact.lower_child) and then DECODES the serialized monomials with the primitive +constructors of clifford_exact (not lower_child) and checks, for every entrance frame, that L_E^-1 S_E R_E^-1 has exactly the +tableau and zero-state vector (global phase included) of fourier(9, range(w)); mutated recipes (wrong phase, swapped sides, wrong +translation, wrong width) must be rejected.""" +if not __debug__: + raise RuntimeError('assertions must remain enabled') # every check of this stage is an assert +import copy, gzip, json, sys +from pathlib import Path +# Package-path adaptation only; the exact wrapper mathematics is unchanged. +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE / 'vendor/clifford')) # BW: the pinned vendor531 clifford_exact (byte copy) +sys.path.insert(0, str(HERE)) +from clifford_exact import canonical_frame, lower_child, fourier, diag, perm, xgate, Op, identity, transpose, inv, parity, monomial as mono_of, mv +import bw_gauss +n = 9; FULL = tuple(1 << i for i in range(n)) +def monomial_op(rec): + """decode a serialized monomial (matrix rows, quadratic rows, Z4 linear part, translation, phase)""" + out = diag(n, tuple(rec['quadratic_rows']), tuple(rec['linear_Z4'])).then(perm(n, tuple(rec['matrix_rows']))).then(xgate(n, rec['offset'])) + return out.then(Op(n, identity(n), [('phase', rec['phase'])])) +def S_of(U, END=FULL): + # HPE: a helper that starts at E=U and ends at END has residual T_END T_E^-1 (END = FULL is the inherited case) + return canonical_frame(n, tuple(U)).adjoint().then(canonical_frame(n, tuple(END))) +def wrapped_ok(U, rec, END=FULL): + """exactly: L^-1 S R^-1 = C_[w] x I (apply order: R^-1, S, L^-1), w = dim END - dim E""" + w = len(END) - len(U); S = S_of(U, END); Rm = monomial_op(rec['right']); Lm = monomial_op(rec['left']) + net = Rm.adjoint().then(S).then(Lm.adjoint()); target = fourier(n, range(w)) + return rec['rank'] == w and net.tab == target.tab and net.zero_state() == target.zero_state() +def _contains(a, b): + a = list(a) + for x in b: + for y in sorted(a, reverse=True): + if x >> (y.bit_length() - 1) & 1: x ^= y + if x: return False + return True +def Kop(G_cols): + """BW: K_G = perm(G) then diag(Q), Q = I + G^-T G^-1: PR2226's monomial() and the conjugator inside clifford_exact.canonical_frame.""" + G = transpose(tuple(G_cols), n); gi = inv(G, n) + Q = tuple((1 << i) ^ sum(parity(gi_i & gi_j) << j for j, gi_j in enumerate(transpose(gi, n))) for i, gi_i in enumerate(transpose(gi, n))) + return perm(n, G).then(diag(n, Q)) +def numeric_K(G_cols): + import numpy as np + pv, ph = bw_gauss.monomial(list(G_cols), n) + N = 1 << n; re = np.zeros((N, N), dtype=np.int64); im = np.zeros((N, N), dtype=np.int64) + unit = [(1, 0), (0, 1), (-1, 0), (0, -1)] + for x in range(N): re[pv[x], x], im[pv[x], x] = unit[ph[x]] + return re, im, 0 +def warp_ok(G_cols, rec): + """BW: the serialized monomial equals PR2226's exact numpy K_G on all 512 columns (indep. decode) and its op decodes to K_G exactly.""" + m = bw_gauss.recipe_matrix(rec, n) + if not bw_gauss.equal_scaled(numeric_K(G_cols), m): return False + dec = monomial_op(rec); ref = Kop(G_cols) + return dec.tab == ref.tab and dec.zero_state() == ref.zero_state() + +def main(): + c = json.load(gzip.open(sys.argv[1])); frames = c['frames']; v = c['v'] + starts = sorted({c['start'][r] for r in range(2 * v, len(c['start'])) if c['start'][r] != 0 and c['final'][r] == 1}) + # HPE: (entrance, terminal) pairs of helpers ending at a proper subspace; key 'E:U'. Inherited words have none. + ends = sorted({(c['start'][r], c['final'][r]) for r in range(2 * v, len(c['start'])) if c['final'][r] != 1}) + # COLD-HPE: e == 0 (a cold helper, entrance = bottom, T_0 = I) is allowed: the (0, U) recipe is keyed '0:U' + assert all(len(frames[u]) < n and _contains(frames[u], frames[e]) for e, u in ends) + cold_ends = [(e, u) for e, u in ends if e == 0] + recipes = {} + for f in starts: + U = frames[f]; rec, compiled = lower_child(S_of(U)) + recipes[str(f)] = dict(frame=f, vectors=list(U), entrance_rank=len(U), rank=rec['rank'], left=rec['left'], right=rec['right']) + for e, u in ends: + E, U = frames[e], frames[u]; rec, compiled = lower_child(S_of(E, U)) + recipes['%d:%d' % (e, u)] = dict(frame=e, terminal=u, vectors=list(E), terminal_vectors=list(U), entrance_rank=len(E), + terminal_rank=len(U), rank=rec['rank'], left=rec['left'], right=rec['right']) + # BW: monomial recipes of the warps K_G (anticipatory dirty borrowing, PR2226): one per operator, serialized like a wrapper monomial + warp_recipes = {} + for w in c.get('warps', []): + _, rec_k = mono_of(Kop(w['G_columns'])) + warp_recipes[str(w['op'])] = dict(op=w['op'], from_frame=w['from_frame'], to_frame=w['to_frame'], G_columns=list(w['G_columns']), K=rec_k) + Path(sys.argv[2]).write_text(json.dumps(dict(status='RESIDUAL_ADAPTER_RECIPES', recipes=recipes, warps=warp_recipes), sort_keys=True, separators=(',', ':')) + '\n') + # ---- independent decode of the serialized file + data_all = json.loads(Path(sys.argv[2]).read_text()); data = data_all['recipes'] + dot = lambda a, b: bin(a & b).count('1') & 1 + detail = [] + for f in starts: + rec = data[str(f)]; U = frames[f] + assert wrapped_ok(U, rec), ('wrapper product is not C_[w] x I', f) + detail.append(dict(frame=f, entrance_rank=len(U), residual_width=n - len(U), vectors=list(U), all_even_weight=all(bin(x).count('1') % 2 == 0 for x in U), + totally_isotropic=all(dot(a, b) == 0 for a in U for b in U))) + hdetail = [] + for e, u in ends: # HPE: independent decode, residual width = dim U - dim E + rec = data['%d:%d' % (e, u)]; E, U = frames[e], frames[u] + assert wrapped_ok(E, rec, U), ('HPE wrapper product is not C_[w] x I', e, u) + hdetail.append(dict(frame=e, terminal=u, entrance_rank=len(E), terminal_rank=len(U), residual_width=len(U) - len(E))) + controls = [] + def reject(name, fn): + f = starts[0]; rec = copy.deepcopy(data[str(f)]); fn(rec) + if wrapped_ok(frames[f], rec): raise AssertionError('mutated wrapper accepted: ' + name) + controls.append(name) + reject('wrong global phase', lambda r: r['right'].__setitem__('phase', (r['right']['phase'] + 1) % 4)) + reject('wrong translation', lambda r: r['left'].__setitem__('offset', r['left']['offset'] ^ 1)) + reject('wrong quadratic form', lambda r: r['right'].__setitem__('quadratic_rows', [x ^ 2 if i == 0 else x for i, x in enumerate(r['right']['quadratic_rows'])]) if False else r['right']['linear_Z4'].__setitem__(0, (r['right']['linear_Z4'][0] + 2) % 4)) + reject('sides swapped', lambda r: (r.__setitem__('left', r['right']), r.__setitem__('right', r['left']))) + reject('wrong width', lambda r: r.__setitem__('rank', r['rank'] + 1)) + if ends: # HPE controls on the first (E, U) pair + e, u = next((p for p in ends if p[0] != 0), ends[0]); rec0 = data['%d:%d' % (e, u)] # COLD-HPE: an entering pair if any (= ends[0] without cold ends) + def hreject(name, ok): + if ok: raise AssertionError('HPE mutation accepted: ' + name) + controls.append(name) + hreject('hpe: U-wrapper decoded against a FULL ending', wrapped_ok(frames[e], rec0)) + hreject('hpe: width misreported as 9 - dim E', wrapped_ok(frames[e], dict(rec0, rank=n - len(frames[e])), frames[u])) + other = next(f for f in range(len(frames)) if f != u and len(frames[f]) == len(frames[u]) and _contains(frames[f], frames[e])) + hreject('hpe: wrong terminal hyperplane', wrapped_ok(frames[e], rec0, frames[other])) + fe = next(((e2, u2) for e2, u2 in ends if str(e2) in data), None) + if fe: # an entrance shared with FULL-ended helpers: R_{E,FULL} must not serve as R_{E,U} + r2 = data['%d:%d' % fe] + hreject('hpe: pre wrapper resolved to the FULL recipe R_{E,FULL}', wrapped_ok(frames[fe[0]], dict(r2, right=data[str(fe[0])]['right']), frames[fe[1]])) + hreject('hpe: wrong global phase', wrapped_ok(frames[e], dict(rec0, left=dict(rec0['left'], phase=(rec0['left']['phase'] + 1) % 4)), frames[u])) + if cold_ends: # COLD-HPE controls on the first cold pair (0, U): factor_iff_pre says only R_{0,U} itself may precede + e, u = cold_ends[0]; recc = data['%d:%d' % (e, u)]; E, U = frames[e], frames[u] + ID = dict(matrix_rows=[1 << i for i in range(n)], offset=0, quadratic_rows=[0] * n, linear_Z4=[0] * n, phase=0) + assert monomial_op(ID).tab == identity(n) # the control's wrapper really is the identity + def creject(name, ok): + if ok: raise AssertionError('cold HPE mutation accepted: ' + name) + controls.append(name) + creject('cold hpe: identity pre wrapper instead of R_{0,U}', wrapped_ok(E, dict(recc, right=ID), U)) + creject('cold hpe: identity post wrapper instead of L_{0,U}', wrapped_ok(E, dict(recc, left=ID), U)) + creject('cold hpe: no wrappers (cold FULL convention L = R = I)', wrapped_ok(E, dict(recc, left=ID, right=ID), U)) + creject('cold hpe: U-wrapper decoded against a FULL ending', wrapped_ok(E, recc)) + creject('cold hpe: width misreported as 9', wrapped_ok(E, dict(recc, rank=n), U)) + other = next(f for f in range(len(frames)) if f != u and len(frames[f]) == len(frames[u])) + creject('cold hpe: wrong terminal hyperplane', wrapped_ok(E, recc, frames[other])) + creject('cold hpe: wrong global phase', wrapped_ok(E, dict(recc, right=dict(recc['right'], phase=(recc['right']['phase'] + 1) % 4)), U)) + ent = next((p for p in ends if p[0] != 0 and p[1] == u), None) + same = lambda x, y: monomial_op(x).tab == monomial_op(y).tab and monomial_op(x).zero_state() == monomial_op(y).zero_state() + if ent and not same(data['%d:%d' % ent]['right'], recc['right']): # an entering helper ending at the same U: its R_{E,U} must not serve as R_{0,U} + creject('cold hpe: pre wrapper resolved to an entering recipe R_{E,U}', wrapped_ok(E, dict(recc, right=data['%d:%d' % ent]['right']), U)) + wdetail = [] + for w in c.get('warps', []): # BW: independent decode of every warp recipe, then mutation controls on the first warp + rec = data_all['warps'][str(w['op'])] + assert rec['G_columns'] == w['G_columns'] + assert warp_ok(w['G_columns'], rec['K']), ('warp recipe differs from the exact monomial K_G', w['op']) + wdetail.append(dict(op=w['op'], from_frame=w['from_frame'], to_frame=w['to_frame'], columns_checked=1 << n)) + if c.get('warps'): + w0 = c['warps'][0]; k0 = data_all['warps'][str(w0['op'])]['K'] + def wreject(name, ok): + if ok: raise AssertionError('warp mutation accepted: ' + name) + controls.append(name) + wreject('warp: wrong global phase', warp_ok(w0['G_columns'], dict(k0, phase=(k0['phase'] + 1) % 4))) + wreject('warp: wrong translation', warp_ok(w0['G_columns'], dict(k0, offset=k0['offset'] ^ 1))) + wreject('warp: wrong linear phase', warp_ok(w0['G_columns'], dict(k0, linear_Z4=[(k0['linear_Z4'][0] + 2) % 4] + k0['linear_Z4'][1:]))) + wreject('warp: wrong quadratic form', warp_ok(w0['G_columns'], dict(k0, quadratic_rows=[k0['quadratic_rows'][0] ^ 2, k0['quadratic_rows'][1] ^ 1] + k0['quadratic_rows'][2:]))) + wreject('warp: recipe of another operator', warp_ok(w0['G_columns'], data_all['warps'][str(c['warps'][1]['op'])]['K'])) + wreject('warp: inverse recipe used as the warp', warp_ok(w0['G_columns'], mono_of(Kop(w0['G_columns']).adjoint())[1])) + G2 = list(w0['G_columns']); G2[0] ^= G2[1] + wreject('warp: wrong G (frame-changed column)', warp_ok(G2, k0)) + sing = list(w0['G_columns']); sing[1] = sing[0] + try: Kop(sing); raise SystemExit('non-invertible G accepted') + except (AssertionError, StopIteration, ValueError): controls.append('warp: non-invertible G') + res = dict(status='PASS_RESIDUAL_WRAPPERS_ARE_EXACT', frames=len(detail), **({'hyperplane_end_pairs': hdetail} if ends else {}), **({'cold_hyperplane_end_pairs': len(cold_ends)} if cold_ends else {}), wrappers_reject=controls, all_even_weight=all(d['all_even_weight'] for d in detail), **({'warp_recipes_exact_on_all_512_columns': wdetail} if wdetail else {}), + all_totally_isotropic=all(d['totally_isotropic'] for d in detail), detail=detail) + Path(sys.argv[3]).write_text(json.dumps(res, indent=1) + '\n') + print('Lemma A (exact): L^-1 S_E R^-1 = C_[w] x I for', len(detail), 'entrance frames, global phase included;', len(controls), 'wrapper mutations rejected; all-even-weight:', res['all_even_weight']) +if __name__ == '__main__': main() diff --git a/research/coupled-provider-independent-audit/custody/5376/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/t74-native-fast/vendor/native/new/code/borrow/bw_phases.py b/research/coupled-provider-independent-audit/custody/5376/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/t74-native-fast/vendor/native/new/code/borrow/bw_phases.py new file mode 100644 index 0000000000..99f351785e --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/t74-native-fast/vendor/native/new/code/borrow/bw_phases.py @@ -0,0 +1,59 @@ +# Warp-aware copy of phases_full.py (PR425 / icekylinx with Codex assistance, heterogeneous centres). +# BW: exact lowering of every anticipatory-dirty-borrowing warp (PR2226, Cinna Davis @1337isnot1337, with OpenAI Codex assistance): +# each distinct physical warp product T_to K_G^{+-1} T_from^-1 is lowered with the unchanged lower_child and must have rank ZERO +# (a monomial Clifford); its serialized monomial is then compared with an independent exact numpy column product on all 512 columns. +"""Exact phase-aware lowering of every used edge of a BORROW canonical word, warps included. usage: bw_phases.py OUT_DIR""" +if not __debug__: + raise RuntimeError('assertions must remain enabled') # every check of this stage is an assert +import gzip,hashlib,json,sys,time +from collections import Counter +from pathlib import Path +HERE=Path(__file__).resolve().parent +sys.path.insert(0,str(HERE/'vendor/clifford'));sys.path.insert(0,str(HERE)) +from clifford_exact import * +import bw_gauss +from bw_adapters import Kop + +OUT=Path(sys.argv[1]);P=OUT/'CANONICAL-WORD.json.gz' +c=json.load(gzip.open(P));n=c['h'];frames=c['frames'];start=time.monotonic();ops=[] +for U in frames: + op=canonical_frame(n,U) + L=[u|(u<0 else K.adjoint() + op=ops[f0].adjoint().then(Ks).then(ops[f1]);rec,compiled=lower_child(op) + assert rec['rank']==0 and rec['right'] is None,('warp is not a monomial Clifford',sign,op_id,f0,f1) + Z=bw_gauss.warp_product(G,frames[f0],frames[f1],sign*op_id,n) + assert bw_gauss.equal_scaled(Z,bw_gauss.recipe_matrix(rec['left'],n)),('recipe differs from the exact column product',sign,op_id,f0,f1) + hist['warp']+=1;warps.append({'sign':sign,'op':op_id,'old':f0,'new':f1,'G_columns':G,**rec}) +raw=json.dumps({'children':recipes,'endpoint_adapters':adapters,'warps':warps},sort_keys=True,separators=(',',':')).encode() +(OUT/'CLIFFORD-RECIPES.json').write_bytes(raw) +result={'status':'PASS_NEW_WORD_EXACT_LOCAL_PHASE_RECIPES', + 'canonical_word_sha256':hashlib.sha256(P.read_bytes()).hexdigest(), + 'frames':len(frames),'directed_edges':len(edges),'ranks':{str(k):x for k,x in hist.items()}, + 'endpoint_adapters':len(adapters),'warp_recipes':len(warps),'warp_recipes_rank_zero':all(w['rank']==0 for w in warps), + 'warp_recipes_equal_exact_512_column_product':True, + 'all_child_equalities_include_global_phase':True, + 'recipe_sha256':hashlib.sha256(raw).hexdigest(),'seconds':time.monotonic()-start, + 'scope':'Every local frame, centre transition and warp. Expanded scalar-interface integration and global emitted program are separate obligations.'} +(OUT/'CLIFFORD-REVIEW.json').write_text(json.dumps(result,indent=2)+'\n') +print('PASS exact local phases',result['seconds'],'seconds',flush=True) diff --git a/research/coupled-provider-independent-audit/custody/5376/provenance-sources/7c472563474e60185e6ca101a17622133d047e56/certificates/selected-result.json b/research/coupled-provider-independent-audit/custody/5376/provenance-sources/7c472563474e60185e6ca101a17622133d047e56/certificates/selected-result.json new file mode 100644 index 0000000000..c35482cd90 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/provenance-sources/7c472563474e60185e6ca101a17622133d047e56/certificates/selected-result.json @@ -0,0 +1,85 @@ +{ + "status": "Selected maintainer-reviewed conditional joint-helper construction; source-bound foundation reuse is explicit", + "kappa": "60403/20000000", + "decimal": "0.00302015", + "source_prs": [ + 4470, + 4447, + 4441, + 4440, + 4416, + 4433, + 4359, + 4268, + 3945, + 4085, + 2979, + 4076, + 4088, + 1673, + 1758, + 1786, + 23, + 555, + 589 + ], + "source_manifest": "certificates/frontier4470-source.json", + "certificate": "certificates/frontier4470/CLAIM.json", + "certificate_sha256": "d962932a6971b8f0054462c59f4ad699dcf3d1fbf886e1f856a6fa9e97491232", + "proof": "docs/research/pr-intake-evidence/pr4470/PROOF-REVIEW.md", + "proof_supplements": { + "notes/batched-bit-rows.tex": "ef72c0ead19373cbc19c8a3aacb44dd0f75353ee5f4d055f775a986a4878022c", + "notes/batched-complex-rows.tex": "64c70926a8705874f1c9b42a2f703e42cad4e90f927f544458cfdf729540236c", + "notes/compact-control-movement.tex": "b963c3d2f4e1b7059aa289bb4b4ac89b688920bcf42f5b20d7698cdef0132cc6", + "notes/general-clifford-frames.tex": "c9bb9655b594583c6b4bab8cb485233f1d1e588f83858cf1e4c3530cee8fed54", + "notes/stopped-product-complex.tex": "4738089103a4b263b3b0ef458f5ef35519c696f1ea871ae79e508d3720f5870a", + "notes/three-stage-cover-bit.tex": "47123a756f823c83a0d48cca2bf5add6472cd88410b13aed345e70c8834fb511", + "notes/three-stage-cover-rows.tex": "6ad97a5cd7d6aecf978a81226e1c2763d37840caca130c61f3bf5c4ac111c5c8", + "references/semantic-bulk/pr23/semantic-bulk-17-note.tex": "652242b05174bb776ffc6165af170df9c8cf220dbd0fc26c24d778f320dbabc8", + "research/e8-bit-carrier-skeleton/code/bit/export_records.py": "8a5999601f917dbb492bb9ae9a344611f18cc7cedc53dc3c76496a369e530eb3", + "research/e8-bit-carrier-skeleton/code/nine/geometry.py": "36eeda3184bd009e89462b65c8725d10860c444f8da8f1f87e5f6e50120011ca", + "research/e8-bit-p111-tuned/code/gen_p3.py": "438b83f10d70ceca7cf78049420204b7de2dc61682f913c50a62596106ad84cd", + "research/e8-bit-p111-tuned/code/xcheck_p.py": "af3decc877e27c00001cf56f50c6c09566e8e101297ab34c7860aed96a06d80e", + "research/e8-bit-p111-tuned/tune/EXPECTED.json": "b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4", + "research/e8-bit-p111-tuned/tune/apply.py": "806ae4cb2648e4f05dcf56bd089891fd3ba33a6ee5fe76d3329e322c6770c1a1", + "research/e8-bit-p111-tuned/tune/wlib.py": "a37fdf3cdf5f62945c2a90193401c0e9edc9dd3cda8d8cb36a3b9c329ebe4dbc", + "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962", + "docs/research/pr-intake-evidence/pr4359/PROOF-REVIEW.md": "7d67bb814285f7634029fbd378c6457156545f0b38858cc1c6ec34b68cd9d162", + "docs/research/pr-intake-evidence/pr4470/PROOF-REVIEW.md": "5c111dd56beb53dc44ab727d96e1af03aaf50f3023d4342e2b0a89ede6cf585b", + "docs/research/pr-intake-evidence/pr4416/PROOF-REVIEW.md": "2c2bbe6fe1bab44778192118f27e59a0d23dbe02c47aa8a42845093f1ce46f49" + }, + "review": "docs/research/pr-intake-evidence/pr4470/PROOF-REVIEW.md", + "validation": "docs/research/pr-intake-evidence/pr4470/VALIDATION.json", + "integration": "docs/research/pr-intake-evidence/pr4470/INTEGRATION.json", + "reproduce": "make frontier4470-verify", + "scope": "Maintainer-reviewed conditional PR4470 construction. Inherited native/all-column, owned-erasure, whole-job, compiler, precision/tape, analytic, prime and recovery hypotheses remain. Uniform words are not materialized.", + "previous_kappa": "23/10000", + "previous_record": "certificates/checkpoints/frontier4359.json", + "audited_source_head": "b9a13c1673e0e9697de410de16e8bbf3207a7363", + "source_certificate": "research/joint-helper-lattice/RESULT.json", + "source_certificate_sha256": "c7b2388f6511c19976b337d8c8ac374610af616866a249d75dace704eb5d9e21", + "replay_mode": "fresh changed-construction replay with exact-source prior foundation review reuse", + "contributors": "docs/research/community-joint4470-contributors.md", + "assumptions": [ + { + "id": "native_all_columns", + "statement": "Retained native operators, phase conventions, spectators and whole-job adapters work at every positive column multiplicity." + }, + { + "id": "owned_erasure", + "statement": "Owned streams and suspended centers obey the retained allocation, erasure and ownership contracts." + }, + { + "id": "compiler", + "statement": "The finite mixed-target compiler and chronological product, completion and splitting satisfy the retained uniform closure contract." + }, + { + "id": "precision_tape", + "statement": "Retained fixed-tape movement and precision/storage prescriptions apply to the new fixed finite template." + }, + { + "id": "analytic_recovery", + "statement": "Analytic decomposition, fine-prime avoidance and exact integer recovery follow the retained upstream/outer framework." + } + ] +} diff --git a/research/coupled-provider-independent-audit/custody/5376/provenance-sources/7c472563474e60185e6ca101a17622133d047e56/docs/research/agent-task-catalog.json b/research/coupled-provider-independent-audit/custody/5376/provenance-sources/7c472563474e60185e6ca101a17622133d047e56/docs/research/agent-task-catalog.json new file mode 100644 index 0000000000..f126dd2e2d --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/provenance-sources/7c472563474e60185e6ca101a17622133d047e56/docs/research/agent-task-catalog.json @@ -0,0 +1,1242 @@ +{ + "schema_version": 1, + "priority_revision": 7, + "priority_log": "docs/research/research-priority-log.md", + "assessed_on": "2026-10-20", + "status": "Research suggestions, not reservations or assertions that these questions are unclaimed. Check current main and live PRs.", + "tracks": [ + { + "id": "bit-mechanisms", + "weight": 20, + "tasks": [ + { + "id": "bit-helper-contract", + "question": "Can one precisely specified helper-mixing word satisfy a replacement for the inherited H2/K interface?", + "starting_points": [ + "docs/research/research-family-status.md", + "research/r439-bsection-stars-seed01/README.md", + "research/r439-copy-path-sharing-barrier/README.md" + ], + "methods": [ + "Derive a replacement interface lemma and price its implementation.", + "Seek an exact dirty-input or chronological-cut counterexample to the proposed replacement." + ], + "acceptance_gate": "A full boundary contract and paid profile; unchanged scalar counts alone are insufficient. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "research/r439-bsection-stars-seed01/verify.py" + ], + "expected": "PASS_R439_BSECTION_STARS", + "inspect": "Compare the two false H2/K flags with the unchanged paid profile in its README.", + "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay." + }, + "first_experiment": "Write one replacement H2/K implication for a single helper-star operation, then try to falsify it on dirty inputs.", + "bottleneck_link": "A legitimate replacement could admit a cheaper bit circuit; scalar savings alone do not alter the selected moment.", + "allowed_variations": [ + "Choose one helper-star or quartet instance; narrow to one boundary implication." + ], + "scope_change_triggers": [ + "Changing only source count or scalar addition count without an interface argument." + ], + "overlap_terms": [ + "H2_D_frame0_targets_from_helpers", + "K_equals_D", + "helper-star" + ] + }, + { + "id": "bit-new-register-model", + "question": "Can an explicitly larger or nonabelian register model escape the scoped three-register obstruction?", + "starting_points": [ + "docs/research/research-family-status.md", + "research/bit-three-register-lower-bound/README.md", + "certificates/selected-result.json", + "research/bit-gl3-mixed-targets-length10/README.md", + "docs/research/community-efficient1000-review.md" + ], + "methods": [ + "Construct the smallest exact identity in a newly specified legal operation alphabet.", + "Derive a target-specific relaxation bound for that same explicit alphabet." + ], + "acceptance_gate": "Name the changed hypothesis, all counted roles and a uniform identity; finite column tests alone do not certify it. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read Model section 1 of the three-register bound and identify the exact excluded free operations.", + "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay." + }, + "first_experiment": "First compare the alphabet, role count and length with the fully replayed #1974 census and #2027 mixed-root tariff. Identify a changed premise and a legal native implementation; then price one smallest completed instance before searching larger words.", + "bottleneck_link": "A small-width completed saving changes the bit primitive; a finite-address identity alone is insufficient.", + "allowed_variations": [ + "Choose a fixed larger register count or a specified nonabelian operation family." + ], + "scope_change_triggers": [ + "Remaining inside the already-excluded three-register abelian model.", + "Repeating the two-register GL3 census or a covered three-register length without changing a hypothesis; a formal group-algebra word without native conversion is a partial result." + ], + "overlap_terms": [ + "three-register", + "nonabelian", + "group algebra" + ] + }, + { + "id": "r437-carrier-integration", + "question": "Can the paid R437 two-window carrier improvement be admitted by the actual pooled compiler and physical caller?", + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/r437-two-window-carrier/README.md", + "research/r437-reverse-row-coefficient/README.md" + ], + "methods": [ + "Close one compiler/request, caller or precision/stock implication for the pinned paid exchange.", + "Falsify that exact interface with an arbitrary-dirty-state or chronology counterexample." + ], + "acceptance_gate": "Pin the complete source and destination contracts, exact paid and scalar deltas, and all remaining assumptions. A local moment gain is not a physical or all-size supplier admission.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read #4067 paid profile and open integration obligations; #4147 covers the reverse row coefficient. Three additional ADDs per call and all helpers remain charged. This is not a selected supplier.", + "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately." + }, + "first_experiment": "Choose one unclaimed obligation: pooled compiler codebook/request alignment, actual physical caller, or precision/stock envelope using the already reported reverse coefficient. Pin the input and receiver, preserve dirty/source windows, and test one binding with a rejection control. Stop at unresolved dependencies; do not rederive the coefficient or quote the local moment as a completed bound.", + "bottleneck_link": "The exchange changes the paid profile; integration must establish that its gain survives the complete caller.", + "allowed_variations": [ + "One compiler rebind, one actual caller boundary, or one precision/stock implication." + ], + "scope_change_triggers": [ + "Ignoring added ADDs, retaining an obsolete reverse coefficient, or declaring global admission from the local histogram." + ], + "overlap_terms": [ + "R437", + "two-window carrier", + "4067", + "4147", + "pooled compiler", + "request alignment", + "reverse row coefficient" + ], + "existing_checks": [ + { + "scope": "PR #4067: source-bound two-window carrier with (2,2) to (1,3) paid exchange and fixed OQ4 host.", + "evidence": "research/r437-two-window-carrier/README.md", + "remaining": "Pooled compiler/request rebind, physical caller and precision/stock admission.", + "status": "author-checked", + "source_commit": "a95f11c52e3ca1e4c5171b3c20d8f4b0815aee2e", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4147: reverse row coefficient follow-up.", + "evidence": "research/r437-reverse-row-coefficient/README.md", + "remaining": "Use the exact coefficient in a caller-bound precision/stock proof rather than repeat the arithmetic.", + "status": "author-checked", + "source_commit": "72e7bb797adf82aeb525a399f56ab8adbab8e93c", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + } + ] + }, + { + "id": "complex-mechanisms", + "weight": 20, + "tasks": [ + { + "id": "p104-side-correction", + "question": "Can a changed P104 producer/consumer contract escape the scoped slot, chart and completion obstructions with a favorable full bill?", + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/p104-literal-slot-defect/README.md", + "research/p104-uniform-commutation-gap/README.md", + "research/p104-uniform-encoding-gap/README.md", + "research/p104-source-chart-shortcut/README.md", + "research/p104-fiber-tag-seam/README.md" + ], + "methods": [ + "Construct one side-correction word at an explicit chronological cut with the needed frames still available.", + "Derive a lower bound on the side correction and hosting costs that decides whether this channel can beat the selected budget." + ], + "acceptance_gate": "An exact arbitrary-input identity, source/target frame availability and restoration at the chosen cut, plus the complete channel+correction+idle/hosting bill or an explicit favorable bound. The native channel alone is not a supplier. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read the named successor obstructions before extending #2981 static flags. Distinguish literal-slot action, commutation, uniform encoding, source-chart shortcut and fiber-tag seam scopes; none excludes all P104 mechanisms.", + "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately." + }, + "first_experiment": "Name one hypothesis changed from these exact interfaces. Write a literal producer-to-consumer timeline and an arbitrary-dirty-input positive/control pair, then charge acquisition, coefficients, completion, hosting and restoration. Stop if the same slot/fiber mismatch persists or the favorable full budget already fails. A scoped independent audit remains useful; another static count is not a new completion.", + "bottleneck_link": "Completing an already realized changed channel tests a concrete construction opportunity, instead of refining the incumbent packing. A positive local result still needs global and all-size admission.", + "allowed_variations": [ + "One correction factorization, one chronological cut, or one explicit hosting obstruction.", + "A changed correction schedule with an updated full bill and native frame contract." + ], + "scope_change_triggers": [ + "Recompiling the already certified low-rank channel without closing a new obligation.", + "Treating a pending ancestor, local histogram or unpriced side correction as an admitted global supplier.", + "Repeating a correction or physical conversion already supplied by a pending follow-up without adding independent coverage or a different unresolved obligation.", + "Repeating the 208-flag static matching or calling a static nested cover a chronological correction program. Independent audit of that certificate is distinct and remains useful.", + "Repeating a static cover, source-chart shortcut or fiber-tag seam without changing the hypothesis responsible for its obstruction." + ], + "overlap_terms": [ + "P104", + "I-G/2", + "side correction", + "native channel", + "1972", + "1991", + "2586", + "endpoint transport", + "physical dual", + "relay composition", + "2981", + "joint unit flags", + "acquisition delivery", + "static nesting", + "4133", + "4136", + "4140", + "4153", + "4154", + "p104-literal-slot-defect", + "p104-uniform-commutation-gap", + "p104-uniform-encoding-gap", + "p104-source-chart-shortcut", + "p104-fiber-tag-seam" + ], + "existing_checks": [ + { + "scope": "PR #4133: literal-slot defect", + "evidence": "research/p104-literal-slot-defect/README.md", + "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.", + "status": "author-checked", + "source_commit": "88666f1dee93fbd85b31fd5d6f91a219e111b5f4", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4136: uniform commutation gap", + "evidence": "research/p104-uniform-commutation-gap/README.md", + "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.", + "status": "author-checked", + "source_commit": "281ce601a8be9db470de630759179c23e1dfaa88", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4140: uniform encoding gap", + "evidence": "research/p104-uniform-encoding-gap/README.md", + "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.", + "status": "author-checked", + "source_commit": "de25c6525aa866962309df5d107b32d55e6e5628", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4153: source-chart shortcut exhausts its optimistic allowance", + "evidence": "research/p104-source-chart-shortcut/README.md", + "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.", + "status": "author-checked", + "source_commit": "9123241fea53df77e51ffe30d9aca1625d4bf3a8", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4154: fiber-tag seam mismatch", + "evidence": "research/p104-fiber-tag-seam/README.md", + "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.", + "status": "author-checked", + "source_commit": "4ffcdaee5d6255a9cea1fe53a5424435068089d0", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + }, + { + "id": "complex-rank-shape-decoder", + "question": "Can a decoder deliver the local paid mass in fewer, larger-rank children (block frame climbs instead of rank-1 to rank-3 steps)?", + "starting_points": [ + "docs/research/research-family-status.md", + "research/complex-local-word-ceiling/README.md", + "research/complex-decoder-field-extension-seed44/README.md", + "research/complex-frame-pair-decoders/README.md", + "research/selected-k8-unrestricted-ends/README.md", + "research/eisenstein-reduction-copy-floor/README.md" + ], + "methods": [ + "Find one exact small decoding identity whose frame path climbs in blocks, and price its complete per-call profile.", + "Bound the best effective child rank achievable for one fixed support alphabet, including copies, frames and restoration." + ], + "acceptance_gate": "A per-call local profile, with all copied information, frames and restoration counted, whose ceiling exceeds the selected word's by at least 5%; masked or overcomplete supports must change an assumption of the eight-term all-pairs bound. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "research/complex-local-word-ceiling/verify.py" + ], + "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING", + "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.", + "scope": "Positive control and planning budget only; this is not a new construction or full cold replay." + }, + "first_experiment": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin. Ideal budget: rank-16 delivery is 2.31x (levers.py).", + "bottleneck_link": "Rank-1 children are about half of recursive cost; the selected word's effective child rank is about 3.9. Larger-rank delivery lowers recursive cost per unit of paid mass.", + "allowed_variations": [ + "One masked, overcomplete or block decoder family with exact labels and supports.", + "A scoped lower bound on effective rank for one alphabet.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "scope_change_triggers": [ + "Repacking idle remainders of an unchanged word (covered by the packing ceiling).", + "Repeating the eight-term all-pairs search inside its proved scope.", + "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.", + "Searching below C=40 in the #2017 Eisenstein binary scalar-rectangle or fixed-support block-linear additive pairing model; specify a changed premise instead. This bound does not cover every complex decoder.", + "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts." + ], + "overlap_terms": [ + "rank shape", + "block climb", + "masked decoder", + "overcomplete", + "effective rank" + ] + }, + { + "id": "complex-new-helper-inventory", + "question": "Can a new local cost interface change the deficit-to-recursive-cost ratio beyond current packing?", + "starting_points": [ + "docs/research/research-family-status.md", + "research/complex-local-word-ceiling/README.md", + "research/heterogeneous-owner-assembly/README.md", + "certificates/selected-result.json", + "research/selected-k8-unrestricted-ends/README.md" + ], + "methods": [ + "Propose a changed helper inventory and derive an optimistic exact moment.", + "Design a small completed instance and independently verify its endpoint and rank bill." + ], + "acceptance_gate": "A new physically realizable contract outside the frozen catalogue whose per-call profile, screened with ceiling.ceiling(), beats the selected word's packing ceiling; a lower cap does not establish identical circuitry or order attainable optima, and is insufficient to pass the stronger-budget target under this model. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "research/complex-local-word-ceiling/verify.py" + ], + "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING", + "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.", + "scope": "Positive control and planning budget only; this is not a new construction or full cold replay." + }, + "first_experiment": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin.", + "bottleneck_link": "Packing of the selected word is capped at +0.87% (ceiling model); only a lower local excess spend or a changed coverage law raises the cap.", + "allowed_variations": [ + "Narrow to one changed boundary or helper type with explicit counts.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "scope_change_triggers": [ + "Mixing only providers already inside the pinned catalogue.", + "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.", + "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts." + ], + "overlap_terms": [ + "helper inventory", + "heterogeneous-owner", + "mutable leaver" + ] + } + ] + }, + { + "id": "recursive-interfaces", + "weight": 20, + "tasks": [ + { + "id": "joint-query-controller", + "question": "Can the installed QQ16 caller win a complete matched protocol bill, or can a changed demand eliminate actual paid work?", + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/qq16-caller-install/README.md" + ], + "methods": [ + "Derive the matched whole-caller physical bill for installed and baseline protocols.", + "Change the actual demanded observations and prove a cheaper legal producer/consumer contract." + ], + "acceptance_gate": "Name the changed premise of the fixed F0/B1 observation obstruction. Show exactly which query is recovered, legal native reads and restoration, and a full favorable budget including cover maps, helpers and endpoints. Local inverse identities alone do not close the global controller. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read #4166 COST.md and ADMISSION.json. An actual caller connection is now proposed. Its native-component profile loses; parent park/restore versus external-call costs remain unresolved. Retain the producer and recovery lineage rather than rebuild it.", + "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately." + }, + "first_experiment": "At the actual installed cut, compare matched complete parent park/restore and external input/return protocols at the same bank/packet geometry, including every later root call and service cost. Alternatively pin both bridge observations and derive a genuinely smaller source-compatible demand. Stop if the complete necessary inequality fails or an essential cost is unknown; no larger decoder scan from a local tape-action saving.", + "bottleneck_link": "The native local words exist; retained query information and its physical access are the missing link to a composed recursive interface.", + "allowed_variations": [ + "One paid query, one changed first pair, or one precisely specified affine helper state.", + "A counterexample or lower bound for that exact proposed repair.", + "One unresolved obligation of a newer local decoder, with exact source heads and a distinct claim/domain." + ], + "scope_change_triggers": [ + "Retaining the fixed first pair and ordinary schedule while allowing only homogeneous selected-only control, already excluded by the witness.", + "Treating cover-map counts as zero-cost physical address operations.", + "Recreating the pending complete local decoder or early-record/output-bank coalescing already under investigation without a distinct audit or changed premise.", + "Treating a completed-output defect inequality as a producer-interior, dirty-range or physical-cost certificate.", + "Recreating completed-output recovery or caller wiring already supplied by #4166 without new independent coverage.", + "Dropping retained later root calls or claiming native-profile dominance from the isolated publication saving." + ], + "overlap_terms": [ + "QQ16", + "joint-query", + "changing-chart controller", + "selected observation", + "1969", + "2540", + "early record", + "output-bank retention", + "complete native decoder", + "2965", + "producer defect", + "dirty-helper range", + "F17 consumer", + "4166", + "qq16-caller-install" + ], + "existing_checks": [ + { + "scope": "PR #4166: author-checked installed producer/service/return/bridge connection; native-component comparison loses.", + "evidence": "research/qq16-caller-install/README.md", + "remaining": "Complete matched physical protocol bill, or changed source-compatible demand/circuit; no affordable supplier yet.", + "status": "author-checked", + "source_commit": "0b082d22a0e9a442d264ab0633e35ef26c790630", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + }, + { + "id": "centre-path-sharing", + "question": "Can the 64-per-call centre path (eight rank-8 COPY/ERASE totals through the private temporary) be shared across calls or shrunk?", + "starting_points": [ + "docs/research/research-family-status.md", + "research/complex-local-word-ceiling/README.md", + "research/split-centres-global/proofs/PR386-BIT-GEOMETRY.txt", + "certificates/selected-result.json" + ], + "methods": [ + "Derive a fully charged favorable relaxation for sharing one centre path across k calls, including restoration, hosting and precision.", + "Prove a lower bound on copied information per call for the selected decoder contract." + ], + "acceptance_gate": "Show the changed centre charge and copy profile per call with every added restoration or hosting cost charged, and its ceiling via ceiling.ceiling(centre=...). A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "research/complex-local-word-ceiling/verify.py" + ], + "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING", + "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.", + "scope": "Positive control and planning budget only; this is not a new construction or full cold replay." + }, + "first_experiment": "Write the per-call centre charge and copy children for sharing across k = 2 calls, charge the sharing overhead, and screen it; stop this route if even the ideal sharing gains under 10%. Ideal budgets: free 2.80x, shared by two 1.90x (levers.py).", + "bottleneck_link": "The centre path consumes 64 of about 99.6 unpaid coordinates per call, i.e. about 64% of the raw deficit.", + "allowed_variations": [ + "One sharing pattern across a fixed number of calls.", + "One reduced copied-total contract for the existing decoder.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "scope_change_triggers": [ + "Removing copies without a replacement contract for the decoder's copied totals.", + "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts." + ], + "overlap_terms": [ + "centre path", + "copied totals", + "private temporary", + "shared centre", + "batching" + ] + }, + { + "id": "coverage-law-change", + "question": "Can a template or call contract leave two or more unpaid coordinates per live family?", + "starting_points": [ + "docs/research/research-family-status.md", + "research/complex-local-word-ceiling/README.md", + "research/idle-axis-hosting/PROOF.md", + "certificates/selected-result.json" + ], + "methods": [ + "State a replacement for the coverage identity (mass = 72W + 64N) and the contract change that realizes it, with its implementation cost.", + "Find an obstruction: show which data-endpoint obligation forces exactly one unpaid coordinate in the current template." + ], + "acceptance_gate": "An explicit replacement identity, verified on a small complete instance with dirty inputs, priced with ceiling.ceiling(unpaid=...). A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "research/complex-local-word-ceiling/verify.py" + ], + "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING", + "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.", + "scope": "Positive control and planning budget only; this is not a new construction or full cold replay." + }, + "first_experiment": "Explain where the single unpaid coordinate per family comes from in the hosted template; propose one change and price it. Ideal budget: two unpaid coordinates per family is 3.77x (levers.py).", + "bottleneck_link": "The deficit is one coordinate per family minus the centre charge; doubling unpaid coordinates per family scales it directly.", + "allowed_variations": [ + "One template change or one endpoint-contract change.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "scope_change_triggers": [ + "Counting a coordinate as unpaid while leaving it unadvanced in the data endpoint.", + "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts." + ], + "overlap_terms": [ + "coverage identity", + "unpaid coordinate", + "deficit law", + "W - 64N" + ] + }, + { + "id": "connector-alphabet-change", + "question": "Does one explicit extension of the connector alphabet offer a favorable completed budget?", + "starting_points": [ + "docs/research/research-family-status.md", + "research/universal-connector-boundary/README.md", + "certificates/selected-result.json" + ], + "methods": [ + "Construct and charge a legal extra operation on a minimal instance.", + "Prove a target-specific bound after adding one specified operation family." + ], + "acceptance_gate": "State which fixed-alphabet premise changes and charge its implementation; do not declare it free. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "research/universal-connector-boundary/verify.py" + ], + "expected": "PASS_UNIVERSAL_CONNECTOR_BOUNDARY", + "inspect": "Reproduce the 945-pairing control, then read Exact interface to list the allowed calls.", + "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay." + }, + "first_experiment": "Add exactly one legally priced operation and test a tiny dirty-input instance before enumerating larger cases.", + "bottleneck_link": "A new legal connector operation could change recursive interface cost; a larger census in the same alphabet is a separate side result.", + "allowed_variations": [ + "Choose one additional operation and a small source count for its first counterexample." + ], + "scope_change_triggers": [ + "Keeping the alphabet and only increasing the source count; record this as a changed assignment.", + "Extending a source-count census without naming a supplier/interface decision it could change; audit #2973 pruning concerns before relying on the affected predecessor exclusions." + ], + "overlap_terms": [ + "universal connector", + "source-toggle", + "connector alphabet" + ] + } + ] + }, + { + "id": "adversarial-audit", + "weight": 15, + "tasks": [ + { + "id": "selected-stock-envelope", + "question": "What explicit uniform stock envelope does the actual selected stopped producer supply at one bootstrap stage?", + "starting_points": [ + "research/selected-bootstrap-stock-audit/README.md", + "research/bootstrap-cutoff-time-space-split/README.md", + "certificates/selected-result.json", + "docs/research/community-efficient1000-review.md", + "research/stock-margin-chain/README.md" + ], + "methods": [ + "Derive a source-bound reserve recurrence at the actual selected atom widths, separating parent stock from completed inner borrowing.", + "Find an exact missing implication or counterexample to a proposed selected-stage stock envelope." + ], + "acceptance_gate": "Bind every coefficient and depth factor to the selected producer and state the width domain. Compare a proved envelope with the sufficient cutoff guard; a large numerical headroom or a historical m=120 coefficient is not a selected m=73 proof.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read #2972 stock-margin chain and the selected stock audit. The new source archive reports the remaining cutoff comparisons, but leaves every actual stock coefficient unresolved; it is not an independently validated reserve envelope.", + "scope": "Source-bound orientation only. Read the named package and review before relying on its local evidence; this command is not its replay or supplier admission." + }, + "first_experiment": "Choose one actual selected producer/stage and derive its parent reserve and depth coefficient from source. Check whether newer handoffs already cover that exact obligation. Stop with the missing implementation lemma if it cannot be bounded; do not rerun #2972 cutoff/headroom arithmetic as a new contribution.", + "bottleneck_link": "This reduces a concrete inherited implementation obligation without confusing unchanged kappa arithmetic with a completed theorem.", + "allowed_variations": [ + "One stage or one explicit reserve/depth implication.", + "An independently checked same-domain proof repair, retaining all remaining assumptions." + ], + "scope_change_triggers": [ + "Importing the historical 57604 or 252 allowance without a selected-producer binding.", + "Calling a conditional fit lemma a full outer-proof adoption.", + "Replacing an actual selected stock coefficient with cutoff comparisons or a conditional fit inequality." + ], + "overlap_terms": [ + "selected stock", + "stock envelope", + "bootstrap cutoff", + "1956", + "1965", + "1990", + "2972", + "stock-margin-chain", + "actual_stock_coefficient" + ], + "existing_checks": [ + { + "scope": "Retained stock audit identifies missing actual selected-stage coefficients; later cutoff-chain arithmetic does not supply them.", + "evidence": "docs/research/research-family-status.md#revision-6-handoffs-source-archives-awaiting-independent-validation", + "remaining": "Derive one actual reserve/depth coefficient from the selected producer.", + "status": "reviewed", + "source_commit": "836b19bfa309ceafbc8ee32a15e8c4b10dde7e11", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + }, + { + "id": "supplier-boundary-audit", + "question": "Can the #4088 four-provider dispatch satisfy the complete ordinary/outer admission contract?", + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/staged544-mixed-fourth-entry/README.md", + "research/scatter-boundary-decision/README.md" + ], + "methods": [ + "Trace one hypothesis through the source, checker and complete caller.", + "Construct one semantically invalid but superficially well-formed fixture and test rejection." + ], + "acceptance_gate": "Pin the current sources and one obligation; the historical owner audit is an example, not evidence of a current bug.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read #4088 Scope and Open next questions: local words, native receipts and literal fill do not include a rerun of the mixed four-provider ordinary/outer engine. #3801 is the newer scatter-boundary decision; do not restart #2977 as if untouched.", + "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately." + }, + "first_experiment": "Pin the provider registry, four native source closures and dispatch. Make a bounded acceptance coverage map or one registry adapter preserving every inherited admission predicate and rejection control (including an omitted fourth provider). Record remaining ordinary/outer obligations and a resource estimate before heavy execution. Stop at unresolved source/caller dependencies; no selected-result promotion from a local pass.", + "bottleneck_link": "Closing a current acceptance gap or proof obligation strengthens reliability even without changing kappa.", + "allowed_variations": [ + "One provider-registry, dispatch, native-closure or admission-predicate obligation; separate branches must name distinct coverage." + ], + "scope_change_triggers": [ + "Reporting the historical timing-only diagnostic as a new current acceptance bug.", + "Calling a malformed mutant a failure of the selected construction, or importing an opt-in repair without testing the exporter boundary.", + "Running another root enclosure instead of validating dispatch or weakening an inherited predicate to make mixed admission pass." + ], + "overlap_terms": [ + "owner boundary", + "bridge omission", + "hosting", + "2977", + "scatter export", + "duplicate index", + "parity semantics", + "4088", + "3801", + "staged544-mixed-fourth-entry", + "scatter-boundary-decision" + ], + "existing_checks": [ + { + "scope": "PR #4088: author-checked local words, native receipts, owner/phase fill and exact moment.", + "evidence": "research/staged544-mixed-fourth-entry/README.md", + "remaining": "Rebind and validate ordinary/outer admission with all four providers; full mixed release not established.", + "status": "author-checked", + "source_commit": "72d7efc181edb21806a878f174847c96dd410ab0", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #3801: successor scatter-boundary decision package.", + "evidence": "research/scatter-boundary-decision/README.md", + "remaining": "Consult its exact acceptance scope before any new exporter audit; not proof of a selected failure.", + "status": "author-checked", + "source_commit": "911f8800ba7a4b03603ef62c5ffc6240e53cb5fd", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + }, + { + "id": "uniform-transfer-audit", + "question": "Does one quantified step of the proposed #4100 all-size construction hold at its actual caller?", + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/unconditional-batched-crt/README.md" + ], + "methods": [ + "Prove one missing implication with explicit quantified hypotheses.", + "Find an exact counterexample at the claimed interface boundary." + ], + "acceptance_gate": "Identify the proposition and what would change downstream; do not equate a finite replay with a universal proof.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read PROOF.md and AUDIT.md in #4100. Select one distinct obligation: CRT total repair, native/free-algebra lifting, precision/conditioning, or complete fixed-tape cost. This is an author-submitted proof, not an accepted unconditional theorem.", + "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately." + }, + "first_experiment": "Check live handoffs; name one proposition, its caller, quantified domain and dependency closure. Independently prove the implication or exhibit a precise gap/counterexample. Prioritize CRT.md total repair or COMPLEX.md free-algebra lift only if unclaimed. Stop at the chosen obligation; do not substitute finite samples or root arithmetic for an all-size proof, or launch the complete package by default.", + "bottleneck_link": "Finite supplier improvements are useful only under the retained transfer obligations.", + "allowed_variations": [ + "One CRT repair, native lift, precision/conditioning or tape-cost proposition, with its exact caller." + ], + "scope_change_triggers": [ + "Replacing a quantified obligation with another finite smoke test.", + "Treating archive intake, an author PASS receipt or a finite composed fixture as discharge of the universal hypotheses." + ], + "overlap_terms": [ + "uniform transfer", + "all-size", + "precision", + "4100", + "unconditional-batched-crt" + ], + "existing_checks": [ + { + "scope": "PR #4100: proposed unconditional construction and finite checks, without independent acceptance.", + "evidence": "research/unconditional-batched-crt/README.md", + "remaining": "Independent proof audit of one caller-bound all-size implication; all other premises remain explicit.", + "status": "author-checked", + "source_commit": "337d04939571a637aeab54a0f58f54fde811663a", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + }, + { + "id": "census-pruning-audit", + "question": "Does the reported word-census parity-pruning error invalidate a specific exclusion we still rely on, and what bounded repair is justified?", + "starting_points": [ + "research/f7-weight-parity-census-correction/README.md", + "docs/research/research-family-status.md" + ], + "methods": [ + "Independently reconstruct the tiny counterexample and trace one affected exclusion to its exact pruning code.", + "Compare corrected and unpruned enumeration on a small exhaustive domain, then audit the changed pruning implication." + ], + "acceptance_gate": "Pin the old and proposed corrected engines, distinguish a disproved pruning rule from a disproved final bound, and state exactly which downstream exclusions need revalidation. #2973 is an author-checked source archive; neither its new f(7) claim nor all old conclusions are automatically accepted or rejected.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read #2973 error description and MATH.md; manually reconstruct the prefix states of 01021323 before running any large census.", + "scope": "Source-binding orientation only; no full enumeration or mathematical validation." + }, + "first_experiment": "Reconstruct the eight prefix states of 01021323 and compare bit-0 versus Hamming-weight parity budgets independently. Trace the reported false prune to one pinned predecessor (#2542, #2634 or #2691), then test a small exhaustive domain. Stop after a source-impact handoff or corrected-prune proof; a full seven-label replay needs a separate resource budget and a named research decision it can change.", + "bottleneck_link": "An unsound exclusion can wrongly close a mechanism; correcting its dependency boundary is more useful than extending the same census.", + "allowed_variations": [ + "One predecessor pruning rule, one independently exhaustive small domain, or one downstream dependency audit." + ], + "scope_change_triggers": [ + "Launching a larger census before validating the prune and explaining which active decision it changes.", + "Treating a small-domain counterexample to the old rule as a counterexample to every reported seven-label bound." + ], + "overlap_terms": [ + "2973", + "2542", + "2634", + "2691", + "weight parity", + "bit-0", + "01021323", + "census pruning" + ] + } + ] + }, + { + "id": "independent-verification", + "weight": 10, + "tasks": [ + { + "id": "independent-moment", + "question": "Does a new paid-profile or mixture-ceiling claim have independent source-bound coverage of its actual changed ledger?", + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/staged544-mixed-fourth-entry/README.md", + "research/staged-fourth-mixture-ceiling/README.md", + "research/r437-two-window-carrier/README.md" + ], + "methods": [ + "Independently reconstruct one changed paid ledger or pooled dual with exact source and model binding.", + "Check a genuinely uncovered moment implication with a different enclosure method and semantic controls." + ], + "acceptance_gate": "Demonstrate independence, source binding, positive cases and semantic failure controls. Name the existing checks and the missing coverage. More digits or another equivalent evaluation of an unchanged root is not by itself new verification coverage.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Choose one uncovered implication in #4088 literal mixed fill, #4091 pooled dual/model binding or #4067 changed frame/host bill. #4091 pins an earlier #4088 head: validate word, capacity and stock equivalence before applying that ceiling to the later fill.", + "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately." + }, + "first_experiment": "Independently reconstruct one changed ledger or pooled certificate with a positive case and a semantic failure control. Compare exact sources and name what existing checks miss. Keep this separate from supplier-boundary-audit (ordinary/outer dispatch) and uniform-transfer-audit (all-size proof). Stop after the chosen implication; more digits of an unchanged root are not additional mechanism coverage.", + "bottleneck_link": "Independent pricing prevents unsupported frontier claims and can reveal genuine accounting slack.", + "allowed_variations": [ + "Reconstruct either a source ledger or a numeric enclosure with a different method." + ], + "scope_change_triggers": [ + "Importing the primary function and calling its output independent verification.", + "Calling an aggregate histogram or source archive an independently accepted physical supplier." + ], + "overlap_terms": [ + "independent moment", + "rank histogram", + "exact enclosure", + "2979", + "rank7 joint endframes", + "paired extraction", + "joint lowering", + "4088", + "4091", + "4067", + "staged544-mixed-fourth-entry", + "staged-fourth-mixture-ceiling", + "r437-two-window-carrier" + ], + "existing_checks": [ + { + "scope": "PR #4088: mixed local/owner/phase ledger and moment reported.", + "evidence": "research/staged544-mixed-fourth-entry/README.md", + "remaining": "Independent binding of changed construction to paid histogram, distinct from full admission.", + "status": "author-checked", + "source_commit": "72d7efc181edb21806a878f174847c96dd410ab0", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4091: sharp pooled ceiling proposed for fixed THREE/FOUR words and inventory.", + "evidence": "research/staged-fourth-mixture-ceiling/README.md", + "remaining": "Validate dual, exhaustive pattern scope and exact source equivalence before applying to newer fills.", + "status": "author-checked", + "source_commit": "a29bdd8f56cd18b805917775cdec09ff935eddc4", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4067: paid (2,2) to (1,3) exchange and fixed OQ4 host reported.", + "evidence": "research/r437-two-window-carrier/README.md", + "remaining": "Independent full cost delta; remaining caller/precision/stock obligations are separate.", + "status": "author-checked", + "source_commit": "a95f11c52e3ca1e4c5171b3c20d8f4b0815aee2e", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + }, + { + "id": "formal-interface-lemma", + "question": "Can one uncovered interface implication be formalized with exact caller and certificate bindings?", + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/gate-operand-parity-lean/README.md", + "research/staged544-certified-endpoint/README.md", + "research/unconditional-batched-crt/README.md" + ], + "methods": [ + "Formalize a missing boundary lemma identified by the selected review.", + "Audit a formal theorem-to-certificate binding independently." + ], + "acceptance_gate": "State the exact formalized proposition and remaining assumptions; avoid duplicate arithmetic formalizations already present.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Inventory the gate-operand parity lemma (#3807) and certified endpoint arithmetic (#3857). Neither is a full multiplication proof. For #4100, audit the compact-switch statement and its hypotheses before formalizing it.", + "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately." + }, + "first_experiment": "Write one missing statement with quantified hypotheses, actual caller and existing coverage. A compact-switch lemma is a candidate only after its mathematical contract is reviewed. Establish a bounded proof plan before a separately budgeted proof-assistant build; do not rerun large Lean jobs as orientation.", + "bottleneck_link": "A missing interface proof can reduce the conditional gap even if it does not change kappa.", + "allowed_variations": [ + "Narrow to one formal lemma or one theorem-to-certificate binding." + ], + "scope_change_triggers": [ + "Formalizing already-covered arithmetic and claiming the full multiplication theorem." + ], + "overlap_terms": [ + "hyperplane end", + "formal interface", + "Lean binding", + "3807", + "3857", + "4100", + "gate-operand-parity-lean", + "staged544-certified-endpoint", + "unconditional-batched-crt" + ], + "existing_checks": [ + { + "scope": "PR #3807: scoped gate-operand parity formalization.", + "evidence": "research/gate-operand-parity-lean/README.md", + "remaining": "Exact theorem-to-caller binding and genuinely uncovered interface lemmas.", + "status": "author-checked", + "source_commit": "4c3530f42a6abcc48e7a6bcffd6c901911dc8269", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #3857: certified real-power moment/endpoint arithmetic.", + "evidence": "research/staged544-certified-endpoint/README.md", + "remaining": "Uniform algorithmic implications, not another endpoint digit.", + "status": "author-checked", + "source_commit": "ef4315b8caa605e47a2515004845eb2d2ed71a86", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4100: compact-switch formalization proposed as future validation.", + "evidence": "research/unconditional-batched-crt/README.md", + "remaining": "Audit the statement and assumptions before a formal proof campaign.", + "status": "author-checked", + "source_commit": "337d04939571a637aeab54a0f58f54fde811663a", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + } + ] + }, + { + "id": "verifier-engineering", + "weight": 8, + "tasks": [ + { + "id": "replay-runtime", + "question": "Can one measured replay bottleneck be sped up without dropping coverage?", + "starting_points": [ + "scripts/run_isolated_tests.py", + "scripts/verify_replay_coverage.py", + "certificates/selected-result.json" + ], + "methods": [ + "Profile one isolated replay and optimize the measured bottleneck.", + "Design source-bound reuse with explicit dependency invalidation and negative controls." + ], + "acceptance_gate": "Report before/after wall time on the same fixture, retained checks and invalidation behavior.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read the selected reproduction command and choose a single replay stage for profiling.", + "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay." + }, + "first_experiment": "Measure one unchanged fixture, preserve check coverage, and test one optimization with invalidation controls.", + "bottleneck_link": "Faster trustworthy replays increase review throughput and let mechanism candidates be checked sooner.", + "allowed_variations": [ + "Profile one stage or design one source-bound cache boundary." + ], + "scope_change_triggers": [ + "Skipping coverage or comparing different fixtures to claim speedup." + ], + "overlap_terms": [ + "replay runtime", + "cache invalidation", + "isolated tests" + ] + }, + { + "id": "portable-replay", + "question": "Can one reproducible environment or artifact-comparison failure be repaired?", + "starting_points": [ + "research/gzip-container-reproducibility/README.md", + "docs/ci-verification.md" + ], + "methods": [ + "Reproduce one portability failure and add a minimal cross-environment fix.", + "Audit one canonical-payload comparison for omitted proof-relevant fields." + ], + "acceptance_gate": "Preserve immutable source hashes and proof-relevant content; a different compressed byte stream alone is not a mathematical mismatch.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read the gzip-container reproducibility examples and distinguish frozen source bytes from regenerated payloads.", + "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay." + }, + "first_experiment": "Reproduce one specific mismatch or audit one canonical comparison for omitted proof-relevant fields.", + "bottleneck_link": "Portable exact checks prevent environment failures from blocking valid contributions.", + "allowed_variations": [ + "One interpreter/version mismatch or one payload field comparison." + ], + "scope_change_triggers": [ + "Removing immutable-source pins because generated compressed bytes differ." + ], + "overlap_terms": [ + "gzip container", + "reproducibility", + "canonical payload" + ] + } + ] + }, + { + "id": "consolidation", + "weight": 5, + "tasks": [ + { + "id": "overlap-receipt", + "question": "What exact content and credit of a small named PR set has already been retained?", + "starting_points": [ + "docs/research/pr-ledger.md", + "CONTRIBUTORS.md" + ], + "methods": [ + "Compare exact heads and retained artifacts to write a source-bound disposition receipt.", + "Audit an existing receipt for missing content or predecessor attribution." + ], + "acceptance_gate": "Separate complete integration, partial retention and changed heads; make no autonomous closures.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read one small PR set in the ledger and identify exact reviewed heads and unresolved content.", + "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay." + }, + "first_experiment": "Compare that set to retained artifacts; produce a complete or explicitly partial disposition receipt.", + "bottleneck_link": "Reliable overlap evidence preserves credit and prevents repeated review of already-retained material.", + "allowed_variations": [ + "One small related PR family or one existing integration receipt." + ], + "scope_change_triggers": [ + "Treating matching titles or one shared blob as proof of full incorporation." + ], + "overlap_terms": [ + "overlap receipt", + "partial integration", + "attribution" + ] + }, + { + "id": "scope-navigation", + "question": "Can one misleading historical-current claim or missing research cross-reference be corrected?", + "starting_points": [ + "docs/research/current-status.md", + "docs/research/pr-ledger.md", + "certificates/selected-result.json" + ], + "methods": [ + "Trace one confusing path from onboarding to its authoritative source.", + "Index one tightly related family of obstructions with explicit excluded and open hypotheses." + ], + "acceptance_gate": "Produce evidence-backed navigation, preserve historical records and avoid a duplicate global survey.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Follow one link from the selected record to its review and compare a potentially stale historical claim.", + "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay." + }, + "first_experiment": "Repair one confusing path or produce a scoped map of one related obstruction family.", + "bottleneck_link": "Clear navigation lowers entry cost for central research; a global survey without a concrete fix is not required.", + "allowed_variations": [ + "One historical-current ambiguity or one bounded family index." + ], + "scope_change_triggers": [ + "Rewriting frozen scientific packages just to change their historical wording." + ], + "overlap_terms": [ + "current status", + "historical checkpoint", + "scope navigation" + ] + } + ] + }, + { + "id": "incumbent-optimization", + "weight": 2, + "tasks": [ + { + "id": "selected-packing", + "question": "Does a named residual packing task have meaningful uncovered headroom after its exact fixed-inventory ceiling?", + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/staged-fourth-mixture-ceiling/README.md", + "research/staged544-mixed-fourth-entry/README.md" + ], + "methods": [ + "Check a fixed-inventory ceiling and source equivalence before any explicitly bounded residual search.", + "Price a genuinely changed word/interface under a newly applicable model." + ], + "acceptance_gate": "Check live overlap and exact model/source binding first. Distinguish a chronological construction from a pooled optimum. State the applicable fixed-inventory ceiling and remaining headroom; changed words or interfaces require a new fully charged model. Do not launch a residual search without an explicit scope and time cap.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read #4091 fixed-word pooled ceiling and #4088 later 1090-call literal fill. Bind the unchanged local invoices/capacities/stock before transferring the ceiling; its earlier 1080-call residual-bin recipe is historical.", + "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately." + }, + "first_experiment": "Default to a bounded headroom/source-equivalence check. Only start residual search with an explicit unclaimed domain, time cap and reason the tiny remaining gain matters. Otherwise hand off or select a changed-word mechanism. A changed word or interface needs a fresh cost model, not the old ceiling. Stop at the fixed-inventory cap; do not extend by new random seeds.", + "bottleneck_link": "An actual paid-profile gain can improve the frontier up to the other supplier cap.", + "allowed_variations": [ + "One bounded residual packing instance or exact relaxation.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "scope_change_triggers": [ + "Rerunning an existing search with only a different seed as a separate mathematical contribution." + ], + "overlap_terms": [ + "T16", + "owner exchange", + "packing", + "4091", + "4088", + "staged-fourth-mixture-ceiling", + "staged544-mixed-fourth-entry" + ], + "existing_checks": [ + { + "scope": "PR #4091: pooled optimum at one-third staging for pinned fixed words; not a chronological fill.", + "evidence": "research/staged-fourth-mixture-ceiling/README.md", + "remaining": "Independent scope/source check; any residual optimization is explicitly bounded and optional.", + "status": "author-checked", + "source_commit": "a29bdd8f56cd18b805917775cdec09ff935eddc4", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4088: later 1090-call literal fill improves the earlier 1080-call witness.", + "evidence": "research/staged544-mixed-fourth-entry/README.md", + "remaining": "Complete admission remains separate; old residual-bin instructions must not be copied blindly.", + "status": "author-checked", + "source_commit": "72d7efc181edb21806a878f174847c96dd410ab0", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + }, + { + "id": "scalar-to-moment", + "question": "Can a changed frame itinerary remove a paid transition beyond the already covered scalar A2 contractions?", + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/staged544-a2-graph-rewrite/README.md", + "research/staged544-separated-a2/README.md", + "research/staged544-a2-composition-audit/README.md", + "research/staged544-a1858-contraction-audit/README.md" + ], + "methods": [ + "Derive the changed legal frame itinerary and exact child histogram.", + "Prove a scoped obstruction showing why that scalar gain cannot change the paid contract." + ], + "acceptance_gate": "An unchanged histogram is not a kappa gain; record any separate runtime or proof benefit explicitly.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read the A2 and separated-A2 constructions and their composition/contraction audits. Scalar contractions can preserve the complete recursive histogram; fewer ADDs alone do not justify further scans.", + "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately." + }, + "first_experiment": "Identify an actual paid transition to remove and construct a legal replacement frame itinerary, charging restoration, source windows and changed helpers. Compare complete before/after histograms. Stop if only scalar count changes; report that benefit honestly, without expanding the same scalar-only census.", + "bottleneck_link": "A legal change to the histogram, not addition count alone, is the bridge to an exponent gain.", + "allowed_variations": [ + "One existing scalar simplification and one proposed frame-path change." + ], + "scope_change_triggers": [ + "Submitting only another scalar count as completion of a paid-profile task." + ], + "overlap_terms": [ + "scalar simplification", + "paid profile", + "R439", + "3998", + "4019", + "4112", + "4152", + "staged544-a2-graph-rewrite", + "staged544-separated-a2", + "staged544-a2-composition-audit", + "staged544-a1858-contraction-audit" + ], + "existing_checks": [ + { + "scope": "PR #3998: consecutive A2 scalar contraction", + "evidence": "research/staged544-a2-graph-rewrite/README.md", + "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.", + "status": "author-checked", + "source_commit": "389268a6b5e0373a3125d5c6fcd6995f4ea324f5", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4019: separated A2 sites with unchanged recursive histogram", + "evidence": "research/staged544-separated-a2/README.md", + "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.", + "status": "author-checked", + "source_commit": "f408e09df300b575235f7f77f81948071397e16d", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4112: composition audit", + "evidence": "research/staged544-a2-composition-audit/README.md", + "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.", + "status": "author-checked", + "source_commit": "205b7380656ba4b6316a8a493b1a3c679b8f7a0e", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4152: A1858 contraction audit", + "evidence": "research/staged544-a1858-contraction-audit/README.md", + "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.", + "status": "author-checked", + "source_commit": "caaa14cde5962adc372fdca71f63d0f29e73c8b2", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + } + ] + } + ], + "selection_context": { + "refreshed_on": "2026-10-22", + "kappa": "60403/20000000", + "source_pr": 4470, + "record": "certificates/selected-result.json", + "review": "docs/research/pr-intake-evidence/pr4470/PROOF-REVIEW.md", + "orientation_command": "python3 -B scripts/research_selected_baseline.py", + "scope": "Metadata refresh only. Revision-7 weights and cards remain historical suggestions pending separate strategic reassessment; check current contracts and overlap before adopting them." + } +} diff --git a/research/coupled-provider-independent-audit/custody/5376/provenance-sources/7c472563474e60185e6ca101a17622133d047e56/research/inverse-dirty-certificates/PROOF.md b/research/coupled-provider-independent-audit/custody/5376/provenance-sources/7c472563474e60185e6ca101a17622133d047e56/research/inverse-dirty-certificates/PROOF.md new file mode 100644 index 0000000000..d2433c24ca --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/provenance-sources/7c472563474e60185e6ca101a17622133d047e56/research/inverse-dirty-certificates/PROOF.md @@ -0,0 +1,246 @@ +# Compact certificates with actual inverse calls + +This is a scoped written proof for the register grammar below. The implementation +and finite tests corroborate it; there is no proof-assistant or independent human +verification claim. The contribution answers the inverse-frontend question in +[zxv's PR5235](https://github.com/CrocSwap/integer-mult-bounds/pull/5235), pinned at +`48976daa4dce59b4867ef046da72a370e389925d`. That package supplies the +independent-operator register bridge, invariant certificates and unipotent +witness method. Here inverse occurrences denote the **actual inverse of the +same generator**, and therefore need a different, cyclic realization and a +sound passage from formal series to arbitrary invertible substitutions. + +Recognizable rational series, the Magnus substitution and weighted-automata +equivalence are classical. See Stefan Kiefer, +[Notes on Equivalence and Minimization of Weighted Automata](https://arxiv.org/abs/2009.01217), +and Retakh, Reutenauer and Vaintrob, +[Noncommutative rational functions and Farber's invariants of boundary links](https://arxiv.org/abs/math/0004112), +Remark 2.3 and Proposition 2.4, which recall the Magnus embedding and the +Schutzenberger/Fliess characterization. We claim a project-specific interface, +explicit state bound and executable certificate bridge, not a new general +automata/PIT algorithm or a new Magnus theorem. The argument below is +self-contained and does not require the injectivity theorem for the group +algebra embedding. + +## 1. Grammar and statement + +Fix a field K, a finite alphabet of independently chosen invertible operators +G_a on a common finite-dimensional K-vector space, and r >= 1 named registers. +All r initial vectors are independent; no dirty helper is assumed zero. +A program is a finite sequence of: + +1. scalar linear assignment to a register, with all sources read before the + assignment, including when the destination is also a source; +2. `dst <- G_a^s dst`, where s is +1 or -1; +3. `dst <- dst + c G_a^s src`, with the old source and destination, also when + `src == dst`. + +All scalar coefficients lie in K. Compare two such programs on the same +ordered roles and alphabet, returning **every** final register. Let q be the +total number of unary occurrences in both programs, including queries, inverse +occurrences, and queries with coefficient zero. Put D = r + q. + +**Theorem.** There are effectively constructed scalar matrices +U in K^(r x D), V in K^(D x r), and T_a in K^(D x D) such that: + +- the complete endpoint difference, expanded at G_a = I + Y_a, has coefficient + matrix U T_a1 ... T_ak V at every word a1...ak, including k=0; +- the programs have equal complete endpoints for every payload dimension and + every invertible substitution if and only if all these coefficients vanish; +- equality has a finite certificate consisting of at most D path rows, their + initial-span coordinates and transition-closure coordinates; +- failure has a nonzero coefficient word of length k < D and an explicit + simultaneous unipotent substitution in dimension k+1 <= D witnessing it. + +The search below finds a shortest nonzero coefficient word. The independent +certificate checker certifies its nonzeroness, **not shortestness**. It does +not claim a least-dimensional witness among arbitrary invertible matrices. + +The executable supports K=Q and prime fields F_p with p <= 2^31-1. Rational +input denominators must be nonzero in F_p. The written theorem holds over any +field. There are no commutation, involution, Clifford, adjoint or other +relations; a failure need not persist after imposing such extra relations. +Only inverses of named generators are in the grammar, not inverses of arbitrary +operator sums or matrices of operators. + +## 2. One atom per unary occurrence + +Create r leaf atoms x_i. Maintain each register as a scalar row in the atom +list. Each linear instruction updates that row. Each unary occurrence with +pre-instruction source row e creates a fresh atom z_j = G_a^s (e z). +An apply instruction replaces the destination by z_j; a query adds c z_j to +the old destination. Even a self-source query takes e before the update. + +Compile the two programs with separate mutable register tables but the same r +leaf atoms. Append all unary atoms from both sides to one list. Their source +rows use earlier atoms only. Thus there are exactly D atoms. U is the +left-minus-right matrix of all final role expressions; it retains each input +role and each output role independently. An atom is an algebraic compiler +record, not a clean physical register or a free allocation. + +Work in noncommutative formal series K<> and put G_a=1+Y_a. Its inverse +is the formal geometric series, well-defined over every characteristic. For a +forward occurrence and an inverse occurrence, respectively, the defining +equations are + + z_j = e z + Y_a e z, + z_j = e z - Y_a z_j. + +The second equation follows by multiplying z_j=(1+Y_a)^(-1)e z by 1+Y_a. +It is the inverse-aware step: a negative diagonal feedback term, not a new +independent operator label and not a truncated polynomial expansion. + +Let E have row e at every unary atom and zero leaf rows. Let V0 embed the r +input roles at the leaf rows. For each a, let A_a have row e at a forward +a-occurrence, row -unit_j at an inverse a-occurrence, and zero elsewhere. +Then, with scalar matrices commuting entrywise with the series letters, + + z = E z + V0 x + sum_a Y_a A_a z. + +E is strictly lower triangular. Consequently H=(I-E)^(-1) is the finite +scalar matrix I+E+...+E^(D-1). Set V=H V0 and T_a=H A_a. The equations become + + z = V x + sum_a Y_a T_a z. + +This system has a unique formal solution: each coefficient of positive length +is determined by shorter coefficients. Iterating gives exactly + + [a1 ... ak](U z) = U T_a1 ... T_ak V. + +Word order is matrix-product order: `[B,A]` means BA and applies A first. +The inverse feedback means T_a need not be nilpotent. Infinite nonzero tails +are allowed even though D is finite. + +The producer uses the equivalent triangular recurrences + + V_j = e V, + (T_b)_j = e T_b + 1_(b=a) e (forward), + (T_b)_j = e T_b - 1_(b=a) unit_j (inverse), + +where e only reads earlier rows. The checker instead reconstructs E,A_a and +the triangular inverse H. These are separately transcribed compilers. + +## 3. Finite closure certificates + +A positive certificate provides b <= D path rows B_l=U_o T_w and scalar +coordinate matrices L and C_a satisfying + + U = L B, B T_a = C_a B for every a, B V = 0. + +These finite equations imply U T_w V=0 for every word by induction. +Independence, minimality and reachability of B are unnecessary for soundness; +the supplied paths merely specify B compactly and bind it to the program. + +Conversely, if every coefficient is zero, the reachable space +R=span{U_o T_w} has dimension at most D, is transition-stable and annihilates V. +Choose a basis from reachable path rows. Its initial and closure coordinates +give the displayed certificate. A basis of paths shorter than D exists: +R_k, the span of paths of length at most k, cannot stop increasing and later +increase again, since R_(k+1)=R_k+sum_a R_k T_a. If R_0=0, everything is zero; +otherwise at most D-1 strict increases are possible. + +Breadth-first search tests output projections of accepted independent path +rows and appends their independent successors. Rejected dependent rows add no +possible earlier distinguishing length: their expression uses accepted rows +of no greater length, whose successors span their successors. Hence a first +nonzero projection occurs at a shortest coefficient word, of length < D. +Exact elimination is in the producer only. The checker rebuilds the path rows +and verifies the displayed equations, or verifies one claimed nonzero +coefficient on failure. No acceptance check relies on Python `assert`. + +With alphabet size s, dense production takes polynomially many field +operations (O(s D^3) for reachable-space search and coordinates, plus parsing +and compilation). Coordinate storage is O(s D^2+rD), with at most O(D^2) +path letters. The simple checker may rebuild each path from scratch, costing +O(D^4+sD^3) field operations. These are arithmetic bounds, not bounds on +rational coefficient bit lengths or a practical scaling guarantee. + +## 4. Why zero series implies every invertible substitution + +Formal series cannot be evaluated directly at arbitrary matrices by summing an +infinite series. The following argument supplies the missing step. + +Fix any dimension n and any tuple of invertible matrices M_a over K. Introduce +one central indeterminate t and substitute + + G_a(t) = I + t(M_a-I). + +Each G_a(t) has determinant with constant term 1, so is invertible over K(t) +and its inverse has a well-defined expansion in K[[t]]. The program endpoint +is therefore a matrix of rational functions regular at t=0. Its formal +expansion is precisely the specialization Y_a -> t(M_a-I) of the series from +Section 2: in each degree there are only finitely many words, so substitution +is legitimate. + +If the noncommutative endpoint series is zero, this matrix has identically +zero power series at t=0. A rational function regular at zero with zero formal +expansion is zero in K(t): multiply by its denominator, whose constant term is +nonzero. Finally every inverse occurrence is regular at t=1, since +det G_a(1)=det M_a != 0. Evaluating the zero rational endpoint at t=1 proves +equality for this arbitrary invertible tuple M_a. This is valid over finite +fields as well; it uses a formal indeterminate, not sampling field elements. + +Thus a finite closure certificate proves the complete universal invertible +endpoint claim, without assuming convergence, generic numerical invertibility +or an infinite-field polynomial identity heuristic. + +## 5. Nonzero series gives an explicit invertible witness + +Suppose c=(U T_a1 ... T_ak V)_(o,i) is nonzero. On the basis e_0,...,e_k let + + N_a = sum_(j=0 to k-1, a_(j+1)=a) E_(j,j+1), + G_a = I + N_a. + +All N_a share the same strictly upper-triangular flag. All products of more +than k such matrices vanish, and each inverse G_a^(-1) is the finite sum +I-N_a+N_a^2-...+(-N_a)^k. Therefore the formal-series substitution now really +is a finite calculation, also for programs containing inverse calls. + +In matrix entry (0,k), shorter words give zero, longer words give zero, and a +word of length k gives one exactly when its labels are a1,...,ak in order. +The literal endpoint difference in block (o,i), entry (0,k), equals c. +Use input e_k in role i and zero vectors in other roles to exhibit a concrete +failure. The universal check had kept all roles independent; this choice of +one witness input imposes no clean-state assumption on the theorem. +For k=0 take dimension one and all G_a=I. + +This proves the converse in Section 1 and the constructive dimension bound. +The literal matrix oracle computes inverses by Gaussian elimination and +executes the original instructions; it does not reuse T_a or the producer. + +## 6. Boundaries and discriminating examples + +The dirty-sandwich example has roles x,h,y, all arbitrary. It temporarily +changes h to h+A x, adds B h to y, restores h, and subtracts B h. Its complete +endpoint is (x,h,y+B A x). The reference program temporarily applies A to x, +queries B x into y, and applies A^(-1) to x. Both full endpoints agree. +Deleting any one of the eight left-side instructions yields a detectable +failure in each tested field. This example certifies the stated algebraic +boundary; it is not a proposed faster physical implementation or a new echo +construction. + +A false commutator identity B^(-1)A^(-1)BA=I has a nonzero degree-two +coefficient. Scalar/one-dimensional substitutions cannot reveal that error; +the certificate's unipotent witness does. Self-source queries, omitted helper +returns and wrong inverse signs have distinct rejecting fixtures. + +The family G^(-1)(I-G)^d expands to (-Y)^d/(1+Y), so its first coefficient +occurs at degree d and its tail continues indefinitely. The replay checks +coefficients beyond the program's number of unary occurrences. In F_p, +G^p-I=Y^p supplies a characteristic-sensitive delayed witness. + +The stress example computes (A+B)^64 x, which has 2^64 distinct noncommutative +words, on both sides, and inserts a C^(-1),C cancellation on one side. +The complete two-role comparison uses D=260 states and no expanded words. +The helper is explicitly overwritten on both sides in this stress program; +the separate dirty-sandwich example tests actual helper restoration. + +For a termwise tensor substitution choose the new generators G_a^(tensor f) +and their actual inverses. The theorem then applies at the enlarged payload +dimension. Scalar coefficients stay scalar; no tensor power of a sum or of +the whole register-role matrix is taken. This is only an algebraic interface +lemma. Native realizations, phases, rounding, rectangular typing, precision, +stock, hosting, fixed-tape cost, complete paid invoices and supplier admission +are not proved here. No selected frontier or kappa changes. + +Prepared by Krzysztof Wójt with substantial OpenAI Codex assistance. Apache-2.0. diff --git a/research/coupled-provider-independent-audit/custody/5376/provenance-sources/7c472563474e60185e6ca101a17622133d047e56/research/passive-saved-query-ceiling/evidence/frozen/pr4948-saved-query-macro-gate/UNIFORM-ALPHABET-ADDENDUM.md b/research/coupled-provider-independent-audit/custody/5376/provenance-sources/7c472563474e60185e6ca101a17622133d047e56/research/passive-saved-query-ceiling/evidence/frozen/pr4948-saved-query-macro-gate/UNIFORM-ALPHABET-ADDENDUM.md new file mode 100644 index 0000000000..d742381500 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/provenance-sources/7c472563474e60185e6ca101a17622133d047e56/research/passive-saved-query-ceiling/evidence/frozen/pr4948-saved-query-macro-gate/UNIFORM-ALPHABET-ADDENDUM.md @@ -0,0 +1,11 @@ +# Uniform finite alphabet for the large-width argument + +This clarification leaves the six-file freeze and its manifest unchanged. Independent reviewer B requested that the finite-alphabet premise be explicit. + +All one-column literal address maps in this gate lie in the Clifford group on the **fixed 17-axis ambient space**. Its projective quotient is finite. Scalar root phases are absorbed into the coefficients after tensor lift; they do not change Fourier grade. The finite universe of projective one-column Clifford maps is therefore independent of column width f. + +The Gram argument in `PROOF.md` can be applied once to representatives of this whole finite projective universe, rather than merely to the words appearing in a single chosen decoder. For sufficiently large f its tensor-power Gram matrix is positive definite. This gives a uniform threshold even when scalar reconstruction coefficients, selections of allowed controls, or numbers of passive scalar operations depend on f. The source one-column C1/C3 entries and all their allowed left expansions remain in the monomial subset and preserve the grade support proved in the frozen packet. + +This does not include f-dependent payload permutations outside the fixed columnwise Clifford alphabet. Such maps are not granted by this gate's scalar-owner/actual finite-code contract. It also does not turn the source's finite coefficients into coefficients raised to tensor powers. + +No new scan, emitter, cost claim, or κ result is added. diff --git a/research/coupled-provider-independent-audit/custody/5376/provenance-sources/7c472563474e60185e6ca101a17622133d047e56/research/projection-recursion-check/README.md b/research/coupled-provider-independent-audit/custody/5376/provenance-sources/7c472563474e60185e6ca101a17622133d047e56/research/projection-recursion-check/README.md new file mode 100644 index 0000000000..1d8c9f7b1b --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/provenance-sources/7c472563474e60185e6ca101a17622133d047e56/research/projection-recursion-check/README.md @@ -0,0 +1,191 @@ +# Independent check of #4628's block-5 and block-6 bounds (2.99172, 2.97290, 2.9447) + +No new κ. Nothing here is about integer multiplication. This is an independent check of one hand-argued claim of +open PR #4628 (Jacob Alan Sussman, head `ee4fd87f064017c23e5a86fc1dcfe0a5237caed3`): + +> m ≥ 4: at least 2.9447 calls per array (2.99172 at m = 5, 2.97290 at m = 6), engine game, argued by hand +> (two AI reviewers reproduced the numbers). + +PROOF.md §7 of #4628 says only "The block-4 hook is carried upward through projections between the frame graphs of +the engine, controlled by a coupling argument", and refers to the author's repository for the argument. + +## Result + +| Item | Verdict | How | +|---|---|---| +| Projection counts N_r(s) | **correct** | own derivation (section 3); brute force over **all** 15, 135 and 2,295 Lagrangians at m = 2, 3, 4 and every nonzero p, plus 60 sampled Lagrangians at m = 5 | +| T_5 = 834241/278850 = 2.991720, T_6 = 1188222/399685 = 2.972896 | **reproduced exactly** | own recursion in exact fractions | +| ≥ 2.9447 for every m ≥ 4 | **reproduced** | exact for m = 4..60 (minimum 2.944709234, decreasing in m); for m ≥ 60 by a monotone coupling whose transition inequalities I prove for every k (section 4; the author's `tail.py` checks them for k ≤ 80 only), c* = 2.944709234 | +| Soundness of the recursion | **a sound route exists** (my reconstruction, argued by hand, section 2) | induced representations over the nonzero Paulis plus Bruhat transitivity for the engine's frame group | +| Inputs | **the numbers rest on two block-4 values that nobody re-checked**: a_3 ≥ 68,320 (enters T_5) and a_2 ≥ 48,576 (enters T_6) | section 5 | + +Gaps found, none of which refutes the claim: + +1. **The written argument is not public.** #4628 says "The programs and the written argument are in my repository". + At commit `86e575e2` of jacobalansussman/wht-power-saving-lean only the programs and their outputs are public + (`research/block-bounds-and-new-rules/programs/engine-bounds-blocks-5-and-6/`). The proof they cite ("PROOF.md, + Theorem 3", "Lemma 1(c)", "Lemma 2", "Theorems 4 and 5") is in the folder `proofs/induction/` of a private archive + (that repository's `block-bounds-and-new-rules/README.md`, Sources). So the hand argument cannot be read by + reviewers. Section 2 gives an independent route. +2. **Two inputs come from one program.** T_5 = (N_5(4)·a_4 + N_5(3)·a_3)/(N_5,1(1)·a_1) uses the block-4 hook values + a_1 = 27,456 (cap, proved in Lean), a_4 ≥ 86,592 (demand, determinant certificate, C author evidence) and + **a_3 ≥ 68,320**; T_6 also uses **a_2 ≥ 48,576**. The last two are mod-p rank lower bounds printed by the author's + `hookG.py` (`data/block4-hook/out_rank2_blocks.txt`). Mod-p rank is the safe direction, but no certificate is + stored, and #4628's `verify.py` does not check them. The author's README calls the three-move value "computed + modulo a prime but not certified" (that remark is about using it as an upper bound; here it is used as a lower + bound). With only the triangle bounds a_2 ≥ a_4 − 2a_1 = 31,680 and a_3 ≥ a_4 − a_1 = 59,136 the route gives + T_5 ≥ 2.83219, T_6 ≥ 2.77245, T_60 ≥ 2.70821. +3. **The tail was checked numerically only up to k = 80.** The coupling needs two inequalities at every block k. + They hold for all k (section 4), so this gap is closed here. +4. **Status of the soundness step.** My reconstruction in section 2 is argued by hand, like the original. It is + independent: I did not see the author's proof. + +Bearing on the open shapes: with T_5 and T_6 and the bound W + m (not checked here), the smallest shapes left open are +2 in 7 and 3 in 9 at block 5, and 2 in 8 and 3 in 9 at block 6. These match #4628's table. 3 in 9 needs more than +3 calls per array. This route cannot give that: its limit is 2.94471, and it falls with m. Excluded by T_m alone: +3 in 8 and 4 in 11 at blocks 5 and 6, 5 in 14 at block 6, and W in 3W − 1 for W ≤ 120 (block 5) and W ≤ 36 (block 6). +All of these match #4628. + +## 1. The claim, in the form checked + +Frames are Lagrangian subspaces of F_2^(2m), the symplectic space of the m-qubit Paulis. The engine's free letters +are shifts (X Paulis), invertible XOR-linear address maps, and phases i^(z·x + c). Conjugating S-phases by address +maps gives CZ. Together these generate every Pauli and every Clifford that fixes the Z-frame L_0. Their image in +Sp(2m, 2) is the whole Siegel parabolic P = {[[A, B], [0, A^(-T)]]}. A call C_v = (1+i)/2·I + (1−i)/2·X_v is √X_v, +a Clifford at frame distance 1 from L_0, and the target C^(⊗m) is at distance m. +For a subspace N kept by every free letter, raise(f g f′) = raise(g) for free f, f′. So the double cosets P\Sp/P, +which are the distances d = m − dim(L_0 ∩ gL_0), make raise a function a_d of the distance alone (with a_0 = 0). +The brute-force count confirms that every Lagrangian at the same distance gives the same projection counts. + +The recursion (author's `induct.py`, re-implemented here) is a^(m)_r = Σ_s N^(m)_r(s)·a^(m−1)_s. Here N^(m)_r(s) +is the number of nonzero p ∈ F_2^(2m) for which the reductions π_p L = (L ∩ p^⊥) + ⟨p⟩ of a distance-r pair have +distance s in p^⊥/⟨p⟩. The bound at block m is T_m = a^(m)_m / a^(m)_1, by Theorem R (#4628 PROOF.md §1). + +## 2. Why the recursion is a valid lower bound (independent reconstruction; argued by hand) + +Let N′ be a block-(m−1) certificate kept by the block-(m−1) frame group, with profile a′. The steps: + +- **Copies of N′ for each p.** For each nonzero p, pick a Clifford h_p with h_p p = z_1 and h_p(π_p L_0) = L_0. + This is possible because the stabiliser of z_1 acts transitively on the Lagrangians containing z_1. Let U_p be + the sum of the two eigenspaces of P taken in all f columns at once (V_+(P)^(⊗f) ⊕ V_−(P)^(⊗f)). Put the copy + N_p = h_p^(−1)(N′ ⊗ both Z_1-eigenspaces) inside U_p; the X_1 Pauli identifies the two eigenspaces. +- **The new space.** Set U = ⊕_p U_p. A Clifford g maps U_p to U_(gp), and the eigenvalue signs cancel because all + f columns carry the same sign. U is a representation of the finite group G generated by the letters. +- **The program identity holds on U.** A program right at every width f ≥ 1 is an identity in C[G]. Burnside–Brauer + (faithful V, the Vandermonde argument run with exponents n ≥ 1) puts every irreducible of G into some V^(⊗f) with + f ≥ 1. So Theorem R applies on U, with any linear (complex) mixing. +- **Free letters keep N = ⊕_p N_p.** For a free b, the map h_(bp)·b·h_p^(−1) fixes z_1 and L_0. Its reduction is + therefore a block-(m−1) free element, which keeps N′. +- **Raise splits over p.** raise_U(g) = Σ_q raise_(N′)(h_q g h_(g⁻¹q)^(−1)). The reduced map sends the standard + frame to h_q(π_q gL_0). Its distance from the standard frame h_q(π_q L_0) is d(π_q L_0, π_q gL_0). So raise_U(g) + = Σ_q a′_(d(π_q L_0, π_q gL_0)), which is the recursion, up to a uniform factor 2 that cancels in T_m. + +In which direction each input is needed: the cap at block m is N_1(1)·a′_1 and needs a′_1 as an upper bound, with +a′_0 = 0. The demands need a′_(m−1) and a′_(m−2) as lower bounds. The optional triangle step a_r ≥ a_m − (m−r)·a_1 +is valid (raise is subadditive) and changes nothing here. The checks agree: with and without it the tops are +identical. + +This route uses the frame group of the engine (Lagrangians, the Siegel parabolic). As #4628 says, it does not carry +over to the widened game (Toffoli is not Clifford). + +## 3. The projection counts (own derivation) + +Let L, M be at distance r, so I = L ∩ M has dim m − r and L + M = I^⊥. The cases for p: + +| p | number of such p | reduced distance s | +|---|---|---| +| in I | 2^(m−r) − 1 | r | +| outside L + M | 4^m − 2^(m+r) | r (π_pL ∩ π_pM = (I ∩ p^⊥) + p) | +| in exactly one of L, M | 2(2^m − 2^(m−r)) | r − 1 (the intersection is I + p) | +| p = l + m′ (l ∈ L∖I, m′ ∈ M∖I), ω(l, m′) = 1 | (2^r − 1)·2^(r−1)·2^(m−r) | r − 1 | +| same, ω(l, m′) = 0 | (2^r − 1)(2^(r−1) − 1)·2^(m−r) | r − 2 (l also lies in the intersection) | + +ω(l, m′) is well defined modulo I. The pairing L/I × M/I → F_2 is nondegenerate, which gives the split +(2^r − 1)·2^(r−1) against (2^r − 1)(2^(r−1) − 1). This is the author's closed form. `verify.py` confirms it against +brute force. + +## 4. The tail for m > 60 (independent proof of the coupling inequalities) + +Write j = k − r for the deficit. A random p moves block k to block k − 1, and the deficit +- goes up with probability p_up = N_r(r−2)/(4^k − 1) = (2^r − 1)(2^(r−1) − 1)·2^j/(4^k − 1); +- goes down with probability p_down = N_r(r)/(4^k − 1) = (2^j − 1 + 4^k − 2^(2k−j))/(4^k − 1). + +R^(k)_r = a^(k)_r/a^(k)_1 = (1/q_k)·E[R^(k−1)_s] with q_k = N_1(1)/(4^k − 1) ≤ 1. Hence +T_m ≥ E[R^(60)_(60 − J)], where J is the deficit at block 60. + +- **Up-probability.** The numerator equals 2^(2k−j−1) − 3·2^(k−1) + 2^j ≤ 2^(2k−j−1) − 2^k. This is less than + 2^(−(j+1))·(4^k − 1), so p_up ≤ 2^(−(j+1)). +- **Down-probability.** p_down ≥ 1 − 2^(−j) is equivalent to 2^j ≥ 2^(−j). Once r = 0 the chain only goes down. +- **The dominating chain.** It moves up with probability 2^(−(j+1)) and down with probability 1 − 2^(−j). It is + monotone, since Q_up(j) + Q_down(j+1) = 1, and its stationary law is π*(j) ∝ Π_(i≤j) 1/(2^i − 1). +- **Comparison.** Started at deficit 0, J ≤_st π*. The block-60 profile is nondecreasing in r (checked), so T_m ≥ + Σ_j π*(j)·R^(60)_(60−j). The tail of the normaliser is bounded by 2w_J with J = 80 (w_(j+1)/w_j ≤ 1/3). This gives + c* = 2.944709234 > 2.9447, the same constant as the author's. + +## 5. Inputs, and what each number rests on + +| input (block-4 hook, k = 8, f = 9) | used in | status | +|---|---|---| +| a_1 = 27,456 (cap) | all | proved in Lean (`hook_cap`), as an upper bound | +| a_4 ≥ 86,592 (demand) | all | 5,412 × 5,412 minor, C checker (author evidence in #4628; about an hour) | +| a_3 ≥ 68,320 | T_5 and later | mod-p rank in the author's `hookG.py`; no stored certificate; not re-checked by #4628 | +| a_2 ≥ 48,576 | T_6 and later | as above. The README of #4628 also cites 48,576 as a certified **upper** bound (two calls in a row); the induction needs it as a **lower** bound, which is again only the mod-p rank | + +## Reproduce + +```sh +python3.12 -B research/projection-recursion-check/verify.py # PASS_PROJECTION_RECURSION_CHECK, about 35 s, stdlib +python3 scripts/research_package.py --package research/projection-recursion-check --check-only +python3.12 scripts/research_package.py --package research/projection-recursion-check +``` + +`verify.py` imports nothing from #4628 or from the author's repository. Ten controls must be rejected, and are: + +- a closed form with one count moved; +- T_5 and T_6 off by one in the denominator; +- a_3 + 1 reproducing T_5; +- two weakened dominating chains; +- 3 in 9 at block 6 claimed excluded; +- 3 in 8 at block 5 claimed allowed; +- 2.99172 claimed from the triangle inputs alone; +- a nonmonotone profile. + +## NOT covered + +- The block-4 hook values themselves. I did not recompute a_2, a_3 or a_4 (dimension 102,960), or the Lean proofs + of the cap. +- The author's private written proof. Section 2 is my own reconstruction; it is argued by hand, and no person has + checked it. +- The other claims of #4628: W + m and 2W, one array, no-phase block 3, the widened-game keptness, and section 7. + The shapes above use W + m as stated in #4628. +- Whether #288's or Harvey's models lie inside the engine game. + +## Open next questions + +See `open_questions` in [TASK.json](TASK.json): + +1. Certify a_3 ≥ 68,320 and a_2 ≥ 48,576 with a stored minor and a separate checker. +2. Write section 2 as a full proof, or in Lean. +3. Exclude 3 in 9 at block 5 or 6. That needs a certificate above 3 calls per array, which this route cannot give. + +## Sources (pins in SOURCES.json; external files by sha256) + +- #4628 at head `ee4fd87f064017c23e5a86fc1dcfe0a5237caed3`: `research/complex-small-m-lower-bounds/README.md` + (table of section 1, section 6) and `PROOF.md` §7. +- jacobalansussman/wht-power-saving-lean at `86e575e28ed94890872dcff1bb2621d7ff559cbd`, read only to locate the + claim and its inputs; no code reused. Files under `research/block-bounds-and-new-rules/`: + - `README.md`, sha256 `47c99107…54f50a`; + - `data/engine-bounds-blocks-5-and-6/out_induct.txt`, `e4cf4402…bb4072`; + - `data/engine-bounds-blocks-5-and-6/out_tail.txt`, `9861aa2c…778c2b`; + - `programs/engine-bounds-blocks-5-and-6/induct.py`, `dabe7190…2c428c`; + - `programs/engine-bounds-blocks-5-and-6/nrs_closed.py`, `54ba1ab4…71eeb`; + - `programs/engine-bounds-blocks-5-and-6/tail.py`, `2ac28e4c…12e717d5d4`; + - `data/block4-hook/out_rank2_blocks.txt` (the a_2, a_3 values). + +## Credit + +The claim, the projection recursion, the block-4 hook and its numbers are Jacob Alan Sussman's (#4628 and his +repository, written with AI agents). The certificate method (Theorem R / the FO lemma) is eumemic's (#288), with +Swapnil Jain's P1/P2 as cited there. The engine and cost model are OpenAI's. + +Prepared by lm1909 with Claude Code (Claude Opus 5.5) assistance. Apache-2.0. diff --git a/research/coupled-provider-independent-audit/custody/5376/provenance-sources/7c472563474e60185e6ca101a17622133d047e56/research/t74-native-fast/LICENSE b/research/coupled-provider-independent-audit/custody/5376/provenance-sources/7c472563474e60185e6ca101a17622133d047e56/research/t74-native-fast/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/provenance-sources/7c472563474e60185e6ca101a17622133d047e56/research/t74-native-fast/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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Its alias rule, changed-reference K_G handoffs, initial compensation and exact free-operator replay (vendored under new/code/borrow/vendor, see new/code/borrow/NOTICE-PR2226.md) are applied here to the T74 pivot-566+554 words; the native lowering, window-exact owner fill and independent audit of the borrow words are new in this package. Bootstrap carried-cutoff repair: PR1956 (Josie Elliston); Lemma G label/adapter checks and X/Y/Z mutants: PR1964 (thakrarsagar), extended here with borrow warp/zero-buffer controls. + +New research prepared by Rohan Arun with substantial OpenAI Codex assistance. Apache-2.0. Parent words and build recipe method derive from Jeremy Kothe PR1274 and Rohan Arun PR1218, with lineage credited in README.md. All inherited mathematical qualifications are retained. +Additional pivot555 and567 composition by Rohan Arun with substantial OpenAI Codex assistance. + +T74 exact-fill owner construction by Rohan Arun with substantial OpenAI Codex assistance. + +PR1377 grid refinement credited to Jeremy Kothe. Outer witness refinement by Rohan Arun with OpenAI Codex assistance; construction unchanged. + +Pivot-566 kernel, words, edits, rebuild.py and rebind.py: PR1625 (mdumitrean). Endpoint/outer-witness stacking, fine_cache.py and oracle stage by jeremykothe2 with oh-my-pi assistance. + +The preceding paragraphs are inherited source notices, not attribution of this derivative. +This joint twelve-source construction, generator, independent replay, hosting composition and package: Tekalign (@tekuuu), with substantial OpenAI Codex assistance. No independent human review claimed. +Credits: Cinna Davis/PR2226 anticipatory dirty borrowing; Tekalign/PR2436 four lifted targets; Jeremy Kothe/PR2462,2588,2673 source pipeline, source-label swap and order/fill; zxv/PR2530 eight aliases; Mason Hale/PR2696 concentrated source-partner assignment and independent local interpreter; Philippe Van Velzen/PR2559,2679 evacuation, six pre-life hosts and refit/alias; themilkman216/PR2621 priority order; Marius-Paul Dumitrean/PR2733 independent concentrated/pre-life composition; Vlado Vojdanovski/PR2322 generator utilities. PR2720's fixed-old-path cut obstruction motivates the changed premise. The retained owner/native/bit/modern outer lineage and their notices remain in the pinned source. New work Apache-2.0. diff --git a/research/coupled-provider-independent-audit/custody/5376/provenance-sources/7c472563474e60185e6ca101a17622133d047e56/research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py b/research/coupled-provider-independent-audit/custody/5376/provenance-sources/7c472563474e60185e6ca101a17622133d047e56/research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py new file mode 100644 index 0000000000..166841a037 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/provenance-sources/7c472563474e60185e6ca101a17622133d047e56/research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py @@ -0,0 +1,149 @@ +"""Small exact Gaussian-dyadic Clifford compiler, independent of gx internals. +Paulis use i^p X^x Z^z. State vectors use integer Gaussian numerators / 2^d. +The tableau is supplemented by a literal circuit, so global phases are kept. +""" +from dataclasses import dataclass + +def parity(x):return x.bit_count()&1 +def rank(rows): + p={} + for x in rows: + while x: + b=x.bit_length()-1 + if b not in p:p[b]=x;break + x^=p[b] + return len(p) +def transpose(rows,n):return tuple(sum(((rows[j]>>i)&1)<>j&1);a[j],a[k]=a[k],a[j] + for i in range(n): + if i!=j and a[i]>>j&1:a[i]^=a[j] + assert [r&((1<>n for r in a) +def basis_extend(cols,n): + out=[] + for x in list(cols)+[1<len(out):out.append(x) + assert len(out)==n + return tuple(out) +def nullspace(rows,n): + a=list(rows);p=[];k=0 + for j in range(n): + t=next((i for i in range(k,len(a)) if a[i]>>j&1),None) + if t is None:continue + a[t],a[k]=a[k],a[t] + for i in range(len(a)): + if i!=k and a[i]>>j&1:a[i]^=a[k] + p.append(j);k+=1 + return tuple((1<>j)&1)<>i&1:out=pmul(out,T[i]) + for i in range(n): + if z>>i&1:out=pmul(out,T[n+i]) + return out +def compose(A,B):return tuple(apply(A,p) for p in B) +def inverse(T): + n=len(T)//2;cols=[x|(z<>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4)) + return tuple(out) +def qvalue(Q,alpha,x,n): + return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4 +def mul_i(a,p): + x,y=a;p%=4 + return [(x,y),(-y,x),(-x,-y),(y,-x)][p] +@dataclass +class Op: + n:int + tab:tuple + circuit:list + def then(self,b): + assert self.n==b.n + return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit) + def adjoint(self): + circ=[] + for e in reversed(self.circuit): + if e[0]=='P':circ.append(('P',inv(e[1],self.n))) + elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2]))) + elif e[0]=='C':circ.append(('C',e[1],-e[2])) + elif e[0]=='phase':circ.append(('phase',(-e[1])%4)) + else:circ.append(e) + return Op(self.n,inverse(self.tab),circ) + def zero_state(self,basis=0): + N=1<>i)&1 for i in range(n)) + assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n)) + return Op(n,tuple([(1<>i&1 else 0,1<>i&1 else 0) for i in range(n)]),[('C',q,sgn)]) +def xgate(n,b):return Op(n,tuple([(1<>i)&1)) for i in range(n)]),[('X',b)]) +def fourier(n,axes=None): + out=ident(n) + for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<len(selected):picks.append(j);selected.append(x) + assert len(picks)==r and all(x>>r==0 for x in Bcols) + Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1<=i^parity(q.x)|x>`; port0 is +an actual noncommuting control because parity(q.t)=1. Conjugating the +literal words by an admitted central monomial keeps rawD0 in that subgroup +and H9 outside it, even when the resulting central queries do not commute. +This uses subgroup membership, not a false commutation identity. + +These calculations reuse the actual recipe and normalizer observation of +the independent source/accounting agent, with exact source bytes retained. +They do not rerun the whole native632-field execution or the outer compiler. + +## Algebraic statement, including all retained pure helper jobs + +Let G be a fixed finite-phase Clifford group for one column, and H a +subgroup. At width f work in a finite-dimensional central-character twisted +group algebra A_f with subgroup algebra B_f on H/Z, over a characteristic- +zero splitting field K. Write d=dim_K B_f. Let pi:A_f->B_f retain only +subgroup basis classes. It is a B_f-bimodule map. Membership and this +projection are unchanged by scalar phases. No domain assumption is made. + +For the source application, H grants all transverse Clifford operations +and central monomial operations, retaining their tensor-factor separation. +It includes the raw d_s, their translations and admitted central monomial +wrappers. A full rank17 main target is outside H. Equation(1) shows the +literal fullH9 helpers are outside H: their central factor is Q or Q^-1, +which is not monomial, while D_A is purely transverse. This is an exact +factor statement; it does not homogenize a rank4 helper to rank9. + +Consider two main owners, m1 non-H helper jobs emitted in the first call, +m2 other non-H helper jobs emitted in the second call, and s further owners +whose desired maps lie in H (including restored identity scratch). Thus + + n=2+m1+m2+s. + +Each call has ONE elementary main shear with a pure query outside H. +Its diagonal factors on the main owners are units in B_f. On its own +helper owners it performs the specified pure group jobs; other helpers are +identity spectators. Any H-valued helper factors are units in B_f and +included among the s ordinary owners. Helper owner sets are disjoint. +Allow arbitrary L,W,R in GL_n(B_f), and arbitrary noncommuting queries and +helper group words outside H. Suppose the endpoint is the two independent +non-H main jobs together with every original helper job and its required +H-valued spectators. Then no such endpoint exists. + +### Compression proof + +Write M=T2 W T1, with diagonal factors before the source shears as above. +Let U contain all output rows except the second shear's destination main +row and the m2 non-H helpers transformed in the second call. Let C contain +all input columns except the m1 non-H first-call helper owners. Thus + + |U|=n-m2-1, |C|=n-m1. + +For rows in U the second shear contributes no non-H term and its diagonal +factor is a unit in B_f. For columns in C, T1's diagonal is a unit in B_f; +its only other possible term contains the SINGLE first query outside H. +Multiplication by B_f on either side keeps that term outside H. Therefore + + (pi(M))_(U,C) = (D2)_U W_(U,C) (D1)_C. (2) + +No product of two non-H words is evaluated or assumed to lie in H. In +particular Q2, Q1 and the helpers need not commute or normalize B_f. + +View W as an invertible K-linear map on the regular right module B_f^n. +Restricting its input to C gives an injective map on a |C|d-dimensional +space. Projecting its output to U can destroy at most (n-|U|)d dimensions. +Consequently + + rank_K W_(U,C) >= (|U|+|C|-n)d = (s+1)d. + +The B_f-unit diagonal factors in(2) preserve this rank. A compression +cannot have greater rank than the whole matrix, so + + rank_K pi(M) >= (s+1)d. (3) + +The desired diagonal endpoint instead projects to zero on its two main +jobs and all m1+m2 non-H helper jobs. Its s H-valued target words are group +units, so its projected rank is exactly s*d. Because pi is a bimodule map, +invertible outer L,R preserve projected rank. This contradicts(3). +Zero divisors in B_f do not affect this finite vector-space argument. + +For the natural four-owner case, m1=m2=1,s=0. The two U rows are the source +main row of the second shear and the FIRST helper row. If pi(M)=0, both +rows of W must be supported on the first helper's single column. They +cannot jointly surject onto two independent B_f output modules. This is +the shortest form of the obstruction. It does not depend on a common Q, +the first shear orientation, or the quadratic double-query product. + +## All-width faithfulness and exact free-control boundary + +Let Z be the scalar subgroup of the chosen finite-phase group G; H contains +Z. At width f specialize every scalar z=ζI as ζ^f. The quotient A_f has +one basis class per projective group element G/Z. The proof of injective +tensor evaluation is short. Choose representatives v_t. For each t and +each other u choose a linear functional vanishing on v_u and nonzero at +v_t. Their product isolates v_t in degree |G/Z|-1. Multiplying by a power +of a functional nonzero at v_t extends this to every larger degree f. +Applying it to the tensor vectors proves independence for every +f>=|G/Z|-1. Thus the operator endpoint would give a forbidden A_f identity +at all sufficiently large widths. Width-dependent scalar coefficients and +free choices within this same finite alphabet are allowed. Accidental +small-width linear relations between Clifford matrices are not used. + +The theorem grants a large but SPECIFIC free grammar: central monomials +and transverse Cliffords, with their separation preserved. Arbitrary +central/fresh address mixing is outside B_f. The theorem also retains +invertible global owner controls and restored spectator contracts. It +does not inherit the separate4856 maximal-grade proof's arbitrary +rectangular COPY/DROP conclusion. Discarding or erasing main-dependent +garbage can lower projected rank and is a different endpoint. Zero clean +work fields cleared at exit can be included by the equivalent kernel +form: (3) gives nullity at most (m1+m2+1)d, while the 2+m1+m2 required +non-H original input columns would all have zero projected output. +This requires a reversible global B_f extension and full cleanup, not an +unproved permission to erase arbitrary dirty state. + +## Invoice, nearest predecessor and next actual lever + +Retaining all816 autonomous helper rewards leaves the hypothetical invoice +`224H17+2H-2P`, with supplied optimistic margin39.063938114801903 at +C=.0030217758. That positive budget motivates testing a changed resource; +it is not an endpoint certificate. This gate closes the separated-resource +realization even with retained transformed helper operations. No kappa gain +or complete native obstruction is claimed. + +PR4712, head b75a27bf07f1584b20babfddf887493981cd5949, already gives the +dirty-helper word `h+=x; h=Fh; y+=h; h=F^-1h; h-=x; h=Fh; y-=h`. +It returns `(x,y+Fx,Fh)`, with three F/F^-1 calls and four scalar ADDs. +Its paid-minus-helper bill is2*r^t against one replaced owned centre's +r^t. It is not a new saving and is credited here rather than rediscovered. + +The nearest method is PR4920 at7eb4ef5251f7ba96c7e5d78c42fc98e66b7be4ba: +its separated theorem allowed identity scratch, while its full-monomial +grade theorem allowed exactly two owners. The present compression argument +adds simultaneously transformed productive helper operations to the first +scope; it does not combine the two old scopes into a universal result. +The parent independently checked the rank argument and supplied the +commuting-Q row-kill precursor. Native operators and source interfaces are +credited to Cinna Davis/1337isnot1337 and the upstream contributors. Source +normalizer reuse and backward-ABI correction are credited to the independent +accounting/source agent and shared-producer agent. New derivation and +portable corroboration: OpenAI Codex gpt-6.1-sol/high. Apache-2.0. + +The smallest constructive change is a literal central/fresh monomial route +on the actual native role boundaries. It must preserve both distinct helper +jobs and pay for any entrance-chart conversion. X begins in a rank1 chart; +Y and the full helper begin empty. Common full exit charts do not make +swapping X and helper inputs free. An already transformed arbitrary value +Hh, supplied before all controls and returned unchanged, is just an arbitrary +dirty coordinate after renaming w=Hh; useful resource access must involve +the producer H itself or a correlated saved original input. No routing +family search or native word was emitted for this gate. diff --git a/research/coupled-provider-independent-audit/custody/5376/provenance-sources/7c472563474e60185e6ca101a17622133d047e56/research/universal-dirty-certificates/fields.py b/research/coupled-provider-independent-audit/custody/5376/provenance-sources/7c472563474e60185e6ca101a17622133d047e56/research/universal-dirty-certificates/fields.py new file mode 100644 index 0000000000..f1b6dc83e2 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/provenance-sources/7c472563474e60185e6ca101a17622133d047e56/research/universal-dirty-certificates/fields.py @@ -0,0 +1,140 @@ +"""Small exact scalar layer shared by producer and checker (part of their trust base). + +Prepared for zxv with substantial OpenAI Codex assistance. Apache-2.0. +""" +from fractions import Fraction +from math import isqrt +from functools import lru_cache +import re + + +class Gaussian: + """Q(i); input strings use a+bi with rational a,b, or just i/-i.""" + def __init__(self, value=0): + if isinstance(value, Gaussian): + self.real, self.imag = value.real, value.imag + elif type(value) is str and value.endswith("i"): + body = value[:-1] + rational = r"\d+(?:/\d+)?" + match = re.fullmatch(r"([+-]?"+rational+r")([+-](?:"+rational+r")?)", body) + if match: + self.real = Fraction(match[1]) + self.imag = Fraction(match[2]+"1" if match[2] in ("+", "-") else match[2]) + else: + if body in ("", "+", "-"): + body += "1" + self.real, self.imag = Fraction(0), Fraction(body) + else: + self.real, self.imag = Fraction(value), Fraction(0) + + @classmethod + def pair(cls, real, imag): + out = cls() + out.real, out.imag = real, imag + return out + + def __add__(self, other): + z = Gaussian(other) + return self.pair(self.real+z.real, self.imag+z.imag) + + __radd__ = __add__ + + def __mul__(self, other): + z = Gaussian(other) + return self.pair(self.real*z.real-self.imag*z.imag, self.real*z.imag+self.imag*z.real) + + __rmul__ = __mul__ + + def __neg__(self): + return self.pair(-self.real, -self.imag) + + def __sub__(self, other): + return self+-Gaussian(other) + + def __rsub__(self, other): + return Gaussian(other)+-self + + def __truediv__(self, other): + z = Gaussian(other) + norm = z.real*z.real+z.imag*z.imag + return self*self.pair(z.real/norm, -z.imag/norm) + + def __rtruediv__(self, other): + return Gaussian(other)/self + + def __eq__(self, other): + z = Gaussian(other) + return self.real == z.real and self.imag == z.imag + + def __bool__(self): + return bool(self.real or self.imag) + + def __str__(self): + if not self.imag: + return str(self.real) + return str(self.real)+("+" if self.imag >= 0 else "")+str(self.imag)+"i" + + __repr__ = __str__ + + +def scalars(problem): + p = problem.get("field", "Q") + if p == "Q": + return Fraction + if p == "Qi": + return Gaussian + if type(p) is not int: + raise ValueError("field must be Q, Qi or a prime at most 2^31-1") + return prime_scalars(p) + + +@lru_cache(maxsize=32) +def prime_scalars(p): + if not 2 <= p <= 2**31-1 or any(p % d == 0 for d in range(2, isqrt(p)+1)): + raise ValueError("field must be Q, Qi or a prime at most 2^31-1") + + class Prime: + def __init__(self, x=0): + if isinstance(x, Prime): + self.value = x.value + else: + q = Fraction(x) + self.value = q.numerator*pow(q.denominator, -1, p) % p + + def __add__(self, other): + return Prime(self.value+Prime(other).value) + + __radd__ = __add__ + + def __mul__(self, other): + return Prime(self.value*Prime(other).value) + + __rmul__ = __mul__ + + def __neg__(self): + return Prime(-self.value) + + def __sub__(self, other): + return self+-Prime(other) + + def __rsub__(self, other): + return Prime(other)+-self + + def __truediv__(self, other): + return Prime(self.value*pow(Prime(other).value, -1, p)) + + def __rtruediv__(self, other): + return Prime(other)/self + + def __eq__(self, other): + return self.value == Prime(other).value + + def __bool__(self): + return bool(self.value) + + def __str__(self): + return str(self.value) + + __repr__ = __str__ + + return Prime diff --git a/research/coupled-provider-independent-audit/custody/5376/registered-driver/848cdce9003262c4b6e02ec4558f302e4fae56ad.commit b/research/coupled-provider-independent-audit/custody/5376/registered-driver/848cdce9003262c4b6e02ec4558f302e4fae56ad.commit new file mode 100644 index 0000000000..3a10165169 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/registered-driver/848cdce9003262c4b6e02ec4558f302e4fae56ad.commit @@ -0,0 +1,6 @@ +tree eb1a7e9f6b14f6a651f679fbfd9dfb2c23382697 +parent aef3c2f91a10d4c41e814ea264a9d64c9423bcb2 +author Ali Romman <226877337+aliromman@users.noreply.github.com> 1792796110 -0500 +committer Ali Romman <226877337+aliromman@users.noreply.github.com> 1792796110 -0500 + +Allocate provider replay time within the fixed package budget diff --git a/research/coupled-provider-independent-audit/custody/5376/registered-driver/d50934faea13c2c1d72a4edd7f53875541ceae5e.tree b/research/coupled-provider-independent-audit/custody/5376/registered-driver/d50934faea13c2c1d72a4edd7f53875541ceae5e.tree new file mode 100644 index 0000000000..27368f2527 Binary files /dev/null and b/research/coupled-provider-independent-audit/custody/5376/registered-driver/d50934faea13c2c1d72a4edd7f53875541ceae5e.tree differ diff --git a/research/coupled-provider-independent-audit/custody/5376/registered-driver/eb1a7e9f6b14f6a651f679fbfd9dfb2c23382697.tree b/research/coupled-provider-independent-audit/custody/5376/registered-driver/eb1a7e9f6b14f6a651f679fbfd9dfb2c23382697.tree new file mode 100644 index 0000000000..b07cce8431 Binary files /dev/null and b/research/coupled-provider-independent-audit/custody/5376/registered-driver/eb1a7e9f6b14f6a651f679fbfd9dfb2c23382697.tree differ diff --git a/research/coupled-provider-independent-audit/custody/5376/registered-driver/research_package.py b/research/coupled-provider-independent-audit/custody/5376/registered-driver/research_package.py new file mode 100644 index 0000000000..ef9b52c392 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/registered-driver/research_package.py @@ -0,0 +1,1022 @@ +#!/usr/bin/env python3 +"""Validate and replay explicitly registered research packages, never every verify.py. + +Douglas Colkitt, with OpenAI Codex assistance. Apache-2.0. +""" +import argparse +import errno +from contextlib import closing, contextmanager +from itertools import chain +import hashlib +import importlib.metadata +import json +import os +from pathlib import Path, PurePosixPath +import re +import signal +import stat +import subprocess +import sys +import tempfile +import threading + +ROOT = Path(__file__).resolve().parents[1] +GIT_BLOB_RESPONSE_TIMEOUT = 90 + + +def require(ok, message): + if not ok: + raise ValueError(message) + + +def canonical_relative_path(name): + # Git's changed paths use one repository-relative POSIX spelling. Accepting + # aliases here would let a declared input evade the planner's exact match. + require(isinstance(name, str), "canonical relative path must be a string") + path = PurePosixPath(name) + require(bool(path.parts) and not path.is_absolute() and ".." not in path.parts + and "\\" not in name and path.as_posix() == name, + "use a canonical repository-relative POSIX path: " + name) + return path + + +def symlink_free_relative_path(root, name): + """Reject symlink components without requiring a deleted input to exist. + + Git reports changes under the target's path, not a symlink alias declared + by its consumer. Inspect existing components below the repository root; + the checkout must remain stable during planning, validation and replay. + """ + parts = canonical_relative_path(name).parts + current = root + for part in parts: + current = current / part + try: + mode = current.lstat().st_mode + except (FileNotFoundError, NotADirectoryError): + break + require(not stat.S_ISLNK(mode), "symlink in repository-relative path: " + name) + return root / name + + +def relative_file(root, name): + result = symlink_free_relative_path(root, name) + require(result.resolve().is_relative_to(root.resolve()) and result.is_file(), + "missing or external file: " + name) + return result + + +# Adapted from the package-local policy in +# research/t74-2530-source-partner-audit/audit_common.py (Apache-2.0). +# Keep repository configuration and linked-worktree .git discovery intact; +# inherited shell overrides must not choose a different repository or index. +_GIT_REDIRECT_VARS = frozenset(( + "GIT_DIR", "GIT_WORK_TREE", "GIT_INDEX_FILE", "GIT_OBJECT_DIRECTORY", + "GIT_ALTERNATE_OBJECT_DIRECTORIES", "GIT_NAMESPACE", "GIT_CEILING_DIRECTORIES", + "GIT_COMMON_DIR", "GIT_CONFIG_PARAMETERS", "GIT_CONFIG_COUNT", +)) +_GIT_CONFIG_PREFIXES = ("GIT_CONFIG_KEY_", "GIT_CONFIG_VALUE_") + + +def git_source_env(): + """Use cwd's repository and stored objects, without changing the parent. + + Git can ignore cwd when inherited selection variables point elsewhere. + Config-injection variables can also redirect worktree/index operations. + This policy is only for Git metadata/source subprocesses, not verifiers. + """ + env = {name: value for name, value in os.environ.items() + if name not in _GIT_REDIRECT_VARS and not name.startswith(_GIT_CONFIG_PREFIXES)} + # Replacement refs can report an original ID while returning other bytes. + env["GIT_NO_REPLACE_OBJECTS"] = "1" + return env + + +def git(root, *args): + return subprocess.run(["git", *args], cwd=root, env=git_source_env(), + capture_output=True, check=True).stdout + + +def tracked_input_paths(root): + """Use HEAD spelling, never case folding, filesystem resolution or the index. + + Staged/untracked files are not replay inputs until committed. NUL framing + preserves Git filenames containing whitespace, including CR and LF. + """ + raw = subprocess.run( + ["git", "ls-tree", "-r", "--name-only", "-z", "HEAD"], cwd=root, env=git_source_env(), + capture_output=True, check=True, timeout=30).stdout + return frozenset(name.decode("utf-8") for name in raw.split(b"\0") if name) + + +def require_tracked_input(name, paths): + canonical_relative_path(name) + require(name in paths, "use an exact Git-tracked input path from HEAD: " + name) + + +def git_source_rows(root, base, names): + """Read one pinned object at a time through one Git process; no persistent cache. + + Each request is consumed before the next is sent. This avoids pipe deadlocks + and retains the old one-blob memory bound, even for large source archives. + Newline paths and non-blob objects retain the legacy Git-show semantics. + The caller must close this generator if source validation fails mid-stream. + """ + with subprocess.Popen(["git", "cat-file", "--batch"], cwd=root, env=git_source_env(), + stdin=subprocess.PIPE, stdout=subprocess.PIPE, + stderr=subprocess.PIPE) as process: + try: + for name in names: + expression = base + ":" + name + if "\n" in expression or "\r" in expression: + yield git(root, "rev-parse", expression).decode().strip(), git(root, "show", expression) + continue + process.stdin.write(expression.encode("utf-8") + b"\n") + process.stdin.flush() + header = process.stdout.readline().rstrip(b"\n").split(b" ") + require(len(header) == 3 and re.fullmatch(rb"[0-9a-f]{40,64}", header[0]) + and header[2].isdigit(), "missing or invalid Git source: " + name) + size = int(header[2]) + payload = process.stdout.read(size) + require(len(payload) == size and process.stdout.read(1) == b"\n", + "truncated Git source: " + name) + if header[1] != b"blob": + payload = git(root, "show", expression) + yield header[0].decode("ascii"), payload + process.stdin.close() + code = process.wait(timeout=90) + require(code == 0, "Git source reader failed: " + process.stderr.read().decode("utf-8", errors="replace")) + finally: + if not process.stdin.closed: + process.stdin.close() + if process.poll() is None: + try: + process.wait(timeout=5) + except subprocess.TimeoutExpired: + process.kill() + process.wait() + + +class _UnsupportedNulBatch(Exception): + """Git rejected the initial NUL-mode request before yielding any source.""" + + +def _closed_stdin_error(error): + # Windows can report EINVAL instead of EPIPE when a child closes stdin. + # This classifies the pipe error only; the retry still requires exit 129. + return (isinstance(error, BrokenPipeError) + or (os.name == "nt" and error.errno == errno.EINVAL)) + + +def _stop_git_blob_process(process): + """Stop this reader's owned POSIX group even after its leader exits.""" + try: + if os.name == "posix": + # Reap an exited leader first: signaling a group containing only + # its unreaped zombie can report EPERM on macOS. A surviving + # descendant keeps the group alive after the leader is reaped. + process.poll() + os.killpg(process.pid, signal.SIGKILL) + else: + process.kill() + except ProcessLookupError: + pass + + +@contextmanager +def _git_blob_response_deadline(stop): + """Bound one response, excluding time spent by its consumer. + + On POSIX the reader owns a session: ordinary descendants retaining a pipe + are stopped with the leader. Escaped sessions and separate git() calls are + outside this contract; non-POSIX retains the direct-child deadline. + """ + expired = threading.Event() + + def terminate(): + expired.set() + stop() + + timer = threading.Timer(GIT_BLOB_RESPONSE_TIMEOUT, terminate) + timer.start() + try: + yield + finally: + timer.cancel() + timer.join() + if expired.is_set(): + raise subprocess.TimeoutExpired("git cat-file blob response", GIT_BLOB_RESPONSE_TIMEOUT) + + +def _git_blob_batch(root, specs, nul): + argv = ["git", "cat-file", "--batch"] + (["-z"] if nul else []) + # Usage diagnostics from the unsupported-option probe are expected. Avoid + # a second pipe that could block while we consume the framed stdout reply. + with subprocess.Popen(argv, cwd=root, env=git_source_env(), stdin=subprocess.PIPE, + stdout=subprocess.PIPE, stderr=subprocess.DEVNULL, + start_new_session=(os.name == "posix")) as process: + stopped = False + + def stop(): + nonlocal stopped + if not stopped: + _stop_git_blob_process(process) + stopped = True + + try: + for index, spec in enumerate(specs): + require("\0" not in spec, "invalid Git object request") + request = spec + if not nul and ("\n" in spec or "\r" in spec): + # Resolve one literal argument, never split a path into requests. + request = git(root, "rev-parse", "--verify", "--end-of-options", spec).decode("ascii").strip() + require(re.fullmatch(r"[0-9a-f]{40,64}", request), "invalid Git object ID") + with _git_blob_response_deadline(stop): + try: + process.stdin.write(request.encode("utf-8") + (b"\0" if nul else b"\n")) + process.stdin.flush() + except OSError as exc: + if not _closed_stdin_error(exc): + raise + header = b"" + else: + header = process.stdout.readline() + if nul and index == 0 and not header and process.wait(timeout=90) == 129: + raise _UnsupportedNulBatch(spec) + fields = header.rstrip(b"\n").split(b" ") + require(len(fields) == 3 and re.fullmatch(rb"[0-9a-f]{40,64}", fields[0]) + and fields[1] == b"blob" and fields[2].isdigit(), + "missing or non-blob Git source: " + spec) + size = int(fields[2]) + pinned = process.stdout.read(size) + require(len(pinned) == size and process.stdout.read(1) == b"\n", + "incomplete Git blob response: " + spec) + yield fields[0].decode("ascii"), pinned + process.stdin.close() + require(process.wait(timeout=90) == 0, "Git source reader failed") + finally: + # Terminate ordinary descendants before closing buffered pipes. This + # also covers successful leader exit and an early generator close. + if os.name == "posix": + stop() + # Option rejection can close stdin before our first write/flush. + try: + process.stdin.close() + except OSError as exc: + if not _closed_stdin_error(exc): + raise + process.stdout.close() + if process.poll() is None: + try: + process.wait(timeout=5) + except subprocess.TimeoutExpired: + process.kill() + process.wait() + + +def git_blobs(root, specs): + """Stream exact blobs, retaining the one-process NUL protocol on newer Git. + + Git without -z rejects it with usage status 129. Retry only before any + response, replaying the consumed first request through the line protocol. + The fallback resolves CR/LF paths to object IDs before requesting content. + The caller must close this iterator if validation stops before exhaustion. + """ + specs = iter(specs) + sentinel = object() + first = next(specs, sentinel) + if first is sentinel: + return + with closing(_git_blob_batch(root, chain((first,), specs), nul=True)) as rows: + try: + yield from rows + except _UnsupportedNulBatch as exc: + with closing(_git_blob_batch(root, chain((exc.args[0],), specs), nul=False)) as legacy: + yield from legacy + + +def meaningful(value): + return isinstance(value, str) and bool(value.strip()) and not re.search(r"\bTODO\b", value, re.I) + + +def brief(value): + text = json.dumps(value, ensure_ascii=True, sort_keys=True) + return text if len(text) <= 120 else text[:117] + "..." + + +def require_key(mapping, key, where, shape=None): + """Name the missing key and its expected shape instead of a bare KeyError.""" + require(isinstance(mapping, dict), + where + " must be a JSON object; found " + type(mapping).__name__ + ": " + brief(mapping)) + require(key in mapping, where + "." + key + " is missing" + + ("; expected " + shape if shape else "")) + return mapping[key] + + +def require_text(mapping, key, where, shape="a non-empty string without TODO"): + """Name the key and distinguish missing, wrong-shaped and weak values.""" + require(isinstance(mapping, dict), + where + " must be a JSON object; found " + type(mapping).__name__ + ": " + brief(mapping)) + require(key in mapping, where + "." + key + " is missing; expected " + shape) + value = mapping[key] + require(isinstance(value, str) and meaningful(value), + where + "." + key + " must be " + shape + "; found " + type(value).__name__ + ": " + brief(value)) + + +def card_differences(own, pinned): + """Name every key by which a TASK.json original_card differs from its pin.""" + if not isinstance(own, dict): + return "TASK.json original_card is " + type(own).__name__ + ", expected a JSON object" + details = [] + missing = [key for key in pinned if key not in own] + extra = [key for key in own if key not in pinned] + if missing: + details.append("missing keys: " + ", ".join(missing)) + if extra: + details.append("unexpected keys: " + ", ".join(extra)) + for key in (key for key in pinned if key in own and own[key] != pinned[key]): + details.append(key + " differs (TASK.json: " + brief(own[key]) + "; pinned: " + brief(pinned[key]) + ")") + return "; ".join(details) or "cards compare unequal without a key difference" + + +def source_pin(row, base): + """Resolve one SOURCES.json row to its exact Git object expression. + + Rows without an explicit pin keep the historical base_commit: form. + A file vendored from a pull-request head is pinned exactly with + head:<40-hex sha>:, so its bytes resolve at that commit, not at the + package base. An explicit but unparseable pin fails closed. + """ + name = row["path"] + pin = row.get("pin") + if pin is None: + return base + ":" + name + if pin == "base_commit:" + name: + return base + ":" + name + # Git filenames can contain LF; it is part of the exact path, not a delimiter. + match = re.fullmatch(r"head:([0-9a-f]{40}):(.+)", pin, re.DOTALL) if isinstance(pin, str) else None + if match is not None and match.group(2) == name: + return match.group(1) + ":" + name + raise ValueError("SOURCES.json pin for " + name + " is not a supported pin form: " + brief(pin) + + "; accepted pin forms are base_commit: and head:<40-hex sha>:") + + +def validate(root, package, check_pins=True): + parts = PurePosixPath(package).parts + require(len(parts) == 2 and parts[0] == "research" and re.fullmatch(r"[a-z0-9][a-z0-9-]*", parts[1]), + "package must be research/") + data = {} + for name in ("TASK.json", "SOURCES.json", "VERIFY.json"): + data[name] = json.loads(relative_file(root, package + "/" + name).read_text(encoding="utf-8")) + version = require_key(data[name], "schema_version", name) + require(version == 1, name + ".schema_version must be 1; found " + brief(version)) + task, sources, manifest = (data[n] for n in ("TASK.json", "SOURCES.json", "VERIFY.json")) + scope_status = require_key(task, "scope_status", "TASK.json", "unchanged, refined or changed") + require(scope_status in ("unchanged", "refined", "changed"), + "TASK.json.scope_status must be unchanged, refined or changed; found " + brief(scope_status)) + for field in ("actual_scope", "bottleneck_link", "stop_rule", "evidence", "author", "ai_assistance"): + require_text(task, field, "TASK.json") + if scope_status == "unchanged": + question = require_key(require_key(task, "original_card", "TASK.json", + "the pinned catalogue card object"), + "question", "TASK.json.original_card") + require(task["actual_scope"] == question, + "different wording/scope requires refined or changed plus a reason" + + " (TASK.json.actual_scope " + brief(task["actual_scope"]) + + " differs from TASK.json.original_card.question " + brief(question) + ")") + else: + require_text(task, "scope_change_reason", "TASK.json", + "a non-empty string without TODO explaining the scope refinement/change") + outcome = require_key(task, "outcome", "TASK.json", + "partial, completed, blocked or negative-result") + require(outcome in ("partial", "completed", "blocked", "negative-result"), + "TASK.json.outcome must be partial, completed, blocked or negative-result; found " + brief(outcome)) + questions = task.get("open_questions") + require(isinstance(questions, list), + "TASK.json.open_questions must be a list; found " + type(questions).__name__ + ": " + brief(questions)) + if not questions: + require_text(task, "no_open_questions_reason", "TASK.json", + "a non-empty string without TODO explaining an empty next-question list") + for position, question in enumerate(questions): + for field in ("question", "why_it_matters", "first_step", "blocked_by"): + require_text(question, field, "TASK.json.open_questions[" + str(position) + "]") + readme = relative_file(root, package + "/README.md").read_text(encoding="utf-8") + require("## Open next questions" in readme, "README.md needs an \"## Open next questions\" section") + status = require_key(manifest, "status", "VERIFY.json") + require(status == "ready", + "VERIFY.json.status must be \"ready\"; complete the draft before requesting replay; found " + brief(status)) + python = require_key(manifest, "python", "VERIFY.json") + require(python == "3.12", + "VERIFY.json.python must be \"3.12\" (generic replay currently uses Python 3.12); found " + brief(python)) + requirements = manifest.get("requirements", []) + require(isinstance(requirements, list), + "VERIFY.json.requirements must be a list of exact \"name==version\" pins; found " + + type(requirements).__name__ + ": " + brief(requirements)) + require(len(requirements) == len(set(requirements)), "VERIFY.json.requirements must not repeat a pin") + for item in requirements: + require(isinstance(item, str) + and re.fullmatch(r"(?:numpy|sympy|scipy)==[0-9]+(?:\.[0-9]+){1,2}", item), + "generic CI supports exact numpy/sympy/scipy pins; use a dedicated workflow for other environments" + + "; offending entry: " + brief(item)) + names = [item.split("==")[0] for item in requirements] + require(len(names) == len(set(names)), "declare only one version per dependency") + # Validation already treats an omitted list as empty; execution must receive + # that same default without rewriting the contributor's manifest on disk. + manifest["requirements"] = requirements + commands = manifest.get("commands") + require(isinstance(commands, list) and 1 <= len(commands) <= 8, + "VERIFY.json.commands must be a list of 1..8 explicit verification commands; found " + + type(commands).__name__ + ": " + brief(commands)) + total = 0 + for position, command in enumerate(commands): + path = "VERIFY.json.commands[" + str(position) + "]" + require(isinstance(command, dict), + path + " must be a JSON object; found " + type(command).__name__ + ": " + brief(command)) + argv = command.get("argv") + require(isinstance(argv, list) and len(argv) >= 2 and all(isinstance(a, str) for a in argv), + path + ".argv must be a list of at least 2 strings; found " + brief(argv)) + require(argv[0] == "{python}", path + ".argv must explicitly use {python}; no implicit shell") + require_text(command, "checks", path, "a non-empty string without TODO describing command coverage") + seconds = command.get("timeout_seconds") + require(type(seconds) is int, + path + ".timeout_seconds must be an integer number of seconds; found " + + type(seconds).__name__ + ": " + brief(seconds)) + require(1 <= seconds <= 600, + path + ".timeout_seconds " + str(seconds) + + (" exceeds the 600 s per-command cap" if seconds > 600 + else " is below the 1 s per-command minimum")) + total += seconds + require(total <= 1200, "declared replay budget " + str(total) + + " s (sum of timeout_seconds) exceeds the 1200 s total cap" + + "; use a dedicated job for larger checks") + inputs = manifest.get("inputs") + require(isinstance(inputs, list), + "VERIFY.json.inputs must be a list of canonical repository-relative paths; found " + + type(inputs).__name__ + ": " + brief(inputs)) + tracked = tracked_input_paths(root) + for name in inputs: + symlink_free_relative_path(root, name) + require_tracked_input(name, tracked) + relative_file(root, name) + files = require_key(sources, "files", "SOURCES.json") + require(files, "SOURCES.json.files is empty; declare the source inventory") + base = require_key(sources, "base_commit", "SOURCES.json", "a 40-64 hex string pinning an exact base commit") + require(isinstance(base, str) and re.fullmatch(r"[0-9a-f]{40,64}", base), + "SOURCES.json.base_commit must be a 40-64 hex string pinning an exact base commit; found " + brief(base)) + task_base = require_key(task, "base_commit", "TASK.json", + "a 40-64 hex string equal to SOURCES.json.base_commit") + require(task_base == base, "TASK.json.base_commit " + brief(task_base) + + " must equal SOURCES.json.base_commit " + brief(base)) + for row in files: + require(isinstance(row, dict) and isinstance(row.get("path"), str), + "SOURCES.json.files rows must be JSON objects with a string path; offending row: " + brief(row)) + require(row.get("usage") in ("input", "provenance"), + "SOURCES.json.files row " + row["path"] + " must declare usage \"input\" or \"provenance\"; found " + + brief(row.get("usage"))) + undeclared = sorted({r["path"] for r in sources["files"] if r["usage"] == "input"} - set(inputs)) + require(not undeclared, + "every SOURCES.json files row with usage \"input\" must also be declared in VERIFY.json inputs" + + " (they drive CI invalidation); undeclared: " + ", ".join(undeclared)) + if check_pins: + catalog_name = "docs/research/agent-task-catalog.json" + require(catalog_name in {r["path"] for r in sources["files"]}, + "SOURCES.json.files must pin the originating task catalogue " + catalog_name + + " (a provenance row pinned at base_commit)") + names = [r["path"] for r in sources["files"]] + for name in names: + p = PurePosixPath(name) + require(not p.is_absolute() and ".." not in p.parts, "invalid source path") + specs = [source_pin(row, sources["base_commit"]) for row in sources["files"]] + require(all(spec == sources["base_commit"] + ":" + catalog_name + for name, spec in zip(names, specs) if name == catalog_name), + "originating task catalogue must be pinned at base_commit") + with closing(git_blobs(root, specs)) as objects: + for index, (obj, pinned) in enumerate(objects): + row = sources["files"][index] + name = row["path"] + require(obj == row["git_blob"], "source blob provenance mismatch: " + name) + require(hashlib.sha256(pinned).hexdigest() == row["sha256"], "source SHA256 provenance mismatch: " + name) + if row["usage"] == "input": + require(pinned == relative_file(root, name).read_bytes(), "working source drift: " + name) + if name == catalog_name: + catalog = json.loads(pinned) + cards = [t for tr in catalog["tracks"] for t in tr["tasks"] if t["id"] == task["task_id"]] + require(len(cards) == 1, + "TASK.json task_id " + brief(task["task_id"]) + " matches " + str(len(cards)) + + " cards in pinned " + catalog_name + " at base_commit " + sources["base_commit"] + + "; need exactly one") + original_card = require_key(task, "original_card", "TASK.json", + "the pinned catalogue card object (copy --print-card output verbatim)") + if original_card != cards[0]: + raise ValueError("original card in TASK.json must equal the pinned catalogue card object exactly; " + "copy it verbatim from " + catalog_name + " at base_commit " + sources["base_commit"] + + ": " + card_differences(original_card, cards[0])) + return task, manifest + + +def catalogue_card(root, package, task_id): + """The exact original_card object a hand-authored TASK.json must copy. + + Reads the catalogue blob pinned at the package base commit, never the + working tree, because validate() compares original_card against that pin. + """ + sources = json.loads(relative_file(root, package + "/SOURCES.json").read_text(encoding="utf-8")) + name = "docs/research/agent-task-catalog.json" + rows = require_key(sources, "files", "SOURCES.json") + row = next((r for r in rows if isinstance(r, dict) and r.get("path") == name), None) + require(row is not None, "SOURCES.json.files must pin the originating task catalogue " + name) + base = require_key(sources, "base_commit", "SOURCES.json", "a 40-64 hex string pinning an exact base commit") + spec = source_pin(row, base) + require(spec == base + ":" + name, "originating task catalogue must be pinned at base_commit") + catalog = json.loads(git(root, "show", spec)) + cards = [t for tr in catalog["tracks"] for t in tr["tasks"] if t["id"] == task_id] + require(len(cards) == 1, + "task_id " + brief(task_id) + " matches " + str(len(cards)) + + " cards in pinned " + name + " at base_commit " + base + "; need exactly one") + return cards[0] + + +_WINDOWS_GATE = r""" +import ctypes +from ctypes import wintypes +import json +import subprocess +import sys +api = ctypes.WinDLL('kernel32', use_last_error=True) +api.OpenEventW.argtypes = [wintypes.DWORD, wintypes.BOOL, wintypes.LPCWSTR] +api.OpenEventW.restype = wintypes.HANDLE +api.WaitForSingleObject.argtypes = [wintypes.HANDLE, wintypes.DWORD] +api.WaitForSingleObject.restype = wintypes.DWORD +api.CloseHandle.argtypes = [wintypes.HANDLE] +api.CloseHandle.restype = wintypes.BOOL +event = api.OpenEventW(0x00100000, False, sys.argv[1]) +if not event: + raise ctypes.WinError(ctypes.get_last_error()) +try: + if api.WaitForSingleObject(event, 30000) != 0: + raise RuntimeError('replay ownership gate was not released') +finally: + api.CloseHandle(event) +# No verification command or descendant starts until the parent owns this job. +sys.exit(subprocess.call(json.loads(sys.argv[2]))) +""" + +def run_windows_command(argv, cwd, timeout, env): + """Own ordinary verification descendants even after their leader exits. + + The gated launcher joins a kill-on-close Job Object before it may spawn + the requested command. A late taskkill cannot recover an exited leader's + tree. Job handles are not inherited and breakaway is not enabled. + """ + import ctypes + from ctypes import wintypes + import time + import uuid + + class BasicLimits(ctypes.Structure): + _fields_ = [("ProcessTime", ctypes.c_int64), ("JobTime", ctypes.c_int64), + ("Flags", wintypes.DWORD), ("MinWorkingSet", ctypes.c_size_t), + ("MaxWorkingSet", ctypes.c_size_t), ("ActiveProcessLimit", wintypes.DWORD), + ("Affinity", ctypes.c_size_t), ("Priority", wintypes.DWORD), + ("Scheduling", wintypes.DWORD)] + + class IOCounts(ctypes.Structure): + _fields_ = [(name, ctypes.c_uint64) for name in + ("ReadOps", "WriteOps", "OtherOps", "ReadBytes", "WriteBytes", "OtherBytes")] + + class ExtendedLimits(ctypes.Structure): + _fields_ = [("Basic", BasicLimits), ("IO", IOCounts), + ("ProcessMemory", ctypes.c_size_t), ("JobMemory", ctypes.c_size_t), + ("PeakProcessMemory", ctypes.c_size_t), ("PeakJobMemory", ctypes.c_size_t)] + + class Accounting(ctypes.Structure): + _fields_ = [(name, ctypes.c_int64) for name in + ("UserTime", "KernelTime", "PeriodUserTime", "PeriodKernelTime")] + [ + (name, wintypes.DWORD) for name in + ("PageFaults", "TotalProcesses", "ActiveProcesses", "TerminatedProcesses")] + + api = ctypes.WinDLL("kernel32", use_last_error=True) + + def native(name, result, *arguments): + fn = getattr(api, name) + fn.restype, fn.argtypes = result, arguments + return fn + + handle, dword, boolean = wintypes.HANDLE, wintypes.DWORD, wintypes.BOOL + create_job = native("CreateJobObjectW", handle, ctypes.c_void_p, wintypes.LPCWSTR) + set_info = native("SetInformationJobObject", boolean, handle, ctypes.c_int, ctypes.c_void_p, dword) + assign = native("AssignProcessToJobObject", boolean, handle, handle) + terminate = native("TerminateJobObject", boolean, handle, wintypes.UINT) + query = native("QueryInformationJobObject", boolean, handle, ctypes.c_int, + ctypes.c_void_p, dword, ctypes.c_void_p) + create_event = native("CreateEventW", handle, ctypes.c_void_p, boolean, boolean, wintypes.LPCWSTR) + set_event = native("SetEvent", boolean, handle) + close = native("CloseHandle", boolean, handle) + + def checked(ok): + if not ok: + raise ctypes.WinError(ctypes.get_last_error()) + return ok + + job = checked(create_job(None, None)) + event, process, assigned = None, None, False + try: + limits = ExtendedLimits() + limits.Basic.Flags = 0x2000 # JOB_OBJECT_LIMIT_KILL_ON_JOB_CLOSE + checked(set_info(job, 9, ctypes.byref(limits), ctypes.sizeof(limits))) + name = "Local\\research-replay-" + uuid.uuid4().hex + event = checked(create_event(None, True, False, name)) + # A name collision must not attach to an already-signaled event. + if ctypes.get_last_error() == 183: + raise ValueError("replay ownership gate name already exists") + process = subprocess.Popen( + # The gate itself must not run sitecustomize/PYTHONPATH startup + # code before ownership. The requested command retains env/argv. + # Windows accepts Unicode argv directly. ASCII JSON escaping can + # expand an otherwise valid command past its UTF-16 launch limit. + [sys.executable, "-I", "-S", "-c", _WINDOWS_GATE, name, + json.dumps(argv, ensure_ascii=False)], + cwd=cwd, env=env, start_new_session=True) + checked(assign(job, int(process._handle))) + assigned = True + checked(set_event(event)) + try: + return process.wait(timeout=timeout) + except subprocess.TimeoutExpired: + raise ValueError("verification timed out") from None + finally: + try: + if process is not None: + if assigned: + checked(terminate(job, 1)) + # Termination is asynchronous. Require the job to report + # no active processes before releasing its ownership handle. + deadline = time.monotonic() + 10 + while True: + state = Accounting() + checked(query(job, 1, ctypes.byref(state), ctypes.sizeof(state), None)) + if not state.ActiveProcesses: + break + if time.monotonic() >= deadline: + raise ValueError("verification process cleanup timed out") + time.sleep(0.01) + elif process.poll() is None: + # Assignment failed before the gate opened: no command child + # exists, so only this known gated launcher needs stopping. + process.kill() + process.wait(timeout=10) + finally: + try: + if event: + checked(close(event)) + finally: + checked(close(job)) + +def run_command(argv, cwd, timeout): + # Assertion checks must not disappear because of the caller's environment. + # Keep explicit manifest options (including deliberate -O controls) intact. + # PYTHONPATH precedes the standard library on a child's sys.path, so a stray + # same-named module could end a verifier with exit code 0 before any check. + env = os.environ.copy() + env.pop("PYTHONOPTIMIZE", None) + # Ambient inspection can turn a verifier exception into a successful REPL + # exit at terminal EOF. Keep explicit -i and the caller's stdin unchanged. + env.pop("PYTHONINSPECT", None) + env.pop("PYTHONPATH", None) + if os.name == "nt": + code = run_windows_command(argv, cwd, timeout, env) + require(code == 0, f"verification command exited {code}") + return + previous_handler = None + terminating = False + waiting = False + process = None + + def terminate(signum, frame): + nonlocal terminating + if not terminating: + terminating = True + # Only interrupt the protected wait. Launch/assignment and cleanup + # defer delivery; repeated signals cannot interrupt group cleanup. + if waiting: + raise SystemExit(128 + signum) + + # Own a group for POSIX cleanup of this command and its descendants. + try: + if (threading.current_thread() is threading.main_thread() + and signal.getsignal(signal.SIGTERM) == signal.SIG_DFL): + previous_handler = signal.SIG_DFL + signal.signal(signal.SIGTERM, terminate) + if terminating: + raise SystemExit(143) + process = subprocess.Popen(argv, cwd=cwd, env=env, start_new_session=True) + try: + try: + waiting = True + if terminating: + raise SystemExit(143) + code = process.wait(timeout=timeout) + finally: + waiting = False + except subprocess.TimeoutExpired: + raise ValueError("verification timed out") from None + require(code == 0, f"verification command exited {code}") + finally: + try: + if process is not None: + if hasattr(os, "killpg"): + # The leader may have exited while descendants hold its group. + try: + os.killpg(process.pid, signal.SIGKILL) + except ProcessLookupError: + pass + elif process.poll() is None: + subprocess.run(["taskkill", "/F", "/T", "/PID", str(process.pid)], capture_output=True) + process.wait() + finally: + if previous_handler is not None: + signal.signal(signal.SIGTERM, previous_handler) + if terminating: + raise SystemExit(143) + + +def isolated_python_argv(argv, cache_directory): + """Place our cache option after interpreter flags, before the entry point. + + -B prevents writes, not reads of existing .pyc files. A fresh namespace + keeps preexisting source-adjacent and externally configured caches out of + this registered interpreter. It is not inherited by child interpreters. + """ + require(argv and argv[0] == sys.executable, "cache isolation requires the registered Python interpreter") + index = 1 + options = [argv[0]] + while index < len(argv): + option = argv[index] + if option in ("-", "--") or not option.startswith("-"): + break + if option == "--check-hash-based-pycs": + require(index + 1 < len(argv), "missing Python hash-cache option argument") + options.extend(argv[index:index + 2]) + index += 2 + continue + if option.startswith("--"): + options.append(option) + index += 1 + continue + # Python permits combined short flags, attached -c/-m payloads, and + # attached or separate -W/-X arguments. Stop scanning an option once + # its argument begins: letters inside that argument are not flags. + entry = False + consumed = 1 + replace_cache = False + for offset, flag in enumerate(option[1:], start=1): + if flag in "cm": + entry = True + break + if flag in "WX": + if offset == len(option) - 1: + require(index + 1 < len(argv), "missing Python interpreter option argument") + consumed = 2 + value = argv[index + 1] if consumed == 2 else option[offset + 1:] + if flag == "X" and value.split("=", 1)[0] == "pycache_prefix": + replace_cache = True + if offset > 1: + options.append(option[:offset]) + break + if entry: + break + if not replace_cache: + options.extend(argv[index:index + consumed]) + index += consumed + # CPython's effective prefix can use the first duplicate -X value even + # when sys._xoptions shows the last. Remove only earlier cache-prefix + # settings; script arguments remain untouched, even when spelled -X. + return [*options, "-X", "pycache_prefix=" + str(cache_directory), *argv[index:]] + + +def run_python_replay(argv, cwd, timeout): + with tempfile.TemporaryDirectory(prefix="research-replay-pycache-") as cache: + run_command(isolated_python_argv(argv, cache), cwd, timeout) + + +def run_package(root, package, install=False): + task, manifest = validate(root, package) + require(sys.version_info[:2] == (3, 12), "run replay with Python 3.12 (metadata check is version-independent)") + if install and manifest["requirements"]: + run_command([sys.executable, "-m", "pip", "install", "--disable-pip-version-check", *manifest["requirements"]], root, 300) + for requirement in manifest["requirements"]: + name, version = requirement.split("==") + require(importlib.metadata.version(name) == version, "dependency version mismatch: " + requirement) + # Coverage labels are UTF-8 metadata but a redirected Windows stdout may + # use cp1252. Escape unrepresentable display characters instead of aborting + # before replay. This changes only our stream, not child encoding or env. + if hasattr(sys.stdout, "reconfigure"): + sys.stdout.reconfigure(errors="backslashreplace") + for command in manifest["commands"]: + argv = [sys.executable if item == "{python}" else item.replace("{package}", package) for item in command["argv"]] + print("CHECK " + command["checks"], flush=True) + run_python_replay(argv, root, command["timeout_seconds"]) + print("PASS_REGISTERED_RESEARCH_PACKAGE " + package + " outcome=" + task["outcome"]) + + +def planning_manifests(root, tracked): + """Include deliberate sparse omissions without disguising deletions or drift. + + The fallback follows the chooser's PR3102 contract: one stage-zero regular + skip-worktree index entry must match the exact HEAD mode and blob. This is + declaration discovery only, not permission to replay absent package code. + """ + committed = {name for name in tracked + if name.startswith("research/") and name.count("/") == 2 + and name.endswith("/VERIFY.json")} + # Explicit scandir retains error detection; only an absent directory is OK. + try: + with os.scandir(root / "research") as entries: + local = {Path(entry.path) / "VERIFY.json" for entry in entries} + except FileNotFoundError: + local = set() + present, missing = {}, set() + for path in sorted(local | {root / name for name in committed}): + name = path.relative_to(root).as_posix() + symlink_free_relative_path(root, name) + try: + mode = path.lstat().st_mode + except (FileNotFoundError, NotADirectoryError): + if name in committed: + missing.add(name) + continue + require(stat.S_ISREG(mode), "non-regular replay manifest: " + name) + present[name] = path + fallback = {} + if missing: + indexed, objects = {}, {} + for record in git(root, "ls-files", "-t", "--stage", "-z", "--", "research").split(b"\0"): + if not record: + continue + header, raw_name = record.split(b"\t", 1) + name = raw_name.decode("utf-8") + if name in missing: + indexed.setdefault(name, []).append(header.split()) + for record in git(root, "ls-tree", "-r", "-z", "HEAD", "--", "research").split(b"\0"): + if not record: + continue + header, raw_name = record.split(b"\t", 1) + name = raw_name.decode("utf-8") + if name in missing: + objects[name] = header.split() + for name in sorted(missing): + metadata = objects.get(name, []) + require(len(metadata) == 3 and metadata[0] in (b"100644", b"100755") + and metadata[1] == b"blob" + and indexed.get(name) == [[b"S", metadata[0], metadata[2], b"0"]], + "missing replay manifest is not an unchanged sparse HEAD input: " + name + + "; materialize it or commit its intended deletion") + # A regular file occupying the package directory is not an omission. + require(not (root / name).parent.exists() or (root / name).parent.is_dir(), + "non-directory replay package: " + name) + names = sorted(missing) + with closing(git_blobs(root, [objects[n][2].decode("ascii") for n in names])) as rows: + for (oid, raw), name in zip(rows, names): + require(oid.encode("ascii") == objects[name][2], "sparse manifest blob mismatch: " + name) + fallback[name] = raw + # Preserve Path's component ordering: package "a" precedes "a-extra". + for name in sorted(present.keys() | fallback.keys(), key=lambda name: PurePosixPath(name).parts): + yield root / name, fallback[name] if name in fallback else present[name].read_bytes(), name in fallback + + +def plan_details(root, changed): + """One selection pass with exact causes; no replay or acceptance decision.""" + changed = set(changed) + # A removed input is absent from HEAD, including an old case-only rename + # spelling on case-insensitive filesystems. Git's exact changed paths remain + # eligible so its consumer is selected, rather than rejected or skipped. + head_tracked = tracked_input_paths(root) + tracked = head_tracked | changed + replay_changed = sorted(changed.intersection({ + "scripts/research_package.py", ".github/workflows/research-packages.yml", + ".github/workflows/research-package-batch.yml"})) + # Group literal Git paths once. Keep removed paths and exact spellings. + changed_packages = {} + for name in sorted(changed): + parts = name.split("/", 2) + if len(parts) == 3 and parts[0] == "research": + changed_packages.setdefault("/".join(parts[:2]), []).append(name) + packages = [] + sparse_count = 0 + for path, raw, sparse in planning_manifests(root, head_tracked): + sparse_count += sparse + package = path.parent.relative_to(root).as_posix() + manifest = json.loads(raw.decode("utf-8")) + # Parse only for selection; validate fully in the isolated replay job. + inputs = manifest.get("inputs", []) + require(isinstance(inputs, list), "declare input paths for CI invalidation") + for name in inputs: + # Do not require existence: a deleted input must still trigger replay. + symlink_free_relative_path(root, name) + require_tracked_input(name, tracked) + causes = { + "declared_inputs": sorted(changed.intersection(inputs)), + "package_files": changed_packages.get(package, []), + "shared_controls": replay_changed, + } + if any(causes.values()): + packages.append({"package": package, "causes": causes, + "manifest_sha256": hashlib.sha256(raw).hexdigest()}) + if sparse_count: + print(f"Planning includes {sparse_count} unchanged sparse manifests from HEAD; " + "materialize packages and inputs before replay.", file=sys.stderr) + return packages + + +def plan(root, changed): + return [row["package"] for row in plan_details(root, changed)] + + +def write_plan_explanation(path, base, head, changed, details): + """Publish a complete sidecar before stdout/GitHub matrix publication.""" + matched = {name for row in details for names in row["causes"].values() for name in names} + report = { + "schema_version": 1, "base": base, "head": head, + "mode": "all-tracked" if base is None else "commit-diff", + "scope": "Selection from working or authenticated sparse HEAD manifests, not replay or mathematical acceptance. " + "Manifest hashes bind the declarations read; checkout must remain stable.", + "changed_paths": sorted(set(changed) - {""}), "selected": details, + "unmatched_paths": sorted(set(changed) - matched - {""}), + } + fd, temporary = tempfile.mkstemp(prefix=".replay-plan-", dir=path.parent) + try: + with os.fdopen(fd, "w", encoding="utf-8") as stream: + json.dump(report, stream, indent=2) + stream.write("\n") + os.replace(temporary, path) + finally: + Path(temporary).unlink(missing_ok=True) + + +def replay_matrix(packages, batch_size=None): + """Retain the flat CLI format, or group complete coverage into bounded matrices.""" + if batch_size is None: + return {"include": [{"package": p} for p in packages]} + require(type(batch_size) is int and 1 <= batch_size <= 256, + "matrix batch size must be 1..256") + batches = [packages[i:i + batch_size] for i in range(0, len(packages), batch_size)] + require(len(batches) <= 256, + "more than 256 matrix batches required; no packages were truncated") + return {"include": [{"packages": batch} for batch in batches]} + + +def main(): + ap = argparse.ArgumentParser(description=__doc__) + ap.add_argument("--package") + ap.add_argument("--check-only", action="store_true") + ap.add_argument("--print-card", metavar="TASK_ID", + help="print the exact pinned catalogue card object to copy into TASK.json original_card") + ap.add_argument("--install-deps", action="store_true", help="explicit opt-in to install manifest's allowed pinned dependencies") + ap.add_argument("--changed-since", help="plan affected opt-in packages relative to this Git commit") + ap.add_argument("--github-output", type=Path) + ap.add_argument("--explain-plan", type=Path, + help="write exact replay-selection causes to JSON; matrix output stays unchanged") + ap.add_argument("--matrix-batch-size", type=int, + help="group planned packages for bounded reusable-workflow matrices (1..256)") + args = ap.parse_args() + if args.explain_plan and (not args.changed_since or args.package or args.print_card): + ap.error("--explain-plan requires --changed-since without --package or --print-card") + if args.explain_plan and args.github_output and args.explain_plan.resolve() == args.github_output.resolve(): + ap.error("--explain-plan and --github-output must use different files") + try: + if args.print_card: + require(args.package, + "--print-card needs --package research/ to resolve its pinned catalogue") + sys.stdout.write(json.dumps(catalogue_card(ROOT, args.package, args.print_card), indent=2) + "\n") + elif args.changed_since: + if set(args.changed_since) == {"0"}: + base = None + changed = git(ROOT, "ls-files", "-z").decode().split("\0") + else: + base = git(ROOT, "rev-parse", "--verify", args.changed_since + "^{commit}").decode().strip() + # A rename must invalidate both the removed input and its new path. + changed = git(ROOT, "diff", "--no-renames", "--name-only", "-z", base, "HEAD").decode().split("\0") + details = plan_details(ROOT, changed) + packages = [row["package"] for row in details] + matrix = json.dumps(replay_matrix(packages, args.matrix_batch_size)) + if args.explain_plan: + head = git(ROOT, "rev-parse", "--verify", "HEAD^{commit}").decode().strip() + write_plan_explanation(args.explain_plan, base, head, changed, details) + print(matrix) + if args.github_output: + with args.github_output.open("a", encoding="utf-8") as out: + out.write(f"matrix={matrix}\ncount={len(packages)}\n") + elif args.package: + if args.check_only: + validate(ROOT, args.package) + print("PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)") + else: + run_package(ROOT, args.package, args.install_deps) + else: + ap.error("use --package, --print-card or --changed-since") + except (OSError, ValueError, KeyError, TypeError, subprocess.SubprocessError, importlib.metadata.PackageNotFoundError) as exc: + ap.exit(1, str(exc) + "\n") + + +if __name__ == "__main__": + main() diff --git a/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/ADVANCES-MUTATIONS.json b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/ADVANCES-MUTATIONS.json new file mode 100644 index 0000000000..cadc0398be --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/ADVANCES-MUTATIONS.json @@ -0,0 +1,45 @@ +{ + "cases": [ + { + "mutation": "conjugate native C factor", + "optimized": false, + "rejection": "Native trace phase" + }, + { + "mutation": "conjugate native C factor", + "optimized": true, + "rejection": "Native trace phase" + }, + { + "mutation": "ignore native inverse sign", + "optimized": false, + "rejection": "Native entry phase" + }, + { + "mutation": "ignore native inverse sign", + "optimized": true, + "rejection": "Native entry phase" + }, + { + "mutation": "omit output prefix constraint", + "optimized": false, + "rejection": "Native partial inner product" + }, + { + "mutation": "omit output prefix constraint", + "optimized": true, + "rejection": "Native partial inner product" + }, + { + "mutation": "omit final native return", + "optimized": false, + "rejection": "Compact complete endpoint" + }, + { + "mutation": "omit final native return", + "optimized": true, + "rejection": "Compact complete endpoint" + } + ], + "status": "PASS_CLIFFORD_ADVANCE_MUTATIONS" +} diff --git a/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/ADVANCES-RESULT.json b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/ADVANCES-RESULT.json new file mode 100644 index 0000000000..2e8e73ba23 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/ADVANCES-RESULT.json @@ -0,0 +1,50 @@ +{ + "code_fourier_values": 256, + "complete_programs": 48, + "controls": [ + "singular permutation", + "diagonal parity", + "asymmetric diagonal", + "wrong C sign", + "unknown gate", + "coordinate out of range", + "invalid prefix", + "negative axes" + ], + "exact_native_relations": 9, + "exhaustive_quadratic_forms": 640, + "filter_axis_counts": 65, + "general_test_widths": "8n-3 through 8n+4 for n>=2", + "large_native_programs": [ + { + "axes": 64, + "base_dimension": "18446744073709551616", + "equivalent": false + }, + { + "axes": 65, + "base_dimension": "36893488147419103232", + "equivalent": true + } + ], + "literal_witnesses": 48, + "native_entries": 3328, + "native_traces": 128, + "native_words": 128, + "one_axis": { + "group_sha256": "32481fd502c5f388244bcd56d20fbc0e0ca3933f47dbbdbbd8215397cea0238d", + "image_of_i": 256, + "prime": 65537, + "rank": 96, + "widths": [ + 5, + 6, + 7, + 8 + ] + }, + "partial_inner_products": 304, + "scalar_phase_traps": 1, + "stable_separation": "75/76", + "status": "PASS_CLIFFORD_ADVANCES_NO_NEW_KAPPA" +} diff --git a/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/ADVANCES.md b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/ADVANCES.md new file mode 100644 index 0000000000..340c54f752 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/ADVANCES.md @@ -0,0 +1,251 @@ +# Fewer widths and exact computation without dense matrices + +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. + +This note extends [PROOF.md](PROOF.md). It uses the same group C_n, exact +global phases, complete register endpoints and coefficients that do not +depend on the positive tensor width f. Set D=2^n. No result changes kappa. + +## 1. Eight widths suffice for every axis count + +For n>=1, a fixed residual vanishes at every positive width if and only if +it vanishes at the eight widths + + 8n-3, 8n-2, ..., 8n+4. + +For n=0, use widths 1,2,3,4. For n=1, Section 3 improves the test to +widths 5,6,7,8. The number of tests and the largest tested width are +different quantities. The general maximum 8n+4 has not decreased. + +Let E be the binary code generated by the four length-eight rows +11111111, 11110000, 11001100 and 10101010. It has dimension four. Its +weights are 0,4,8, and E=E-perp for the binary dot product. Define T_n +in (C^D) tensor-power 8 by summing the basis vectors whose n binary rows +all belong to E. This vector is nonzero. + +The vector T_n is fixed by the eighth tensor power of each native generator: + +- S on one axis contributes i to the power of that row's weight. This is 1. +- CNOT adds one code row to another. It permutes the summands. +- The native Hadamard is ((1+i)/2) times the binary Fourier matrix. + Its eighth tensor power has coefficient 1/16. The Fourier sum of E + is 16 times the indicator of E-perp=E. Thus it fixes T_n, with phase 1. +- The scalar iI has eighth power 1. + +These gates generate C_n. Here is a direct reduction argument. The image +of Z_1 under a Clifford is a nonidentity Pauli. Single-axis H and S gates +convert each nonzero component to Z. CNOT gates reduce the resulting +nonempty Z string to Z_1. An X gate corrects its sign. The image of X_1 +then anticommutes with Z_1. CNOT and controlled-Z gates with control 1 +remove its components on the other axes. An S gate removes its remaining +Z_1 component, and Z_1 corrects its sign. These changes preserve Z_1. +The remaining operator fixes X_1 and Z_1, so it has the form I tensor V. +Repeat on V. The final scalar is a dyadic Gaussian unit of absolute value +one, hence one of 1,i,-1,-i, as proved in PROOF.md. Replace each ordinary +H in this argument by the native Hadamard. The Pauli action is unchanged; +the final scalar still belongs to the same four-element group. + +Normalize T_n to a unit vector tau. The injection J_f(v)=v tensor tau +satisfies + + (sum_g c_g g^(tensor(f+8))) J_f + = J_f (sum_g c_g g^(tensor f)). + +Thus vanishing at f+8 implies vanishing at f. Every integer from 1 to +F=8n+4 can be increased by a multiple of eight to a member of F-7,...,F. +The first theorem in PROOF.md now gives the stated eight-width test. +Apply the argument separately to every input and output role. + +This argument does not transfer the dimension-free stability constant +to the eight selected widths. The bound in Section 2 uses all widths +1,...,8n+4. A direct restriction argument loses powers of D. + +The code invariant is classical. See Runge's prior results as credited in +[Nebe, Rains and Sloane, The invariants of the Clifford groups, Sections 4 +and 6](https://arxiv.org/pdf/math/0001038). The contribution here is its +use in the fixed-coefficient endpoint test, with the native phase checked. + +## 2. Uniform separation improves from 14/15 to 75/76 + +For distinct exact operators and M=sum_g |c_g|^2, let +E_f=D^(-f)||sum_g c_g g^(tensor f)||_HS^2. Then + + max_(1<=f<=8n+4) E_f >= (75/76) M. + +Use the same filter as PROOF.md. Write r=-1/4, m=2n and + + P_m(t) = product_(j=1..m) (t-r^j)/(1-r^j), + q_n(z) = (z+z^2+z^3+z^4) P_m(z^4)/4. + +The four residue classes of coefficients do not overlap. Therefore the +sum of absolute coefficients of q_n equals that of P_m. + +In descending degree, the coefficient with index l has sign +s_l=(-1)^(l(l+3)/2), namely ++--++--. To check this, the elementary +symmetric function in r,...,r^m equals + + r^(l(l+1)/2) product_(k=1..l) (1-r^(m-l+k))/(1-r^k). + +This identity follows by separating subsets that contain the last root; +the empty product gives the initial case. Every factor in the product +is positive. Include the coefficient sign (-1)^l to get s_l. + +Let u_l be the absolute coefficients of P_(2n), L their sum, and U_odd +their sum over odd l. Add the next two roots -a,b, where +b=16^(-(n+1)) and a=4b. The new factor is +(t^2+(a-b)t-ab)/((1+a)(1-b)). The sign rule gives + + L_new - L = [2ab L - 2(a-b) U_odd]/((1+a)(1-b)). + +For n>=1, the unnormalized coefficient of t^(2n-1) has magnitude +(1-16^(-n))/5 >=3/16. The sum of the unnormalized absolute coefficients +is at most product_j(1+4^(-j)) <=3/2. The last inequality follows by +expanding the product and bounding it by the geometric series whose +ratio is sum_j 4^(-j)<=1/3. Hence U_odd/L>=1/8. On the other hand, +ab/(a-b)=4b/3<=1/192. Thus L_new=1. + +For n=1, P_2(t)=(64t^2+12t-1)/75, so L=77/75. For n=0, L=1. +Consequently the positive coefficient mass of q_n is at most +(1+77/75)/2=76/75. The exact identity sum_f b_f E_f=M and E_f>=0 +give the claimed bound. This is a bound for this filter; optimality of +the operator stability constant is not claimed. + +The implementation forms the integer numerator +product_j(4^j t-(-1)^j) and the common denominator +product_j(4^j-(-1)^j) first. It reduces fractions only when it emits q_n. +This gives the same polynomial and avoids repeated large rational reductions. + +## 3. The one-axis maximum cutoff is exactly eight + +The frozen native C and S gates generate all 96 exact operators of C_1. +Their closure and phases are checked in verify.py. Let + + K[g,h] = sum_(f=5..8) (tr(g* h)/2)^f. + +The file [ONE-AXIS-RANK.json](ONE-AXIS-RANK.json) contains an inverse of K +after reduction to F_65537 with i mapped to 256. The checker reconstructs +K, checks that 65537 is prime and 256^2=-1, and multiplies K by this +inverse. It does not use the elimination routine to check the inverse. +All original denominators are powers of two. A nonzero reduced determinant +therefore proves that the characteristic-zero determinant is nonzero. +The positive semidefinite Gram sum K has zero kernel. This proves that +widths 5,6,7,8 suffice for every fixed residual on C_1. + +The Reynolds example in PROOF.md vanishes at widths 1 through 7 and is +nonzero at width 8. The maximum cutoff eight is therefore sharp. +At least four tested widths are required: for each residue r modulo four, +the four scalar operators give the residual + + sum_(k=0..3) i^(-rk) (i^k I)^(tensor f). + +It vanishes unless f is congruent to r modulo four. A test set that omits +one residue cannot detect this residual. Thus four is also the minimum +number of widths for a fixed universal test on C_1. Neither conclusion +establishes a sharp cutoff for n>=2. + +## 4. A phase-exact quadratic path calculation + +[quadratic.py](quadratic.py) accepts the frozen native P, X, D, C and +phase gate grammar. It keeps a list of binary affine output bits and a +phase polynomial modulo four. The polynomial has arbitrary linear +coefficients and even cross coefficients. It also keeps an exact Gaussian +scalar factor. It never allocates an array indexed by the 2^n base states. + +Start with n input variables. P and X change only the affine output bits. +D adds its stated linear and even quadratic phase. For C(q,s), use + + C(q,s) = ((1+s i)/2) (I + i^(-s) X_q). + +Add one binary path variable a, multiply the scalar factor by (1+s i)/2, +add -s a to the phase and add a q to the output bits. Keep the literal +phase gate. The formula also covers q=0. The number of variables is +m=n+h, where h is the number of C gates in the literal word. + +An affine parity has, modulo four, its constant and linear terms plus +even pair terms. Terms of degree at least three vanish modulo four. +Twice a product of parities needs only the product over F_2. Thus every +gate preserves this representation, including affine translations. + +An entry fixes the input and output bits. A trace equates them. Binary +elimination either rejects inconsistent equations or gives an affine +parametrization with one assignment per solution. Substitute this map +in the phase. The remaining unconstrained sum is evaluated as follows: + +- For an odd linear coefficient a of variable x, write its part as + a x+2 x L. Summing x gives (1+i^a) i^(-a L). Remove x and add the + indicated parity phase. This keeps the same quadratic form class. +- If every linear coefficient is even and a cross term remains, sum one + variable x. The result is twice the sum subject to a binary affine + constraint on its neighbors. Eliminate that constraint. +- If no cross terms remain, a linear coefficient 2 makes the sum zero. + Otherwise each remaining variable supplies a factor two. + +Each step removes at least one variable. The code uses direct polynomial +substitution. A conservative bound is O(m^5) arithmetic operations per +sum, plus O(L m^4) to build a path form for L native gates. It uses +polynomial space. This bound is not a +claim of optimal stabilizer simulation or constant-time integer arithmetic. +Coefficient bit lengths are polynomial in the literal word length. + +The use of binary quadratic forms for Clifford operations is classical; +see [Dehaene and De Moor, Sections III-V](https://arxiv.org/pdf/quant-ph/0304125). +The new implementation derives its phases directly from the pinned native +kernel. The dense frozen kernel remains a separate finite test oracle. + +## 5. Bitwise witness extraction removes the D^2 scan + +For two operators g,h and fixed prefixes of the output and input bits, +define B(g,h) as the sum of conjugate(g[x,y])h[x,y] over the unspecified +bits. Combine two path sums, negate the left phase, equate their input +and output bits, and impose the prefix equations. Section 4 computes B +in polynomial time, with at most the sum of both path-variable counts. + +With r tensor factors still after the current factor, the conditional +squared norm is + + sum_(g,h) conjugate(c_g)c_h B(g,h) (tr(g* h)/D)^r. + +It is real and nonnegative. The two choices for the next coordinate bit +partition its sum. Choose the larger child. After 2n choices, the current +base coordinate pair is fixed; multiply each coefficient by g[x,y] and +continue with the next tensor factor. There are 2nf bit choices, each +with two children, instead of fD^2 coordinate trials. + +At the start of one factor the conditional norm is D E. The 2n splits +lose at most D^2. Induction gives the same final entry bound as PROOF.md: + + |entry|^2 >= E_f D^(-f). + +[compact.py](compact.py) also expands complete register endpoints as +signed native words. It retains every input and return role. It merges +two unitary words exactly when tr(g* h)/D=1; the identity +||g-h||_HS^2=2D-2 Re tr(g* h) proves this test. Global phases stay inside +the operator keys, not in coefficients outside the tensor power. + +For expanded support s and a maximum literal path size m, pair traces +cost O(s^2 poly(m)). A witness costs O(n f s^2 poly(m)) arithmetic +operations, with polynomial space in these parameters. No 2^n matrix or +2^(nf) tensor is built. The symbolic support s can still grow exponentially +in the register-program length. This result does not remove that obstacle. + +## Verification and limits + +[verify_advances.py](verify_advances.py) checks the code invariant, exact +filter bounds, modular inverse certificate, exhaustive small quadratic +sums, frozen native entries and traces, conditional inner products, and +complete programs against the original dense compiler. It checks larger +native examples without a dense matrix. ADVANCES-RESULT.json records the +executed counts. Normal and optimized Python must produce the same receipt. + +The proofs above are written arguments, not proof-kernel certificates. +The code invariant and quadratic-form method have classical predecessors. +The sparse full-program adapter, finite-width refinements and native phase +bindings are the present contribution. No complete current provider or +physical cost invoice has been run. No selected frontier changes here. + +## Open next questions + +1. Prove a sharper maximum cutoff for n>=2, or give a matching obstruction. +2. Bound support growth on one complete current provider before a large run. +3. Derive a useful stability constant for the eight selected widths. +4. Improve the quadratic elimination cost after a measured provider needs it. diff --git a/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/LICENSE b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/MUTATIONS.json new file mode 100644 index 0000000000..9263be8739 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/MUTATIONS.json @@ -0,0 +1,45 @@ +{ + "cases": [ + { + "mutation": "omit final trace root", + "optimized": false, + "rejection": "Polynomial endpoints" + }, + { + "mutation": "omit final trace root", + "optimized": true, + "rejection": "Polynomial endpoints" + }, + { + "mutation": "ignore inverse", + "optimized": false, + "rejection": "Signed-word complete endpoint" + }, + { + "mutation": "ignore inverse", + "optimized": true, + "rejection": "Signed-word complete endpoint" + }, + { + "mutation": "omit final return", + "optimized": false, + "rejection": "Zero-axis scalar group" + }, + { + "mutation": "omit final return", + "optimized": true, + "rejection": "Zero-axis scalar group" + }, + { + "mutation": "remove Gram normalization", + "optimized": false, + "rejection": "Independent dense norm" + }, + { + "mutation": "remove Gram normalization", + "optimized": true, + "rejection": "Independent dense norm" + } + ], + "status": "PASS_CLIFFORD_GRAM_MUTATIONS" +} diff --git a/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/ONE-AXIS-RANK.json b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/ONE-AXIS-RANK.json new file mode 100644 index 0000000000..6138b717d1 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/ONE-AXIS-RANK.json @@ -0,0 +1,9422 @@ +{ + "group_sha256": "32481fd502c5f388244bcd56d20fbc0e0ca3933f47dbbdbbd8215397cea0238d", + "image_of_i": 256, + "inverse": [ + [ + 32344, + 51075, + 51075, + 43700, + 17417, + 17417, + 43700, + 60702, + 38637, + 38637, + 38637, + 38637, + 38637, + 60702, + 7672, 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b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/PROOF.md @@ -0,0 +1,268 @@ +# A finite and stable tensor test for dyadic Clifford programs + +The [continuation](ADVANCES.md) reduces the number of tested widths, +improves 14/15 to 75/76, proves the sharp one-axis cutoff, and supplies +a compact native implementation. This note retains the original proof. + +## Result + +Let R = Z[i,1/2], let D = 2^n, and let C_n be the unitary matrices in +M_D(R) that normalize the n-axis Pauli group. Keep their exact global phase. +This class includes the source Gaussian gate + + C_v = (1+i)I/2 + (1-i)X_v/2, + +its inverse, quadratic phase gates, affine binary permutations and the +source Hadamard gate. It is larger than the monomial subgroup. + +Consider two finite scalar register programs. Each role has an independent +arbitrary input in (C^D)^(tensor f). Instructions can add a scalar multiple +of one role to another, scale a role, exchange roles, or apply U^(tensor f) +for U in C_n. Queries can add c U^(tensor f) v_s to v_d. Self queries are +permitted. Both programs and their scalar coefficients are fixed as f varies. +Every input and return role is part of the contract. + +**Theorem.** The complete endpoints agree for every positive integer f if +and only if they agree for f = 1,...,8n+4. There is no program-length or +support-size term in this cutoff. This is not a claim that these widths are +minimal, or that dense tensor matrices can be tested at low cost. + +There is a stronger quantitative statement. In one endpoint entry, combine +equal exact native matrices and write the residual as + + A_f = sum_(g in S) c_g g^(tensor f), + +where the matrices in S are distinct. Set + + M = sum_g |c_g|^2, + E_f = D^(-f) ||A_f||_HS^2. + +Then + + max_(1 <= f <= 8n+4) E_f >= (14/15) M. (1) + +The proof gives explicit rational weights b_f such that + + sum_(f=1)^(8n+4) b_f E_f = M. (2) + +Each E_f can be computed from base-dimension pair traces. It does not require +a tensor matrix. A nonzero E_f gives an exact nonzero tensor entry by a finite +sequence of conditional norm tests. The executable uses Q(i); the theorem +allows arbitrary complex scalar coefficients. + +This result changes an infinite algebraic obligation into a finite test for +this native class. It does not supply a native layout, a physical cost bound, +rounding, stock, a recursive supplier, or a change to the complete kappa. + +## 1. The exact trace alphabet + +Use Hermitian Paulis P_v, labelled by v in F_2^(2n), as an orthogonal basis +of M_D(C). A Clifford U acts by + + U P_v U* = epsilon(v) P_(S v), + +where S is symplectic and each epsilon(v) is 1 or -1. On the fixed space +L = ker(S-I), the signs form an additive character. Indeed, multiplication +P_u P_v = gamma(u,v) P_(u+v), followed by conjugation, cancels the same +nonzero gamma on both sides and gives epsilon(u+v)=epsilon(u)epsilon(v). + +The trace of conjugation on all matrices is |tr U|^2. The Pauli basis gives +the same trace as sum_(v in L) epsilon(v). A nontrivial sign character sums +to zero; the trivial character sums to |L|. Thus + + |tr U|^2 is zero or 2^d, with 0 <= d <= 2n. (3) + +We also need the phase of this trace. C_n is a finite group. Its conjugation +action on the finite Pauli group has finite image. Its kernel consists of +scalar matrices: commuting with all Z generators forces a diagonal matrix, +and commuting with all X generators makes that diagonal constant. A scalar +in R with absolute value one is in {1,i,-1,-i}. To see this, write it as +(a+bi)/2^k. Unique factorization in Z[i], with 2=-i(1+i)^2, shows that a +Gaussian rational with denominator a power of two and norm one is a unit. +The kernel therefore has four elements. + +Every U has finite order. Its eigenvalues are roots of unity, so its trace +is an algebraic integer. The trace is also in Q(i). The ring of integers of +Q(i) is Z[i], so tr U is a Gaussian integer. Factoring its norm in (3) now +shows + + tr U in {0} union {i^k (1+i)^d : 0 <= k < 4, + 0 <= d <= 2n}. (4) + +The same statement holds for U*V. In particular, no arbitrary rational +unit-circle phase may be admitted. For example (3+4i)I/5 is unitary and +normalizes Paulis, but is outside the dyadic hypothesis. + +Finally tr(U*V)=D holds exactly when U=V. All eigenvalues of U*V have absolute +value one. Equality in their sum being the positive real number D forces +every eigenvalue to be one; a unitary matrix with those eigenvalues is I. + +## 2. An explicit polynomial that selects the identity + +Let z = tr U / D. In addition to zero and the four scalar values 1,i,-1,-i, +every possible z satisfies + + z^4 = (-1)^j 4^(-j), for some 1 <= j <= 2n. + +Define the rational polynomial + + q_n(z) = z(1+z+z^2+z^3)/4 + * product_(j=1)^(2n) + (z^4 - (-1)^j 4^(-j))/(1 - (-1)^j 4^(-j)). (5) + +It has zero constant term, degree 8n+4, and q_n(1)=1. It vanishes at every +other value in the trace alphabet. Therefore, for exact matrices U,V in C_n, + + q_n(tr(U*V)/D) = 1 if U=V, and 0 otherwise. (6) + +Write q_n(z)=sum_f b_f z^f. The triangle inequality for polynomial +coefficient norms gives a dimension-independent bound. The first factor +has coefficient norm one. Each odd-j factor has nonnegative coefficients +whose sum is one. The norm of the even factor j=2k is + + (1+16^(-k))/(1-16^(-k)). + +For nonnegative a,b with a+b<1, + + [(1+a)/(1-a)] [(1+b)/(1-b)] + = (1+t)/(1-t), where t=(a+b)/(1+ab) <= a+b. + +Induction and sum_(k>=1) 16^(-k)=1/15 show + + sum_f |b_f| <= product_(k=1)^n (1+16^(-k))/(1-16^(-k)) < 8/7. (7) + +For n=0 the norm is one and the same strict bound holds. Also sum_f b_f=1. +It follows that the sum of the positive coefficients is less than 15/14. + +## 3. The Gram identity and stable separation + +The Hilbert-Schmidt inner product is multiplicative under tensor products. +Thus + + E_f = sum_(g,h in S) conjugate(c_g)c_h (tr(g^* h)/D)^f, (8) + +where g* denotes the adjoint, so the trace argument is g* h. Apply (6) to +(8) and sum against b_f. All terms with g != h vanish and the diagonal +terms give M. This proves (2). + +Each E_f is a nonnegative real number. Terms with b_f<0 can be removed from +the right side of (2) when taking an upper bound. Hence + + M <= (sum_(b_f>0) b_f) max_f E_f < (15/14) max_f E_f + +when M>0. The weaker non-strict form (1) also covers M=0. If the first 8n+4 +residual matrices vanish, (2) forces M=0. Every exact coefficient c_g is then +zero, so A_f vanishes at every positive width. The reverse implication is +immediate. Apply this argument to each input/output entry to obtain the full +dirty-register theorem. + +This proof uses only pair traces and a rational polynomial. It does not need +an irreducible character table or a census of C_n. Burnside-Brauer supplies +a related classical tensor-generation argument; (5)-(8) give the explicit +native cutoff, quantitative bound and computational certificate used here. + +## 4. Extract a tensor entry without a tensor matrix + +Suppose E_f>0. For one output coordinate x and input coordinate y in the +first tensor factor, put c'_g=c_g g[x,y]. The remaining tensor operator is +sum_g c'_g g^(tensor (f-1)). Its normalized squared norm is obtained from +the same pair-trace matrix by (8). The sum of these conditional norms over +the D^2 choices of (x,y) is D E_f. At least one choice is positive, and a +maximizing choice is at least E_f/D. + +Repeat until no tensor factors remain. The final scalar is exactly the +chosen entry of A_f. It is nonzero and its squared absolute value is at +least E_f/D^f. Start at a width attaining the maximum in (1) to obtain + + |entry|^2 >= (14/15) M D^(-f). (9) + +The independent witness checker uses a separate signed-word interpreter, +multiplies the base matrices in their literal order, and computes this one +entry as a product of base entries. It does not use traces, the cutoff, +the interpolation polynomial, or the producer's register compiler. + +## 5. Cost, input validation and trust + +For s distinct residual operators supplied as D-by-D matrices, all pair +traces cost O(s^2 D^2) exact scalar operations. Equal traces can be collected +into at most 8n+5 buckets, including zero. The full norm sequence then costs +O(n^2+s^2) further scalar operations after the pair traces, apart from +coefficient storage. Coefficient bit sizes are not bounded by this count. + +The direct entry extractor uses O(f D^2 s^2 log(f+1)) scalar operations in the +worst case, with base matrices and their Gram matrix in memory. The logarithm +accounts for repeated squaring of pair traces. It never allocates +a D^f-by-D^f matrix. Word support can grow exponentially during compilation; +the program compiler is not asserted to be polynomial in instruction count. +The base dimension D itself is exponential in n. No practical full-supplier +speedup is inferred from these bounds. + +The frontend checks every supplied matrix for dyadic entries, unitarity and +Pauli normalization on all 2n generators. The last check is sufficient: +the generators generate the Pauli group, and invertible conjugation gives +an injective map of that finite group into itself. Products and adjoints +remain in C_n. Exact matrix keys include global phase. Scalar coefficients +remain outside tensor powers. The checker does not move a scalar phase +from an operator into a coefficient. + +The actual source kernel uses precisely the gates in the first section. +Its C formula has eigenvalues 1 and i. Its Hadamard convention is S C S, +so H^2=iI, not I. The retained source bytes and the independent column +formula are checked in verify.py. These checks bind the algebraic grammar; +they do not run a complete native supplier or its physical implementation. + +The proof is written mathematics. Python, the compiler, the frozen Gaussian +arithmetic and the native-source transcription remain trusted. The direct +tensor, signed-word and source-column checks test different implications. +They are not an independent human review or a proof-assistant theorem. + +## 6. A finite test that misses a real failure + +The one-axis source C and S gates generate a group G of 96 exact matrices. +There are at most 24 signed images of an ordered anticommuting Pauli pair, +and at most four scalar lifts of each image. Thus this group is the complete +one-axis dyadic normalizer, not just a proper subgroup used for calibration. +Let one dirty target receive + + y <- y + (1/96) sum_(g in G) g^(tensor f) x. + +The source x is unchanged. The average is an orthogonal projector, so its +trace equals its rank. Complete exact enumeration gives rank zero at widths +1 through 7 and rank 15 at width 8. The all-zero input/output tuple has +entry 5/24 at width 8. Thus seven full small-width checks can all accept +a false all-width identity. The registered example and literal witness +checker reproduce this counterexample without building its tensor matrix. + +## 7. Scope and credit + +The program must have fixed scalar coefficients and a fixed native word as +width changes. This theorem does not cover a different program at each f, +arbitrary continuous phases, nonunitary scaled operators, non-Clifford gates, +positive characteristic, nonlinear leaves or physical aliasing. A caller +with restricted clean inputs needs its own input contract. Rounded equality +is not exact equality. No complete multiplication theorem or kappa changes. + +The finite-group algebra viewpoint is prior work. The repository's +projection-recursion-check already uses positive-width Burnside-Brauer +separation, following Jacob Alan Sussman's engine model. The free-word +tensor audit of Cinna Davis's programs and the certificates by zxv and +Krzysztof Wojt retain their separate contributions. Chris R's retained-helper +and passive-query proofs already use finite Clifford alphabets and tensor +Gram separation. For fixed scalar coefficients, this package supplies the +explicit filter and dimension-independent stability constant above. It does +not replace their statements about width-dependent coefficients. The +concurrent PR #5369 targets the smaller +affine-quadratic monomial class with four selected widths. This package does +not claim its result. README.md links these related sources. + +Classical provenance: Burnside and Brauer's tensor-generation theorem, as +reviewed by Benjamin Steinberg in +[On the Burnside-Brauer-Steinberg theorem](https://arxiv.org/abs/1409.7632), +the Pauli conjugation basis, Gaussian-integer factorization, polynomial +interpolation and Gram identities. No global mathematical priority is +claimed. The new package provides the explicit dyadic-Clifford trace +filter, stable bound, complete program frontend, compressed failure +certificate and source-bound checks. The exact source and credit map is +in README.md and SOURCES.json. + +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. diff --git a/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/PROVIDER.md b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/PROVIDER.md new file mode 100644 index 0000000000..7b7dfa9e48 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/PROVIDER.md @@ -0,0 +1,281 @@ +# Complete selected-provider check and a pair-fusion obstruction + +The new verifier passes the complete local provider selected from PR4610. +It also excludes **30,328 fixed pair fusions at every positive tensor width**. +This contribution does not increase kappa. The paid profile does not change. + +The provider is the exact word at main commit +`1ec1119972c9aefe42525172d07b332fcff81cb4`. Its author head is +`20bb93cd990d2ff683e4d0fc56b87a42cd5d3296`. The paid catalogue comes from +the independent PR5241 admission at +`13efb5fc5f3b7c14ec2cfa181dd9eb6480972cf2`. +`provider/SOURCES.json` binds each copied input to its source Git object and +SHA-256. Frozen source files are not changed. + +## Result and coverage + +Each direction has 21,449 source events, 632 independent persistent inputs, +and one independent owned input. Every persistent output is checked. The owned +output must be zero. All 408 helper inputs remain arbitrary. Their outputs +have their specified native frame changes; they are not assumed to be zero. + +The new quadratic-sum engine checks 7,000 oriented recipe classes: + +| Class | Checks | Coverage | +| --- | ---: | --- | +| Paid transitions | 5,710 | All 6,596 event instances across both directions | +| Native warps | 360 | All 480 signed event instances | +| Helper boundaries | 34 | All 408 roles in each direction | +| Main adapters | 896 | All 448 adapter events in each direction | + +These counts refer to labelled classes. They do not count distinct matrices. +For two unitary circuits U,V on D=512 coordinates, the checker requires +`tr(U* V)/D = 1`. Here `*` is the conjugate transpose. This equality proves +U=V, including absolute phase. Each circuit then has the same tensor power at +every positive width. A recipe's stored PASS status is not an input to this +test. The main adapter generator only proposes data. Acceptance does not +import or execute that generator or its native compiler. + +The complete physical programs are also passed directly to `compact.certify`. +Their references contain every input and output role. The result is equality +at every positive width, with no nonzero endpoint entry. The complete sparse +expansion gives these measured support counts: + +| Direction | Scalar/native instructions | Native symbols | Peak total terms | Peak terms in one row | Final terms | +| --- | ---: | ---: | ---: | ---: | ---: | +| Forward | 24,827 | 1,297 | 22,331 | 156 | 744 | +| Backward | 24,819 | 1,297 | 12,930 | 148 | 744 | + +These are counts for this fixed provider. General program support can still +grow exponentially. No dense tensor matrix is made. The separate check of +the displayed failure witnesses uses base-space vectors with 512 entries. + +## Exact boundary and translation + +Let F_U be the source canonical frame, C_q the source Gaussian gate, and +F_full the full frame. Write E_i for the entrance frame of persistent role i +and H_i for its exit frame. In the forward orientation: + +- For 0<=i<112, E_i=C_(q_i) and H_i=F_full. +- For 112<=i<224, E_i=I and H_i=F_full C_(q_(i-112))^-1. +- For 224<=i<632, E_i=F_(start_i) and H_i=F_(final_i). + +The backward orientation uses the entrywise conjugate of each native frame +and operator. A negative warp uses the inverse before this conjugation. +Conjugation is not replaced by the adjoint. + +In these logical coordinates, the forward endpoint is +`L_(112+j) <- L_(112+j) + L_j` for 0<=j<112. The backward endpoint is +`L_j <- L_j - L_(112+j)`. All other persistent logical coordinates return +unchanged. Thus the persistent physical endpoint is + + diag(H_i^tensor f) T diag((E_i^-1)^tensor f). + +This operator is invertible for every positive f. The owned input is erased, +and its output is zero. All scalar coefficients remain outside tensor powers. + +The importer expands a paid transition a->b as F_b F_a^-1. A signed warp +becomes F_b K_signed F_a^-1. A scalar ADD retains its literal rational +coefficient. Owned CLEAR becomes scalar multiplication by zero. Owned COPY +becomes CLEAR followed by ADD. Borrowed CLEAR and COPY are rejected. + +The 448 main adapter markers are included. An entrance adapter is +F_start E_i^-1. An exit adapter is H_i F_final^-1. There is a source detail +that must not be hidden: some identity exit markers precede the final climb. +The importer permits a marker at a different current frame only when the +adapter circuit is exactly the identity. A nonidentity marker must use its +actual current frame. +Every nonidentity entrance adapter must precede all uses of its role. Every +nonidentity exit adapter must follow all uses. The word audit checks both +conditions. Thus an adapter inside a candidate interval changes its endpoint +frame and has the identity logical map. + +The sparse interpreter expands all independent inputs together. The existing +`compact.certify` interpreter expands one input at a time. Both complete +endpoints agree with the same explicit physical reference. The earlier +PR5241 free-group argument already proves this provider's algebraic lift. +The new contribution here is an executable application of the new Gram +engine, complete support measurements, and the obstruction below. It is not +a priority claim for that earlier lift argument. + +## Fusion class + +For each persistent role, list its paid climbs in chronological order. Take +every pair in this list, at all positive ranks. Paid events on the same role +or on other roles may occur between the two climbs. Native warps, scalar contacts, +adapters and complete owned-center windows may also occur between them. +There are **7,582 pairs per direction**. No adjacency or common middle-frame +condition is imposed. The domain includes all 2,658 adjacent pairs, including +all 1,363 adjacent rank-one pairs, per direction. + +Let A and B be the literal physical operators of the first and second climb. +Let T be the complete interval between them. The original local map is BTA. +Two replacements are tested: + +- Early fusion: apply BA at the first slot and remove the second slot. The + local map becomes TBA. +- Late fusion: remove the first slot and apply BA at the second slot. The + local map becomes BAT. + +Every other physical operation is fixed. In particular, no scalar contact +is changed to a new native query. The product BA is used with its exact +phase, even when the middle frames differ. This gives 2*2*7582=30,328 candidate +rewrites. The domain does not include a new intermediate placement, a +changed pair of operators, simultaneous fusions, or a pair on different roles. + +The initial invoice opportunity was two H1 jobs replaced by one H2 job. +For a legal replacement in each of 18 local calls, the complete delta would +be -36 H1 +18 H2. This is the physical-pair gap in the PR5243 handoff. +The proof also applies to the other rank pairs. The endpoint obstruction +rejects every candidate before a new complete pricing step. +No such saving is charged to the complete kappa calculation. + +## Closed-cut lemma + +At every persistent climb in this source, the owned register is either +unused and about to be initialized before any read, or is zero after a +completed lifetime. The word audit checks this property. It also checks +that only the owned register can be overwritten and that all reads occur +after initialization. + +Set the unused owned entry to zero. At either end of each candidate interval, +the state is therefore determined by the 632 persistent fields. Each prefix, +interval and suffix defines a square linear map on those fields. This remains +true when the interval contains a whole owned-center window. + +For a fixed positive f, write the complete baseline as S(BTA)P on persistent +fields. The complete endpoint above is invertible. A product of square +matrices over Q(i) can be invertible only when every factor is invertible. +Thus P and S are invertible. It follows that + + S(C-BTA)P = 0 if and only if C-BTA = 0. + +A nonzero interval defect therefore survives to the complete provider's +return. This argument does not require the persistent prefix or suffix to +be unitary. It does not carry a numerical norm bound through those maps. +It would fail at a cut with live owned information omitted from the state. + +## A quantitative contact obstruction + +Use the moving logical frames at the interval boundaries. Let M be the +interval's logical matrix. Frame changes and adapter changes are identity +maps in these coordinates. Scalar instructions remain scalar instructions. +Each native warp is the corresponding phase-bearing K operator. + +For each candidate, the saved certificate gives an off-diagonal block of M +that touches the changed role r. That block is exactly + + M_(r,j) = q U^tensor f or M_(j,r) = q U^tensor f, j != r, + +where q is a nonzero rational and U is a signed word of native unitary maps. +The coefficient is obtained by exact free-group arithmetic. It is not a +sampled equality and holds for all positive f. The second replay checks every +saved coefficient with the earlier independent-input engine. A separate +role-list census checks that the saved pairs cover the entire declared class. + +For early fusion, let G1 and G2 be the diagonal physical frames immediately +after A and immediately before B. Let G3 be the frame immediately after B. +Then the changed logical interval is L M R, where + + L = G3^-1 G2, + R = G1^-1 B G1. + +Both corrections act only on role r. Their r-blocks are conjugates of B^-1 +and B. For late fusion the corresponding corrections have r-blocks conjugate +to A and A^-1. These formulas do not require the two middle frames to agree. + +On the saved off-diagonal block, only one correction acts. The defect is a +unitary left or right multiple of q(V^tensor f-I), where V is a conjugate of +the relevant paid operator or its inverse. Let + + tau = tr(V)/D, D=512. + +The normalized squared Hilbert-Schmidt defect of this block is exactly + + q^2 (2 - 2 Re(tau^f)). + +The new quadratic-sum engine calculates every required trace with exact +Gaussian rational arithmetic. In every case it checks + + Re(tau) <= 1/2, |tau|^2 <= 1/2. + +For f=1, the first inequality gives Re(tau^f)<=1/2. For f>=2, the second +gives |tau|^f<=1/2. The same bounds hold for the inverse, whose trace is the +complex conjugate. Consequently every saved block has normalized squared +defect at least **q^2>0 at every positive width**. The closed-cut lemma lifts +this obstruction to the complete provider. +The smallest saved q^2 is **1/256**, which is a uniform lower bound on the +selected cut-block defects. It is not a lower bound on the full-provider +defect after multiplication by its prefix and suffix. + +`provider/FUSIONS.json.gz` contains all 15,164 contact certificates, the exact +event positions, ranks, four frame IDs, native word, scalar coefficient and two +traces. Each certificate excludes the early and late replacement. +`provider/WITNESSES.json` also gives twelve literal width-one basis witnesses +from the complete physical programs. They cover both directions, both +placements, equal and unequal middle frames, and nonadjacent pairs with a +higher-rank climb. The native source +amplitude evaluator checks each value without Gram traces or quadratic sums. + +## Verification and limits + +From the repository root, with Python 3.12 and the standard library: + +```sh +python3.12 -I -W error -B research/clifford-tensor-gram/verify_provider.py +python3.12 -I -O -W error -B research/clifford-tensor-gram/verify_provider.py +``` + +Expected final line: + +```text +PASS_COMPLETE_PR4610_PROVIDER_AND_30328_FUSION_OBSTRUCTIONS +``` + +The replay checks source bytes, every recipe class, both complete programs, +the complete pair census, every contact coefficient, exact trace bounds and +the full-program witnesses. Negative controls cover an omitted paid class, +a wrong absolute phase, borrowed erasure, a cut with live owned data and a +missing contact. An identity interval is a positive control: no obstruction +is inferred merely from the presence of two paid operations. + +The local paid profile remains `{1:2201,2:412,3:510,4:127,5:40,8:8}`: 3,298 jobs +and rank mass 5,327 per direction. The complete selected kappa remains +0.0030217758. This work does not reprice the controller, run a new outer +admission, or change the selected record. The five selected framework +assumptions remain. The result covers this ideal finite local provider and +its tensor substitution; it does not prove physical tape, precision, stock, +analytic recovery or the complete multiplication theorem. + +The obstruction does not exclude changed contacts, joint use of several +fields, simultaneous rewrites, interior placement, owned-center pairs, +new operators or later source providers. In particular, it does not +subsume the separate frozen eight-relation row argument in PR5393. + +## Open next questions + +1. Can a changed scalar contact supply the missing transformed operand at a + lower complete cost? Start from a saved contact certificate. Replace that + actual contact, retain dirty restoration, and price the replacement query. +2. Can several coordinated fusions cancel their endpoint defects? Start with + a small explicit set of saved pairs. Run the complete native endpoint test; + individual rejection does not prove joint rejection. +3. Can the eight-width criterion help with a complete program whose endpoint + cannot first be reduced by free-group identities? This provider gives a + manageable support example, not a bound for other programs. + +## Credit + +Cao Yifan / intqwq supplies the selected PR4610 construction. Chris R / +Clear1nsight supplies the PR5241 independent paid catalogue, complete admission +and earlier quantified lift proof. Cinna Davis / 1337isnot1337 supplies the +retained controller, native warp and helper chain. zxv, Jacob Alan Sussman, +Dugongue, Rohan Arun, Jeremy Kothe, icekylinx, DreamingOfClouds and chafreaky +retain credit for the relevant native, frame, helper and adapter sources. +The source notices and `provider/NOTICE.md` give the source links. The scalar +arithmetic and frozen native kernel retain their existing notices. + +The new provider importer, Gram application, cut proof, complete pair census +and receipts are by Ali Romman with substantial OpenAI Codex assistance. +The checks are author checks. Independent human review and a proof-kernel +verification are not claimed. Apache-2.0. diff --git a/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/README.md b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/README.md new file mode 100644 index 0000000000..9f6cdf24c5 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/README.md @@ -0,0 +1,234 @@ +# Finite, stable tensor tests for the full dyadic Clifford group + +**A uniform algebraic interface theorem and an exact verifier; no new kappa.** +For fixed scalar register programs on n binary axes, with unitary dyadic +Clifford operators and every dirty input/return retained, equality at the +**eight widths 8n-3 through 8n+4 implies equality at every positive width** +for n>=2. For one axis, **widths 5,6,7,8 suffice**, and both the maximum +cutoff eight and the number of tests four are sharp. For zero axes use +widths 1,2,3,4. This +covers Gaussian and Hadamard gates as well as phase-monomial maps. The cutoff +does not depend on program length or expanded support. + +The [original proof](PROOF.md) and [extensions](ADVANCES.md) give a stable test. +Let M be the squared coefficient +norm after equal exact native operators are combined. Some tested width has +normalized squared Hilbert-Schmidt residual at least **(75/76)M** among all +widths 1 through 8n+4. An explicit +rational polynomial recovers M from the finite norm sequence. Base-space pair +traces suffice. The compact implementation uses exact quadratic sums and +bitwise conditional norms. It builds **neither a dense base matrix nor a +tensor matrix**, and it removes the original D^2 coordinate scan. + +For the source's nine binary axes, **eight tests at widths 69 through 76** suffice. +This is an algebraic bound, not a full supplier replay or a minimal cutoff. +The complete kappa calculation and selected frontier are unchanged. + +The [complete-provider application](PROVIDER.md) now passes both directions +of the selected PR4610 local provider: all 633 inputs and returns, 7,000 +oriented native recipe classes, and the full physical programs. It also +excludes **30,328 early/late pair fusions at every positive tensor width**. +The domain contains every pair of paid climbs on one persistent role, at +all ranks and without an adjacency condition. The [result](provider/RESULT.json), +[full-program witnesses](provider/WITNESSES.json), and +[research notes](provider/RESEARCH-NOTES.md) preserve the evidence and limits. +No paid job is removed and kappa does not increase. + +## A concrete small-width trap + +The [Reynolds example](examples/reynolds.json) adds the average of the 96 +one-axis native group operators to a dirty target. It preserves the source. +Its complete endpoint is the identity at widths **1 through 7**, but fails at +width **8**, with a literal entry **5/24**. The +[certificate](examples/reynolds.certificate.json) gives the roles and coordinates. +This example uses the full group, not a numerical sample. + +## Use + +Python 3.12 and the standard library suffice. From the repository root: + +```sh +python3.12 -B scripts/research_package.py --package research/clifford-tensor-gram +``` + +The registered commands print `PASS_CLIFFORD_TENSOR_GRAM_NO_NEW_KAPPA` and +`PASS_CLIFFORD_ADVANCES_NO_NEW_KAPPA` in normal and optimized Python. +The provider commands also print +`PASS_COMPLETE_PR4610_PROVIDER_AND_30328_FUSION_OBSTRUCTIONS`. +Direct commands also work in a Git-free export: + +```sh +python3.12 -I -W error -B research/clifford-tensor-gram/verify.py +python3.12 -I -O -W error -B research/clifford-tensor-gram/verify.py +python3.12 -I -W error -B research/clifford-tensor-gram/verify_advances.py +python3.12 -I -O -W error -B research/clifford-tensor-gram/verify_advances.py +python3.12 -I -W error -B research/clifford-tensor-gram/verify_provider.py +python3.12 -I -O -W error -B research/clifford-tensor-gram/verify_provider.py +python3.12 -I -B research/clifford-tensor-gram/compact.py \ + research/clifford-tensor-gram/examples/native-64.json +python3.12 -I -B research/clifford-tensor-gram/certify.py \ + research/clifford-tensor-gram/examples/native-relation.json +python3.12 -I -B research/clifford-tensor-gram/check_witness.py \ + research/clifford-tensor-gram/examples/reynolds.json \ + research/clifford-tensor-gram/examples/reynolds.certificate.json +python3.12 -I -B research/clifford-tensor-gram/audit_mutations.py +python3.12 -I -B research/clifford-tensor-gram/audit_advances.py +``` + +The producer prints JSON. Read `equivalent_at_all_positive_widths`; a successful +process means the decision completed, and a counterexample is a valid result. +The independent witness checker prints `PASS_LITERAL_TENSOR_WITNESS 5/24`. +Relative to the original dense producer, it uses a separate signed-word +interpreter and literal matrix entries, with +no producer import, trace calculation or interpolation argument. Only the +frozen scalar arithmetic is shared. +It checks the literal nonzero entry, not the claimed norms or the universal +cutoff theorem. + +The compact producer reuses that signed-word expansion. Its differential +checks use the original dense compiler, frozen source matrices and literal +entries. It is not an independent checker of itself. The research record is +saved in [RESEARCH-NOTES.md](RESEARCH-NOTES.md). + +## Input contract + +`compact.py` uses the same roles and instructions below, but each value in +`operators` is a literal native circuit. See the +[64-axis example](examples/native-64.json) and +[65-axis phase relation](examples/native-65.json). The native gate forms are +`["P", rows]`, `["X", offset]`, `["D", rows, alpha]`, `["C", mask, sign]` +and `["phase", exponent]`. Binary matrix rows are integer masks. Diagonal +alpha values belong to 0,1,2,3 and have the diagonal row parity. C signs +are +1 or -1. The parser checks the native gate conditions. + +The compact certificate records the reduced decision widths. For a negative +result it still computes all 8n+4 norm values to use the stronger stability +bound and select its witness. The eight-width theorem alone does not give +that dimension-free bound on the selected eight norms. + +The [native relation example](examples/native-relation.json) gives the format. +`axes` is n; `roles` counts arbitrary independent inputs and returns. +`operators` contains exact 2^n-by-2^n matrices, with integer entries or +Gaussian-rational strings such as `1/2-1/2i`. Floats are rejected. The frontend +checks dyadic entries, unitarity and normalization of all Pauli generators. +`program` and `reference` are complete instruction lists. An empty reference +is identity on every role. + +| Instruction | Required fields | Action | +| --- | --- | --- | +| `add` | `src`, `dst` | Add a scalar multiple of a role | +| `query` | `src`, `dst`, `symbol` | Add an operator image of a role | +| `apply` | `dst`, `symbol` | Apply an operator to a role | +| `scale` | `dst`, `coefficient` | Scale a role | +| `swap` | `src`, `dst` | Exchange roles | + +`add` and `query` accept an optional `coefficient`, default one. `query` and +`apply` accept Boolean `inverse`, default false. Self queries read the previous +value. Global phase stays inside the tensor power; scalar coefficients stay +outside. The source convention has H^2=iI. Replacing that operator with scalar +scaling by i passes width one and fails width two, as the +[phase example](examples/phase-trap.json) shows. Scalar coefficients need not +be dyadic. + +## Evidence and limits + +[ADVANCES-RESULT.json](ADVANCES-RESULT.json) records the continuation: +256 code Fourier values, exact filter bounds for n=0,...,64, a rank-96 +modular inverse certificate, 640 exhaustive small quadratic sums, 3,328 +native entries, 128 native traces, 304 partial inner products, 48 complete +program comparisons and literal witnesses, nine exact native relations, +a scalar-phase trap and eight rejection controls. The large cases use +64 and 65 axes. Their base dimensions are 2^64 and 2^65; no dense base +array is allocated. The 64-axis witness is the exact entry 1/4294967296. +The 65-axis relation retains H^2=iI as a native operator identity. + +[RESULT.json](RESULT.json) records 96 group elements, 689 exact trace-filter +values, 2,124 source columns, 48 entangling trace cases, 60 explicit tensor +norms, 72 complete endpoint comparisons, 24 full tensor program comparisons, +16 random literal witnesses, two zero-axis boundary cases and 20 controls. +The source columns include both +orientations of an actual nine-axis Gaussian gate. Controls reject nonunitary +inputs, non-dyadic phases, Toffoli, malformed instructions, wrong tensor phases, +missing helper returns and false witnesses. Source hashes are checked before +the replay imports the frozen files. + +[MUTATIONS.json](MUTATIONS.json) records four private-copy defects rejected in +both Python modes: a missing trace factor, an ignored inverse, an omitted +dirty return and a missing Gram normalization. The audit prints +`PASS_CLIFFORD_GRAM_MUTATIONS`. The local runs used CPython 3.12.13 on macOS +with no third-party packages. + +[ADVANCES-MUTATIONS.json](ADVANCES-MUTATIONS.json) records four additional +defects rejected in both modes: a wrong native C phase, an ignored native +inverse sign, a missing prefix constraint and an omitted dirty return. +The audit prints `PASS_CLIFFORD_ADVANCE_MUTATIONS`. + +The written proof supplies the universal quantifiers. Finite tests corroborate +it. This is author-checked with substantial AI assistance, not independent +human or proof-kernel acceptance. Compilation can expand exponentially many +terms. The compact path and witness algorithms use polynomial work in the +axis count, literal word length, tensor width and expanded support. The +original dense frontend still uses base dimension 2^n. No polynomial-time claim in instruction +length or practical full-supplier speedup follows. The provider application +checks the complete selected local word and its native recipes. A selected +controller/compiler cold replay, new admission, Lean and Docker are not run. +Physical storage, tapes, stock, precision and outer recovery remain separate. +Programs that change with f, non-Clifford gates, continuous phases, nonunitary +native operators, rounded leaves and restricted clean-input contracts are excluded. + +## Sources and credit + +Base: canonical main `7c472563474e60185e6ca101a17622133d047e56`, priority 7. +[SOURCES.json](SOURCES.json) binds exact sources. No predecessor is modified. +The provider application has the separate current-main pin +`1ec1119972c9aefe42525172d07b332fcff81cb4`; its source copies and full credit +are in [provider/SOURCES.json](provider/SOURCES.json) and +[provider/NOTICE.md](provider/NOTICE.md). +Rohan Arun supplies the retained native compiler, following Jeremy Kothe and +the native lineage. Tekalign's retention and Cinna Davis's borrowing work keep +their credit. The complete [notice](vendor/NATIVE-LINEAGE-NOTICE) accompanies +the byte-identical kernel. + +zxv's [PR #5235](https://github.com/CrocSwap/integer-mult-bounds/pull/5235) +supplies the independent-symbol interface and frozen Gaussian arithmetic. +Krzysztof Wojt's [PR #5262](https://github.com/CrocSwap/integer-mult-bounds/pull/5262) +supplies the inverse-aware interface and native-relation handoff. lm1909's +[projection-recursion check](https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/research/projection-recursion-check/README.md) +already uses positive-width group separation, following Jacob Alan Sussman's +engine model. Cinna Davis, ToikY, Sagar Thakrar, roger-sato and the retained +free-word/tensor audits keep their earlier results and attribution. + +Chris R's [PR #4928](https://github.com/CrocSwap/integer-mult-bounds/pull/4928) +and [PR #4978](https://github.com/CrocSwap/integer-mult-bounds/pull/4978) +already use finite Clifford alphabets and tensor Gram separation. Their +[general separation proof](https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/research/two-full-retained-helper-ceiling/science/PROOF.md) +and [passive-query clarification](https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/research/passive-saved-query-ceiling/evidence/frozen/pr4948-saved-query-macro-gate/UNIFORM-ALPHABET-ADDENDUM.md) +retain that credit. This package adds an explicit linear cutoff and constant +stability bound for fixed scalar coefficients in the full dyadic class. + +Concurrent [PR #5369](https://github.com/CrocSwap/integer-mult-bounds/pull/5369) +proves a four-width criterion for affine-quadratic monomial maps. +Its scope excludes Hadamard gates. The +[coordination claim](https://github.com/CrocSwap/integer-mult-bounds/discussions/5236#discussioncomment-19153620) +records this package's larger class, Gram test and stability claim. Public +PR/Discussion bodies and relevant main notes were checked. Historical diffs +and unpublished work remain outside coverage. + +Classical ingredients are credited in [PROOF.md](PROOF.md). No new general +Burnside-Brauer theorem, general circuit identity algorithm or global priority +is claimed. The contribution is the explicit native trace filter, stable +cutoff, program frontend, compact witness and source-bound validation. +The code invariant follows Runge and Nebe, Rains and Sloane. The binary +quadratic-form method follows Dehaene and De Moor. [ADVANCES.md](ADVANCES.md) +links those sources and derives the native phase conventions used here. + +## Open next questions + +1. Find the sharp maximum cutoff for n>=2. The one-axis maximum eight is + now sharp. The general eight-width test still reaches 8n+4. +2. Prove a useful stability constant on the eight selected widths. The + present 75/76 bound uses the full range 1,...,8n+4. +3. Bind a complete current provider and measure support growth. Retain every + input/return and native phase. Physical admission and a full bill remain open. + +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. diff --git a/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/RESEARCH-NOTES.md b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/RESEARCH-NOTES.md new file mode 100644 index 0000000000..dc3244e15d --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/RESEARCH-NOTES.md @@ -0,0 +1,133 @@ +# Continuation research record + +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. + +## Starting point + +The first result is commit 0db0609042d3bee25028ef6515fcee40a33e958d in +[PR #5376](https://github.com/CrocSwap/integer-mult-bounds/pull/5376). +It proves the 8n+4 positive-width cutoff and a 14/15 separation bound. +Both local modes, the export, mutation checks and hosted CI passed. +The continuation refresh found main at +1ec1119972c9aefe42525172d07b332fcff81cb4. Priority revision 7 and both +consumed kernels are unchanged. The selected kappa is not part of this work. + +## Questions and acceptance tests + +1. Can a degree-eight invariant reduce the number of widths to eight? + Prove invariance under a complete native generating set. Prove the + resulting kernel inclusion, with all width and coefficient quantifiers. +2. Can the filter bound improve from 14/15 to 75/76? + Prove the coefficient signs and control their total absolute value for + every n. Numerical samples do not establish the uniform bound. +3. What is the sharp one-axis positive-width cutoff? + Combine an exact full-rank Gram certificate with an explicit lower-bound + example. Do not generalize a one-axis result to other axis counts. +4. Can exact traces and entries avoid a dense 2^n base matrix? + Derive a phase-exact quadratic-sum algorithm. Compare it with the frozen + source and independent dense cases, including inverses and zero traces. + Preserve possible exponential growth in expanded circuit support. + +## Initial observations, not yet new accepted results + +For n=1,...,12, exact filter coefficient sums give reciprocal positive mass +at least 75/76. The n=1 value is exactly 75/76. The later values increase +toward approximately 0.9887179563. These samples suggest a monotonicity +proof; they do not prove it. + +The extended binary Hamming code of length eight is self-dual and doubly +even. Its row-code tensor is a candidate invariant for every axis count. +The classical code-invariant construction is prior work of Runge and +Nebe, Rains and Sloane, not a new invariant discovered here. + +The original direct witness search examines all D^2 coordinate pairs at +each tensor factor. Even a compact trace routine alone does not remove +that search. A complete scalable extractor needs a separate argument. + +## Results of the continuation + +The proofs and algorithms are saved in [ADVANCES.md](ADVANCES.md), +[quadratic.py](quadratic.py) and [compact.py](compact.py). + +1. The length-eight code invariant gives kernel inclusion from f+8 to f. + Eight selected widths now suffice. For nine axes these are 69 through 76. +2. The coefficient sign pattern ++-- gives a monotonicity proof for the + filter norm. Its maximum is 77/75 at n=1. Positive mass is at most 76/75, + so the stable separation improves from 14/15 to 75/76. +3. The one-axis Gram sum at widths 5,6,7,8 has rank 96. A saved inverse + over F_65537 proves this rank in characteristic zero. The previous + Reynolds example proves that the maximum cutoff eight is sharp. + Central scalar characters also prove that four widths are necessary. +4. Exact quadratic path sums retain the native global phase. Conditional + sums with coordinate prefixes give a bitwise witness extractor. This + removes both the dense base matrix and the D^2 coordinate scan. + +The first modular experiment gave cumulative ranks modulo 65537 of +4,14,34,57,77,91,95,96 at widths 1 through 8. These are modular ranks; +the lower-width values alone are not characteristic-zero rank certificates. +The final proof uses the rank-96 inverse and the separate Reynolds obstruction. + +The replay includes 640 exhaustive small quadratic sums, every one-axis +native group word, entangling two- and three-axis words, complete register +programs and exact positive relations. The large cases certify an explicit +64-axis entry and the phase relation on 65 axes. Full counts and literal +certificates are saved with the package. + +## Performance correction + +The initial filter routine repeatedly reduced rational coefficients. The +continuation instead multiplies integer numerator factors and keeps one +denominator. A direct comparison with the function from commit +0db0609042d3bee25028ef6515fcee40a33e958d gave identical coefficient lists +at n=0,1,2,9,16,32. One local CPython 3.14.7 measurement at n=32 took +0.283 seconds before and 0.0149 seconds after. This is one measurement of +the filter builder, not a full-verifier or provider speed claim. +The registered validation uses CPython 3.12.13 and checks the original +receipts as well as the new results. + +The first read-only continuation replay found a receipt-comparison defect: +native gate tuples serialize as JSON arrays. Comparing the loaded arrays +with in-memory tuples fails even when the serialized bytes agree. The +receipt check now compares canonical serialized bytes. This fixes the +serialization boundary without changing mathematical values or certificates. + +## Limits and routes not established + +The eight-width embedding does not preserve the dimension-free stability +constant. The 75/76 bound still uses all widths from 1 through 8n+4. A +trace routine alone would not remove the coordinate search; the conditional +two-path sum is needed for that step. The general maximum cutoff is not +proved sharp, and the one-axis result cannot be extrapolated to n>=2. + +The code invariant and binary quadratic-form method are classical. No +literature priority claim is made for those methods. The native phase +derivation, program binding, width refinements and reproducible certificates +are the contribution here. Symbolic word support can still be exponential. +No complete current provider, physical invoice or kappa improvement follows. +The written proofs remain author-checked with substantial AI assistance. + +The final upstream refresh kept main at +1ec1119972c9aefe42525172d07b332fcff81cb4. The selected result and source +pins did not change. The canonical Discussion claim remains the coordination +point. This continuation updates the same focused PR. + +## Local verification closeout + +The registered runner passed all four commands on CPython 3.12.13: +the original replay and the continuation replay, each in normal and +optimized mode. One complete local run took 88.42 seconds. The original +receipts remain unchanged after the integer filter optimization. + +Both mutation audits passed. Each of eight defects was rejected in both +Python modes, for 16 negative runs. The new defects change a native phase, +an inverse sign, a coordinate constraint and a dirty return. The metadata +and pinned-source check also passed. Exact commands are in README.md. + +The final advisory overlap refresh at 2026-10-23 21:12 UTC covered 337 +open PRs and 4,676 Discussion records, with complete remote pagination. +The new-term matches were this contribution and an unrelated occurrence +of 75/76 in a prior pencil-selection note. The sparse local checkout covers +only 16 of 7,269 note paths. Relevant predecessor proofs were read +separately. Historical diffs and unpublished work remain outside coverage. +The concurrent monomial PR remains at its previously reviewed head and +has not been changed by this work. diff --git a/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/RESULT.json b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/RESULT.json new file mode 100644 index 0000000000..bd440a4b06 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/RESULT.json @@ -0,0 +1,98 @@ +{ + "closure_edges": 192, + "complete_endpoint_comparisons": 72, + "controls": [ + "wrong witness value", + "wrong witness width", + "wrong certificate schema", + "wrong certificate problem_sha256", + "wrong certificate axes", + "wrong certificate cutoff", + "nonunitary", + "continuous rational phase", + "wrong shape", + "floating scalar", + "non-Clifford dyadic unitary", + "invalid instruction 11", + "invalid instruction 12", + "invalid instruction 13", + "invalid instruction 14", + "invalid instruction 15", + "invalid instruction 16", + "omitted helper return detected", + "noncommuting order detected", + "phase outside tensor detected" + ], + "cutoff": "8n+4", + "dense_norm_cases": 60, + "entangling_trace_cases": 48, + "full_tensor_programs": 24, + "native_source_columns": 2124, + "one_axis_group_order": 96, + "polynomial_values": 689, + "random_literal_witnesses": 16, + "reynolds": { + "coefficient_norm_squared": "1/96", + "first_nonzero_width": 8, + "input_role": 0, + "normalized_squared_norms": [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "15/256", + "0", + "0", + "0", + "155/4096" + ], + "output_role": 1, + "support": 96, + "trace_buckets": 13, + "witness": { + "discrepancy": "5/24", + "input_tuple": [ + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1 + ], + "output_tuple": [ + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1 + ], + "width": 8 + } + }, + 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"c5907050a9a7fa36d4fcba3ad4fe440d1bec2063360c095013891785ba65c3ce" + } + ], + "attribution": "Rohan Arun and the retained native lineage supply the exact kernel; Tekalign retained its source. zxv supplies fields.py. Krzysztof Wojt supplies the inverse-interface handoff. lm1909 and Jacob Alan Sussman supply the prior positive-width group-separation use. See README.md and the retained notice. New material by Ali Romman with substantial OpenAI Codex assistance; Apache-2.0. Chris R / Clear1nsight supplies the related finite-alphabet tensor separation in PR4928 and PR4978. The current provider application retains Cao Yifan / intqwq, Chris R / Clear1nsight, Cinna Davis and all source frame/helper/adapter credit in provider/NOTICE.md. Current source bytes are copied and authenticated inside the package; their source paths are provenance pins." +} diff --git a/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/TASK.json b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/TASK.json new file mode 100644 index 0000000000..220174d087 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/TASK.json @@ -0,0 +1,133 @@ +{ + "schema_version": 1, + "task_id": "formal-interface-lemma", + "priority_revision": 7, + "base_commit": "7c472563474e60185e6ca101a17622133d047e56", + "original_card": { + "id": "formal-interface-lemma", + "question": "Can one uncovered interface implication be formalized with exact caller and certificate bindings?", + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/gate-operand-parity-lean/README.md", + "research/staged544-certified-endpoint/README.md", + "research/unconditional-batched-crt/README.md" + ], + "methods": [ + "Formalize a missing boundary lemma identified by the selected review.", + "Audit a formal theorem-to-certificate binding independently." + ], + "acceptance_gate": "State the exact formalized proposition and remaining assumptions; avoid duplicate arithmetic formalizations already present.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Inventory the gate-operand parity lemma (#3807) and certified endpoint arithmetic (#3857). Neither is a full multiplication proof. For #4100, audit the compact-switch statement and its hypotheses before formalizing it.", + "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately." + }, + "first_experiment": "Write one missing statement with quantified hypotheses, actual caller and existing coverage. A compact-switch lemma is a candidate only after its mathematical contract is reviewed. Establish a bounded proof plan before a separately budgeted proof-assistant build; do not rerun large Lean jobs as orientation.", + "bottleneck_link": "A missing interface proof can reduce the conditional gap even if it does not change kappa.", + "allowed_variations": [ + "Narrow to one formal lemma or one theorem-to-certificate binding." + ], + "scope_change_triggers": [ + "Formalizing already-covered arithmetic and claiming the full multiplication theorem." + ], + "overlap_terms": [ + "hyperplane end", + "formal interface", + "Lean binding", + "3807", + "3857", + "4100", + "gate-operand-parity-lean", + "staged544-certified-endpoint", + "unconditional-batched-crt" + ], + "existing_checks": [ + { + "scope": "PR #3807: scoped gate-operand parity formalization.", + "evidence": "research/gate-operand-parity-lean/README.md", + "remaining": "Exact theorem-to-caller binding and genuinely uncovered interface lemmas.", + "status": "author-checked", + "source_commit": "4c3530f42a6abcc48e7a6bcffd6c901911dc8269", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #3857: certified real-power moment/endpoint arithmetic.", + "evidence": "research/staged544-certified-endpoint/README.md", + "remaining": "Uniform algorithmic implications, not another endpoint digit.", + "status": "author-checked", + "source_commit": "ef4315b8caa605e47a2515004845eb2d2ed71a86", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4100: compact-switch formalization proposed as future validation.", + "evidence": "research/unconditional-batched-crt/README.md", + "remaining": "Audit the statement and assumptions before a formal proof campaign.", + "status": "author-checked", + "source_commit": "337d04939571a637aeab54a0f58f54fde811663a", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + }, + "scope_status": "changed", + "actual_scope": "Eight-width full dyadic Clifford tests, compact exact native certificates, complete selected-provider replay and a uniform obstruction to all 30328 early/late fusions of two paid climbs on one persistent role.", + "scope_change_reason": "Supply a written native-relation interface theorem and executable certificate rather than repeat a formal arithmetic endpoint.", + "bottleneck_link": "A fixed native program needs an all-width endpoint proof. The trace filter supplies a uniform finite test and a quantified failure certificate for the full dyadic Clifford class.", + "budget_minutes": 60, + "stop_rule": "Prove the stated cutoff and stability bound, check source and independent tensor fixtures, then publish one scoped package. No supplier or selected-frontier update.", + "outcome": "completed", + "evidence": "PROOF.md, ADVANCES.md, PROVIDER.md, all result and mutation receipts, source-bound complete provider inputs and registered normal/optimized replays.", + "author": "Ali Romman with substantial OpenAI Codex assistance", + "ai_assistance": "Substantial OpenAI Codex assistance in derivation, implementation, self-review, validation and publication. No independent human or proof-kernel review.", + "open_questions": [ + { + "question": "What is the sharp maximum cutoff for n>=2?", + "why_it_matters": "Eight tests still reach width 8n+4.", + "first_step": "Find a smaller representation-theoretic bound or a matching explicit residual.", + "blocked_by": "The one-axis modular certificate does not generalize." + }, + { + "question": "Can the eight selected widths retain a dimension-free stability constant?", + "why_it_matters": "The 75/76 bound uses the full range of widths.", + "first_step": "Bound the selected-width Gram spectrum.", + "blocked_by": "The invariant embedding alone loses powers of the base dimension." + }, + { + "question": "Can a changed contact provide the transformed operand at lower complete cost?", + "why_it_matters": "Every fixed pair fusion retains a nonzero contact defect.", + "first_step": "Use one saved contact certificate and replace its literal scalar contact with a priced native query.", + "blocked_by": "Whole-caller endpoint, dirty restoration and full cost remain." + }, + { + "question": "Can coordinated pair rewrites cancel their defects?", + "why_it_matters": "The obstruction covers one pair at a time.", + "first_step": "Name a small joint rewrite and run its complete native endpoint.", + "blocked_by": "No joint-rewrite or physical invoice certificate exists." + } + ], + "coordination": "https://github.com/CrocSwap/integer-mult-bounds/discussions/5236#discussioncomment-19153620", + "continuation": { + "user_requested": true, + "main_checkpoint": "1ec1119972c9aefe42525172d07b332fcff81cb4", + "previous_result": "0db0609042d3bee25028ef6515fcee40a33e958d", + "source_pins_changed": false, + "notes": "RESEARCH-NOTES.md" + }, + "provider_application": { + "user_requested": true, + "main_checkpoint": "1ec1119972c9aefe42525172d07b332fcff81cb4", + "verifier_predecessor": "5370f4465388dbbfff3ba45d5d6ae99d447b1766", + "scope": "Complete selected local provider in both directions, then early/late fusion of every pair of paid persistent climbs on one role. All positive tensor widths.", + "decision": "Narrow after the full fixed pair-fusion domain fails. Changed contacts or coordinated rewrites require a new test.", + "outcome": "No kappa improvement; complete provider certificates and a uniform scoped obstruction.", + "paid_profile_changed": false, + "unknown_costs": "No changed physical, compiler or outer cost is assumed zero. All candidate rewrites fail the algebraic endpoint.", + "notes": "provider/RESEARCH-NOTES.md", + "sources": "provider/SOURCES.json" + } +} diff --git a/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/VERIFY.json b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/VERIFY.json new file mode 100644 index 0000000000..b41360ab97 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/VERIFY.json @@ -0,0 +1,87 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py", + "research/universal-dirty-certificates/fields.py" + ], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-W", + "error", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 90, + "checks": "Exact trace filter, complete one-axis group, source columns, independent tensor norms and endpoints, literal witnesses and rejection controls." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-W", + "error", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 90, + "checks": "Exact trace filter, complete one-axis group, source columns, independent tensor norms and endpoints, literal witnesses and rejection controls." + }, + { + "argv": [ + "{python}", + "-I", + "-W", + "error", + "-B", + "{package}/verify_advances.py" + ], + "timeout_seconds": 90, + "checks": "Code invariant, stronger filter bound, one-axis rank certificate, quadratic sums, complete native programs, bitwise witnesses and large-axis phase cases." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-W", + "error", + "-B", + "{package}/verify_advances.py" + ], + "timeout_seconds": 90, + "checks": "Code invariant, stronger filter bound, one-axis rank certificate, quadratic sums, complete native programs, bitwise witnesses and large-axis phase cases." + }, + { + "argv": [ + "{python}", + "-I", + "-W", + "error", + "-B", + "{package}/verify_provider.py" + ], + "timeout_seconds": 420, + "checks": "All 7000 native recipe classes, both complete selected provider directions, all 30328 pair fusions, separate contact and coverage replays, literal full-program witnesses and controls." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-W", + "error", + "-B", + "{package}/verify_provider.py" + ], + "timeout_seconds": 420, + "checks": "All 7000 native recipe classes, both complete selected provider directions, all 30328 pair fusions, separate contact and coverage replays, literal full-program witnesses and controls." + } + ] +} diff --git a/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/audit_advances.py b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/audit_advances.py new file mode 100644 index 0000000000..0429c569ab --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/audit_advances.py @@ -0,0 +1,58 @@ +"""Reject compact-computation defects in private package copies. + +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +""" +import argparse +import json +from pathlib import Path +import shutil +import subprocess +import sys +import tempfile + +HERE = Path(__file__).resolve().parent +MUTATIONS = [ + ("conjugate native C factor", "quadratic.py", "G.pair(1, sign)/2", "G.pair(1, -sign)/2", "Native trace phase"), + ("ignore native inverse sign", "quadratic.py", "out.append((kind, gate[1], -gate[2]))", + "out.append((kind, gate[1], gate[2]))", "Native entry phase"), + ("omit output prefix constraint", "quadratic.py", + "equations += [left.outputs[j] ^ x for j, x in enumerate(output_prefix)]", + "equations += []", "Native partial inner product"), + ("omit final native return", "compact.py", "enumerate(zip(left, right))", + "enumerate(zip(left[:-1], right[:-1]))", "Compact complete endpoint"), +] + + +def audit(write=False): + results = [] + for label, filename, old, new, expected in MUTATIONS: + for optimized in (False, True): + with tempfile.TemporaryDirectory(prefix="clifford-advance-mutation-") as directory: + target = Path(directory) / "package" + shutil.copytree(HERE, target, ignore=shutil.ignore_patterns("__pycache__")) + source = target / filename + original = source.read_text(encoding="utf-8") + if original.count(old) != 1: + raise ValueError("Mutation target is not unique: "+label) + source.write_text(original.replace(old, new), encoding="utf-8") + command = [sys.executable, "-I", "-W", "error", "-B"] + if optimized: + command.append("-O") + command += [str(target / "verify_advances.py"), "--write"] + run = subprocess.run(command, text=True, capture_output=True, timeout=180) + if run.returncode == 0 or "ValueError: "+expected not in run.stderr: + raise ValueError("Mutation did not fail at its semantic check: "+label+"\n"+run.stdout+run.stderr) + results.append({"mutation": label, "optimized": optimized, "rejection": expected}) + receipt = {"status": "PASS_CLIFFORD_ADVANCE_MUTATIONS", "cases": results} + path = HERE / "ADVANCES-MUTATIONS.json" + if write: + path.write_text(json.dumps(receipt, indent=2, sort_keys=True)+"\n", encoding="utf-8") + elif json.loads(path.read_text(encoding="utf-8")) != receipt: + raise ValueError("Committed advance mutation receipt mismatch") + print(receipt["status"]) + + +if __name__ == "__main__": + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--write", action="store_true", help="Regenerate the advance mutation receipt") + audit(parser.parse_args().write) diff --git a/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/audit_mutations.py b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/audit_mutations.py new file mode 100644 index 0000000000..11fd235740 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/audit_mutations.py @@ -0,0 +1,57 @@ +"""Check that semantic defects fail in private package copies. + +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +""" +import argparse +import json +from pathlib import Path +import shutil +import subprocess +import sys +import tempfile + +HERE = Path(__file__).resolve().parent +MUTATIONS = [ + ("omit final trace root", "range(1, 2*n+1)", "range(1, 2*n)", "Polynomial endpoints"), + ("ignore inverse", "adjoint(operators[symbol]) if inverse else operators[symbol]", + "operators[symbol]", "Signed-word complete endpoint"), + ("omit final return", "enumerate(zip(left, right))", "enumerate(zip(left[:-1], right[:-1]))", + "Zero-axis scalar group"), + ("remove Gram normalization", "G(0))/d\n for right", "G(0))\n for right", + "Independent dense norm"), +] + + +def audit(write=False): + results = [] + for label, old, new, expected in MUTATIONS: + for optimized in (False, True): + with tempfile.TemporaryDirectory(prefix="clifford-gram-mutation-") as directory: + target = Path(directory) / "package" + shutil.copytree(HERE, target, ignore=shutil.ignore_patterns("__pycache__")) + source = target / "certify.py" + original = source.read_text(encoding="utf-8") + if original.count(old) != 1: + raise ValueError("Mutation target is not unique: "+label) + source.write_text(original.replace(old, new), encoding="utf-8") + command = [sys.executable, "-I", "-W", "error", "-B"] + if optimized: + command.append("-O") + command += [str(target / "verify.py"), "--write"] + run = subprocess.run(command, text=True, capture_output=True, timeout=180) + if run.returncode == 0 or "ValueError: "+expected not in run.stderr: + raise ValueError("Mutation did not fail at its semantic check: "+label+"\n"+run.stdout+run.stderr) + results.append({"mutation": label, "optimized": optimized, "rejection": expected}) + receipt = {"status": "PASS_CLIFFORD_GRAM_MUTATIONS", "cases": results} + path = HERE / "MUTATIONS.json" + if write: + path.write_text(json.dumps(receipt, indent=2, sort_keys=True)+"\n", encoding="utf-8") + elif json.loads(path.read_text(encoding="utf-8")) != receipt: + raise ValueError("Committed mutation receipt mismatch") + print(receipt["status"]) + + +if __name__ == "__main__": + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--write", action="store_true", help="Regenerate the mutation receipt") + audit(parser.parse_args().write) diff --git a/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/certify.py b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/certify.py new file mode 100644 index 0000000000..95c1cbf710 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/certify.py @@ -0,0 +1,329 @@ +"""Decide complete tensor identities for dyadic Clifford register programs. + +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +The trace interpolation proof is in PROOF.md. No tensor matrix is built. +""" +import argparse +from fractions import Fraction as Q +import hashlib +import json +from pathlib import Path +import sys + +sys.path.insert(0, str(Path(__file__).resolve().parent / "vendor")) +from fields import Gaussian as G + + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def conjugate(z): + return G.pair(z.real, -z.imag) + + +def norm2(z): + return z.real*z.real + z.imag*z.imag + + +def power(z, k): + result = G(1) + while k: + if k & 1: + result = result*z + z = z*z + k //= 2 + return result + + +def scalar(x): + require(type(x) in (str, int), "Use an integer or an exact Gaussian string") + return G(x) + + +def identity(d): + return tuple(tuple(G(int(i == j)) for j in range(d)) for i in range(d)) + + +def adjoint(a): + return tuple(tuple(conjugate(a[j][i]) for j in range(len(a))) for i in range(len(a))) + + +def multiply(a, b): + d = len(a) + out = [[G(0) for _ in range(d)] for _ in range(d)] + sparse_b = [[(j, x) for j, x in enumerate(row) if x] for row in b] + for i, row in enumerate(a): + for k, x in enumerate(row): + if x: + for j, y in sparse_b[k]: + out[i][j] = out[i][j] + x*y + return tuple(tuple(row) for row in out) + + +def key(a): + return tuple(tuple((z.real, z.imag) for z in row) for row in a) + + +def pauli(n, x, z, phase=0): + d = 1 << n + unit = power(G("i"), phase % 4) + return tuple( + tuple(unit*(-1 if (z & j).bit_count() % 2 else 1) if i == j ^ x else G(0) + for j in range(d)) for i in range(d)) + + +def pauli_signature(a): + """Return the exact X/Z/phase label, or reject a non-Pauli matrix.""" + d = len(a) + n = d.bit_length()-1 + first = [(i, row[0]) for i, row in enumerate(a) if row[0]] + require(len(first) == 1, "Conjugated generator is not a Pauli") + x, unit = first[0] + units = [G(1), G("i"), G(-1), G("-i")] + require(unit in units, "Conjugated generator has a non-Pauli phase") + z = 0 + for j in range(n): + value = a[x ^ (1 << j)][1 << j] + require(value in (unit, -unit), "Conjugated generator is not a Pauli") + if value == -unit: + z |= 1 << j + phase = units.index(unit) + require(a == pauli(n, x, z, phase), "Conjugated generator is not a Pauli") + return x, z, phase + + +def validate_operator(a, n): + d = 1 << n + require(len(a) == d and all(len(row) == d for row in a), "Operator shape") + for row in a: + for value in row: + for part in (value.real, value.imag): + den = part.denominator + require(den & (den-1) == 0, "Operator entry is not dyadic") + star = adjoint(a) + require(multiply(star, a) == identity(d), "Operator is not unitary") + return [pauli_signature(multiply(multiply(a, pauli(n, x, z)), star)) + for x, z in [(1 << j, 0) for j in range(n)] + [(0, 1 << j) for j in range(n)]] + + +def parse_problem(problem): + require(type(problem) is dict and set(problem) == {"axes", "roles", "operators", "program", "reference"}, + "Problem keys") + n, r = problem["axes"], problem["roles"] + require(type(n) is int and n >= 0 and type(r) is int and r > 0, "Axes or roles") + require(type(problem["operators"]) is dict, "Operators must be an object") + matrices = {} + for name, rows in problem["operators"].items(): + require(type(name) is str and bool(name) and type(rows) is list and + all(type(row) is list for row in rows), "Operator format") + a = tuple(tuple(scalar(x) for x in row) for row in rows) + validate_operator(a, n) + matrices[name] = a + return n, r, matrices + + +def accumulate(out, label, coefficient): + value = out.get(label, G(0)) + coefficient + if value: + out[label] = value + else: + out.pop(label, None) + + +def compile_difference(problem): + """Keep phases in matrix keys and keep scalar coefficients outside them.""" + n, roles, operators = parse_problem(problem) + eye = identity(1 << n) + bank = {key(eye): eye} + products = {} + + def execute(instructions): + require(type(instructions) is list, "Instruction list") + rows = [{(i, key(eye)): G(1)} for i in range(roles)] + for instruction in instructions: + require(type(instruction) is dict, "Instruction object") + kind = instruction.get("op") + allowed = {"add": {"op", "src", "dst", "coefficient"}, + "scale": {"op", "dst", "coefficient"}, + "swap": {"op", "src", "dst"}, + "apply": {"op", "dst", "symbol", "inverse"}, + "query": {"op", "src", "dst", "symbol", "inverse", "coefficient"}} + require(kind in allowed and set(instruction) <= allowed[kind], "Instruction keys") + dst = instruction.get("dst") + require(type(dst) is int and 0 <= dst < roles, "Destination role") + src = instruction.get("src", dst) + require(type(src) is int and 0 <= src < roles, "Source role") + if kind in ("add", "query", "swap"): + require("src" in instruction, "Missing source role") + if kind == "swap": + rows[src], rows[dst] = rows[dst], rows[src] + continue + if kind == "scale": + coefficient = scalar(instruction["coefficient"]) + rows[dst] = {k: coefficient*v for k, v in rows[dst].items() if coefficient*v} + continue + image = rows[src].copy() + if kind in ("apply", "query"): + symbol = instruction.get("symbol") + inverse = instruction.get("inverse", False) + require(type(inverse) is bool and type(symbol) is str and symbol in operators, "Operator reference") + a = adjoint(operators[symbol]) if inverse else operators[symbol] + image = {} + for (i, old), coefficient in rows[src].items(): + cache_key = symbol, inverse, old + if cache_key not in products: + product = multiply(a, bank[old]) + new = key(product) + bank[new] = product + products[cache_key] = new + accumulate(image, (i, products[cache_key]), coefficient) + if kind == "apply": + rows[dst] = image + else: + coefficient = scalar(instruction.get("coefficient", 1)) + updated = rows[dst].copy() + for label, value in image.items(): + accumulate(updated, label, coefficient*value) + rows[dst] = updated + return rows + + left, right = execute(problem["program"]), execute(problem["reference"]) + result = [] + for output, (a, b) in enumerate(zip(left, right)): + row = a.copy() + for label, coefficient in b.items(): + accumulate(row, label, -coefficient) + for input_role in range(roles): + terms = [(coefficient, bank[operator]) for (i, operator), coefficient in row.items() if i == input_role] + if terms: + result.append((output, input_role, terms)) + return n, result + + +def cutoff_polynomial(n): + require(type(n) is int and n >= 0, "Nonnegative axis count") + coefficients, denominator = [1], 1 + for j in range(1, 2*n+1): + scale, sign = 4**j, (-1)**j + new = [0]*(len(coefficients)+1) + for degree, coefficient in enumerate(coefficients): + new[degree] -= sign*coefficient + new[degree+1] += scale*coefficient + coefficients = new + denominator *= scale-sign + return [Q(0)]+[Q(a, 4*denominator) for a in coefficients for _ in range(4)] + + +def gram(matrices): + d = len(matrices[0]) + return [[sum((conjugate(a)*b for row_a, row_b in zip(left, right) + for a, b in zip(row_a, row_b)), G(0))/d + for right in matrices] for left in matrices] + + +def energy(coefficients, inner, width): + value = sum((conjugate(a)*b*power(inner[i][j], width) + for i, a in enumerate(coefficients) for j, b in enumerate(coefficients)), G(0)) + require(value.imag == 0 and value.real >= 0, "Invalid squared residual norm") + return value.real + + +def trace_buckets(coefficients, inner): + out = {} + for i, a in enumerate(coefficients): + for j, b in enumerate(coefficients): + value = inner[i][j] + accumulate(out, (value.real, value.imag), conjugate(a)*b) + return out + + +def bucket_energies(buckets, cutoff): + powers = {label: G(1) for label in buckets} + answer = [] + for _ in range(cutoff): + for label in powers: + powers[label] = powers[label]*G.pair(*label) + value = sum((coefficient*powers[label] for label, coefficient in buckets.items()), G(0)) + require(value.imag == 0 and value.real >= 0, "Invalid bucket norm") + answer.append(value.real) + return answer + + +def tensor_entry(coefficients, matrices, output, input_tuple): + answer = G(0) + for coefficient, a in zip(coefficients, matrices): + value = coefficient + for x, y in zip(output, input_tuple): + value = value*a[x][y] + answer = answer+value + return answer + + +def entry_witness(coefficients, matrices, inner, width): + """Choose an entry by exact conditional squared norms.""" + d = len(matrices[0]) + initial = energy(coefficients, inner, width) + require(initial > 0, "The requested width has zero residual") + current = list(coefficients) + output, input_tuple = [], [] + for remaining in range(width-1, -1, -1): + best = None + for x in range(d): + for y in range(d): + candidate = [c*a[x][y] for c, a in zip(current, matrices)] + value = energy(candidate, inner, remaining) + if best is None or value > best[0]: + best = value, x, y, candidate + require(best[0] > 0, "Conditional tensor norm lost the witness") + _, x, y, current = best + output.append(x) + input_tuple.append(y) + value = sum(current, G(0)) + require(norm2(value)*d**width >= initial, "Tensor entry lower bound") + return {"width": width, "output_tuple": output, "input_tuple": input_tuple, + "discrepancy": str(value)} + + +def analyze(n, terms): + """Analyze distinct validated Clifford matrices with nonzero coefficients.""" + coefficients, matrices = zip(*terms) + require(len(set(key(a) for a in matrices)) == len(matrices), "Merge equal exact operators first") + inner = gram(matrices) + polynomial = cutoff_polynomial(n) + buckets = trace_buckets(coefficients, inner) + energies = bucket_energies(buckets, len(polynomial)-1) + mass = sum(norm2(c) for c in coefficients) + require(sum(b*v for b, v in zip(polynomial[1:], energies)) == mass, "Trace interpolation failed") + require(max(energies) >= Q(14, 15)*mass, "Stable separation failed") + width = 1 + max(range(len(energies)), key=energies.__getitem__) + witness = entry_witness(coefficients, matrices, inner, width) + return {"support": len(terms), "trace_buckets": len(buckets), "coefficient_norm_squared": str(mass), + "normalized_squared_norms": [str(x) for x in energies], + "first_nonzero_width": 1+next(i for i, x in enumerate(energies) if x), + "witness": witness} + + +def certify(problem): + n, residuals = compile_difference(problem) + digest = hashlib.sha256(json.dumps(problem, sort_keys=True, separators=(",", ":")).encode()).hexdigest() + result = {"schema": "clifford-tensor-gram/v1", "problem_sha256": digest, + "axes": n, "cutoff": 8*n+4, "equivalent_at_all_positive_widths": not residuals, + "nonzero_endpoint_entries": len(residuals)} + if residuals: + output, input_role, terms = residuals[0] + result["failure"] = {"output_role": output, "input_role": input_role, **analyze(n, terms)} + return result + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("problem", type=Path) + args = parser.parse_args() + result = certify(json.loads(args.problem.read_text(encoding="utf-8"))) + print(json.dumps(result, indent=2, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/check_witness.py b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/check_witness.py new file mode 100644 index 0000000000..a3bca57b43 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/check_witness.py @@ -0,0 +1,150 @@ +"""Check a tensor entry by a separate signed-word interpreter. + +This module does not import the certificate producer or use Gram traces. +It shares only the frozen exact scalar arithmetic. Word support can grow. +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +""" +import argparse +import hashlib +import json +from pathlib import Path +import sys + +sys.path.insert(0, str(Path(__file__).resolve().parent / "vendor")) +from fields import Gaussian as G + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def star(a): + return tuple(tuple(G.pair(a[j][i].real, -a[j][i].imag) + for j in range(len(a))) for i in range(len(a))) + + +def product(a, b): + return tuple(tuple(sum((x*y for x, y in zip(row, column)), G(0)) + for column in zip(*b)) for row in a) + + +def eye(d): + return tuple(tuple(G(int(i == j)) for j in range(d)) for i in range(d)) + + +def add_term(row, word, coefficient): + row[word] = row.get(word, G(0))+coefficient + if not row[word]: + del row[word] + + +def word_endpoint(problem, instructions, input_role): + r = problem["roles"] + rows = [{(): G(1)} if j == input_role else {} for j in range(r)] + for instruction in instructions: + kind, d = instruction["op"], instruction["dst"] + need(type(d) is int and 0 <= d < r, "Destination role") + s = instruction.get("src", d) + need(type(s) is int and 0 <= s < r, "Source role") + if kind == "swap": + rows[d], rows[s] = rows[s], rows[d] + continue + if kind == "scale": + coefficient = G(instruction["coefficient"]) + rows[d] = {w: coefficient*c for w, c in rows[d].items() if coefficient*c} + continue + image = rows[s].copy() + if kind in ("query", "apply"): + symbol, inverse = instruction["symbol"], instruction.get("inverse", False) + need(symbol in problem["operators"] and type(inverse) is bool, "Operator reference") + letter = (symbol, inverse) + image = {} + for word, coefficient in rows[s].items(): + if word and word[0] == (symbol, not inverse): + new_word = word[1:] + else: + new_word = (letter,)+word + add_term(image, new_word, coefficient) + if kind == "apply": + rows[d] = image + else: + need(kind in ("add", "query"), "Instruction kind") + coefficient = G(instruction.get("coefficient", 1)) + updated = rows[d].copy() + for word, value in image.items(): + add_term(updated, word, coefficient*value) + rows[d] = updated + return rows + + +def matrices(problem): + d = 1 << problem["axes"] + bank = {} + for name, rows in problem["operators"].items(): + a = tuple(tuple(G(x) for x in row) for row in rows) + need(len(a) == d and all(len(row) == d for row in a), "Matrix shape") + inverse = star(a) + need(product(a, inverse) == eye(d), "Inverse requires a unitary matrix") + bank[name, False], bank[name, True] = a, inverse + return bank + + +def evaluate_word(word, bank, d): + out = eye(d) + for letter in word: + out = product(out, bank[letter]) + return out + + +def discrepancy(problem, output_role, input_role, output_tuple, input_tuple): + width = len(output_tuple) + d, r = 1 << problem["axes"], problem["roles"] + need(width > 0 and len(input_tuple) == width, "Positive tensor width") + need(all(type(x) is int and 0 <= x < d for x in output_tuple+input_tuple), "Tensor coordinate") + need(type(output_role) is int and 0 <= output_role < r and + type(input_role) is int and 0 <= input_role < r, "Endpoint role") + bank = matrices(problem) + left = word_endpoint(problem, problem["program"], input_role)[output_role] + right = word_endpoint(problem, problem["reference"], input_role)[output_role] + words = left.copy() + for word, coefficient in right.items(): + add_term(words, word, -coefficient) + answer = G(0) + for word, coefficient in words.items(): + a = evaluate_word(word, bank, d) + value = coefficient + for x, y in zip(output_tuple, input_tuple): + value = value*a[x][y] + answer = answer+value + return answer + + +def check(problem, certificate): + need(certificate.get("schema") == "clifford-tensor-gram/v1", "Certificate schema") + digest = hashlib.sha256(json.dumps(problem, sort_keys=True, separators=(",", ":")).encode()).hexdigest() + need(certificate.get("problem_sha256") == digest, "Problem digest") + need(type(certificate.get("axes")) is int and certificate["axes"] == problem["axes"], "Axis count") + need(type(certificate.get("cutoff")) is int and certificate["cutoff"] == 8*problem["axes"]+4, "Cutoff") + need(certificate["equivalent_at_all_positive_widths"] is False, "Expected a negative certificate") + failure = certificate["failure"] + witness = failure["witness"] + need(type(witness["width"]) is int and 1 <= witness["width"] <= certificate["cutoff"], "Witness width") + need(witness["width"] == len(witness["input_tuple"]) == len(witness["output_tuple"]), "Width mismatch") + value = discrepancy(problem, failure["output_role"], failure["input_role"], + witness["output_tuple"], witness["input_tuple"]) + need(value != 0 and value == G(witness["discrepancy"]), "The literal discrepancy does not match") + return str(value) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("problem", type=Path) + parser.add_argument("certificate", type=Path) + args = parser.parse_args() + value = check(json.loads(args.problem.read_text()), json.loads(args.certificate.read_text())) + print("PASS_LITERAL_TENSOR_WITNESS", value) + + +if __name__ == "__main__": + main() diff --git a/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/compact.py b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/compact.py new file mode 100644 index 0000000000..aa83f0f565 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/compact.py @@ -0,0 +1,182 @@ +"""Certify complete native programs with quadratic sums and bitwise witnesses. + +Program support can grow exponentially. No base or tensor matrix is built. +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +""" +import argparse +from fractions import Fraction as Q +import hashlib +import json +from pathlib import Path +import sys + +sys.path.insert(0, str(Path(__file__).resolve().parent)) +import certify as c +from check_witness import word_endpoint, add_term +from quadratic import Paths, partial_inner, inverse_circuit + + +def decision_widths(n): + if n == 0: + return list(range(1, 5)) + if n == 1: + return list(range(5, 9)) + return list(range(8*n-3, 8*n+5)) + + +def validate(problem): + c.require(type(problem) is dict and set(problem) == {"axes", "roles", "operators", "program", "reference"}, + "Native problem keys") + n, roles = problem["axes"], problem["roles"] + c.require(type(n) is int and n >= 0 and type(roles) is int and roles > 0, "Axes or roles") + c.require(type(problem["operators"]) is dict, "Native operators") + bank = {} + for name, circuit in problem["operators"].items(): + c.require(type(name) is str and bool(name) and type(circuit) is list, "Native operator format") + Paths(n, circuit) + bank[name, False] = circuit + bank[name, True] = inverse_circuit(n, circuit) + allowed = {"add": {"op", "src", "dst", "coefficient"}, + "scale": {"op", "dst", "coefficient"}, "swap": {"op", "src", "dst"}, + "apply": {"op", "dst", "symbol", "inverse"}, + "query": {"op", "src", "dst", "symbol", "inverse", "coefficient"}} + for instructions in (problem["program"], problem["reference"]): + c.require(type(instructions) is list, "Native instruction list") + for op in instructions: + c.require(type(op) is dict and op.get("op") in allowed, "Instruction object") + kind = op["op"] + c.require(set(op) <= allowed[kind], "Instruction keys") + c.require(type(op.get("dst")) is int and 0 <= op["dst"] < roles, "Destination role") + if kind in ("add", "query", "swap"): + c.require(type(op.get("src")) is int and 0 <= op["src"] < roles, "Source role") + if kind in ("query", "apply"): + c.require(type(op.get("symbol")) is str and op["symbol"] in problem["operators"] and + type(op.get("inverse", False)) is bool, "Operator reference") + if kind == "scale": + c.require("coefficient" in op, "Scale coefficient") + if "coefficient" in op: + c.scalar(op["coefficient"]) + return bank + + +def merge_terms(coefficients, paths): + """For unitary matrices, normalized inner product one means equality.""" + d = 1 << paths[0].n + inner = [[partial_inner(a, b)/d for b in paths] for a in paths] + representatives, merged = [], [] + for j, coefficient in enumerate(coefficients): + i = next((i for i, k in enumerate(representatives) if inner[k][j] == 1), None) + if i is None: + representatives.append(j) + merged.append(coefficient) + else: + merged[i] = merged[i]+coefficient + keep = [i for i, coefficient in enumerate(merged) if coefficient] + indices = [representatives[i] for i in keep] + return ([merged[i] for i in keep], [paths[j] for j in indices], + [[inner[i][j] for j in indices] for i in indices]) + + +def residuals(problem): + bank = validate(problem) + n = problem["axes"] + paths = {} + out = [] + for input_role in range(problem["roles"]): + left = word_endpoint(problem, problem["program"], input_role) + right = word_endpoint(problem, problem["reference"], input_role) + for output_role, (a, b) in enumerate(zip(left, right)): + words = a.copy() + for word, coefficient in b.items(): + add_term(words, word, -coefficient) + if not words: + continue + for word in words: + if word not in paths: + circuit = [gate for letter in reversed(word) for gate in bank[letter]] + paths[word] = Paths(n, circuit) + coefficients, operators, inner = merge_terms(list(words.values()), [paths[word] for word in words]) + if coefficients: + out.append((output_role, input_role, coefficients, operators, inner)) + return out + + +def entry_witness(coefficients, paths, inner, width): + """Choose each coordinate bit from two exact conditional norms.""" + n, d = paths[0].n, 1 << paths[0].n + initial = c.energy(coefficients, inner, width) + c.require(initial > 0, "Positive residual norm") + current = list(coefficients) + output, inputs = [], [] + partial_cache = {} + + def score(x, y, remaining): + key = tuple(x), tuple(y) + if key not in partial_cache: + partial_cache[key] = [[partial_inner(a, b, x, y) for b in paths] for a in paths] + partial = partial_cache[key] + value = sum((c.conjugate(a)*b*partial[i][j]*c.power(inner[i][j], remaining) + for i, a in enumerate(current) for j, b in enumerate(current)), c.G(0)) + c.require(value.imag == 0 and value.real >= 0, "Conditional squared norm") + return value.real + + for remaining in range(width-1, -1, -1): + x, y = [], [] + parent = d*c.energy(current, inner, remaining+1) + for coordinate in (x, y): + for _ in range(n): + children = [] + for bit in (0, 1): + coordinate.append(bit) + children.append(score(x, y, remaining)) + coordinate.pop() + c.require(sum(children) == parent, "Conditional norm split") + bit = int(children[1] > children[0]) + coordinate.append(bit) + parent = children[bit] + c.require(parent > 0, "Conditional witness vanished") + a, b = sum(bit << j for j, bit in enumerate(x)), sum(bit << j for j, bit in enumerate(y)) + output.append(a) + inputs.append(b) + current = [coefficient*path.entry(a, b) for coefficient, path in zip(current, paths)] + value = sum(current, c.G(0)) + c.require(c.norm2(value)*d**width >= initial, "Compact entry lower bound") + return {"width": width, "output_tuple": output, "input_tuple": inputs, "discrepancy": str(value)} + + +def analyze(n, coefficients, paths, inner): + polynomial = c.cutoff_polynomial(n) + mass = sum(c.norm2(a) for a in coefficients) + norms = c.bucket_energies(c.trace_buckets(coefficients, inner), 8*n+4) + c.require(sum(b*v for b, v in zip(polynomial[1:], norms)) == mass, "Compact trace interpolation") + c.require(max(norms) >= Q(75, 76)*mass, "Improved stable separation") + c.require(any(norms[f-1] for f in decision_widths(n)), "Reduced width criterion") + width = 1+max(range(len(norms)), key=norms.__getitem__) + return {"support": len(paths), "coefficient_norm_squared": str(mass), + "normalized_squared_norms": [str(x) for x in norms], + "witness": entry_witness(coefficients, paths, inner, width)} + + +def certify(problem): + entries = residuals(problem) + n = problem["axes"] + result = {"schema": "clifford-tensor-gram/native-v1", "axes": n, + "problem_sha256": hashlib.sha256(json.dumps(problem, sort_keys=True, separators=(",", ":")).encode()).hexdigest(), + "cutoff": 8*n+4, "decision_widths": decision_widths(n), + "equivalent_at_all_positive_widths": not entries, "nonzero_endpoint_entries": len(entries)} + if entries: + output, input_role, coefficients, paths, inner = entries[0] + result["failure"] = {"output_role": output, "input_role": input_role, + **analyze(n, coefficients, paths, inner)} + return result + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("problem", type=Path) + args = parser.parse_args() + print(json.dumps(certify(json.loads(args.problem.read_text())), indent=2, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/examples/native-64.certificate.json b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/examples/native-64.certificate.json new file mode 100644 index 0000000000..e2a64e17cc --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/examples/native-64.certificate.json @@ -0,0 +1,552 @@ +{ + "axes": 64, + "cutoff": 516, + "decision_widths": [ + 509, + 510, + 511, + 512, + 513, + 514, + 515, + 516 + ], + "equivalent_at_all_positive_widths": false, + "failure": { + "coefficient_norm_squared": "1", + "input_role": 0, + "normalized_squared_norms": [ + "1", + "1", + "1", + "1", + "1", + "1", + "1", + "1", + "1", + "1", + "1", + "1", + 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No source evaluator is imported. +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +""" +from collections import Counter +from fractions import Fraction as Q +from functools import lru_cache +import gzip +import hashlib +import json +from pathlib import Path + +from check_witness import need +from quadratic import inverse_circuit, rank + +HERE = Path(__file__).resolve().parent +N, D, PERSISTENT, OWNED = 9, 512, 632, 632 + + +def read_inputs(): + manifest = json.loads((HERE / "provider/SOURCES.json").read_bytes()) + objects = {} + for item in manifest["inputs"]: + raw = (HERE / "provider" / item["file"]).read_bytes() + need(hashlib.sha256(raw).hexdigest() == item["sha256"], "Provider source bytes: " + item["file"]) + payload = gzip.decompress(raw) if item["file"].endswith(".gz") else raw + objects[item["name"]] = ([json.loads(line) for line in payload.splitlines()] + if ".jsonl" in item["file"] else json.loads(payload)) + return manifest, objects + + +def transpose(rows): + return [sum(((row >> j) & 1) << k for k, row in enumerate(rows)) for j in range(N)] + + +def inverse(rows): + work = [v | (1 << (N+j)) for j, v in enumerate(rows)] + for j in range(N): + pivot = next((k for k in range(j, N) if work[k] >> j & 1), None) + need(pivot is not None, "Invertible native address map") + work[j], work[pivot] = work[pivot], work[j] + for k in range(N): + if k != j and work[k] >> j & 1: + work[k] ^= work[j] + return [v >> N for v in work] + + +def native_map(columns): + rows = transpose(columns) + inverse_columns = transpose(inverse(rows)) + quadratic = [(1 << j) ^ sum(((a & b).bit_count() % 2) << k + for k, b in enumerate(inverse_columns)) + for j, a in enumerate(inverse_columns)] + return [["P", rows], ["D", quadratic, [(quadratic[j] >> j) & 1 for j in range(N)]]] + + +def conjugate(circuit): + out = [] + for gate in circuit: + if gate[0] == "D": + out.append(["D", gate[1], [(-a) % 4 for a in gate[2]]]) + elif gate[0] in ("C", "phase"): + out.append(list(gate[:-1]) + [-gate[-1]]) + else: + out.append(gate) + return out + + +def normalizer(rec): + need(set(rec) == {"matrix_rows", "quadratic_rows", "linear_Z4", "offset", "phase"}, + "Complete monomial recipe") + need(type(rec["phase"]) is int and 0 <= rec["phase"] < 4, "Canonical native phase") + return [["D", rec["quadratic_rows"], rec["linear_Z4"]], + ["P", rec["matrix_rows"]], ["X", rec["offset"]], ["phase", rec["phase"]]] + + +def recipe(rec): + need(set(rec) == {"left", "right", "rank"}, "Complete paid recipe") + r = rec["rank"] + need(type(r) is int and 0 <= r <= N, "Recipe rank") + if not r: + need(rec["right"] is None, "Rank-zero recipe shape") + return normalizer(rec["left"]) + return normalizer(rec["right"]) + [["C", 1 << j, 1] for j in range(r)] + normalizer(rec["left"]) + + +class Provider: + def __init__(self, word): + self.word = word + self.c = word["canonical"] + c = self.c + need(c["h"] == N and c["v"] == 112 and len(c["start"]) == len(c["final"]) == PERSISTENT, + "Complete selected local boundary") + need(set(word["programs"]) == {"forward", "backward"}, "Both provider directions") + need(all(len(u) <= N and all(type(x) is int and 0 < x < D for x in u) + and rank(u) == len(u) for u in c["frames"]), "Independent native frame bases") + self.maps = {row["op"]: native_map(row["G_columns"]) for row in c["warps"]} + need(set(self.maps) == set(range(1, 73)) and len(c["warps"]) == 72, "All 72 native maps") + + @lru_cache(None) + def frame(self, index): + basis = self.c["frames"][index] + r = len(basis) + if not r: + return [] + if r == N: + return [["C", 1 << j, 1] for j in range(N)] + extended = [] + for v in basis + [1 << j for j in range(N)]: + if rank(extended + [v]) > len(extended): + extended.append(v) + change = native_map(extended) + return inverse_circuit(N, change) + [["C", 1 << j, 1] for j in range(r)] + change + + def edge(self, a, b, direction): + circuit = inverse_circuit(N, self.frame(a)) + self.frame(b) + return conjugate(circuit) if direction == "backward" else circuit + + def warp(self, signed, a, b, direction): + middle = self.maps[abs(signed)] + if signed < 0: + middle = inverse_circuit(N, middle) + circuit = inverse_circuit(N, self.frame(a)) + middle + self.frame(b) + return conjugate(circuit) if direction == "backward" else circuit + + def old_frame(self, role, entrance): + if role >= 224: + return self.frame(self.c["start" if entrance else "final"][role]) + if entrance: + return [["C", self.c["ports"][role], 1]] if role < 112 else [] + return self.frame(1) if role < 112 else [["C", self.c["ports"][role-112], -1]] + self.frame(1) + + def audit_word(self, direction): + """Check every event, frame contact, owned lifetime and paid charge.""" + c, program = self.c, self.word["programs"][direction] + current = list(c["start"]) + [None] + live, paid, counts, adapters, pairs, warps = False, Counter(), Counter(), {}, {}, set() + contacts = {r: [] for r in range(224)} + for j, event in enumerate(program): + kind = event[0] + counts[kind] += 1 + if kind in ("climb", "center"): + if kind == "climb": + _, _, target, a, b, r = event + need(0 <= target < PERSISTENT and not live, "Persistent climb at a closed owned cut") + need(len(c["frames"][b]) > len(c["frames"][a]), "Ascending persistent edge") + else: + _, target, a, b, r = event + need(target == 0 and live, "Live owned center") + target = OWNED + u, v = c["frames"][a], c["frames"][b] + need(current[target] == a and r == abs(len(u)-len(v)) > 0 + and rank(u+v) == max(len(u), len(v)), "Chronological nested paid edge") + current[target] = b + if target < 224: + contacts[target].append(j) + paid[r] += 1 + pairs[a, b] = r + elif kind == "warp": + _, register, signed, a, b = event + target = role(register) + if target < 224: + contacts[target].append(j) + need(current[target] == a and abs(signed) in self.maps, "Chronological signed warp") + rows = transpose(next(row["G_columns"] for row in c["warps"] if row["op"] == abs(signed))) + if signed < 0: + rows = inverse(rows) + mapped = [sum(((v & row).bit_count() % 2) << k for k, row in enumerate(rows)) + for v in c["frames"][a]] + need(rank(mapped+c["frames"][b]) == len(mapped) == len(c["frames"][b]), + "Actual signed warp transports its source subspace") + current[target] = b + warps.add((signed, a, b)) + elif kind == "scalar": + gate, f = event[1:] + target = role(gate[1]) + if target < 224: + contacts[target].append(j) + op = gate[0] + if op in ("clear", "copy"): + need(target == OWNED, "Only owned storage can be overwritten") + if op == "clear": + live = False + current[target] = f + continue + need(current[target] == f, "Scalar receiver frame") + if op in ("add", "copy"): + source = role(gate[2]) + if source < 224: + contacts[source].append(j) + need(source != target and current[source] == f, "Scalar source frame") + need(source != OWNED or live, "Owned source is initialized") + if op == "copy": + need(not live, "Copy starts an owned lifetime") + live = True + else: + q = Q(gate[3], gate[4]) + need(q and q.denominator & (q.denominator-1) == 0, "Nonzero dyadic shear") + if target == OWNED: + live = True + else: + need(op == "scale", "Known scalar operation") + q = Q(gate[2], gate[3]) + a = abs(q.numerator) + need(a and a & (a-1) == 0 and q.denominator & (q.denominator-1) == 0, + "Invertible dyadic scale") + elif kind == "adapter": + _, side, target, f = event + need(0 <= target < 224 and side in ("old_to_new", "new_to_old"), "Main adapter domain") + entrance = side == "old_to_new" + need(f == c["start" if entrance else "final"][target], "Exact main adapter boundary") + need(current[target] == f or self.old_frame(target, entrance) == self.frame(f), + "A moved adapter must be exactly the identity") + need((side, target) not in adapters, "No repeated main adapter") + adapters[side, target] = j + else: + need(kind == "phase", "Known provider event") + need(not live and current[:PERSISTENT] == c["final"], "Complete final frame and owned return") + need(set(adapters) == {(side, r) for side in ("old_to_new", "new_to_old") for r in range(224)}, + "All 448 main adapter events") + for (side, target), position in adapters.items(): + entrance = side == "old_to_new" + f = c["start" if entrance else "final"][target] + if self.old_frame(target, entrance) != self.frame(f): + need(all(position < j if entrance else j < position for j in contacts[target]), + "Nonidentity adapters surround every use of their role") + need(dict(paid) == {int(k): v for k, v in c["local_profile"].items()}, "Complete paid profile") + return dict(events=dict(counts), paid=dict(sorted(paid.items())), pairs=pairs, warps=warps) + + def problem(self, direction): + """Expand every physical event and keep all 633 input and return roles.""" + bank = {} + + def put(name, circuit): + if not circuit: + return None + oriented = conjugate(circuit) if direction == "backward" else circuit + need(name not in bank or bank[name] == oriented, "One circuit per symbol") + bank[name] = oriented + return name + + def frame(index): + return put("frame_" + str(index), self.frame(index)) + + def old(register, entrance): + circuit = self.old_frame(register, entrance) + index = self.c["start" if entrance else "final"][register] + if circuit == self.frame(index): + return frame(index) + return put(("entrance_" if entrance else "exit_") + str(register), circuit) + + def apply(out, target, symbol, inverse=False): + if symbol is not None: + out.append(dict(op="apply", dst=target, symbol=symbol, inverse=inverse)) + + program = [] + offsets = [] + for event in self.word["programs"][direction]: + offsets.append(len(program)) + kind = event[0] + if kind in ("climb", "center", "warp"): + if kind == "climb": + target, a, b = event[2:5] + elif kind == "center": + target, a, b = OWNED, event[2], event[3] + else: + target, signed, a, b = role(event[1]), *event[2:] + apply(program, target, frame(a), True) + if kind == "warp": + apply(program, target, put("warp_" + str(abs(signed)), self.maps[abs(signed)]), signed < 0) + apply(program, target, frame(b)) + elif kind == "adapter": + _, side, target, f = event + if side == "old_to_new": + apply(program, target, old(target, True), True) + apply(program, target, frame(f)) + else: + apply(program, target, frame(f), True) + apply(program, target, old(target, False)) + elif kind == "scalar": + gate = event[1] + target, op = role(gate[1]), gate[0] + if op in ("clear", "copy"): + program.append(dict(op="scale", dst=target, coefficient="0")) + if op in ("copy", "add"): + program.append(dict(op="add", dst=target, src=role(gate[2]), + coefficient=str(Q(1) if op == "copy" else Q(gate[3], gate[4])))) + elif op == "scale": + program.append(dict(op="scale", dst=target, coefficient=str(Q(gate[2], gate[3])))) + else: + need(kind == "phase", "Known physical program marker") + offsets.append(len(program)) + reference = [] + for register in range(PERSISTENT): + apply(reference, register, old(register, True), True) + for j in range(112): + source, target, sign = (112+j, j, -1) if direction == "backward" else (j, 112+j, 1) + reference.append(dict(op="add", dst=target, src=source, coefficient=str(sign))) + for register in range(PERSISTENT): + apply(reference, register, old(register, False)) + reference.append(dict(op="scale", dst=OWNED, coefficient="0")) + return dict(axes=N, roles=PERSISTENT+1, operators=bank, program=program, reference=reference), offsets + + +def role(register): + need(type(register) is list and len(register) == 2, "Register syntax") + tag, index = register + need(type(index) is int and ((tag == "L" and 0 <= index < PERSISTENT) or (tag == "C" and index == 0)), + "Register domain") + return index if tag == "L" else OWNED + + +def add(target, source, coefficient=Q(1)): + for key, value in tuple(source.items()): + value = target.get(key, Q(0)) + coefficient*value + if value: + target[key] = value + else: + target.pop(key, None) + + +def append_letter(word, letter, right=False): + if right: + return word[:-1] if word and word[-1] == -letter else word + (letter,) + return word[1:] if word and word[0] == -letter else (letter,) + word + + +def interval(program, first, second, register, transpose_row=False): + """Compute one full row or column of the logical interval matrix.""" + rows = [{} for _ in range(PERSISTENT+1)] + rows[register][()] = Q(1) + events = program[first+1:second] + for event in reversed(events) if transpose_row else events: + kind = event[0] + if kind == "warp": + target, signed = role(event[1]), event[2] + rows[target] = {append_letter(w, signed, transpose_row): q for w, q in rows[target].items()} + elif kind == "scalar": + gate = event[1] + target, op = role(gate[1]), gate[0] + if op == "clear": + rows[target] = {} + elif op == "copy": + source = role(gate[2]) + if transpose_row: + add(rows[source], rows[target]) + rows[target] = {} + else: + rows[target] = rows[source].copy() + elif op == "add": + source, q = role(gate[2]), Q(gate[3], gate[4]) + add(rows[source], rows[target], q) if transpose_row else add(rows[target], rows[source], q) + else: + need(op == "scale", "Known interval scalar") + q = Q(gate[2], gate[3]) + rows[target] = {w: q*v for w, v in rows[target].items()} + return rows[:PERSISTENT] + + +def fusion_pairs(program): + previous, out = {}, [] + for j, event in enumerate(program): + if event[0] != "climb": + continue + target = event[2] + for k, earlier in previous.get(target, []): + out.append((k, j, target, earlier[3], earlier[4], event[3], event[4])) + previous.setdefault(target, []).append((j, event)) + return out + + +def contact_witness(program, pair): + first, second, target, a, b, c, d = pair + for transposed in (False, True): + rows = interval(program, first, second, target, transposed) + for other, entry in enumerate(rows): + if other != target and len(entry) == 1: + word, coefficient = next(iter(entry.items())) + return dict(first=first, second=second, role=target, frames=[a, b, c, d], + ranks=[program[first][5], program[second][5]], + output=target if transposed else other, input=other if transposed else target, + coefficient=str(coefficient), word=list(word)) + raise ValueError("No single-term contact certificate for " + str(pair)) + + +def complete_endpoint(problem, instructions): + """Expand all independent inputs together. Coefficients remain rational.""" + symbols = {name: j+1 for j, name in enumerate(problem["operators"])} + rows = [{(j, ()): Q(1)} for j in range(problem["roles"])] + total = peak_total = problem["roles"] + peak_row = 1 + for instruction in instructions: + target, op = instruction["dst"], instruction["op"] + total -= len(rows[target]) + if op == "apply": + signed = symbols[instruction["symbol"]] * (-1 if instruction.get("inverse", False) else 1) + rows[target] = {(entry, append_letter(word, signed)): q for (entry, word), q in rows[target].items()} + elif op == "add": + add(rows[target], rows[instruction["src"]], Q(instruction["coefficient"])) + else: + need(op == "scale", "Known complete program instruction") + q = Q(instruction["coefficient"]) + rows[target] = {key: q*value for key, value in rows[target].items()} if q else {} + total += len(rows[target]) + peak_total, peak_row = max(peak_total, total), max(peak_row, len(rows[target])) + return rows, dict(peak_total_terms=peak_total, peak_row_terms=peak_row, final_terms=total) diff --git a/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/provider/FUSIONS.json.gz b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/provider/FUSIONS.json.gz new file mode 100644 index 0000000000..895c0d4c4a Binary files /dev/null and b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/provider/FUSIONS.json.gz differ diff --git a/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/provider/HELPERS.json.gz b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/provider/HELPERS.json.gz new file mode 100644 index 0000000000..0910f74138 Binary files /dev/null and b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/provider/HELPERS.json.gz 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diff --git a/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/provider/NOTICE.md b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/provider/NOTICE.md new file mode 100644 index 0000000000..50ee0013c3 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/provider/NOTICE.md @@ -0,0 +1,55 @@ +# Provider sources and attribution + +New material: Ali Romman, with substantial OpenAI Codex assistance in the +proof, implementation, checks and publication. Apache-2.0. The checks do not +constitute independent human review or a proof-kernel verification. + +The source checkpoint is canonical main +`1ec1119972c9aefe42525172d07b332fcff81cb4`. `SOURCES.json` records exact +source paths, Git objects and SHA-256 values for the copied data. + +- **Cao Yifan / intqwq** supplies the final + [PR #4610](https://github.com/CrocSwap/integer-mult-bounds/pull/4610) + native word and phase data. His + [construction proof](https://github.com/CrocSwap/integer-mult-bounds/blob/1ec1119972c9aefe42525172d07b332fcff81cb4/research/kappa-round3-warp-20261022/PROOF.md) + records the changed construction and its OpenAI assistance. `WORD.json.gz` + and `PHASES.json.gz` are byte-exact copies of that selected source. +- **Chris R / Clear1nsight** supplies the + [PR #5241](https://github.com/CrocSwap/integer-mult-bounds/pull/5241) + independent admission and paid catalogue. `PAID.jsonl.gz` is a byte-exact + copy. The [admission proof](https://github.com/CrocSwap/integer-mult-bounds/blob/1ec1119972c9aefe42525172d07b332fcff81cb4/research/final4610-independent-admission/PROOF.md) + already contains a quantified free-group lift. The new work does not claim + priority for that argument. The prior source uses substantial OpenAI + Codex assistance and retains Apache-2.0. +- **Cinna Davis / 1337isnot1337** supplies the joint-helper, native warp, + query-thinned controller and preceding construction chain. `HELPERS.json.gz` + retains the recipes from the + [joint-helper source](https://github.com/CrocSwap/integer-mult-bounds/blob/1ec1119972c9aefe42525172d07b332fcff81cb4/research/joint-helper-lattice/PROOF.md). + **zxv**, **Jacob Alan Sussman** and **Dugongue** retain credit for productive + helpers, mixed-target recursion and frame/physical interfaces. See the + [selected contributor map](https://github.com/CrocSwap/integer-mult-bounds/blob/1ec1119972c9aefe42525172d07b332fcff81cb4/docs/research/community-native4610-contributors.md). +- **Rohan Arun**, **Jeremy Kothe** and the full native lineage supply the + retained exact Clifford kernel. **Tekalign / tekuuu** retains it in the + source package. The byte-exact kernel, scalar layer and full lineage + notice remain in `../vendor/`. The scalar layer is from **zxv**. +- **icekylinx** supplies the earlier phase-lowering source, with Codex + assistance. **DreamingOfClouds** supplies the wrapper source, with Claude + Opus 5.5 assistance; that source credits **chafreaky** for the residual + wrapper construction. Cinna Davis adds native warp support. The + [phase source](https://github.com/CrocSwap/integer-mult-bounds/blob/1ec1119972c9aefe42525172d07b332fcff81cb4/research/t74-native-fast/vendor/native/new/code/borrow/bw_phases.py) + gives the exact main-adapter formula used here. The + [wrapper source](https://github.com/CrocSwap/integer-mult-bounds/blob/1ec1119972c9aefe42525172d07b332fcff81cb4/research/t74-native-fast/vendor/native/new/code/borrow/bw_adapters.py) + retains the source notice and predecessor credit. + +The [PR #5243 handoff](https://github.com/CrocSwap/integer-mult-bounds/discussions/1166#discussioncomment-19147021) +motivates the initial paid-pair test. The separate +[PR #5393](https://github.com/CrocSwap/integer-mult-bounds/pull/5393) concerns +zero-row deletion and single-field reachability on a frozen eight-relation +provider. It is related work, not an input to this proof or an additional gain. + +The source construction, proposed recipe compiler, new quadratic-sum checker, +complete word interpreters and literal witness checker have different roles. +The Gaussian scalar layer is shared. The proof and implementation are not +independent of all earlier source definitions. No general stabilizer-method +priority is claimed; the classical code and quadratic-form work is credited +in `../ADVANCES.md`. diff --git a/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/provider/PAID.jsonl.gz b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/provider/PAID.jsonl.gz new file mode 100644 index 0000000000..73fa3ced93 Binary files /dev/null and b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/provider/PAID.jsonl.gz differ diff --git a/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/provider/PHASES.json.gz b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/provider/PHASES.json.gz new file mode 100644 index 0000000000..ac77b78547 Binary files /dev/null and b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/provider/PHASES.json.gz differ diff --git a/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/provider/RESEARCH-NOTES.md b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/provider/RESEARCH-NOTES.md new file mode 100644 index 0000000000..83b4901e17 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/provider/RESEARCH-NOTES.md @@ -0,0 +1,97 @@ +# Provider experiment record + +The user requested an application of the new verifier to a complete current +provider, with a real kappa gain or a useful obstruction as the target. + +## Source and decision + +Canonical main was refreshed to +`1ec1119972c9aefe42525172d07b332fcff81cb4`, priority revision 7. The selected +record points to the final PR4610 word and PR5241 admission. The selected +value is 0.0030217758. The older verifier proof inputs remain pinned to their +original base. This application uses a separate current-source manifest. + +The first live overlap check covered 347 open PRs and 4,681 Discussion +records, with complete remote pagination. Local notes were sparse. The +PR5243 handoff asks for a physical H1+H1->H2 pair. PR5393 proves a different +zero-row result on a frozen eight-relation provider. The new scope is the +complete selected local provider and literal early/late fusion on one +persistent role. The first test uses adjacent rank-one climbs. No other +chat's work is changed. + +A second live check at 22:28 UTC on 2026-10-23 covered 350 open PRs and +4,684 Discussion records, with complete remote pagination. The terms were +`pair fusion`, `paid climbs`, `same persistent role`, `30328` and +`clifford-tensor-gram`. No competing claim for this exact provider audit was +found. Local coverage was 16 of 7,269 note paths; this check is not a full +historical novelty certificate. + +## Experiments and corrections + +1. The source has 21,449 events in each direction, 632 persistent roles and + one owned role. The 5,710 paid class records cover 6,596 instances. Only + checking a single native warp would not cover this boundary. +2. The first importer required each adapter marker's frame to be the current + frame. This rejected 82 source exit markers. Source inspection showed that + these adapters are identities. The importer now proves identity for a + moved marker. It still rejects a nonidentity adapter at a wrong frame. +3. The first owned-lifetime tracker marked COPY but not ADD into a cleared + owned register as live. The backward source accumulates its center by + ADD. The tracker was corrected before any complete-provider claim. +4. The native inverse circuit returns tuple gates. The first conjugation + helper combined a tuple with a list. This was a representation error, + not a mathematical failure. The helper now makes the new gate list + explicitly. Both orientations are replayed. +5. All 5,710 paid recipes then passed the new phase-exact Gram test. The + rank-one normalized traces were zero or `(1+i)/2^j` and its conjugate, + with j from 1 to 4. The proof uses the more general checked bounds + `Re(tau)<=1/2` and `|tau|^2<=1/2`. +6. The initial fusion scan required a common middle frame. It found 1,341 + pairs per direction and a single-term off-diagonal contact for every + pair. The two-sided cut formula removed that unnecessary restriction. + The second census covers all 1,363 adjacent rank-one pairs per direction, + including 22 with an intervening change of middle frame. It excludes + both endpoint placements for each pair: 5,452 replacements in total. + The same proof then applies to all 2,658 adjacent pairs at all ranks. + A final extension removes adjacency as well: all 7,582 pairs on one + persistent role per direction have a certificate. The final result + excludes 30,328 endpoint placements. Each extension changes the search + domain explicitly; it does not reuse a smaller-domain receipt as proof. +7. The complete physical programs pass the existing compact verifier. A + separate sparse expansion measures peak total support 22,331 forward + and 12,930 backward. Support growth is manageable for this source. No + general polynomial support bound follows. +8. The proof is stronger than a width-one rejection: each saved contact + defect has normalized squared norm at least q^2 at every positive + width. The full-provider norm need not have that bound, because its + prefix and suffix can be nonunitary. Invertibility transfers nonzero + defect, not a condition-number estimate. +9. The final proof audit checks the positions of all 224 nonidentity main + adapters in each direction. Each entrance precedes all uses of its role; + each exit follows all uses. This check is part of the importer. It makes + the interval's logical-frame interpretation explicit. All receipts keep + the same mathematical values. + A separate negative check moved role 112's nonidentity exit adapter from + event 15,723 to event 14,298, before its last scalar contact. The audit + rejected it with `Nonidentity adapters surround every use of their role`. +10. The first hosted replay on Linux / CPython 3.12.15 passed the four earlier + checks, all native recipe classes and both complete provider endpoints. + Its 240-second provider limit then expired during the remaining checks. + No mathematical failure was reported. The manifest now assigns 90 seconds + to each earlier check and 420 seconds to each provider check. The total + stays 1,200 seconds. Source code, proof and scientific receipts are + unchanged by this budget correction. + +No promising fusion survived the exact endpoint test. The source remains +unchanged. The hypothetical invoice delta is not an achieved saving, so a +new compiler or outer arithmetic run is not warranted by this experiment. + +## Verification record + +`RESULT.json` contains the deterministic complete result. `FUSIONS.json.gz` +contains every contact certificate. `WITNESSES.json` contains full physical +program counterexamples. The same commands run in normal and optimized +Python. The repository replay manifest includes both modes. Final export, +committed-byte and publication results are recorded in the public handoff. + +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. diff --git a/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/provider/RESULT.json b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/provider/RESULT.json new file mode 100644 index 0000000000..0e471c979c --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/provider/RESULT.json @@ -0,0 +1 @@ +{"achieved_paid_delta":{},"admission_head":"13efb5fc5f3b7c14ec2cfa181dd9eb6480972cf2","complete_local_provider":{"backward":{"certificate":{"axes":9,"cutoff":76,"decision_widths":[69,70,71,72,73,74,75,76],"equivalent_at_all_positive_widths":true,"nonzero_endpoint_entries":0,"problem_sha256":"94d24c4876b09ca464c6f3bed1b14f59219dc7ffc3360b7a8a772b14c6b8a2cc","schema":"clifford-tensor-gram/native-v1"},"events":{"adapter":448,"center":8,"climb":3290,"phase":10,"scalar":17453,"warp":240},"instructions":24819,"native_symbols":1297,"paid":{"1":2201,"2":412,"3":510,"4":127,"5":40,"8":8},"support":{"final_terms":744,"peak_row_terms":148,"peak_total_terms":12930}},"forward":{"certificate":{"axes":9,"cutoff":76,"decision_widths":[69,70,71,72,73,74,75,76],"equivalent_at_all_positive_widths":true,"nonzero_endpoint_entries":0,"problem_sha256":"d141a880691f5f0fb79266b5e8a990fa59b399d3f63f3458b7a8582446ecb433","schema":"clifford-tensor-gram/native-v1"},"events":{"adapter":448,"center":8,"climb":3290,"phase":10,"scalar":17453,"warp":240},"instructions":24827,"native_symbols":1297,"paid":{"1":2201,"2":412,"3":510,"4":127,"5":40,"8":8},"support":{"final_terms":744,"peak_row_terms":156,"peak_total_terms":22331}}},"controls":[{"name":"missing_paid_class","rejected":"All oriented paid classes, without gaps"},{"name":"paid_absolute_phase","rejected":"Exact native Gram equality with absolute phase"},{"name":"borrowed_erasure","rejected":"Only owned storage can be overwritten"},{"name":"live_owned_cut","rejected":"Persistent climb at a closed owned cut"},{"name":"missing_contact_is_not_a_certificate","rejected":"No single-term contact certificate for (-1, 0, 0, 0, 2, 2, 3)"}],"full_program_basis_witnesses":12,"fusion":{"contact_types":{"backward_column":6632,"backward_row":950,"forward_column":6640,"forward_row":942},"normalized_squared_cut_defect_lower_bound":"coefficient^2","pairs_by_direction":{"backward":7582,"forward":7582},"rank_pairs":{"[1, 1]":8132,"[1, 2]":1220,"[1, 3]":1098,"[1, 4]":542,"[1, 5]":64,"[2, 1]":1210,"[2, 2]":274,"[2, 3]":150,"[2, 4]":30,"[2, 5]":24,"[3, 1]":1156,"[3, 2]":234,"[3, 3]":476,"[3, 4]":2,"[4, 1]":330,"[4, 2]":70,"[5, 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diff --git a/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/provider/WORD.json.gz b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/provider/WORD.json.gz new file mode 100644 index 0000000000..46d929df83 Binary files /dev/null and b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/provider/WORD.json.gz differ diff --git a/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/provider/generate_adapters.py b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/provider/generate_adapters.py new file mode 100644 index 0000000000..b256bc0ca0 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/provider/generate_adapters.py @@ -0,0 +1,47 @@ +"""Propose main adapter recipes with the frozen source compiler. + +The verifier checks these data with quadratic sums. It does not run this file. +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +""" +import json +from pathlib import Path +import sys + +PACKAGE = Path(__file__).resolve().parent.parent +sys.path.insert(0, str(PACKAGE)) +sys.path.insert(0, str(PACKAGE / "vendor")) +import clifford_exact as source +import provider + + +def generate(): + _, data = provider.read_inputs() + model = provider.Provider(data["word"]) + rows = [] + for entrance in (True, False): + for role in range(224): + f = model.c["start" if entrance else "final"][role] + old = model.old_frame(role, entrance) + circuit = provider.inverse_circuit(9, old) + model.frame(f) + # Tableau generation is part of proposal generation only. + op = source.ident(9) + for gate in circuit: + kind = gate[0] + if kind == "P": + part = source.perm(9, tuple(gate[1])) + elif kind == "D": + part = source.diag(9, tuple(gate[1]), tuple(gate[2])) + else: + provider.need(kind == "C", "Adapter generator gate") + part = source.cgate(9, gate[1], gate[2]) + op = op.then(part) + recipe, _ = source.lower_child(op) + provider.need(recipe["rank"] == 0, "Proposed main adapter is monomial") + rows.append(dict(entrance=entrance, role=role, frame=f, recipe=recipe)) + return rows + + +if __name__ == "__main__": + target = Path(__file__).resolve().parent / "MAIN-ADAPTERS.json" + target.write_text(json.dumps(generate(), sort_keys=True, separators=(",", ":")) + "\n") + print("PROPOSED_448_MAIN_ADAPTERS_REQUIRES_GRAM_CHECK") diff --git a/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/quadratic.py b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/quadratic.py new file mode 100644 index 0000000000..a57ba96a01 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/quadratic.py @@ -0,0 +1,256 @@ +"""Exact sums of native Clifford paths, with no state vector. + +The proof and cost bounds are in ADVANCES.md. Binary affine forms use bit +zero for the constant and bit j+1 for variable j. All phases are retained. +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +""" +from itertools import combinations +from pathlib import Path +import sys + +sys.path.insert(0, str(Path(__file__).resolve().parent / "vendor")) +from fields import Gaussian as G + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def bits(mask): + while mask: + low = mask & -mask + yield low.bit_length()-1 + mask ^= low + + +def parity_sum(values): + out = 0 + for value in values: + out ^= value + return out + + +class Phase: + """A constant plus linear terms and even quadratic terms modulo four.""" + + def __init__(self, variables): + self.constant = 0 + self.linear = [0]*variables + self.cross = set() + + def toggle(self, i, j): + if i == j: + self.linear[i] = (self.linear[i]+2) % 4 + else: + term = tuple(sorted((i, j))) + self.cross.symmetric_difference_update((term,)) + + def add_parity(self, mask, coefficient): + constant = mask & 1 + variables = list(bits(mask >> 1)) + self.constant = (self.constant+coefficient*constant) % 4 + for i in variables: + self.linear[i] = (self.linear[i]+coefficient*(1-2*constant)) % 4 + if coefficient % 2: + self.cross.symmetric_difference_update(combinations(variables, 2)) + + def add_product(self, left, right): + """Add twice the product of two binary affine forms.""" + if left & 1: + self.add_parity(right, 2) + if right & 1: + self.add_parity(left ^ (left & 1), 2) + for i in bits(left >> 1): + for j in bits(right >> 1): + self.toggle(i, j) + + def substitute(self, mapping, variables): + out = Phase(variables) + out.constant = self.constant + for i, coefficient in enumerate(self.linear): + out.add_parity(mapping[i], coefficient) + for i, j in self.cross: + out.add_product(mapping[i], mapping[j]) + return out + + def restrict(self, equations): + pivots = {} + for equation in equations: + while equation > 1: + pivot = equation.bit_length()-1 + if pivot not in pivots: + pivots[pivot] = equation + break + equation ^= pivots[pivot] + if equation == 1: + return None + mapping, free = [], 0 + for j in range(1, len(self.linear)+1): + if j in pivots: + equation = pivots[j] ^ (1 << j) + value = (equation & 1) ^ parity_sum(mapping[k] for k in bits(equation >> 1)) + else: + free += 1 + value = 1 << free + mapping.append(value) + return self.substitute(mapping, free) + + def drop(self, j): + mapping = [0 if k == j else 1 << (k+1-(k > j)) for k in range(len(self.linear))] + return self.substitute(mapping, len(mapping)-1), mapping + + +def gauss_sum(phase, equations=()): + """Sum i**phase over all solutions of the binary equations.""" + phase = phase.restrict(equations) + if phase is None: + return G(0) + factor = G(1) + units = (G(1), G("i"), G(-1), G("-i")) + while phase.linear: + j = next((j for j, a in enumerate(phase.linear) if a % 2), None) + if j is not None: + a = phase.linear[j] + neighbors = [u if v == j else v for u, v in phase.cross if j in (u, v)] + phase, mapping = phase.drop(j) + phase.add_parity(parity_sum(mapping[k] for k in neighbors), -a) + factor = factor*(1+units[a]) + elif phase.cross: + j = min(phase.cross)[0] + constant = phase.linear[j]//2 + neighbors = [u if v == j else v for u, v in phase.cross if j in (u, v)] + phase, mapping = phase.drop(j) + equation = constant ^ parity_sum(mapping[k] for k in neighbors) + phase = phase.restrict((equation,)) + if phase is None: + return G(0) + factor = factor*2 + else: + if any(phase.linear): + return G(0) + factor = factor*(1 << len(phase.linear)) + phase.linear = [] + return factor*units[phase.constant] + + +def rank(rows): + pivots = {} + for row in rows: + while row: + j = row.bit_length()-1 + if j not in pivots: + pivots[j] = row + break + row ^= pivots[j] + return len(pivots) + + +class Paths: + """Build a quadratic path sum from the frozen native gate grammar.""" + + def __init__(self, n, circuit): + need(type(n) is int and n >= 0, "Nonnegative axis count") + self.n = n + self.phase = Phase(n) + self.inputs = [1 << (j+1) for j in range(n)] + self.outputs = self.inputs.copy() + self.factor = G(1) + limit = 1 << n + + def mask(x): + return type(x) is int and 0 <= x < limit + + for gate in circuit: + need(type(gate) in (tuple, list) and bool(gate), "Native gate") + kind = gate[0] + if kind == "P": + need(len(gate) == 2 and len(gate[1]) == n and all(mask(x) for x in gate[1]) + and rank(gate[1]) == n, "Invertible native permutation") + self.outputs = [parity_sum(self.outputs[j] for j in bits(row)) for row in gate[1]] + elif kind == "X": + need(len(gate) == 2 and mask(gate[1]), "Native translation") + self.outputs = [x ^ ((gate[1] >> j) & 1) for j, x in enumerate(self.outputs)] + elif kind == "D": + need(len(gate) == 3 and len(gate[1]) == len(gate[2]) == n, "Native diagonal shape") + rows, alpha = gate[1:] + need(all(mask(x) for x in rows) and all(type(a) is int and 0 <= a < 4 for a in alpha), + "Native diagonal entries") + need(all((rows[i] >> j) & 1 == (rows[j] >> i) & 1 for i in range(n) for j in range(n)) + and all(alpha[j] % 2 == (rows[j] >> j) & 1 for j in range(n)), "Native diagonal parity") + for j, a in enumerate(alpha): + self.phase.add_parity(self.outputs[j], a) + for i, row in enumerate(rows): + for j in bits(row >> (i+1)): + self.phase.add_product(self.outputs[i], self.outputs[j+i+1]) + elif kind == "C": + need(len(gate) == 3 and mask(gate[1]) and type(gate[2]) is int and gate[2] in (-1, 1), + "Native C gate") + q, sign = gate[1:] + self.phase.linear.append((-sign) % 4) + variable = 1 << len(self.phase.linear) + self.outputs = [x ^ (variable if q >> j & 1 else 0) for j, x in enumerate(self.outputs)] + self.factor = self.factor*G.pair(1, sign)/2 + elif kind == "phase": + need(len(gate) == 2 and type(gate[1]) is int, "Native global phase") + self.phase.constant = (self.phase.constant+gate[1]) % 4 + else: + raise ValueError("Unknown native gate") + + def entry(self, output, input_index): + need(type(output) is int and type(input_index) is int and + 0 <= output < 1 << self.n and 0 <= input_index < 1 << self.n, "Base coordinate") + equations = [x ^ ((input_index >> j) & 1) for j, x in enumerate(self.inputs)] + equations += [x ^ ((output >> j) & 1) for j, x in enumerate(self.outputs)] + return self.factor*gauss_sum(self.phase, equations) + + def trace(self): + return self.factor*gauss_sum(self.phase, [x ^ y for x, y in zip(self.inputs, self.outputs)]) + + +def partial_inner(left, right, output_prefix=(), input_prefix=()): + """Sum conjugate(left[x,y])*right[x,y] over the unspecified bits.""" + need(left.n == right.n, "Common axis count") + n = left.n + need(len(output_prefix) <= n and len(input_prefix) <= n and + all(type(b) is int and b in (0, 1) for b in (*output_prefix, *input_prefix)), "Coordinate prefix") + a, b = len(left.phase.linear), len(right.phase.linear) + phase = Phase(a+b) + phase.constant = (-left.phase.constant+right.phase.constant) % 4 + phase.linear = [(-x) % 4 for x in left.phase.linear]+right.phase.linear + phase.cross = left.phase.cross | {(i+a, j+a) for i, j in right.phase.cross} + + def shift(mask): + return (mask & 1) | ((mask >> 1) << (a+1)) + + equations = [x ^ shift(y) for x, y in zip(left.inputs, right.inputs)] + equations += [x ^ shift(y) for x, y in zip(left.outputs, right.outputs)] + equations += [left.outputs[j] ^ x for j, x in enumerate(output_prefix)] + equations += [left.inputs[j] ^ x for j, x in enumerate(input_prefix)] + factor = G.pair(left.factor.real, -left.factor.imag)*right.factor + return factor*gauss_sum(phase, equations) + + +def inverse_circuit(n, circuit): + """Invert a circuit after Paths has checked its gate data.""" + out = [] + for gate in reversed(circuit): + kind = gate[0] + if kind == "P": + rows = [x | (1 << (n+j)) for j, x in enumerate(gate[1])] + for j in range(n): + k = next(k for k in range(j, n) if rows[k] >> j & 1) + rows[j], rows[k] = rows[k], rows[j] + for k in range(n): + if k != j and rows[k] >> j & 1: + rows[k] ^= rows[j] + out.append((kind, tuple(x >> n for x in rows))) + elif kind == "D": + out.append((kind, gate[1], tuple((-a) % 4 for a in gate[2]))) + elif kind == "C": + out.append((kind, gate[1], -gate[2])) + elif kind == "phase": + out.append((kind, -gate[1])) + else: + out.append(gate) + return out diff --git a/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/vendor/NATIVE-LINEAGE-NOTICE b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/vendor/NATIVE-LINEAGE-NOTICE new file mode 100644 index 0000000000..380e979f0e --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/vendor/NATIVE-LINEAGE-NOTICE @@ -0,0 +1,14 @@ +Anticipatory dirty borrowing: PR2226 (Cinna Davis / 1337isnot1337, with substantial OpenAI Codex assistance) is credited first. Its alias rule, changed-reference K_G handoffs, initial compensation and exact free-operator replay (vendored under new/code/borrow/vendor, see new/code/borrow/NOTICE-PR2226.md) are applied here to the T74 pivot-566+554 words; the native lowering, window-exact owner fill and independent audit of the borrow words are new in this package. Bootstrap carried-cutoff repair: PR1956 (Josie Elliston); Lemma G label/adapter checks and X/Y/Z mutants: PR1964 (thakrarsagar), extended here with borrow warp/zero-buffer controls. + +New research prepared by Rohan Arun with substantial OpenAI Codex assistance. Apache-2.0. Parent words and build recipe method derive from Jeremy Kothe PR1274 and Rohan Arun PR1218, with lineage credited in README.md. All inherited mathematical qualifications are retained. +Additional pivot555 and567 composition by Rohan Arun with substantial OpenAI Codex assistance. + +T74 exact-fill owner construction by Rohan Arun with substantial OpenAI Codex assistance. + +PR1377 grid refinement credited to Jeremy Kothe. Outer witness refinement by Rohan Arun with OpenAI Codex assistance; construction unchanged. + +Pivot-566 kernel, words, edits, rebuild.py and rebind.py: PR1625 (mdumitrean). Endpoint/outer-witness stacking, fine_cache.py and oracle stage by jeremykothe2 with oh-my-pi assistance. + +The preceding paragraphs are inherited source notices, not attribution of this derivative. +This joint twelve-source construction, generator, independent replay, hosting composition and package: Tekalign (@tekuuu), with substantial OpenAI Codex assistance. No independent human review claimed. +Credits: Cinna Davis/PR2226 anticipatory dirty borrowing; Tekalign/PR2436 four lifted targets; Jeremy Kothe/PR2462,2588,2673 source pipeline, source-label swap and order/fill; zxv/PR2530 eight aliases; Mason Hale/PR2696 concentrated source-partner assignment and independent local interpreter; Philippe Van Velzen/PR2559,2679 evacuation, six pre-life hosts and refit/alias; themilkman216/PR2621 priority order; Marius-Paul Dumitrean/PR2733 independent concentrated/pre-life composition; Vlado Vojdanovski/PR2322 generator utilities. PR2720's fixed-old-path cut obstruction motivates the changed premise. The retained owner/native/bit/modern outer lineage and their notices remain in the pinned source. New work Apache-2.0. diff --git a/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/vendor/clifford_exact.py b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/vendor/clifford_exact.py new file mode 100644 index 0000000000..166841a037 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/vendor/clifford_exact.py @@ -0,0 +1,149 @@ +"""Small exact Gaussian-dyadic Clifford compiler, independent of gx internals. +Paulis use i^p X^x Z^z. State vectors use integer Gaussian numerators / 2^d. +The tableau is supplemented by a literal circuit, so global phases are kept. +""" +from dataclasses import dataclass + +def parity(x):return x.bit_count()&1 +def rank(rows): + p={} + for x in rows: + while x: + b=x.bit_length()-1 + if b not in p:p[b]=x;break + x^=p[b] + return len(p) +def transpose(rows,n):return tuple(sum(((rows[j]>>i)&1)<>j&1);a[j],a[k]=a[k],a[j] + for i in range(n): + if i!=j and a[i]>>j&1:a[i]^=a[j] + assert [r&((1<>n for r in a) +def basis_extend(cols,n): + out=[] + for x in list(cols)+[1<len(out):out.append(x) + assert len(out)==n + return tuple(out) +def nullspace(rows,n): + a=list(rows);p=[];k=0 + for j in range(n): + t=next((i for i in range(k,len(a)) if a[i]>>j&1),None) + if t is None:continue + a[t],a[k]=a[k],a[t] + for i in range(len(a)): + if i!=k and a[i]>>j&1:a[i]^=a[k] + p.append(j);k+=1 + return tuple((1<>j)&1)<>i&1:out=pmul(out,T[i]) + for i in range(n): + if z>>i&1:out=pmul(out,T[n+i]) + return out +def compose(A,B):return tuple(apply(A,p) for p in B) +def inverse(T): + n=len(T)//2;cols=[x|(z<>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4)) + return tuple(out) +def qvalue(Q,alpha,x,n): + return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4 +def mul_i(a,p): + x,y=a;p%=4 + return [(x,y),(-y,x),(-x,-y),(y,-x)][p] +@dataclass +class Op: + n:int + tab:tuple + circuit:list + def then(self,b): + assert self.n==b.n + return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit) + def adjoint(self): + circ=[] + for e in reversed(self.circuit): + if e[0]=='P':circ.append(('P',inv(e[1],self.n))) + elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2]))) + elif e[0]=='C':circ.append(('C',e[1],-e[2])) + elif e[0]=='phase':circ.append(('phase',(-e[1])%4)) + else:circ.append(e) + return Op(self.n,inverse(self.tab),circ) + def zero_state(self,basis=0): + N=1<>i)&1 for i in range(n)) + assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n)) + return Op(n,tuple([(1<>i&1 else 0,1<>i&1 else 0) for i in range(n)]),[('C',q,sgn)]) +def xgate(n,b):return Op(n,tuple([(1<>i)&1)) for i in range(n)]),[('X',b)]) +def fourier(n,axes=None): + out=ident(n) + for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<len(selected):picks.append(j);selected.append(x) + assert len(picks)==r and all(x>>r==0 for x in Bcols) + Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1<= 0 else "")+str(self.imag)+"i" + + __repr__ = __str__ + + +def scalars(problem): + p = problem.get("field", "Q") + if p == "Q": + return Fraction + if p == "Qi": + return Gaussian + if type(p) is not int: + raise ValueError("field must be Q, Qi or a prime at most 2^31-1") + return prime_scalars(p) + + +@lru_cache(maxsize=32) +def prime_scalars(p): + if not 2 <= p <= 2**31-1 or any(p % d == 0 for d in range(2, isqrt(p)+1)): + raise ValueError("field must be Q, Qi or a prime at most 2^31-1") + + class Prime: + def __init__(self, x=0): + if isinstance(x, Prime): + self.value = x.value + else: + q = Fraction(x) + self.value = q.numerator*pow(q.denominator, -1, p) % p + + def __add__(self, other): + return Prime(self.value+Prime(other).value) + + __radd__ = __add__ + + def __mul__(self, other): + return Prime(self.value*Prime(other).value) + + __rmul__ = __mul__ + + def __neg__(self): + return Prime(-self.value) + + def __sub__(self, other): + return self+-Prime(other) + + def __rsub__(self, other): + return Prime(other)+-self + + def __truediv__(self, other): + return Prime(self.value*pow(Prime(other).value, -1, p)) + + def __rtruediv__(self, other): + return Prime(other)/self + + def __eq__(self, other): + return self.value == Prime(other).value + + def __bool__(self): + return bool(self.value) + + def __str__(self): + return str(self.value) + + __repr__ = __str__ + + return Prime diff --git a/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/verify.py b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/verify.py new file mode 100644 index 0000000000..ff3365a66c --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/verify.py @@ -0,0 +1,351 @@ +"""Check the trace proof, native source and literal tensor failures. + +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +""" +import argparse +from collections import Counter, deque +from fractions import Fraction as Q +import hashlib +import json +from pathlib import Path +import random +import sys + +HERE = Path(__file__).resolve().parent + + +def need(condition, message): + if not condition: + raise ValueError(message) + + +def source_integrity(): + sources = json.loads((HERE / "SOURCES.json").read_text()) + pairs = {"fields.py": "research/universal-dirty-certificates/fields.py", + "clifford_exact.py": "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py"} + for local, original in pairs.items(): + record = next(item for item in sources["files"] if item["path"] == original) + need(hashlib.sha256((HERE / "vendor" / local).read_bytes()).hexdigest() == record["sha256"], "Frozen source: "+local) + + +source_integrity() +sys.path.insert(0, str(HERE)) +sys.path.insert(0, str(HERE / "vendor")) +import certify as c +import check_witness as independent +import clifford_exact as native +G = c.G + + +def source_matrix(op): + columns = [] + for j in range(1 << op.n): + values, exponent = op.zero_state(j) + columns.append([G.pair(Q(a, 1 << exponent), Q(b, 1 << exponent)) for a, b in values]) + return tuple(tuple(column[i] for column in columns) for i in range(1 << op.n)) + + +def example(operators, program, reference=(), axes=1, roles=3): + return {"axes": axes, "roles": roles, "operators": {name: [[str(x) for x in row] for row in a] for name, a in operators.items()}, + "program": list(program), "reference": list(reference)} + + +def group_one_axis(): + generators = [native.cgate(1, 1), native.diag(1, (1,))] + bank = {c.key(c.identity(2)): (c.identity(2), native.ident(1))} + queue = deque(bank.values()) + edges = 0 + while queue: + a, op = queue.popleft() + for generator in generators: + product = c.multiply(source_matrix(generator), a) + label = c.key(product) + edges += 1 + if label not in bank: + following = product, op.then(generator) + bank[label] = following + queue.append(following) + need(len(bank) == 96 and edges == 192, "Complete group closure") + for a, op in bank.values(): + need(a == source_matrix(op), "Literal native word phase") + c.validate_operator(a, 1) + return [a for a, _ in bank.values()] + + +def kron(a, b): + return tuple(tuple(x*y for x in row_a for y in row_b) for row_a in a for row_b in b) + + +def dense_tensor_norm(terms, width): + d = len(terms[0][1])**width + out = [[G(0) for _ in range(d)] for _ in range(d)] + for coefficient, a in terms: + tensor = ((G(1),),) + for _ in range(width): + tensor = kron(tensor, a) + for i in range(d): + for j in range(d): + out[i][j] = out[i][j]+coefficient*tensor[i][j] + return sum(c.norm2(z) for row in out for z in row)/d + + +def dense_program(problem, instructions, width): + d, r = (1 << problem["axes"])**width, problem["roles"] + count = d*r + rows = [[[G(int(i == role*d+j)) for i in range(count)] for j in range(d)] for role in range(r)] + lifted = {} + for name, encoded in problem["operators"].items(): + a = tuple(tuple(G(x) for x in row) for row in encoded) + tensor = ((G(1),),) + for _ in range(width): + tensor = kron(tensor, a) + lifted[name, False], lifted[name, True] = tensor, independent.star(tensor) + for op in instructions: + kind, dst = op["op"], op["dst"] + src = op.get("src", dst) + if kind == "swap": + rows[dst], rows[src] = rows[src], rows[dst] + elif kind == "scale": + rows[dst] = [[G(op["coefficient"])*x for x in row] for row in rows[dst]] + else: + image = rows[src] + if kind in ("apply", "query"): + a = lifted[op["symbol"], op.get("inverse", False)] + image = [[sum((a[j][k]*rows[src][k][i] for k in range(d)), G(0)) for i in range(count)] for j in range(d)] + if kind == "apply": + rows[dst] = image + else: + rows[dst] = [[x+G(op.get("coefficient", 1))*y for x, y in zip(a, b)] for a, b in zip(rows[dst], image)] + return rows + + +def independent_residual(problem): + bank = independent.matrices(problem) + d, r = 1 << problem["axes"], problem["roles"] + result = {} + for input_role in range(r): + left = independent.word_endpoint(problem, problem["program"], input_role) + right = independent.word_endpoint(problem, problem["reference"], input_role) + for output in range(r): + row = {} + for sign, words in [(1, left[output]), (-1, right[output])]: + for word, coefficient in words.items(): + a = independent.evaluate_word(word, bank, d) + c.accumulate(row, (output, input_role, c.key(a)), coefficient*sign) + result.update(row) + return result + + +def verify(write=False): + rng = random.Random(20261023) + group = group_one_axis() + C, S = source_matrix(native.cgate(1, 1)), source_matrix(native.diag(1, (1,))) + H, I = source_matrix(native.hadamard(1, [0])), c.identity(2) + phase_i = tuple(tuple(G("i")*z for z in row) for row in I) + need(c.multiply(H, H) == phase_i, "Source Hadamard phase") + operators = {"C": C, "S": S, "H": H, "iI": phase_i} + zero_axis = example({str(k): ((c.power(G("i"), k),),) for k in range(4)}, + [{"op": "query", "src": 0, "dst": 1, "symbol": str(k), "coefficient": "1/4"} + for k in range(4)], axes=0, roles=2) + zero_certificate = c.certify(zero_axis) + need(not zero_certificate["equivalent_at_all_positive_widths"], "Zero-axis scalar group") + need(zero_certificate["failure"]["normalized_squared_norms"] == ["0", "0", "0", "1"], "Zero-axis scalar group") + independent.check(zero_axis, zero_certificate) + need(c.certify(example({}, [], axes=0, roles=1))["equivalent_at_all_positive_widths"], "Empty zero-axis program") + polynomial_values = 0 + for n in range(13): + polynomial = c.cutoff_polynomial(n) + need(len(polynomial) == 8*n+5 and polynomial[0] == 0 and sum(polynomial) == 1, "Polynomial endpoints") + need(sum(abs(b) for b in polynomial) < Q(8, 7), "Coefficient norm") + need(sum(b for b in polynomial if b > 0) < Q(15, 14), "Positive coefficient mass") + alphabet = [G(0)] + [c.power(G("i"), k)*c.power(G("1+1i"), d)/(1 << n) for d in range(2*n+1) for k in range(4)] + for z in alphabet: + value = G(0) + for b in reversed(polynomial): + value = value*z+b + need(value == int(z == 1), "Trace-filter value") + polynomial_values += 1 + source_columns = 192 + native_fixtures = [] + for n in range(1, 5): + for q in range(1, 1 << n): + for sign in (-1, 1): + a = source_matrix(native.cgate(n, q, sign)) + first, second = G.pair(Q(1, 2), Q(sign, 2)), G.pair(Q(1, 2), Q(-sign, 2)) + expected = tuple(tuple(first if i == j else second if i == (j ^ q) else G(0) for j in range(1 << n)) for i in range(1 << n)) + need(a == expected, "Source C column formula") + c.validate_operator(a, n) + source_columns += 1 << n + if n <= 3: + native_fixtures.append((n, a)) + for sign in (-1, 1): + op = native.cgate(9, 173, sign) + for j in range(512): + values, den = op.zero_state(j) + expected = [(0, 0)]*512 + expected[j], expected[j ^ 173] = (1, sign), (1, -sign) + need(den == 1 and values == expected, "Nine-axis source column") + source_columns += 1 + entangling_trace_cases = 0 + for n in (2, 3): + for _ in range(24): + op = native.ident(n) + for _ in range(4): + source_axis, target_axis = rng.sample(range(n), 2) + rows = [1 << j for j in range(n)] + rows[target_axis] ^= 1 << source_axis + phase_rows = tuple(1 << j if j == target_axis else 0 for j in range(n)) + op = op.then(native.cgate(n, rng.randrange(1, 1 << n), rng.choice([-1, 1]))) + op = op.then(native.diag(n, phase_rows)).then(native.perm(n, rows)) + a = source_matrix(op) + need(tuple(c.validate_operator(a, n)) == op.tab, "Entangling source tableau") + trace = sum((a[j][j] for j in range(1 << n)), G(0)) + fixed_sum = 0 + for x in range(1 << n): + for z in range(1 << n): + phase = (x & z).bit_count() % 4 + u, v, p = native.apply(op.tab, (x, z, phase)) + if (u, v) == (x, z): + need((p-phase) % 4 in (0, 2), "Hermitian Pauli sign") + fixed_sum += 1 if p == phase else -1 + need(c.norm2(trace) == fixed_sum, "Pauli conjugation trace identity") + alphabet = [G(0)] + [c.power(G("i"), k)*c.power(G("1+1i"), d) for d in range(2*n+1) for k in range(4)] + need(trace in alphabet, "Entangling trace alphabet") + native_fixtures.append((n, a)) + source_columns += 1 << n + entangling_trace_cases += 1 + dense_norm_cases = 0 + for n in (1, 2): + pool = group if n == 1 else list({c.key(a): a for k, a in native_fixtures if k == n}.values()) + for _ in range(12): + selected = rng.sample(pool, 4) + terms = [(G(rng.choice([-2, -1, "i", "1/2", "1/2-1/2i"])), a) for a in selected] + inner = c.gram(selected) + for width in range(1, 4 if n == 1 else 3): + need(c.energy([x for x, _ in terms], inner, width) == dense_tensor_norm(terms, width), "Independent dense norm") + dense_norm_cases += 1 + result = c.analyze(n, terms) + w = result["witness"] + need(c.tensor_entry([x for x, _ in terms], selected, w["output_tuple"], w["input_tuple"]) == G(w["discrepancy"]) != 0, "Tensor entry") + differential_cases = literal_witnesses = full_column_cases = 0 + for trial in range(72): + instructions = [] + for _ in range(8): + kind = rng.choice(["add", "query", "apply", "scale", "swap"]) + op = {"op": kind, "dst": rng.randrange(3)} + if kind in ("add", "query", "swap"): + op["src"] = rng.randrange(3) + if kind in ("query", "apply"): + op.update(symbol=rng.choice(list(operators)), inverse=bool(rng.randrange(2))) + if kind in ("add", "query", "scale"): + op["coefficient"] = rng.choice([-1, 0, 1, "1/2", "i"]) + instructions.append(op) + problem = example(operators, instructions, instructions if trial % 3 == 0 else []) + _, differences = c.compile_difference(problem) + observed = {(o, i, c.key(a)): x for o, i, terms in differences for x, a in terms} + need(observed == independent_residual(problem), "Signed-word complete endpoint") + differential_cases += 1 + if trial < 12: + for width in (1, 2): + left = dense_program(problem, problem["program"], width) + right = dense_program(problem, problem["reference"], width) + lookup = {(o, i): terms for o, i, terms in differences} + d = 2**width + for o in range(3): + for i in range(3): + terms = lookup.get((o, i), []) + for x in range(d): + for y in range(d): + xt = [(x >> k) & 1 for k in reversed(range(width))] + yt = [(y >> k) & 1 for k in reversed(range(width))] + value = c.tensor_entry([a for a, _ in terms], [b for _, b in terms], xt, yt) + need(value == left[o][x][i*d+y]-right[o][x][i*d+y], "Full tensor program column") + full_column_cases += 1 + if trial < 24: + certificate = c.certify(problem) + if not certificate["equivalent_at_all_positive_widths"]: + independent.check(problem, certificate) + literal_witnesses += 1 + positive = example(operators, [{"op": "apply", "dst": 1, "symbol": "H"}]*2, + [{"op": "apply", "dst": 1, "symbol": "iI"}]) + need(c.certify(positive)["equivalent_at_all_positive_widths"], "Native relation") + phase_trap = example(operators, positive["program"], [{"op": "scale", "dst": 1, "coefficient": "i"}]) + phase_certificate = c.certify(phase_trap) + need(phase_certificate["failure"]["first_nonzero_width"] == 2, "Phase outside tensor") + independent.check(phase_trap, phase_certificate) + reynolds = example({str(i): a for i, a in enumerate(group)}, + [{"op": "query", "src": 0, "dst": 1, "symbol": str(i), "coefficient": "1/96"} for i in range(96)], roles=2) + reynolds_certificate = c.certify(reynolds) + norms = reynolds_certificate["failure"]["normalized_squared_norms"] + need(norms == ["0"]*7+["15/256", "0", "0", "0", "155/4096"], "Reynolds norm sequence") + independent.check(reynolds, reynolds_certificate) + need(independent.discrepancy(reynolds, 1, 0, [0]*8, [0]*8) == G("5/24"), "Reynolds entry") + for f, expected in enumerate(norms, 1): + rank = sum((c.power(sum((a[i][i] for i in range(2)), G(0)), f) for a in group), G(0))/96 + need(rank.imag == 0 and rank.real.denominator == 1 and rank/(2**f) == G(expected), "Projector rank") + controls = [] + def reject(label, function): + try: + function() + except (ValueError, KeyError, TypeError, ZeroDivisionError): + controls.append(label) + return + raise ValueError("Accepted control: "+label) + bad = json.loads(json.dumps(reynolds_certificate)) + bad["failure"]["witness"]["discrepancy"] = "0" + reject("wrong witness value", lambda: independent.check(reynolds, bad)) + bad_width = json.loads(json.dumps(reynolds_certificate)) + bad_width["failure"]["witness"]["width"] = 7 + reject("wrong witness width", lambda: independent.check(reynolds, bad_width)) + for field, value in [("schema", "other"), ("problem_sha256", "0"*64), ("axes", 2), ("cutoff", 13)]: + altered = json.loads(json.dumps(reynolds_certificate)) + altered[field] = value + reject("wrong certificate "+field, lambda altered=altered: independent.check(reynolds, altered)) + for label, matrix in [("nonunitary", [[2, 0], [0, 2]]), ("continuous rational phase", [["3/5+4/5i", 0], [0, "3/5+4/5i"]]), + ("wrong shape", [[1]]), ("floating scalar", [[1.0, 0], [0, 1]])]: + invalid = example({"C": C}, []) + invalid["operators"]["C"] = matrix + reject(label, lambda invalid=invalid: c.certify(invalid)) + toffoli = [[int(i == (j ^ (4 if j & 3 == 3 else 0))) for j in range(8)] for i in range(8)] + invalid = {"axes": 3, "roles": 1, "operators": {"T": toffoli}, "program": [], "reference": []} + reject("non-Clifford dyadic unitary", lambda: c.certify(invalid)) + for op in [{"op": "apply", "dst": 3, "symbol": "C"}, {"op": "apply", "dst": 0, "symbol": "missing"}, + {"op": "apply", "dst": 0, "symbol": "C", "inverse": 1}, {"op": "add", "src": 0, "dst": 1, "coefficient": 0.5}, + {"op": "query", "dst": 0, "symbol": "C"}, {"op": "apply", "dst": 0, "symbol": "C", "phase": 0}]: + reject("invalid instruction "+str(len(controls)), lambda op=op: c.certify(example(operators, [op]))) + helper = example(operators, [{"op": "query", "src": 0, "dst": 2, "symbol": "C"}]) + helper_certificate = c.certify(helper) + need(helper_certificate["failure"]["output_role"] == 2, "Dirty helper return") + independent.check(helper, helper_certificate) + controls.append("omitted helper return detected") + order = example(operators, [{"op": "apply", "dst": 0, "symbol": "C"}, {"op": "apply", "dst": 0, "symbol": "S"}], + [{"op": "apply", "dst": 0, "symbol": "S"}, {"op": "apply", "dst": 0, "symbol": "C"}]) + independent.check(order, c.certify(order)) + controls += ["noncommuting order detected", "phase outside tensor detected"] + receipt = {"status": "PASS_CLIFFORD_TENSOR_GRAM_NO_NEW_KAPPA", "cutoff": "8n+4", "separation": "14/15", + "one_axis_group_order": 96, "closure_edges": 192, + "trace_histogram": dict(sorted(Counter(str(sum((a[i][i] for i in range(2)), G(0))) for a in group).items())), + "polynomial_values": polynomial_values, "native_source_columns": source_columns, + "entangling_trace_cases": entangling_trace_cases, + "dense_norm_cases": dense_norm_cases, "complete_endpoint_comparisons": differential_cases, + "full_tensor_programs": full_column_cases, "random_literal_witnesses": literal_witnesses, + "zero_axis_cases": 2, + "reynolds": reynolds_certificate["failure"], "controls": controls} + files = {"RESULT.json": receipt, "examples/native-relation.json": positive, "examples/phase-trap.json": phase_trap, + "examples/phase-trap.certificate.json": phase_certificate, "examples/reynolds.json": reynolds, + "examples/reynolds.certificate.json": reynolds_certificate} + for name, data in files.items(): + path = HERE / name + if write: + path.parent.mkdir(parents=True, exist_ok=True) + path.write_text(json.dumps(data, indent=2, sort_keys=True)+"\n", encoding="utf-8") + else: + need(json.loads(path.read_text()) == data, "Committed result mismatch: "+name) + print(receipt["status"]) + return receipt + + +if __name__ == "__main__": + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--write", action="store_true", help="Regenerate the receipt and examples") + verify(parser.parse_args().write) diff --git a/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/verify_advances.py b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/verify_advances.py new file mode 100644 index 0000000000..22437672d9 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/verify_advances.py @@ -0,0 +1,288 @@ +"""Replay the width refinements and compact native computation. + +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +""" +import argparse +from collections import deque +from fractions import Fraction as Q +import hashlib +import json +from pathlib import Path +import random +import sys + +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE)) +import verify as v +import compact as compact +import quadratic as q + + +def saved(name, data, write): + path = HERE / name + encoded = json.dumps(data, indent=2, sort_keys=True)+"\n" + if write: + path.write_text(encoded, encoding="utf-8") + else: + v.need(path.read_text(encoding="utf-8") == encoded, "Committed advance receipt: "+name) + + +def modular_inverse(matrix, p): + n = len(matrix) + rows = [row[:] + [int(i == j) for j in range(n)] for i, row in enumerate(matrix)] + for j in range(n): + k = next(k for k in range(j, n) if rows[k][j]) + rows[k], rows[j] = rows[j], rows[k] + scale = pow(rows[j][j], -1, p) + rows[j] = [x*scale % p for x in rows[j]] + for k in range(n): + if k != j: + scale = rows[k][j] + rows[k] = [(x-scale*y) % p for x, y in zip(rows[k], rows[j])] + return [row[n:] for row in rows] + + +def one_axis_certificate(group, write): + p, root = 65537, 256 + v.need(all(p % d for d in range(2, 257)) and root*root % p == p-1, "Prime field") + inner = v.c.gram(group) + + def reduce(z): + def part(x): + return x.numerator*pow(x.denominator, -1, p) + return (part(z.real)+root*part(z.imag)) % p + + matrix = [[sum(pow(reduce(z), f, p) for f in range(5, 9)) % p for z in row] for row in inner] + digest = hashlib.sha256(json.dumps([[[str(z) for z in row] for row in a] for a in group]).encode()).hexdigest() + path = HERE / "ONE-AXIS-RANK.json" + if write: + inverse = modular_inverse(matrix, p) + else: + inverse = json.loads(path.read_text())["inverse"] + v.need(type(inverse) is list and len(inverse) == 96 and all(type(row) is list and len(row) == 96 and + all(type(x) is int and 0 <= x < p for x in row) for row in inverse), "Modular inverse shape") + for i, row in enumerate(matrix): + for j, column in enumerate(zip(*inverse)): + v.need(sum(x*y for x, y in zip(row, column)) % p == int(i == j), "One-axis inverse product") + certificate = {"prime": p, "image_of_i": root, "widths": [5, 6, 7, 8], + "group_sha256": digest, "rank": 96, "inverse": inverse} + saved("ONE-AXIS-RANK.json", certificate, write) + return {key: value for key, value in certificate.items() if key != "inverse"} + + +def check_forms(rng): + count = 0 + units = (q.G(1), q.G("i"), q.G(-1), q.G("-i")) + for m in range(8): + for _ in range(80): + phase = q.Phase(m) + phase.constant = rng.randrange(4) + phase.linear = [rng.randrange(4) for _ in range(m)] + phase.cross = {(i, j) for i in range(m) for j in range(i+1, m) if rng.randrange(2)} + equations = [rng.randrange(1 << (m+1)) for _ in range(rng.randrange(m+1))] + expected = q.G(0) + for x in range(1 << m): + if any((e & 1) ^ (((e >> 1) & x).bit_count() % 2) for e in equations): + continue + exponent = phase.constant+sum(a*((x >> i) & 1) for i, a in enumerate(phase.linear)) + exponent += 2*sum(((x >> i) & 1)*((x >> j) & 1) for i, j in phase.cross) + expected = expected+units[exponent % 4] + v.need(q.gauss_sum(phase, equations) == expected, "Exhaustive constrained quadratic sum") + count += 1 + return count + + +def native_words(): + bank = {v.c.key(v.c.identity(2)): v.native.ident(1)} + queue = deque(bank.values()) + generators = (v.native.cgate(1, 1), v.native.diag(1, (1,))) + while queue: + op = queue.popleft() + for generator in generators: + new = op.then(generator) + label = v.c.key(v.source_matrix(new)) + if label not in bank: + bank[label] = new + queue.append(new) + v.need(len(bank) == 96, "Native word group closure") + return list(bank.values()) + + +def check_native(rng): + words = native_words() + for n in (2, 3): + for _ in range(16): + op = v.native.ident(n) + for _ in range(8): + raw = [rng.randrange(1 << n) for _ in range(n)] + rows = [sum(((raw[min(i, j)] >> max(i, j)) & 1) << j for j in range(n)) for i in range(n)] + alpha = [((rows[i] >> i) & 1)+2*rng.randrange(2) for i in range(n)] + source, target = rng.sample(range(n), 2) + permutation = [1 << j for j in range(n)] + permutation[target] ^= 1 << source + op = op.then(v.native.diag(n, rows, alpha)).then(v.native.perm(n, permutation)) + op = op.then(v.native.cgate(n, rng.randrange(1 << n), rng.choice((-1, 1)))) + op = op.then(v.native.xgate(n, rng.randrange(1 << n))) + words.append(op) + entries, traces, partials = 0, 0, 0 + for op in words: + matrix = v.source_matrix(op) + paths = q.Paths(op.n, op.circuit) + inverse = q.Paths(op.n, q.inverse_circuit(op.n, op.circuit)) + star = v.c.adjoint(matrix) + d = 1 << op.n + v.need(paths.trace() == sum((matrix[j][j] for j in range(d)), q.G(0)), "Native trace phase") + traces += 1 + for x in range(d): + for y in range(d): + v.need(paths.entry(x, y) == matrix[x][y] and inverse.entry(x, y) == star[x][y], "Native entry phase") + entries += 2 + for k in range(op.n+1): + xp = [rng.randrange(2) for _ in range(k)] + yp = [rng.randrange(2) for _ in range(op.n-k)] + expected = sum((v.c.conjugate(matrix[x][y])*star[x][y] + for x in range(d) for y in range(d) + if all(((x >> j) & 1) == bit for j, bit in enumerate(xp)) and + all(((y >> j) & 1) == bit for j, bit in enumerate(yp))), q.G(0)) + v.need(q.partial_inner(paths, inverse, xp, yp) == expected, "Native partial inner product") + partials += 1 + return {"native_words": len(words), "native_entries": entries, "native_traces": traces, + "partial_inner_products": partials} + + +def check_programs(rng): + count, witnesses, relations = 0, 0, 0 + for n in range(3): + ops = {"I": v.native.ident(n), "iI": v.native.Op(n, v.native.identity(n), [("phase", 1)])} + if n: + ops.update(C=v.native.cgate(n, (1 << n)-1), H=v.native.hadamard(n, range(n)), + S=v.native.diag(n, tuple(1 << j for j in range(n)))) + for _ in range(16): + program = [] + for _ in range(8): + kind = rng.choice(("query", "apply", "add", "scale", "swap")) + instruction = {"op": kind, "dst": rng.randrange(3)} + if kind in ("query", "add", "swap"): + instruction["src"] = rng.randrange(3) + if kind in ("query", "apply"): + instruction.update(symbol=rng.choice(list(ops)), inverse=bool(rng.randrange(2))) + if kind in ("scale", "query", "add"): + instruction["coefficient"] = rng.choice(("1", "-1", "i", "1/2")) + program.append(instruction) + problem = {"axes": n, "roles": 3, "operators": {s: o.circuit for s, o in ops.items()}, + "program": program, "reference": []} + dense = v.example({s: v.source_matrix(o) for s, o in ops.items()}, program, axes=n) + _, expected_entries = v.c.compile_difference(dense) + expected = {(output, source): {v.c.key(a): coefficient for coefficient, a in terms} + for output, source, terms in expected_entries} + actual = {} + for output, source, coefficients, paths, _ in compact.residuals(problem): + matrices = [tuple(tuple(path.entry(x, y) for y in range(1 << n)) for x in range(1 << n)) for path in paths] + actual[output, source] = {v.c.key(a): coefficient for coefficient, a in zip(coefficients, matrices)} + v.need(actual == expected, "Compact complete endpoint") + certificate = compact.certify(problem) + v.need(certificate["equivalent_at_all_positive_widths"] == (not expected), "Compact decision") + if "failure" in certificate: + f = certificate["failure"] + w = f["witness"] + value = v.independent.discrepancy(dense, f["output_role"], f["input_role"], w["output_tuple"], w["input_tuple"]) + v.need(value != 0 and str(value) == w["discrepancy"], "Compact literal witness") + witnesses += 1 + count += 1 + for n in (1, 2, 3): + ops = {"C": v.native.cgate(n, (1 << n)-1), "H": v.native.hadamard(n, range(n)), + "phase": v.native.Op(n, v.native.identity(n), [("phase", n)])} + cases = [([{"op": "apply", "dst": 2, "symbol": "C"}]*4, []), + ([{"op": "apply", "dst": 1, "symbol": "H"}]*2, + [{"op": "apply", "dst": 1, "symbol": "phase"}]), + ([{"op": "apply", "dst": 0, "symbol": "C"}, + {"op": "apply", "dst": 0, "symbol": "C", "inverse": True}], [])] + for program, reference in cases: + problem = {"axes": n, "roles": 3, "operators": {s: o.circuit for s, o in ops.items()}, + "program": program, "reference": reference} + dense = v.example({s: v.source_matrix(o) for s, o in ops.items()}, program, reference, axes=n) + v.need(compact.certify(problem)["equivalent_at_all_positive_widths"] and + v.c.certify(dense)["equivalent_at_all_positive_widths"], "Compact exact native relation") + relations += 1 + phase_trap = {"axes": 1, "roles": 1, "operators": {"iI": [("phase", 1)]}, + "program": [{"op": "apply", "dst": 0, "symbol": "iI"}], + "reference": [{"op": "scale", "dst": 0, "coefficient": "i"}]} + norms = compact.certify(phase_trap)["failure"]["normalized_squared_norms"] + v.need(norms[0] == "0" and Q(norms[1]) > 0, "Compact phase stays inside tensor") + return {"complete_programs": count, "literal_witnesses": witnesses, "exact_native_relations": relations, + "scalar_phase_traps": 1} + + +def verify(write=False): + rng = random.Random(5376) + code = {q.parity_sum(row for j, row in enumerate((255, 240, 204, 170)) if mask >> j & 1) for mask in range(16)} + v.need(len(code) == 16 and all(x.bit_count() % 4 == 0 for x in code), "Doubly even code") + for y in range(256): + v.need(sum((-1)**((x & y).bit_count() % 2) for x in code) == 16*int(y in code), "Code Fourier invariant") + h = v.source_matrix(v.native.hadamard(1, [0])) + v.need(h == ((q.G("1/2+1/2i"), q.G("1/2+1/2i")), + (q.G("1/2+1/2i"), q.G("-1/2-1/2i"))) and v.c.power(h[0][0], 8) == q.G("1/16"), + "Eight-copy native phase") + previous = None + for n in range(65): + polynomial = v.c.cutoff_polynomial(n) + norm = sum(abs(x) for x in polynomial) + v.need(norm <= Q(77, 75) and sum(x for x in polynomial if x > 0) <= Q(76, 75), "Improved filter bound") + descending = list(reversed(polynomial[1::4])) + v.need(all((x > 0) == ((-1)**(j*(j+3)//2) == 1) for j, x in enumerate(descending)), "Filter coefficient signs") + if n >= 2: + v.need(norm < previous, "Filter norm decreases") + previous = norm + forms = check_forms(rng) + rank_certificate = one_axis_certificate(v.group_one_axis(), write) + native = check_native(rng) + programs = check_programs(rng) + large = [] + for n in (64, 65): + h = v.native.hadamard(n, range(n)) + operators = {"H": h.circuit, "iI": [("phase", 1)]} + if n == 64: + program = [{"op": "query", "src": 0, "dst": 1, "symbol": "H"}] + reference = [] + else: + program = [{"op": "apply", "dst": 0, "symbol": "H"}]*2 + reference = [{"op": "apply", "dst": 0, "symbol": "iI"}] + problem = {"axes": n, "roles": 2, "operators": operators, "program": program, "reference": reference} + certificate = compact.certify(problem) + v.need(certificate["equivalent_at_all_positive_widths"] == (n == 65), "Large native decision") + if n == 64: + v.need(certificate["failure"]["witness"] == {"width": 1, "output_tuple": [0], "input_tuple": [0], + "discrepancy": "1/4294967296"}, "Large literal Hadamard entry") + saved(f"examples/native-{n}.json", problem, write) + saved(f"examples/native-{n}.certificate.json", certificate, write) + large.append({"axes": n, "base_dimension": str(1 << n), "equivalent": n == 65}) + controls = [] + for label, function in [ + ("singular permutation", lambda: q.Paths(2, [("P", [1, 1])])), + ("diagonal parity", lambda: q.Paths(1, [("D", [1], [0])])), + ("asymmetric diagonal", lambda: q.Paths(2, [("D", [2, 0], [0, 0])])), + ("wrong C sign", lambda: q.Paths(1, [("C", 1, 0)])), + ("unknown gate", lambda: q.Paths(1, [("H", 0)])), + ("coordinate out of range", lambda: q.Paths(1, []).entry(2, 0)), + ("invalid prefix", lambda: q.partial_inner(q.Paths(1, []), q.Paths(1, []), [2])), + ("negative axes", lambda: q.Paths(-1, [])), + ]: + try: + function() + except ValueError: + controls.append(label) + else: + raise ValueError("Accepted control: "+label) + receipt = {"status": "PASS_CLIFFORD_ADVANCES_NO_NEW_KAPPA", "general_test_widths": "8n-3 through 8n+4 for n>=2", + "stable_separation": "75/76", "filter_axis_counts": 65, "code_fourier_values": 256, + "one_axis": rank_certificate, "exhaustive_quadratic_forms": forms, + **native, **programs, "large_native_programs": large, "controls": controls} + saved("ADVANCES-RESULT.json", receipt, write) + print(receipt["status"]) + return receipt + + +if __name__ == "__main__": + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--write", action="store_true", help="Regenerate the advance receipts") + verify(parser.parse_args().write) diff --git a/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/verify_provider.py b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/verify_provider.py new file mode 100644 index 0000000000..6a63161f9d --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/clifford-tensor-gram/verify_provider.py @@ -0,0 +1,310 @@ +"""Check the complete selected provider and the fixed pair-fusion domain. + +Use --write to save receipts. Normal replay does not change package files. +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +""" +from collections import Counter +from copy import deepcopy +from fractions import Fraction as Q +import gzip +import hashlib +import json +from pathlib import Path +import sys + +sys.path.insert(0, str(Path(__file__).resolve().parent)) +import compact +import certify as c +import provider as p +from check_witness import word_endpoint +from quadratic import Paths, partial_inner, inverse_circuit +from verify import source_integrity + +HERE = Path(__file__).resolve().parent + + +def canonical(value): + return (json.dumps(value, sort_keys=True, separators=(",", ":")) + "\n").encode() + + +def saved(name, value, write): + raw = canonical(value) + path = HERE / "provider" / name + if write: + path.write_bytes(gzip.compress(raw, mtime=0) if name.endswith(".gz") else raw) + else: + expected = path.read_bytes() + if name.endswith(".gz"): + expected = gzip.decompress(expected) + p.need(expected == raw, "Provider receipt differs: " + name) + return hashlib.sha256(raw).hexdigest() + + +def equal(left, right): + a, b = Paths(p.N, left), Paths(p.N, right) + value = partial_inner(a, b) / p.D + p.need(value == 1, "Exact native Gram equality with absolute phase") + return a + + +def check_catalogue(model, data, audits): + expected = {(a, b, direction): rank for direction, audit in audits.items() + for (a, b), rank in audit["pairs"].items()} + header, *records = data["paid"] + raw = gzip.decompress((HERE / "provider/WORD.json.gz").read_bytes()) + p.need(header["word_payload_sha256"] == hashlib.sha256(raw).hexdigest() + and not header["partial"], "Complete catalogue bound to the exact word") + seen, traces = set(), {} + for row in records: + a, b, direction = row["input"], row["output"], row["direction"] + key = a, b, direction + p.need(key in expected and key not in seen and row["rank"] == row["recipe"]["rank"] == expected[key], + "Unique actual paid class and rank") + actual = equal(model.edge(a, b, direction), p.recipe(row["recipe"])) + traces[key] = actual.trace() / p.D + seen.add(key) + p.need(seen == set(expected) and len(seen) == header["expected_complete_oriented_classes"], + "All oriented paid classes, without gaps") + + warp_records = {(row["operator"], row["input"], row["output"]): row + for row in data["phases"]["actual_warp_classes"]} + p.need(len(warp_records) == len(data["phases"]["actual_warp_classes"]), "No duplicate warp classes") + for direction, audit in audits.items(): + p.need(set(warp_records) == audit["warps"], "All actual native warp classes") + for (signed, a, b), row in warp_records.items(): + rec = row["recipes"][direction] + p.need(rec["rank"] == 0, "Every warp is a monomial") + equal(model.warp(signed, a, b, direction), p.recipe(rec)) + + helpers = {} + for row in data["helpers"]["new_physical_edges_and_boundaries"]: + helpers[row["old"], row["new"]] = row + for row in data["phases"]["changed_helper_boundaries"]: + helpers[row["input"], row["output"]] = row + actual_helpers = Counter(zip(model.c["start"][224:], model.c["final"][224:])) + helper_profile = Counter() + for (a, b), count in sorted(actual_helpers.items()): + u, v = model.c["frames"][a], model.c["frames"][b] + r = len(v)-len(u) + p.need(r > 0 and p.rank(u+v) == len(v), "Strict productive helper boundary") + helper_profile[r] += count + for direction in ("forward", "backward"): + rec = helpers[a, b]["recipes"][direction] + p.need(rec["rank"] == r, "Complete helper recipe rank") + equal(model.edge(a, b, direction), p.recipe(rec)) + + adapters = json.loads((HERE / "provider/MAIN-ADAPTERS.json").read_bytes()) + adapter_seen = set() + for row in adapters: + entrance, register, f = row["entrance"], row["role"], row["frame"] + p.need(type(entrance) is bool and type(register) is int and 0 <= register < 224, + "Main adapter label") + key = entrance, register + p.need(key not in adapter_seen and f == model.c["start" if entrance else "final"][register], + "Exact complete adapter boundary") + p.need(row["recipe"]["rank"] == 0, "Main adapter is a monomial") + target = inverse_circuit(p.N, model.old_frame(register, entrance)) + model.frame(f) + decoded = p.recipe(row["recipe"]) + for direction in ("forward", "backward"): + equal(target if direction == "forward" else p.conjugate(target), + decoded if direction == "forward" else p.conjugate(decoded)) + adapter_seen.add(key) + p.need(adapter_seen == {(side, r) for side in (False, True) for r in range(224)}, + "All main adapters in both orientations") + return traces, dict(paid_oriented_classes=len(seen), warp_oriented_classes=2*len(warp_records), + helper_oriented_classes=2*len(actual_helpers), helper_roles=sum(actual_helpers.values()), + helper_profile=dict(sorted(helper_profile.items())), + main_adapter_oriented_classes=2*len(adapter_seen)) + + +def fusion_census(model, traces): + evidence, trace_counts, kinds, ranks = {}, Counter(), Counter(), Counter() + for direction, program in model.word["programs"].items(): + rows = [] + for pair in p.fusion_pairs(program): + row = p.contact_witness(program, pair) + a, b, c0, d = row["frames"] + for name, key in (("late_trace", (a, b, direction)), ("early_trace", (c0, d, direction))): + tau = traces[key] + # f=1: Re(tau)<=1/2. f>=2: |tau|^f<=1/2. + p.need(tau.real <= Q(1, 2) and c.norm2(tau) <= Q(1, 2), "Uniform noncentral trace bound") + row[name] = str(tau) + trace_counts[str(tau)] += 1 + p.need(Q(row["coefficient"]) != 0, "Nonzero contact coefficient") + kinds[direction + ("_row" if row["output"] == row["role"] else "_column")] += 1 + ranks[str(row["ranks"])] += 1 + rows.append(row) + evidence[direction] = rows + minimum = min(Q(row["coefficient"])**2 for rows in evidence.values() for row in rows) + return evidence, dict(trace_counts=dict(sorted(trace_counts.items())), contact_types=dict(sorted(kinds.items())), + rank_pairs=dict(sorted(ranks.items())), uniform_squared_cut_block_lower_bound=str(minimum), + pairs_by_direction={d: len(rows) for d, rows in evidence.items()}, + rejected_fusions=2*sum(map(len, evidence.values())), + width_domain="every positive integer", + normalized_squared_cut_defect_lower_bound="coefficient^2") + + +def check_contact_certificates(model, evidence): + """Check coverage by role lists, then use the older input-column engine.""" + count = 0 + for direction, certificates in evidence.items(): + events = model.word["programs"][direction] + expected = set() + for register in range(p.PERSISTENT): + climbs = [(j, event) for j, event in enumerate(events) + if event[0] == "climb" and event[2] == register] + expected.update((a, b) for j, (a, _) in enumerate(climbs) for b, _ in climbs[j+1:]) + p.need(len(certificates) == len(expected) and {(r["first"], r["second"]) for r in certificates} == expected, + "Independent complete same-role pair census") + skeleton = [] + for event in events: + instructions = [] + if event[0] == "warp": + instructions.append(dict(op="apply", dst=p.role(event[1]), symbol=str(abs(event[2])), inverse=event[2] < 0)) + elif event[0] == "scalar": + gate = event[1] + target, op = p.role(gate[1]), gate[0] + if op in ("clear", "copy"): + instructions.append(dict(op="scale", dst=target, coefficient="0")) + if op in ("copy", "add"): + instructions.append(dict(op="add", src=p.role(gate[2]), dst=target, + coefficient=str(Q(1) if op == "copy" else Q(gate[3], gate[4])))) + elif op == "scale": + instructions.append(dict(op="scale", dst=target, coefficient=str(Q(gate[2], gate[3])))) + skeleton.append(instructions) + interface = dict(roles=p.PERSISTENT+1, operators={str(j): None for j in range(1, 73)}) + for row in certificates: + program = [instruction for event in skeleton[row["first"]+1:row["second"]] for instruction in event] + result = word_endpoint(interface, program, row["input"])[row["output"]] + word = tuple((str(abs(signed)), signed < 0) for signed in row["word"]) + p.need(result == {word: c.G(row["coefficient"])}, "Separate complete contact coefficient replay") + count += 1 + return count + + +def fused_program(problem, offsets, pair, early): + first, second, *_ = pair + program = problem["program"] + merged = program[offsets[first]:offsets[first+1]] + program[offsets[second]:offsets[second+1]] + return (program[:offsets[first]] + (merged if early else []) + + program[offsets[first+1]:offsets[second]] + ([] if early else merged) + + program[offsets[second+1]:]) + + +def full_witness(problem, program, reference): + """Find a width-one basis witness, then check a separate input-column replay.""" + actual, _ = p.complete_endpoint(problem, program) + names = list(problem["operators"]) + bank = compact.validate(problem) + for output, (left, right) in enumerate(zip(actual, reference)): + difference = left.copy() + p.add(difference, right, Q(-1)) + for entry in sorted({key[0] for key in difference}): + terms = [(word, q) for (source, word), q in difference.items() if source == entry] + circuits = [[gate for signed in reversed(word) + for gate in bank[names[abs(signed)-1], signed < 0]] for word, q in terms] + coefficients, paths, inner = compact.merge_terms([c.G(q) for word, q in terms], + [Paths(p.N, circuit) for circuit in circuits]) + if not coefficients or c.energy(coefficients, inner, 1) == 0: + continue + witness = compact.entry_witness(coefficients, paths, inner, 1) + literal = word_endpoint(problem, program, entry)[output] + wanted = word_endpoint(problem, problem["reference"], entry)[output] + from check_witness import add_term + for word, q in wanted.items(): + add_term(literal, word, -q) + # Independent source amplitude evaluator; no Gram or path sum. + sys.path.insert(0, str(HERE / "vendor")) + import clifford_exact as source + value = c.G(0) + for word, q in literal.items(): + circuit = [gate for letter in reversed(word) for gate in bank[letter]] + vector, denominator = source.Op(p.N, source.identity(p.N), circuit).zero_state(witness["input_tuple"][0]) + real, imag = vector[witness["output_tuple"][0]] + value += q*c.G.pair(Q(real, 1 << denominator), Q(imag, 1 << denominator)) + p.need(value != 0 and str(value) == witness["discrepancy"], "Independent complete-provider basis witness") + return dict(output_role=output, input_role=entry, **witness, + normalized_squared_norm=str(c.energy(coefficients, inner, 1)), + mutated_program_sha256=hashlib.sha256(canonical(program)).hexdigest()) + raise ValueError("No width-one full-program witness") + + +def rejection(name, action): + try: + action() + except (ValueError, KeyError) as error: + return dict(name=name, rejected=str(error)) + raise ValueError("Accepted negative control: " + name) + + +def verify(write=False): + source_integrity() + manifest, data = p.read_inputs() + model = p.Provider(data["word"]) + audits = {d: model.audit_word(d) for d in ("forward", "backward")} + traces, native = check_catalogue(model, data, audits) + print("PASS_ALL_PROVIDER_NATIVE_CLASSES", native, flush=True) + results, witnesses = {}, [] + for direction in ("forward", "backward"): + problem, offsets = model.problem(direction) + actual, support = p.complete_endpoint(problem, problem["program"]) + reference, _ = p.complete_endpoint(problem, problem["reference"]) + p.need(actual == reference, "Complete sparse physical endpoint") + certificate = compact.certify(problem) + p.need(certificate["equivalent_at_all_positive_widths"], "Complete compact provider certificate") + p.need(not actual[p.OWNED], "Arbitrary owned input is erased at return") + results[direction] = dict(certificate=certificate, support=support, instructions=len(problem["program"]), + native_symbols=len(problem["operators"]), events=audits[direction]["events"], + paid=audits[direction]["paid"]) + pairs = p.fusion_pairs(model.word["programs"][direction]) + selected = [min(pairs, key=lambda row: (row[1]-row[0], row)), + min((row for row in pairs if row[4] != row[5]), key=lambda row: (row[1]-row[0], row))] + events = model.word["programs"][direction] + selected.append(min((row for row in pairs if max(events[row[0]][5], events[row[1]][5]) > 1 + and any(event[0] == "climb" and event[2] == row[2] + for event in events[row[0]+1:row[1]])), + key=lambda row: (row[1]-row[0], row))) + for pair in selected: + for early in (True, False): + witness = full_witness(problem, fused_program(problem, offsets, pair, early), reference) + witnesses.append(dict(direction=direction, placement="early" if early else "late", + pair=list(pair), **witness)) + print("PASS_COMPLETE_PROVIDER", direction, support, flush=True) + fusions, fusion_result = fusion_census(model, traces) + fusion_result["separate_contact_replays"] = check_contact_certificates(model, fusions) + controls = [] + bad = deepcopy(data) + bad["paid"] = bad["paid"][:-1] + controls.append(rejection("missing_paid_class", lambda: check_catalogue(model, bad, audits))) + first = data["paid"][1] + wrong = deepcopy(first["recipe"]) + wrong["left"]["phase"] = (wrong["left"]["phase"]+1) % 4 + controls.append(rejection("paid_absolute_phase", lambda: equal(model.edge(first["input"], first["output"], first["direction"]), p.recipe(wrong)))) + broken = deepcopy(data["word"]) + broken["programs"]["forward"].insert(0, ["scalar", ["clear", ["L", 224]], broken["canonical"]["start"][224]]) + controls.append(rejection("borrowed_erasure", lambda: p.Provider(broken).audit_word("forward"))) + broken_live = deepcopy(data["word"]) + prog = broken_live["programs"]["backward"] + at = next(j for j, event in enumerate(prog) if event[0] == "center") + prog.insert(at, next(event for event in prog if event[0] == "climb")) + controls.append(rejection("live_owned_cut", lambda: p.Provider(broken_live).audit_word("backward"))) + # A block with no contact can permit fusion. The exclusion needs its contact witness. + p.need(all(not row for j, row in enumerate(p.interval([], -1, 0, 0)) if j != 0), "Identity interval positive control") + controls.append(rejection("missing_contact_is_not_a_certificate", lambda: p.contact_witness([], (-1, 0, 0, 0, 2, 2, 3)))) + evidence_sha = saved("FUSIONS.json.gz", fusions, write) + witness_sha = saved("WITNESSES.json", witnesses, write) + result = dict(status="PASS_COMPLETE_PR4610_PROVIDER_AND_30328_FUSION_OBSTRUCTIONS", source_main=manifest["base_commit"], + provider_head=manifest["provider_head"], admission_head=manifest["admission_head"], + complete_local_provider=results, native=native, fusion=fusion_result, + fusion_payload_sha256=evidence_sha, witness_payload_sha256=witness_sha, + full_program_basis_witnesses=len(witnesses), controls=controls, + new_kappa=False, achieved_paid_delta={}, + limits="Fixed early/late fusion of any two persistent paid climbs on one role; no changed contacts, coupled fusions, new controller or physical/outer admission.") + saved("RESULT.json", result, write) + print(result["status"], flush=True) + return result + + +if __name__ == "__main__": + p.need(sys.argv[1:] in ([], ["--write"]), "Use --write or no argument") + verify("--write" in sys.argv) diff --git a/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py new file mode 100644 index 0000000000..166841a037 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5376/source-capsule/research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py @@ -0,0 +1,149 @@ +"""Small exact Gaussian-dyadic Clifford compiler, independent of gx internals. +Paulis use i^p X^x Z^z. State vectors use integer Gaussian numerators / 2^d. +The tableau is supplemented by a literal circuit, so global phases are kept. +""" +from dataclasses import dataclass + +def parity(x):return x.bit_count()&1 +def rank(rows): + p={} + for x in rows: + while x: + b=x.bit_length()-1 + if b not in p:p[b]=x;break + x^=p[b] + return len(p) +def transpose(rows,n):return tuple(sum(((rows[j]>>i)&1)<>j&1);a[j],a[k]=a[k],a[j] + for i in range(n): + if i!=j and a[i]>>j&1:a[i]^=a[j] + assert [r&((1<>n for r in a) +def basis_extend(cols,n): + out=[] + for x in list(cols)+[1<len(out):out.append(x) + assert len(out)==n + return tuple(out) +def nullspace(rows,n): + a=list(rows);p=[];k=0 + for j in range(n): + t=next((i for i in range(k,len(a)) if a[i]>>j&1),None) + if t is None:continue + a[t],a[k]=a[k],a[t] + for i in range(len(a)): + if i!=k and a[i]>>j&1:a[i]^=a[k] + p.append(j);k+=1 + return tuple((1<>j)&1)<>i&1:out=pmul(out,T[i]) + for i in range(n): + if z>>i&1:out=pmul(out,T[n+i]) + return out +def compose(A,B):return tuple(apply(A,p) for p in B) +def inverse(T): + n=len(T)//2;cols=[x|(z<>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4)) + return tuple(out) +def qvalue(Q,alpha,x,n): + return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4 +def mul_i(a,p): + x,y=a;p%=4 + return [(x,y),(-y,x),(-x,-y),(y,-x)][p] +@dataclass +class Op: + n:int + tab:tuple + circuit:list + def then(self,b): + assert self.n==b.n + return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit) + def adjoint(self): + circ=[] + for e in reversed(self.circuit): + if e[0]=='P':circ.append(('P',inv(e[1],self.n))) + elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2]))) + elif e[0]=='C':circ.append(('C',e[1],-e[2])) + elif e[0]=='phase':circ.append(('phase',(-e[1])%4)) + else:circ.append(e) + return Op(self.n,inverse(self.tab),circ) + def zero_state(self,basis=0): + N=1<>i)&1 for i in range(n)) + assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n)) + return Op(n,tuple([(1<>i&1 else 0,1<>i&1 else 0) for i in range(n)]),[('C',q,sgn)]) +def xgate(n,b):return Op(n,tuple([(1<>i)&1)) for i in range(n)]),[('X',b)]) +def fourier(n,axes=None): + out=ident(n) + for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<len(selected):picks.append(j);selected.append(x) + assert len(picks)==r and all(x>>r==0 for x in Bcols) + Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1<= 0 else "")+str(self.imag)+"i" + + __repr__ = __str__ + + +def scalars(problem): + p = problem.get("field", "Q") + if p == "Q": + return Fraction + if p == "Qi": + return Gaussian + if type(p) is not int: + raise ValueError("field must be Q, Qi or a prime at most 2^31-1") + return prime_scalars(p) + + +@lru_cache(maxsize=32) +def prime_scalars(p): + if not 2 <= p <= 2**31-1 or any(p % d == 0 for d in range(2, isqrt(p)+1)): + raise ValueError("field must be Q, Qi or a prime at most 2^31-1") + + class Prime: + def __init__(self, x=0): + if isinstance(x, Prime): + self.value = x.value + else: + q = Fraction(x) + self.value = q.numerator*pow(q.denominator, -1, p) % p + + def __add__(self, other): + return Prime(self.value+Prime(other).value) + + __radd__ = __add__ + + def __mul__(self, other): + return Prime(self.value*Prime(other).value) + + __rmul__ = __mul__ + + def __neg__(self): + return Prime(-self.value) + + def __sub__(self, other): + return self+-Prime(other) + + def __rsub__(self, other): + return Prime(other)+-self + + def __truediv__(self, other): + return Prime(self.value*pow(Prime(other).value, -1, p)) + + def __rtruediv__(self, other): + return Prime(other)/self + + def __eq__(self, other): + return self.value == Prime(other).value + + def __bool__(self): + return bool(self.value) + + def __str__(self): + return str(self.value) + + __repr__ = __str__ + + return Prime diff --git 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The five PR4470 framework assumptions are unchanged. Uniform words are not materialized.", + "previous_kappa": "60403/20000000", + "previous_record": "certificates/checkpoints/frontier4470.json", + "audited_source_head": "20bb93cd990d2ff683e4d0fc56b87a42cd5d3296", + "source_certificate": "research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json", + "source_certificate_sha256": "b4f720a7ccbb5b46e472eaf85dc8739a40598986f19b37d26c4f9ecfbd31f0de", + "replay_mode": "Fresh complete independent admission replay; source-bound preceding controller, ordinary BIT and physical/compiler foundation reuse", + "contributors": "docs/research/community-native4610-contributors.md", + "assumptions": [ + { + "id": "native_all_columns", + "statement": "Retained native operators, phase conventions, spectators and whole-job adapters work at every positive column multiplicity." + }, + { + "id": "owned_erasure", + "statement": "Owned streams and suspended centers obey the retained allocation, erasure and ownership contracts." + }, + { + "id": "compiler", + "statement": "The finite mixed-target compiler and chronological product, completion and splitting satisfy the retained uniform closure contract." + }, + { + "id": "precision_tape", + "statement": "Retained fixed-tape movement and precision/storage prescriptions apply to the new fixed finite template." + }, + { + "id": "analytic_recovery", + "statement": "Analytic decomposition, fine-prime avoidance and exact integer recovery follow the retained upstream/outer framework." + } + ], + "audit_pr": 5241, + "audit_head": "13efb5fc5f3b7c14ec2cfa181dd9eb6480972cf2" +} diff --git a/research/coupled-provider-independent-audit/custody/5402/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/docs/research/agent-task-catalog.json b/research/coupled-provider-independent-audit/custody/5402/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/docs/research/agent-task-catalog.json new file mode 100644 index 0000000000..f126dd2e2d --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5402/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/docs/research/agent-task-catalog.json @@ -0,0 +1,1242 @@ +{ + "schema_version": 1, + "priority_revision": 7, + "priority_log": "docs/research/research-priority-log.md", + "assessed_on": "2026-10-20", + "status": "Research suggestions, not reservations or assertions that these questions are unclaimed. Check current main and live PRs.", + "tracks": [ + { + "id": "bit-mechanisms", + "weight": 20, + "tasks": [ + { + "id": "bit-helper-contract", + "question": "Can one precisely specified helper-mixing word satisfy a replacement for the inherited H2/K interface?", + "starting_points": [ + "docs/research/research-family-status.md", + "research/r439-bsection-stars-seed01/README.md", + "research/r439-copy-path-sharing-barrier/README.md" + ], + "methods": [ + "Derive a replacement interface lemma and price its implementation.", + "Seek an exact dirty-input or chronological-cut counterexample to the proposed replacement." + ], + "acceptance_gate": "A full boundary contract and paid profile; unchanged scalar counts alone are insufficient. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "research/r439-bsection-stars-seed01/verify.py" + ], + "expected": "PASS_R439_BSECTION_STARS", + "inspect": "Compare the two false H2/K flags with the unchanged paid profile in its README.", + "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay." + }, + "first_experiment": "Write one replacement H2/K implication for a single helper-star operation, then try to falsify it on dirty inputs.", + "bottleneck_link": "A legitimate replacement could admit a cheaper bit circuit; scalar savings alone do not alter the selected moment.", + "allowed_variations": [ + "Choose one helper-star or quartet instance; narrow to one boundary implication." + ], + "scope_change_triggers": [ + "Changing only source count or scalar addition count without an interface argument." + ], + "overlap_terms": [ + "H2_D_frame0_targets_from_helpers", + "K_equals_D", + "helper-star" + ] + }, + { + "id": "bit-new-register-model", + "question": "Can an explicitly larger or nonabelian register model escape the scoped three-register obstruction?", + "starting_points": [ + "docs/research/research-family-status.md", + "research/bit-three-register-lower-bound/README.md", + "certificates/selected-result.json", + "research/bit-gl3-mixed-targets-length10/README.md", + "docs/research/community-efficient1000-review.md" + ], + "methods": [ + "Construct the smallest exact identity in a newly specified legal operation alphabet.", + "Derive a target-specific relaxation bound for that same explicit alphabet." + ], + "acceptance_gate": "Name the changed hypothesis, all counted roles and a uniform identity; finite column tests alone do not certify it. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read Model section 1 of the three-register bound and identify the exact excluded free operations.", + "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay." + }, + "first_experiment": "First compare the alphabet, role count and length with the fully replayed #1974 census and #2027 mixed-root tariff. Identify a changed premise and a legal native implementation; then price one smallest completed instance before searching larger words.", + "bottleneck_link": "A small-width completed saving changes the bit primitive; a finite-address identity alone is insufficient.", + "allowed_variations": [ + "Choose a fixed larger register count or a specified nonabelian operation family." + ], + "scope_change_triggers": [ + "Remaining inside the already-excluded three-register abelian model.", + "Repeating the two-register GL3 census or a covered three-register length without changing a hypothesis; a formal group-algebra word without native conversion is a partial result." + ], + "overlap_terms": [ + "three-register", + "nonabelian", + "group algebra" + ] + }, + { + "id": "r437-carrier-integration", + "question": "Can the paid R437 two-window carrier improvement be admitted by the actual pooled compiler and physical caller?", + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/r437-two-window-carrier/README.md", + "research/r437-reverse-row-coefficient/README.md" + ], + "methods": [ + "Close one compiler/request, caller or precision/stock implication for the pinned paid exchange.", + "Falsify that exact interface with an arbitrary-dirty-state or chronology counterexample." + ], + "acceptance_gate": "Pin the complete source and destination contracts, exact paid and scalar deltas, and all remaining assumptions. A local moment gain is not a physical or all-size supplier admission.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read #4067 paid profile and open integration obligations; #4147 covers the reverse row coefficient. Three additional ADDs per call and all helpers remain charged. This is not a selected supplier.", + "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately." + }, + "first_experiment": "Choose one unclaimed obligation: pooled compiler codebook/request alignment, actual physical caller, or precision/stock envelope using the already reported reverse coefficient. Pin the input and receiver, preserve dirty/source windows, and test one binding with a rejection control. Stop at unresolved dependencies; do not rederive the coefficient or quote the local moment as a completed bound.", + "bottleneck_link": "The exchange changes the paid profile; integration must establish that its gain survives the complete caller.", + "allowed_variations": [ + "One compiler rebind, one actual caller boundary, or one precision/stock implication." + ], + "scope_change_triggers": [ + "Ignoring added ADDs, retaining an obsolete reverse coefficient, or declaring global admission from the local histogram." + ], + "overlap_terms": [ + "R437", + "two-window carrier", + "4067", + "4147", + "pooled compiler", + "request alignment", + "reverse row coefficient" + ], + "existing_checks": [ + { + "scope": "PR #4067: source-bound two-window carrier with (2,2) to (1,3) paid exchange and fixed OQ4 host.", + "evidence": "research/r437-two-window-carrier/README.md", + "remaining": "Pooled compiler/request rebind, physical caller and precision/stock admission.", + "status": "author-checked", + "source_commit": "a95f11c52e3ca1e4c5171b3c20d8f4b0815aee2e", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4147: reverse row coefficient follow-up.", + "evidence": "research/r437-reverse-row-coefficient/README.md", + "remaining": "Use the exact coefficient in a caller-bound precision/stock proof rather than repeat the arithmetic.", + "status": "author-checked", + "source_commit": "72e7bb797adf82aeb525a399f56ab8adbab8e93c", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + } + ] + }, + { + "id": "complex-mechanisms", + "weight": 20, + "tasks": [ + { + "id": "p104-side-correction", + "question": "Can a changed P104 producer/consumer contract escape the scoped slot, chart and completion obstructions with a favorable full bill?", + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/p104-literal-slot-defect/README.md", + "research/p104-uniform-commutation-gap/README.md", + "research/p104-uniform-encoding-gap/README.md", + "research/p104-source-chart-shortcut/README.md", + "research/p104-fiber-tag-seam/README.md" + ], + "methods": [ + "Construct one side-correction word at an explicit chronological cut with the needed frames still available.", + "Derive a lower bound on the side correction and hosting costs that decides whether this channel can beat the selected budget." + ], + "acceptance_gate": "An exact arbitrary-input identity, source/target frame availability and restoration at the chosen cut, plus the complete channel+correction+idle/hosting bill or an explicit favorable bound. The native channel alone is not a supplier. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read the named successor obstructions before extending #2981 static flags. Distinguish literal-slot action, commutation, uniform encoding, source-chart shortcut and fiber-tag seam scopes; none excludes all P104 mechanisms.", + "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately." + }, + "first_experiment": "Name one hypothesis changed from these exact interfaces. Write a literal producer-to-consumer timeline and an arbitrary-dirty-input positive/control pair, then charge acquisition, coefficients, completion, hosting and restoration. Stop if the same slot/fiber mismatch persists or the favorable full budget already fails. A scoped independent audit remains useful; another static count is not a new completion.", + "bottleneck_link": "Completing an already realized changed channel tests a concrete construction opportunity, instead of refining the incumbent packing. A positive local result still needs global and all-size admission.", + "allowed_variations": [ + "One correction factorization, one chronological cut, or one explicit hosting obstruction.", + "A changed correction schedule with an updated full bill and native frame contract." + ], + "scope_change_triggers": [ + "Recompiling the already certified low-rank channel without closing a new obligation.", + "Treating a pending ancestor, local histogram or unpriced side correction as an admitted global supplier.", + "Repeating a correction or physical conversion already supplied by a pending follow-up without adding independent coverage or a different unresolved obligation.", + "Repeating the 208-flag static matching or calling a static nested cover a chronological correction program. Independent audit of that certificate is distinct and remains useful.", + "Repeating a static cover, source-chart shortcut or fiber-tag seam without changing the hypothesis responsible for its obstruction." + ], + "overlap_terms": [ + "P104", + "I-G/2", + "side correction", + "native channel", + "1972", + "1991", + "2586", + "endpoint transport", + "physical dual", + "relay composition", + "2981", + "joint unit flags", + "acquisition delivery", + "static nesting", + "4133", + "4136", + "4140", + "4153", + "4154", + "p104-literal-slot-defect", + "p104-uniform-commutation-gap", + "p104-uniform-encoding-gap", + "p104-source-chart-shortcut", + "p104-fiber-tag-seam" + ], + "existing_checks": [ + { + "scope": "PR #4133: literal-slot defect", + "evidence": "research/p104-literal-slot-defect/README.md", + "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.", + "status": "author-checked", + "source_commit": "88666f1dee93fbd85b31fd5d6f91a219e111b5f4", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4136: uniform commutation gap", + "evidence": "research/p104-uniform-commutation-gap/README.md", + "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.", + "status": "author-checked", + "source_commit": "281ce601a8be9db470de630759179c23e1dfaa88", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4140: uniform encoding gap", + "evidence": "research/p104-uniform-encoding-gap/README.md", + "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.", + "status": "author-checked", + "source_commit": "de25c6525aa866962309df5d107b32d55e6e5628", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4153: source-chart shortcut exhausts its optimistic allowance", + "evidence": "research/p104-source-chart-shortcut/README.md", + "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.", + "status": "author-checked", + "source_commit": "9123241fea53df77e51ffe30d9aca1625d4bf3a8", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4154: fiber-tag seam mismatch", + "evidence": "research/p104-fiber-tag-seam/README.md", + "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.", + "status": "author-checked", + "source_commit": "4ffcdaee5d6255a9cea1fe53a5424435068089d0", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + }, + { + "id": "complex-rank-shape-decoder", + "question": "Can a decoder deliver the local paid mass in fewer, larger-rank children (block frame climbs instead of rank-1 to rank-3 steps)?", + "starting_points": [ + "docs/research/research-family-status.md", + "research/complex-local-word-ceiling/README.md", + "research/complex-decoder-field-extension-seed44/README.md", + "research/complex-frame-pair-decoders/README.md", + "research/selected-k8-unrestricted-ends/README.md", + "research/eisenstein-reduction-copy-floor/README.md" + ], + "methods": [ + "Find one exact small decoding identity whose frame path climbs in blocks, and price its complete per-call profile.", + "Bound the best effective child rank achievable for one fixed support alphabet, including copies, frames and restoration." + ], + "acceptance_gate": "A per-call local profile, with all copied information, frames and restoration counted, whose ceiling exceeds the selected word's by at least 5%; masked or overcomplete supports must change an assumption of the eight-term all-pairs bound. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "research/complex-local-word-ceiling/verify.py" + ], + "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING", + "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.", + "scope": "Positive control and planning budget only; this is not a new construction or full cold replay." + }, + "first_experiment": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin. Ideal budget: rank-16 delivery is 2.31x (levers.py).", + "bottleneck_link": "Rank-1 children are about half of recursive cost; the selected word's effective child rank is about 3.9. Larger-rank delivery lowers recursive cost per unit of paid mass.", + "allowed_variations": [ + "One masked, overcomplete or block decoder family with exact labels and supports.", + "A scoped lower bound on effective rank for one alphabet.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "scope_change_triggers": [ + "Repacking idle remainders of an unchanged word (covered by the packing ceiling).", + "Repeating the eight-term all-pairs search inside its proved scope.", + "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.", + "Searching below C=40 in the #2017 Eisenstein binary scalar-rectangle or fixed-support block-linear additive pairing model; specify a changed premise instead. This bound does not cover every complex decoder.", + "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts." + ], + "overlap_terms": [ + "rank shape", + "block climb", + "masked decoder", + "overcomplete", + "effective rank" + ] + }, + { + "id": "complex-new-helper-inventory", + "question": "Can a new local cost interface change the deficit-to-recursive-cost ratio beyond current packing?", + "starting_points": [ + "docs/research/research-family-status.md", + "research/complex-local-word-ceiling/README.md", + "research/heterogeneous-owner-assembly/README.md", + "certificates/selected-result.json", + "research/selected-k8-unrestricted-ends/README.md" + ], + "methods": [ + "Propose a changed helper inventory and derive an optimistic exact moment.", + "Design a small completed instance and independently verify its endpoint and rank bill." + ], + "acceptance_gate": "A new physically realizable contract outside the frozen catalogue whose per-call profile, screened with ceiling.ceiling(), beats the selected word's packing ceiling; a lower cap does not establish identical circuitry or order attainable optima, and is insufficient to pass the stronger-budget target under this model. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "research/complex-local-word-ceiling/verify.py" + ], + "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING", + "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.", + "scope": "Positive control and planning budget only; this is not a new construction or full cold replay." + }, + "first_experiment": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin.", + "bottleneck_link": "Packing of the selected word is capped at +0.87% (ceiling model); only a lower local excess spend or a changed coverage law raises the cap.", + "allowed_variations": [ + "Narrow to one changed boundary or helper type with explicit counts.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "scope_change_triggers": [ + "Mixing only providers already inside the pinned catalogue.", + "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.", + "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts." + ], + "overlap_terms": [ + "helper inventory", + "heterogeneous-owner", + "mutable leaver" + ] + } + ] + }, + { + "id": "recursive-interfaces", + "weight": 20, + "tasks": [ + { + "id": "joint-query-controller", + "question": "Can the installed QQ16 caller win a complete matched protocol bill, or can a changed demand eliminate actual paid work?", + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/qq16-caller-install/README.md" + ], + "methods": [ + "Derive the matched whole-caller physical bill for installed and baseline protocols.", + "Change the actual demanded observations and prove a cheaper legal producer/consumer contract." + ], + "acceptance_gate": "Name the changed premise of the fixed F0/B1 observation obstruction. Show exactly which query is recovered, legal native reads and restoration, and a full favorable budget including cover maps, helpers and endpoints. Local inverse identities alone do not close the global controller. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read #4166 COST.md and ADMISSION.json. An actual caller connection is now proposed. Its native-component profile loses; parent park/restore versus external-call costs remain unresolved. Retain the producer and recovery lineage rather than rebuild it.", + "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately." + }, + "first_experiment": "At the actual installed cut, compare matched complete parent park/restore and external input/return protocols at the same bank/packet geometry, including every later root call and service cost. Alternatively pin both bridge observations and derive a genuinely smaller source-compatible demand. Stop if the complete necessary inequality fails or an essential cost is unknown; no larger decoder scan from a local tape-action saving.", + "bottleneck_link": "The native local words exist; retained query information and its physical access are the missing link to a composed recursive interface.", + "allowed_variations": [ + "One paid query, one changed first pair, or one precisely specified affine helper state.", + "A counterexample or lower bound for that exact proposed repair.", + "One unresolved obligation of a newer local decoder, with exact source heads and a distinct claim/domain." + ], + "scope_change_triggers": [ + "Retaining the fixed first pair and ordinary schedule while allowing only homogeneous selected-only control, already excluded by the witness.", + "Treating cover-map counts as zero-cost physical address operations.", + "Recreating the pending complete local decoder or early-record/output-bank coalescing already under investigation without a distinct audit or changed premise.", + "Treating a completed-output defect inequality as a producer-interior, dirty-range or physical-cost certificate.", + "Recreating completed-output recovery or caller wiring already supplied by #4166 without new independent coverage.", + "Dropping retained later root calls or claiming native-profile dominance from the isolated publication saving." + ], + "overlap_terms": [ + "QQ16", + "joint-query", + "changing-chart controller", + "selected observation", + "1969", + "2540", + "early record", + "output-bank retention", + "complete native decoder", + "2965", + "producer defect", + "dirty-helper range", + "F17 consumer", + "4166", + "qq16-caller-install" + ], + "existing_checks": [ + { + "scope": "PR #4166: author-checked installed producer/service/return/bridge connection; native-component comparison loses.", + "evidence": "research/qq16-caller-install/README.md", + "remaining": "Complete matched physical protocol bill, or changed source-compatible demand/circuit; no affordable supplier yet.", + "status": "author-checked", + "source_commit": "0b082d22a0e9a442d264ab0633e35ef26c790630", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + }, + { + "id": "centre-path-sharing", + "question": "Can the 64-per-call centre path (eight rank-8 COPY/ERASE totals through the private temporary) be shared across calls or shrunk?", + "starting_points": [ + "docs/research/research-family-status.md", + "research/complex-local-word-ceiling/README.md", + "research/split-centres-global/proofs/PR386-BIT-GEOMETRY.txt", + "certificates/selected-result.json" + ], + "methods": [ + "Derive a fully charged favorable relaxation for sharing one centre path across k calls, including restoration, hosting and precision.", + "Prove a lower bound on copied information per call for the selected decoder contract." + ], + "acceptance_gate": "Show the changed centre charge and copy profile per call with every added restoration or hosting cost charged, and its ceiling via ceiling.ceiling(centre=...). A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "research/complex-local-word-ceiling/verify.py" + ], + "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING", + "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.", + "scope": "Positive control and planning budget only; this is not a new construction or full cold replay." + }, + "first_experiment": "Write the per-call centre charge and copy children for sharing across k = 2 calls, charge the sharing overhead, and screen it; stop this route if even the ideal sharing gains under 10%. Ideal budgets: free 2.80x, shared by two 1.90x (levers.py).", + "bottleneck_link": "The centre path consumes 64 of about 99.6 unpaid coordinates per call, i.e. about 64% of the raw deficit.", + "allowed_variations": [ + "One sharing pattern across a fixed number of calls.", + "One reduced copied-total contract for the existing decoder.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "scope_change_triggers": [ + "Removing copies without a replacement contract for the decoder's copied totals.", + "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts." + ], + "overlap_terms": [ + "centre path", + "copied totals", + "private temporary", + "shared centre", + "batching" + ] + }, + { + "id": "coverage-law-change", + "question": "Can a template or call contract leave two or more unpaid coordinates per live family?", + "starting_points": [ + "docs/research/research-family-status.md", + "research/complex-local-word-ceiling/README.md", + "research/idle-axis-hosting/PROOF.md", + "certificates/selected-result.json" + ], + "methods": [ + "State a replacement for the coverage identity (mass = 72W + 64N) and the contract change that realizes it, with its implementation cost.", + "Find an obstruction: show which data-endpoint obligation forces exactly one unpaid coordinate in the current template." + ], + "acceptance_gate": "An explicit replacement identity, verified on a small complete instance with dirty inputs, priced with ceiling.ceiling(unpaid=...). A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "research/complex-local-word-ceiling/verify.py" + ], + "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING", + "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.", + "scope": "Positive control and planning budget only; this is not a new construction or full cold replay." + }, + "first_experiment": "Explain where the single unpaid coordinate per family comes from in the hosted template; propose one change and price it. Ideal budget: two unpaid coordinates per family is 3.77x (levers.py).", + "bottleneck_link": "The deficit is one coordinate per family minus the centre charge; doubling unpaid coordinates per family scales it directly.", + "allowed_variations": [ + "One template change or one endpoint-contract change.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "scope_change_triggers": [ + "Counting a coordinate as unpaid while leaving it unadvanced in the data endpoint.", + "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts." + ], + "overlap_terms": [ + "coverage identity", + "unpaid coordinate", + "deficit law", + "W - 64N" + ] + }, + { + "id": "connector-alphabet-change", + "question": "Does one explicit extension of the connector alphabet offer a favorable completed budget?", + "starting_points": [ + "docs/research/research-family-status.md", + "research/universal-connector-boundary/README.md", + "certificates/selected-result.json" + ], + "methods": [ + "Construct and charge a legal extra operation on a minimal instance.", + "Prove a target-specific bound after adding one specified operation family." + ], + "acceptance_gate": "State which fixed-alphabet premise changes and charge its implementation; do not declare it free. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "research/universal-connector-boundary/verify.py" + ], + "expected": "PASS_UNIVERSAL_CONNECTOR_BOUNDARY", + "inspect": "Reproduce the 945-pairing control, then read Exact interface to list the allowed calls.", + "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay." + }, + "first_experiment": "Add exactly one legally priced operation and test a tiny dirty-input instance before enumerating larger cases.", + "bottleneck_link": "A new legal connector operation could change recursive interface cost; a larger census in the same alphabet is a separate side result.", + "allowed_variations": [ + "Choose one additional operation and a small source count for its first counterexample." + ], + "scope_change_triggers": [ + "Keeping the alphabet and only increasing the source count; record this as a changed assignment.", + "Extending a source-count census without naming a supplier/interface decision it could change; audit #2973 pruning concerns before relying on the affected predecessor exclusions." + ], + "overlap_terms": [ + "universal connector", + "source-toggle", + "connector alphabet" + ] + } + ] + }, + { + "id": "adversarial-audit", + "weight": 15, + "tasks": [ + { + "id": "selected-stock-envelope", + "question": "What explicit uniform stock envelope does the actual selected stopped producer supply at one bootstrap stage?", + "starting_points": [ + "research/selected-bootstrap-stock-audit/README.md", + "research/bootstrap-cutoff-time-space-split/README.md", + "certificates/selected-result.json", + "docs/research/community-efficient1000-review.md", + "research/stock-margin-chain/README.md" + ], + "methods": [ + "Derive a source-bound reserve recurrence at the actual selected atom widths, separating parent stock from completed inner borrowing.", + "Find an exact missing implication or counterexample to a proposed selected-stage stock envelope." + ], + "acceptance_gate": "Bind every coefficient and depth factor to the selected producer and state the width domain. Compare a proved envelope with the sufficient cutoff guard; a large numerical headroom or a historical m=120 coefficient is not a selected m=73 proof.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read #2972 stock-margin chain and the selected stock audit. The new source archive reports the remaining cutoff comparisons, but leaves every actual stock coefficient unresolved; it is not an independently validated reserve envelope.", + "scope": "Source-bound orientation only. Read the named package and review before relying on its local evidence; this command is not its replay or supplier admission." + }, + "first_experiment": "Choose one actual selected producer/stage and derive its parent reserve and depth coefficient from source. Check whether newer handoffs already cover that exact obligation. Stop with the missing implementation lemma if it cannot be bounded; do not rerun #2972 cutoff/headroom arithmetic as a new contribution.", + "bottleneck_link": "This reduces a concrete inherited implementation obligation without confusing unchanged kappa arithmetic with a completed theorem.", + "allowed_variations": [ + "One stage or one explicit reserve/depth implication.", + "An independently checked same-domain proof repair, retaining all remaining assumptions." + ], + "scope_change_triggers": [ + "Importing the historical 57604 or 252 allowance without a selected-producer binding.", + "Calling a conditional fit lemma a full outer-proof adoption.", + "Replacing an actual selected stock coefficient with cutoff comparisons or a conditional fit inequality." + ], + "overlap_terms": [ + "selected stock", + "stock envelope", + "bootstrap cutoff", + "1956", + "1965", + "1990", + "2972", + "stock-margin-chain", + "actual_stock_coefficient" + ], + "existing_checks": [ + { + "scope": "Retained stock audit identifies missing actual selected-stage coefficients; later cutoff-chain arithmetic does not supply them.", + "evidence": "docs/research/research-family-status.md#revision-6-handoffs-source-archives-awaiting-independent-validation", + "remaining": "Derive one actual reserve/depth coefficient from the selected producer.", + "status": "reviewed", + "source_commit": "836b19bfa309ceafbc8ee32a15e8c4b10dde7e11", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + }, + { + "id": "supplier-boundary-audit", + "question": "Can the #4088 four-provider dispatch satisfy the complete ordinary/outer admission contract?", + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/staged544-mixed-fourth-entry/README.md", + "research/scatter-boundary-decision/README.md" + ], + "methods": [ + "Trace one hypothesis through the source, checker and complete caller.", + "Construct one semantically invalid but superficially well-formed fixture and test rejection." + ], + "acceptance_gate": "Pin the current sources and one obligation; the historical owner audit is an example, not evidence of a current bug.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read #4088 Scope and Open next questions: local words, native receipts and literal fill do not include a rerun of the mixed four-provider ordinary/outer engine. #3801 is the newer scatter-boundary decision; do not restart #2977 as if untouched.", + "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately." + }, + "first_experiment": "Pin the provider registry, four native source closures and dispatch. Make a bounded acceptance coverage map or one registry adapter preserving every inherited admission predicate and rejection control (including an omitted fourth provider). Record remaining ordinary/outer obligations and a resource estimate before heavy execution. Stop at unresolved source/caller dependencies; no selected-result promotion from a local pass.", + "bottleneck_link": "Closing a current acceptance gap or proof obligation strengthens reliability even without changing kappa.", + "allowed_variations": [ + "One provider-registry, dispatch, native-closure or admission-predicate obligation; separate branches must name distinct coverage." + ], + "scope_change_triggers": [ + "Reporting the historical timing-only diagnostic as a new current acceptance bug.", + "Calling a malformed mutant a failure of the selected construction, or importing an opt-in repair without testing the exporter boundary.", + "Running another root enclosure instead of validating dispatch or weakening an inherited predicate to make mixed admission pass." + ], + "overlap_terms": [ + "owner boundary", + "bridge omission", + "hosting", + "2977", + "scatter export", + "duplicate index", + "parity semantics", + "4088", + "3801", + "staged544-mixed-fourth-entry", + "scatter-boundary-decision" + ], + "existing_checks": [ + { + "scope": "PR #4088: author-checked local words, native receipts, owner/phase fill and exact moment.", + "evidence": "research/staged544-mixed-fourth-entry/README.md", + "remaining": "Rebind and validate ordinary/outer admission with all four providers; full mixed release not established.", + "status": "author-checked", + "source_commit": "72d7efc181edb21806a878f174847c96dd410ab0", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #3801: successor scatter-boundary decision package.", + "evidence": "research/scatter-boundary-decision/README.md", + "remaining": "Consult its exact acceptance scope before any new exporter audit; not proof of a selected failure.", + "status": "author-checked", + "source_commit": "911f8800ba7a4b03603ef62c5ffc6240e53cb5fd", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + }, + { + "id": "uniform-transfer-audit", + "question": "Does one quantified step of the proposed #4100 all-size construction hold at its actual caller?", + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/unconditional-batched-crt/README.md" + ], + "methods": [ + "Prove one missing implication with explicit quantified hypotheses.", + "Find an exact counterexample at the claimed interface boundary." + ], + "acceptance_gate": "Identify the proposition and what would change downstream; do not equate a finite replay with a universal proof.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read PROOF.md and AUDIT.md in #4100. Select one distinct obligation: CRT total repair, native/free-algebra lifting, precision/conditioning, or complete fixed-tape cost. This is an author-submitted proof, not an accepted unconditional theorem.", + "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately." + }, + "first_experiment": "Check live handoffs; name one proposition, its caller, quantified domain and dependency closure. Independently prove the implication or exhibit a precise gap/counterexample. Prioritize CRT.md total repair or COMPLEX.md free-algebra lift only if unclaimed. Stop at the chosen obligation; do not substitute finite samples or root arithmetic for an all-size proof, or launch the complete package by default.", + "bottleneck_link": "Finite supplier improvements are useful only under the retained transfer obligations.", + "allowed_variations": [ + "One CRT repair, native lift, precision/conditioning or tape-cost proposition, with its exact caller." + ], + "scope_change_triggers": [ + "Replacing a quantified obligation with another finite smoke test.", + "Treating archive intake, an author PASS receipt or a finite composed fixture as discharge of the universal hypotheses." + ], + "overlap_terms": [ + "uniform transfer", + "all-size", + "precision", + "4100", + "unconditional-batched-crt" + ], + "existing_checks": [ + { + "scope": "PR #4100: proposed unconditional construction and finite checks, without independent acceptance.", + "evidence": "research/unconditional-batched-crt/README.md", + "remaining": "Independent proof audit of one caller-bound all-size implication; all other premises remain explicit.", + "status": "author-checked", + "source_commit": "337d04939571a637aeab54a0f58f54fde811663a", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + }, + { + "id": "census-pruning-audit", + "question": "Does the reported word-census parity-pruning error invalidate a specific exclusion we still rely on, and what bounded repair is justified?", + "starting_points": [ + "research/f7-weight-parity-census-correction/README.md", + "docs/research/research-family-status.md" + ], + "methods": [ + "Independently reconstruct the tiny counterexample and trace one affected exclusion to its exact pruning code.", + "Compare corrected and unpruned enumeration on a small exhaustive domain, then audit the changed pruning implication." + ], + "acceptance_gate": "Pin the old and proposed corrected engines, distinguish a disproved pruning rule from a disproved final bound, and state exactly which downstream exclusions need revalidation. #2973 is an author-checked source archive; neither its new f(7) claim nor all old conclusions are automatically accepted or rejected.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read #2973 error description and MATH.md; manually reconstruct the prefix states of 01021323 before running any large census.", + "scope": "Source-binding orientation only; no full enumeration or mathematical validation." + }, + "first_experiment": "Reconstruct the eight prefix states of 01021323 and compare bit-0 versus Hamming-weight parity budgets independently. Trace the reported false prune to one pinned predecessor (#2542, #2634 or #2691), then test a small exhaustive domain. Stop after a source-impact handoff or corrected-prune proof; a full seven-label replay needs a separate resource budget and a named research decision it can change.", + "bottleneck_link": "An unsound exclusion can wrongly close a mechanism; correcting its dependency boundary is more useful than extending the same census.", + "allowed_variations": [ + "One predecessor pruning rule, one independently exhaustive small domain, or one downstream dependency audit." + ], + "scope_change_triggers": [ + "Launching a larger census before validating the prune and explaining which active decision it changes.", + "Treating a small-domain counterexample to the old rule as a counterexample to every reported seven-label bound." + ], + "overlap_terms": [ + "2973", + "2542", + "2634", + "2691", + "weight parity", + "bit-0", + "01021323", + "census pruning" + ] + } + ] + }, + { + "id": "independent-verification", + "weight": 10, + "tasks": [ + { + "id": "independent-moment", + "question": "Does a new paid-profile or mixture-ceiling claim have independent source-bound coverage of its actual changed ledger?", + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/staged544-mixed-fourth-entry/README.md", + "research/staged-fourth-mixture-ceiling/README.md", + "research/r437-two-window-carrier/README.md" + ], + "methods": [ + "Independently reconstruct one changed paid ledger or pooled dual with exact source and model binding.", + "Check a genuinely uncovered moment implication with a different enclosure method and semantic controls." + ], + "acceptance_gate": "Demonstrate independence, source binding, positive cases and semantic failure controls. Name the existing checks and the missing coverage. More digits or another equivalent evaluation of an unchanged root is not by itself new verification coverage.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Choose one uncovered implication in #4088 literal mixed fill, #4091 pooled dual/model binding or #4067 changed frame/host bill. #4091 pins an earlier #4088 head: validate word, capacity and stock equivalence before applying that ceiling to the later fill.", + "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately." + }, + "first_experiment": "Independently reconstruct one changed ledger or pooled certificate with a positive case and a semantic failure control. Compare exact sources and name what existing checks miss. Keep this separate from supplier-boundary-audit (ordinary/outer dispatch) and uniform-transfer-audit (all-size proof). Stop after the chosen implication; more digits of an unchanged root are not additional mechanism coverage.", + "bottleneck_link": "Independent pricing prevents unsupported frontier claims and can reveal genuine accounting slack.", + "allowed_variations": [ + "Reconstruct either a source ledger or a numeric enclosure with a different method." + ], + "scope_change_triggers": [ + "Importing the primary function and calling its output independent verification.", + "Calling an aggregate histogram or source archive an independently accepted physical supplier." + ], + "overlap_terms": [ + "independent moment", + "rank histogram", + "exact enclosure", + "2979", + "rank7 joint endframes", + "paired extraction", + "joint lowering", + "4088", + "4091", + "4067", + "staged544-mixed-fourth-entry", + "staged-fourth-mixture-ceiling", + "r437-two-window-carrier" + ], + "existing_checks": [ + { + "scope": "PR #4088: mixed local/owner/phase ledger and moment reported.", + "evidence": "research/staged544-mixed-fourth-entry/README.md", + "remaining": "Independent binding of changed construction to paid histogram, distinct from full admission.", + "status": "author-checked", + "source_commit": "72d7efc181edb21806a878f174847c96dd410ab0", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4091: sharp pooled ceiling proposed for fixed THREE/FOUR words and inventory.", + "evidence": "research/staged-fourth-mixture-ceiling/README.md", + "remaining": "Validate dual, exhaustive pattern scope and exact source equivalence before applying to newer fills.", + "status": "author-checked", + "source_commit": "a29bdd8f56cd18b805917775cdec09ff935eddc4", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4067: paid (2,2) to (1,3) exchange and fixed OQ4 host reported.", + "evidence": "research/r437-two-window-carrier/README.md", + "remaining": "Independent full cost delta; remaining caller/precision/stock obligations are separate.", + "status": "author-checked", + "source_commit": "a95f11c52e3ca1e4c5171b3c20d8f4b0815aee2e", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + }, + { + "id": "formal-interface-lemma", + "question": "Can one uncovered interface implication be formalized with exact caller and certificate bindings?", + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/gate-operand-parity-lean/README.md", + "research/staged544-certified-endpoint/README.md", + "research/unconditional-batched-crt/README.md" + ], + "methods": [ + "Formalize a missing boundary lemma identified by the selected review.", + "Audit a formal theorem-to-certificate binding independently." + ], + "acceptance_gate": "State the exact formalized proposition and remaining assumptions; avoid duplicate arithmetic formalizations already present.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Inventory the gate-operand parity lemma (#3807) and certified endpoint arithmetic (#3857). Neither is a full multiplication proof. For #4100, audit the compact-switch statement and its hypotheses before formalizing it.", + "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately." + }, + "first_experiment": "Write one missing statement with quantified hypotheses, actual caller and existing coverage. A compact-switch lemma is a candidate only after its mathematical contract is reviewed. Establish a bounded proof plan before a separately budgeted proof-assistant build; do not rerun large Lean jobs as orientation.", + "bottleneck_link": "A missing interface proof can reduce the conditional gap even if it does not change kappa.", + "allowed_variations": [ + "Narrow to one formal lemma or one theorem-to-certificate binding." + ], + "scope_change_triggers": [ + "Formalizing already-covered arithmetic and claiming the full multiplication theorem." + ], + "overlap_terms": [ + "hyperplane end", + "formal interface", + "Lean binding", + "3807", + "3857", + "4100", + "gate-operand-parity-lean", + "staged544-certified-endpoint", + "unconditional-batched-crt" + ], + "existing_checks": [ + { + "scope": "PR #3807: scoped gate-operand parity formalization.", + "evidence": "research/gate-operand-parity-lean/README.md", + "remaining": "Exact theorem-to-caller binding and genuinely uncovered interface lemmas.", + "status": "author-checked", + "source_commit": "4c3530f42a6abcc48e7a6bcffd6c901911dc8269", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #3857: certified real-power moment/endpoint arithmetic.", + "evidence": "research/staged544-certified-endpoint/README.md", + "remaining": "Uniform algorithmic implications, not another endpoint digit.", + "status": "author-checked", + "source_commit": "ef4315b8caa605e47a2515004845eb2d2ed71a86", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4100: compact-switch formalization proposed as future validation.", + "evidence": "research/unconditional-batched-crt/README.md", + "remaining": "Audit the statement and assumptions before a formal proof campaign.", + "status": "author-checked", + "source_commit": "337d04939571a637aeab54a0f58f54fde811663a", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + } + ] + }, + { + "id": "verifier-engineering", + "weight": 8, + "tasks": [ + { + "id": "replay-runtime", + "question": "Can one measured replay bottleneck be sped up without dropping coverage?", + "starting_points": [ + "scripts/run_isolated_tests.py", + "scripts/verify_replay_coverage.py", + "certificates/selected-result.json" + ], + "methods": [ + "Profile one isolated replay and optimize the measured bottleneck.", + "Design source-bound reuse with explicit dependency invalidation and negative controls." + ], + "acceptance_gate": "Report before/after wall time on the same fixture, retained checks and invalidation behavior.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read the selected reproduction command and choose a single replay stage for profiling.", + "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay." + }, + "first_experiment": "Measure one unchanged fixture, preserve check coverage, and test one optimization with invalidation controls.", + "bottleneck_link": "Faster trustworthy replays increase review throughput and let mechanism candidates be checked sooner.", + "allowed_variations": [ + "Profile one stage or design one source-bound cache boundary." + ], + "scope_change_triggers": [ + "Skipping coverage or comparing different fixtures to claim speedup." + ], + "overlap_terms": [ + "replay runtime", + "cache invalidation", + "isolated tests" + ] + }, + { + "id": "portable-replay", + "question": "Can one reproducible environment or artifact-comparison failure be repaired?", + "starting_points": [ + "research/gzip-container-reproducibility/README.md", + "docs/ci-verification.md" + ], + "methods": [ + "Reproduce one portability failure and add a minimal cross-environment fix.", + "Audit one canonical-payload comparison for omitted proof-relevant fields." + ], + "acceptance_gate": "Preserve immutable source hashes and proof-relevant content; a different compressed byte stream alone is not a mathematical mismatch.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read the gzip-container reproducibility examples and distinguish frozen source bytes from regenerated payloads.", + "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay." + }, + "first_experiment": "Reproduce one specific mismatch or audit one canonical comparison for omitted proof-relevant fields.", + "bottleneck_link": "Portable exact checks prevent environment failures from blocking valid contributions.", + "allowed_variations": [ + "One interpreter/version mismatch or one payload field comparison." + ], + "scope_change_triggers": [ + "Removing immutable-source pins because generated compressed bytes differ." + ], + "overlap_terms": [ + "gzip container", + "reproducibility", + "canonical payload" + ] + } + ] + }, + { + "id": "consolidation", + "weight": 5, + "tasks": [ + { + "id": "overlap-receipt", + "question": "What exact content and credit of a small named PR set has already been retained?", + "starting_points": [ + "docs/research/pr-ledger.md", + "CONTRIBUTORS.md" + ], + "methods": [ + "Compare exact heads and retained artifacts to write a source-bound disposition receipt.", + "Audit an existing receipt for missing content or predecessor attribution." + ], + "acceptance_gate": "Separate complete integration, partial retention and changed heads; make no autonomous closures.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read one small PR set in the ledger and identify exact reviewed heads and unresolved content.", + "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay." + }, + "first_experiment": "Compare that set to retained artifacts; produce a complete or explicitly partial disposition receipt.", + "bottleneck_link": "Reliable overlap evidence preserves credit and prevents repeated review of already-retained material.", + "allowed_variations": [ + "One small related PR family or one existing integration receipt." + ], + "scope_change_triggers": [ + "Treating matching titles or one shared blob as proof of full incorporation." + ], + "overlap_terms": [ + "overlap receipt", + "partial integration", + "attribution" + ] + }, + { + "id": "scope-navigation", + "question": "Can one misleading historical-current claim or missing research cross-reference be corrected?", + "starting_points": [ + "docs/research/current-status.md", + "docs/research/pr-ledger.md", + "certificates/selected-result.json" + ], + "methods": [ + "Trace one confusing path from onboarding to its authoritative source.", + "Index one tightly related family of obstructions with explicit excluded and open hypotheses." + ], + "acceptance_gate": "Produce evidence-backed navigation, preserve historical records and avoid a duplicate global survey.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Follow one link from the selected record to its review and compare a potentially stale historical claim.", + "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay." + }, + "first_experiment": "Repair one confusing path or produce a scoped map of one related obstruction family.", + "bottleneck_link": "Clear navigation lowers entry cost for central research; a global survey without a concrete fix is not required.", + "allowed_variations": [ + "One historical-current ambiguity or one bounded family index." + ], + "scope_change_triggers": [ + "Rewriting frozen scientific packages just to change their historical wording." + ], + "overlap_terms": [ + "current status", + "historical checkpoint", + "scope navigation" + ] + } + ] + }, + { + "id": "incumbent-optimization", + "weight": 2, + "tasks": [ + { + "id": "selected-packing", + "question": "Does a named residual packing task have meaningful uncovered headroom after its exact fixed-inventory ceiling?", + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/staged-fourth-mixture-ceiling/README.md", + "research/staged544-mixed-fourth-entry/README.md" + ], + "methods": [ + "Check a fixed-inventory ceiling and source equivalence before any explicitly bounded residual search.", + "Price a genuinely changed word/interface under a newly applicable model." + ], + "acceptance_gate": "Check live overlap and exact model/source binding first. Distinguish a chronological construction from a pooled optimum. State the applicable fixed-inventory ceiling and remaining headroom; changed words or interfaces require a new fully charged model. Do not launch a residual search without an explicit scope and time cap.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read #4091 fixed-word pooled ceiling and #4088 later 1090-call literal fill. Bind the unchanged local invoices/capacities/stock before transferring the ceiling; its earlier 1080-call residual-bin recipe is historical.", + "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately." + }, + "first_experiment": "Default to a bounded headroom/source-equivalence check. Only start residual search with an explicit unclaimed domain, time cap and reason the tiny remaining gain matters. Otherwise hand off or select a changed-word mechanism. A changed word or interface needs a fresh cost model, not the old ceiling. Stop at the fixed-inventory cap; do not extend by new random seeds.", + "bottleneck_link": "An actual paid-profile gain can improve the frontier up to the other supplier cap.", + "allowed_variations": [ + "One bounded residual packing instance or exact relaxation.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "scope_change_triggers": [ + "Rerunning an existing search with only a different seed as a separate mathematical contribution." + ], + "overlap_terms": [ + "T16", + "owner exchange", + "packing", + "4091", + "4088", + "staged-fourth-mixture-ceiling", + "staged544-mixed-fourth-entry" + ], + "existing_checks": [ + { + "scope": "PR #4091: pooled optimum at one-third staging for pinned fixed words; not a chronological fill.", + "evidence": "research/staged-fourth-mixture-ceiling/README.md", + "remaining": "Independent scope/source check; any residual optimization is explicitly bounded and optional.", + "status": "author-checked", + "source_commit": "a29bdd8f56cd18b805917775cdec09ff935eddc4", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4088: later 1090-call literal fill improves the earlier 1080-call witness.", + "evidence": "research/staged544-mixed-fourth-entry/README.md", + "remaining": "Complete admission remains separate; old residual-bin instructions must not be copied blindly.", + "status": "author-checked", + "source_commit": "72d7efc181edb21806a878f174847c96dd410ab0", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + }, + { + "id": "scalar-to-moment", + "question": "Can a changed frame itinerary remove a paid transition beyond the already covered scalar A2 contractions?", + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/staged544-a2-graph-rewrite/README.md", + "research/staged544-separated-a2/README.md", + "research/staged544-a2-composition-audit/README.md", + "research/staged544-a1858-contraction-audit/README.md" + ], + "methods": [ + "Derive the changed legal frame itinerary and exact child histogram.", + "Prove a scoped obstruction showing why that scalar gain cannot change the paid contract." + ], + "acceptance_gate": "An unchanged histogram is not a kappa gain; record any separate runtime or proof benefit explicitly.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read the A2 and separated-A2 constructions and their composition/contraction audits. Scalar contractions can preserve the complete recursive histogram; fewer ADDs alone do not justify further scans.", + "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately." + }, + "first_experiment": "Identify an actual paid transition to remove and construct a legal replacement frame itinerary, charging restoration, source windows and changed helpers. Compare complete before/after histograms. Stop if only scalar count changes; report that benefit honestly, without expanding the same scalar-only census.", + "bottleneck_link": "A legal change to the histogram, not addition count alone, is the bridge to an exponent gain.", + "allowed_variations": [ + "One existing scalar simplification and one proposed frame-path change." + ], + "scope_change_triggers": [ + "Submitting only another scalar count as completion of a paid-profile task." + ], + "overlap_terms": [ + "scalar simplification", + "paid profile", + "R439", + "3998", + "4019", + "4112", + "4152", + "staged544-a2-graph-rewrite", + "staged544-separated-a2", + "staged544-a2-composition-audit", + "staged544-a1858-contraction-audit" + ], + "existing_checks": [ + { + "scope": "PR #3998: consecutive A2 scalar contraction", + "evidence": "research/staged544-a2-graph-rewrite/README.md", + "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.", + "status": "author-checked", + "source_commit": "389268a6b5e0373a3125d5c6fcd6995f4ea324f5", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4019: separated A2 sites with unchanged recursive histogram", + "evidence": "research/staged544-separated-a2/README.md", + "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.", + "status": "author-checked", + "source_commit": "f408e09df300b575235f7f77f81948071397e16d", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4112: composition audit", + "evidence": "research/staged544-a2-composition-audit/README.md", + "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.", + "status": "author-checked", + "source_commit": "205b7380656ba4b6316a8a493b1a3c679b8f7a0e", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4152: A1858 contraction audit", + "evidence": "research/staged544-a1858-contraction-audit/README.md", + "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.", + "status": "author-checked", + "source_commit": "caaa14cde5962adc372fdca71f63d0f29e73c8b2", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + } + ] + } + ], + "selection_context": { + "refreshed_on": "2026-10-22", + "kappa": "60403/20000000", + "source_pr": 4470, + "record": "certificates/selected-result.json", + "review": "docs/research/pr-intake-evidence/pr4470/PROOF-REVIEW.md", + "orientation_command": "python3 -B scripts/research_selected_baseline.py", + "scope": "Metadata refresh only. Revision-7 weights and cards remain historical suggestions pending separate strategic reassessment; check current contracts and overlap before adopting them." + } +} diff --git a/research/coupled-provider-independent-audit/custody/5402/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/coded-native-caller/NORMALIZERS.json b/research/coupled-provider-independent-audit/custody/5402/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/coded-native-caller/NORMALIZERS.json new file mode 100644 index 0000000000..bca92c222c --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5402/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/coded-native-caller/NORMALIZERS.json @@ -0,0 +1,126 @@ +{ + "clifford_sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962", + "code_sha256": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0", + "finite_checks": 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+ ], + "recoding_bill": {"forward_prefix_component_l1_upper":57,"forward_update_coefficient":"-1/4","inverse_output_prefix_component_l1_upper":"69/13","inverse_prefix_component_l1_upper":56,"inverse_update_coefficient":"-1/52","monomial_field_maps":224,"output_scaled_adds":448,"owned_fields":8,"owned_initial_clears":8,"owned_terminal_clears":8,"signed_mode_adds":448}, + "schema": "coded-native-real-normalizers/1", + "scope": "Exact physical central ABI and local gauges; not full-controller or multiplication admission.", + "source_payload_sha256": "cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd", + "status": "PASS_CODED_NATIVE_REAL_NORMALIZERS" +} diff --git a/research/coupled-provider-independent-audit/custody/5402/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/coded-native-caller/PHYSICAL.md b/research/coupled-provider-independent-audit/custody/5402/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/coded-native-caller/PHYSICAL.md new file mode 100644 index 0000000000..da8837ba67 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5402/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/coded-native-caller/PHYSICAL.md @@ -0,0 +1,71 @@ +# Real physical normalizers for the coded producer + +This is local constructive research on canonical/pr4929, not a completed supplier or exponent claim. Source code and Gaussian conventions retain the original authors' credit. + +Let n=9 and let q be any of the source's 112 port vectors (weight 3 or 7). Let e0=1. Construct an orthogonal binary matrix G taking e0 to q. If q_0=0, use the orthogonal transvection T_(e0+q). If q_0=1, select j>0 with q_j=0 and use T_(ej+q) T_(e0+ej). Here T_v(x)=x+(v dot x)v; both v have even weight, hence T_v is orthogonal. Such j exists because q is not the all-ones vector. + +For row j of G put z_j=(wt(row_j G)-1)/2 modulo 2. Define K=Z_z P_G. It is a real signed permutation. The full Gaussian R has entries alpha*(-i)^wt(x+y), with alpha=(1+i)^9/2^9. Orthogonality gives + +wt(G^-1 d)-wt(d) = 2 z dot d (mod 4). + +Indeed the degree-two coefficients vanish modulo four because distinct columns of G^-1 have even dot product; the linear coefficient is the weight of that column minus one. Therefore K R K^-1=R exactly, including absolute phase. K also maps the central line to span(q), and its orthogonal complement to q-perp, at the canonical-frame Lagrangian level. All these statements tensor to every positive digit-column count. + +Let Q be the central C gate, D the product of the other eight C gates, so R=DQ. Let E_i and S_i be the actual retained entrance-line and exit-hyperplane frame operators. With the operator convention that rightmost applies first, use + +input X: E_i K_i Q^-1 +input Y: K_i +output X: K_i^-1 +output Y: D K_i^-1 S_i^-1. + +All four wrappers are monomial. Their Lagrangian incidences prove this for every port, and the scratch verifier checks exact tableaus and absolute phases at every one of the 112 source ports. With A from PR4929, define C_ij= A_ij K_i^-1 K_j. Then the full main endpoint is + +F = diag(D,D) [[I,0],[C Q^-1,I]]. + +C is a physically implementable fixed owner recoding: apply K_i to each owner, apply A among the owners at common physical coordinates, and apply K_i^-1. Its inverse uses A^-1=(A+12I)/13. Since each K_i is real orthogonal and A is real symmetric, C^T=C. Since K_i commutes with R, C commutes with R. The polynomial C^2+12C-13I=0 follows by similarity. The 408 independent helper jobs and every paid Gaussian child are unchanged. + +For the actual raw inverse transpose, F^-T=diag(D^-1,D^-1) [[I,-Q^-1 C],[0,I]], since Q,D are symmetric. Multiply both outputs by D^2, then conjugate the physical X bank by Q^2 (input Q^-2 and output Q^2). These are explicit monomial powers. The result is + +B = diag(D,D) [[I,-Q C],[0,I]]. + +The old source convention using Y-only Q^2 conjugation cannot simply be copied for noncommuting C. The X-only convention above is exact. + +For a prior code B0 commuting with the current D, set G(B0)=diag(B0,Q^-1 B0 Q). The following two constructive local identities hold without requiring C and Q to commute: + +(post X C) F (pre Y C) = G(C B0) F_standard G(B0)^-1, +(post X C^-1) B (pre Y C^-1) = G(C^-1 B0) B_standard G(B0)^-1. + +They use [C,DQ]=0 and [B0,D]=0. Every additional operation on the left is physically cheap fixed recoding. For disjoint fresh blocks, codes from earlier stages commute with the current D. These identities do not yet settle interstage ADD/IDLE compatibility, terminal gauges, productive jobs, or the complete moment. + +## Literal recoding and complete local bill + +The source code has an exact factorization A=I-MM^T/4 with M a 112-by-8 matrix having entries 0,+1,-1 and M^T M=56I. Each mode column has 56 nonzero entries, and each owner row has four. The mode columns are emitted in NORMALIZERS.json and all 12,544 entries are checked against the pinned CODE.json. This factorization is used here as a constructive scalar program, without relying on any common physical address chart for separate Gaussian mode transformations. + +To execute A on arbitrary independent owner fields x, allocate eight owned zero fields t. Compute t=M^T x with 448 signed ADDs; update x-=M t/4 with 448 scaled ADDs; clear the eight owned temporaries. Reading x is finished before any x is updated. Hence no input field is overwritten before its last source read. For A^-1 use the same program with coefficient -1/52, since A^-1=I-MM^T/52. Both are exact rational linear programs. The helper fields of the native producer are never used as scratch, copied as free credit, or erased. + +Conjugating this scalar program by the 112 K_i and their inverses implements C or C^-1. This pays 224 monomial field maps, 896 scalar ADDs and 16 owned CLEARs per recoding, with eight owned fields reusable sequentially. The two additional recodings in either local gauge identity therefore cost at most 448 monomial maps, 1,792 scalar ADDs and 32 CLEARs, with no recursive Gaussian child. The four actual port normalizers contribute 448 monomial maps per native invocation. The displayed backward conversion contributes at most 448 further monomial maps (112 input X powers, 112 output X powers and 224 output D-squares); fusing maps can reduce this upper bound but is not assumed. + +These are field-level operation counts. A lifted K_i is an explicit binary map on nine f-bit address blocks together with signs given by block parity. Its constants, indexed movement and phase passes use the retained native monomial implementation. It is therefore a fixed finite O(V polylog p) nonrecursive operation under that caller's precision/address ABI, not a zero-work instruction. Each fixed rational ADD is likewise charged at its actual scalar precision. In particular the inverse denominator 52 must be implemented and rounded; no free exact real-division oracle is assumed. This lemma makes no independent TM tariff or outer-budget claim. + +The maximum exact component-l1 prefix bound for the scalar A program, including its temporaries, is 57. For A^-1 it is 56 (the output-only bound is 69/13). Signed monomial maps preserve component magnitude. A fixed local sequence has a fixed suffix bound obtained by multiplying elementary bounds 1+|coefficient|; owned CLEAR has bound one. This gives a finite bound for local rounding propagation. The number of local uses, compiler precision and complete outer error allocation still belong to the caller theorem. + +The normalized producer still has its exact PR4929 paid profile + + {1:2201, 2:412, 3:510, 4:127, 5:40} + +and independent helper profile + + {4:28, 7:7, 8:47, 9:326}. + +No productive main ranks are asserted merely from the coupled central ABI. Those depend on the completed caller, its initial/final gauges and every paid correction. + +## Universal scope and reproducible evidence + +PR4929 supplies the arbitrary-input logical identity over Q[FreeGroup72] for its emitted center-free word with ground-chart helper pre-compensation. Its normalized main endpoint is L(A), its raw dual is L(A)^-T, and every one of the 408 helper endpoints is autonomous. This proof is an inherited premise with exact source pins, not a consequence of this normalizer checker. The present wrappers and owner recodings act exclusively on the 224 main fields; new scratch is explicitly owned. Thus the helper block remains autonomous and its independent inputs, requested transforms and paid profile remain unchanged. + +For every f>=1, assign the shared native letters their actual consistent invertible lifted operators. Evaluation of the source free-group algebra is a homomorphism and gives the source logical identity. Independently lift each K_i as its f-fold tensor product, retaining spectator coordinates; its signed-permutation word, the two direct frame identities and its commutation with R lift by operator composition. In every compiled monomial word, P and X act columnwise on the f-bit blocks, D sums its Z4 polynomial over the f columns, and a one-column scalar phase i^gamma becomes i^(f*gamma). Reusing the one-column global phase unchanged would be incorrect. Finally form the owner matrix C_f with entries A_ij K_i,f^-1 K_j,f. One does not tensor the whole 224-by-224 owner matrix and does not assert that tensor powers preserve sums. Instead the finite scalar owner program is evaluated directly in the algebra of these lifted address operators. This proves the central ABI and local gauge identities at every positive width. + +Run `python3 -I -B research/coded-native-caller/normalizers.py` or its optimized `-O` form. The checker authenticates the decompressed actual native payload, CODE.json and retained Clifford source before executing the latter. It verifies all 112 real signed normalizers, 57,344 explicit weight-congruence addresses, 896 forward/backward monomial wrappers and eight exact frame/block identities per port, including absolute phase. Each emitted wrapper is separately lowered to a literal P/D/X/phase-only word and checked against its defining expression by exact tableau and absolute-phase state. No C gate remains in an emitted wrapper. The independent incoming-column and outgoing-row identities imply all 5,824 nonzero off-diagonal code blocks, without sampling those pairs. It also executes the eight-mode recoding on all 112 arbitrary-input basis columns in both directions. Omitting the essential signed phase is rejected at every affected port. The default command compares a regenerated mathematical receipt and performs no writes; `--write` is the explicit authoring path. + +Source pins: canonical main 624de9dc66858af0945e5f8a0942488d62280d43, `research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz`, decompressed SHA-256 cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd; PR4929 head 361f5d4100640177d6a983dd2f336021c75bfd5e, `research/native-center-free-code/CODE.json`, SHA-256 8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0; canonical `research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py`, SHA-256 2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962. Gzip container bytes are not substituted for decompressed source identity. + +Credit Dugongue's PR4929 for the coded producer and stable code; Cinna Davis's PR4694/4698 and the original cache/helper construction; Cao Yifan's PR4610 native word; the retained zxv, Jacob Alan Sussman, Cinna Davis and Clifford/native/compiler lineage. The exact canonical-frame implementation and phase conventions are retained source material. The constructive real centralizing normalizers, their explicit lifted words, X-only raw-dual convention and costed local code gauges are the additions here. New work is Apache-2.0 and has substantial OpenAI Codex assistance; no formal-kernel or independent human acceptance is asserted. diff --git a/research/coupled-provider-independent-audit/custody/5402/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/coded-native-caller/clifford_exact.py b/research/coupled-provider-independent-audit/custody/5402/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/coded-native-caller/clifford_exact.py new file mode 100644 index 0000000000..166841a037 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5402/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/coded-native-caller/clifford_exact.py @@ -0,0 +1,149 @@ +"""Small exact Gaussian-dyadic Clifford compiler, independent of gx internals. +Paulis use i^p X^x Z^z. State vectors use integer Gaussian numerators / 2^d. +The tableau is supplemented by a literal circuit, so global phases are kept. +""" +from dataclasses import dataclass + +def parity(x):return x.bit_count()&1 +def rank(rows): + p={} + for x in rows: + while x: + b=x.bit_length()-1 + if b not in p:p[b]=x;break + x^=p[b] + return len(p) +def transpose(rows,n):return tuple(sum(((rows[j]>>i)&1)<>j&1);a[j],a[k]=a[k],a[j] + for i in range(n): + if i!=j and a[i]>>j&1:a[i]^=a[j] + assert [r&((1<>n for r in a) +def basis_extend(cols,n): + out=[] + for x in list(cols)+[1<len(out):out.append(x) + assert len(out)==n + return tuple(out) +def nullspace(rows,n): + a=list(rows);p=[];k=0 + for j in range(n): + t=next((i for i in range(k,len(a)) if a[i]>>j&1),None) + if t is None:continue + a[t],a[k]=a[k],a[t] + for i in range(len(a)): + if i!=k and a[i]>>j&1:a[i]^=a[k] + p.append(j);k+=1 + return tuple((1<>j)&1)<>i&1:out=pmul(out,T[i]) + for i in range(n): + if z>>i&1:out=pmul(out,T[n+i]) + return out +def compose(A,B):return tuple(apply(A,p) for p in B) +def inverse(T): + n=len(T)//2;cols=[x|(z<>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4)) + return tuple(out) +def qvalue(Q,alpha,x,n): + return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4 +def mul_i(a,p): + x,y=a;p%=4 + return [(x,y),(-y,x),(-x,-y),(y,-x)][p] +@dataclass +class Op: + n:int + tab:tuple + circuit:list + def then(self,b): + assert self.n==b.n + return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit) + def adjoint(self): + circ=[] + for e in reversed(self.circuit): + if e[0]=='P':circ.append(('P',inv(e[1],self.n))) + elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2]))) + elif e[0]=='C':circ.append(('C',e[1],-e[2])) + elif e[0]=='phase':circ.append(('phase',(-e[1])%4)) + else:circ.append(e) + return Op(self.n,inverse(self.tab),circ) + def zero_state(self,basis=0): + N=1<>i)&1 for i in range(n)) + assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n)) + return Op(n,tuple([(1<>i&1 else 0,1<>i&1 else 0) for i in range(n)]),[('C',q,sgn)]) +def xgate(n,b):return Op(n,tuple([(1<>i)&1)) for i in range(n)]),[('X',b)]) +def fourier(n,axes=None): + out=ident(n) + for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<len(selected):picks.append(j);selected.append(x) + assert len(picks)==r and all(x>>r==0 for x in Bcols) + Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1< (X,Y+X,H)`. Physical entrance and exit charts remain exactly those of the frozen source. + +There is a completely emitted constant dyadic pre-compensation, followed by the source word with every center Gaussian operation replaced by an owned CLEAR, whose exact normalized endpoint is + +`X' = X; Y' = Y + A X; H' = H`. + +All 632 persistent inputs are arbitrary and independent; no helper is initialized, discarded, identified or counted twice. The literal backward construction has exact normalized endpoint + +`X' = X - A^T Y; Y' = Y; H' = H`, + +the raw inverse transpose of the forward endpoint. The paid profile in both directions is + +`{1:2201, 2:412, 3:510, 4:127, 5:40}`. + +The helper profile stays `{4:28,7:7,8:47,9:326}`. Relative to the source, exactly eight rank-eight children are removed and no Gaussian child is added. The pre-compensation adds 6,596 scalar ADDs with a retained scalar allowance of 32,652 primitives; all numerator magnitudes and denominators are at most 4. These finite scalar operations do not establish a better recursive exponent on their own. + +## Constructive proof + +Delete all eight center calls by replacing each with CLEAR of the owned center field in the call's destination chart. Zero has every chart, so this is a valid erasure of owned scratch, not a borrowed input overwrite. Retain every other physical instruction and every endpoint chart. + +The exact sparse replay over the rational free group algebra on the 72 native symbols gives + +`M_0 = I + S + E_X + E_H`. + +Here S is the original transfer X to Y. Both error blocks land only in Y. E_X reads X; E_H reads only 106 particular helpers, each with a ground entrance and full-frame exit. Every helper and every X output remains autonomous. All error terms have EMPTY native word: the errors are ordinary constant dyadic matrices, not uncomputed address-operator oracles. The 12,532 nonzero entries split into 5,936 in E_X and 6,596 in E_H. + +Every pairwise product of S, E_X and E_H is zero, because all three maps land in Y and none reads Y. Before executing the center-cleared word, apply `I-E_H`. Every required source and target is in the actual ground chart: the targets are Y and the sources are those 106 ground-ended helpers. The operation is the explicit list of 6,596 dyadic ADDs. + +Consequently + +`M_0 (I-E_H) = I+S+E_X`. + +Thus `A=I+E_X` on the 112 main port indices gives the claimed offer, with no helper contamination. Scalar operations in one common address chart have their exact owner-space action, so this is a physical fixed-template pre-compensation and not an abstract change of logical coordinates. + +For the backward direction, the separately emitted center-cleared source word is verified to equal `I-S^T-E_X^T-E_H^T`, with the source's distinct inverse-transpose native letters. Prepend `I+E_H^T`, again using only actual ground-chart fields. The product is `I-S^T-E_X^T`. The verifier compares all 632 independent rows in both orientations. The owned center field is empty at termination. + +## Explicit code, inverse and conditioning + +The same exact entries satisfy + +`E_X^T = E_X, E_X^2 = -14 E_X, tr(E_X) = -112`. + +Set `P=-E_X/14`. It is a real symmetric idempotent of trace 8, hence an orthogonal projection of rank 8. Therefore + +`A=I-14P`, + +with eigenvalue -13 on the eight-dimensional image of P and eigenvalue +1 on its 104-dimensional kernel. In particular + +`A^-1 = I + E_X/13`, + +and its Euclidean condition number is exactly 13. The complete main shear is I+N_A with N_A^2=0 and ||N_A||_2=13; both it and its inverse have norm at most 14, so its condition number is at most 196. Helpers are an independent identity block, and the physical boundary charts are unitary, so this same bound applies to the complete physical coded offer. Its inverse uses I-N_A and needs no 1/13 arithmetic; 1/13 appears only when separately inverting the main code A. Every diagonal entry of A is zero; its 5,824 nonzero off-diagonal entries are ±1/2. The exact checker verifies the degree-two polynomial entry by entry over rational arithmetic, so the spectrum and inverse are universal consequences of that identity rather than numerical eigenvalue observations. + +The coefficient 1/13 is part of the mathematical inverse formula. This deliverable does not call it a free dyadic SCALE, assume a division oracle, or insert A^-1 across different physical address charts without paying for the resulting adapters. + +## Arbitrary fiber widths + +The replay identities hold over Q[FreeGroup72]. Every consistently shared invertible assignment of the 72 native operators defines an evaluation homomorphism. Hence the logical word identity holds at every positive column multiplicity under the retained source native implementation. It does not rely on one-column matrix testing, erasure of central phases or tensor powers preserving sums. + +Every physical frame, native monomial and Gaussian child is retained from the authenticated source, except the eight deleted owned-center calls. The new instructions are only constant dyadic scalar operations at an explicitly common ground chart. No fresh nonmonomial address implementation is introduced. + +The exact observed maximum prefix coefficient ℓ1 norms are 457 forward and 258 backward, checked on the fixed free-symbol words. Unitary evaluation bounds intermediate exact states and perturbations at the initial input in the maximum-over-fields Euclidean fiber norm by fixed constants independent of fiber width. For discrepancies inserted at later sites, use a separate suffix bound: assign each scalar ADD or SCALE of coefficient c the bound 1+|c|, and every unitary Gaussian/monomial, owned CLEAR or owned COPY the bound 1. The product of these elementary bounds over the finite word bounds every suffix. Thus the sum of local error magnitudes times this fixed product bounds propagated rounding error; no prefix norm is substituted for a suffix norm. Entrywise infinity-norm statements require the appropriate square-root fiber-volume conversion. There is no precision-dependent epsilon and no recursive border-precision claim. + +## Integration boundary + +The old source wrapper's port-dependent entrance lines and exit hyperplanes remain. A is a constant matrix in the stated normalized logical coordinates. It must not be silently treated as a constant free recoding in every physical main chart or in a different standardized central-Q ABI. Its nonzero off-diagonal entries connect distinct entrance-line charts. A useful next step is an actual coded caller or a paid simultaneous adapter that exploits the eight-mode structure, together with complete moment, raw-dual, compiler, finite precision and outer recovery budgets. This document supplies the exact producer and its bill, not those missing consumers. + +## Predecessor overlap and credit + +Cinna Davis's PR #4694, head `2add42d1edf14a263abe90a3bcde67fc1ba30768`, already emits a center-free kernel with paid profile minus eight rank-eight calls, records its coupled cache ABI, constructs its raw dual, and proves that its 106 observed helpers start at the empty chart. The source CACHE.md was read directly. None of center deletion, the cold-helper observation or the abstract block Schur elimination is claimed here as new. PR #4698, scientific head `9079ab66ba9a1717df478a08eb957c20d84d3e61`, already emits a dyadic helper basis of 379 gates in each direction reducing observations to eight helpers, and a conditional consumer. The present deliberately dense 6,596-ADD pre-compensation is easier to audit, not a claim to a better basis count. Its changed sufficient result is the actual fixed-template helper-independent coded offer, explicit A entries, exact eight-mode spectrum/inverse/conditioning, and unchanged independent helper ABI. + + +Cao Yifan / intqwq supplies the joint-helper/native-map round-three word at canonical `research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz`, commit `624de9dc66858af0945e5f8a0942488d62280d43`. Its predecessor and refreshed public lineage includes PR #4610; the exact source package and bytes, rather than an older PR headline, bind this result. Cinna Davis, the PR #4470 native/helper/controller lineage, Dugongue's exact native and complementary-provider work, DaysSky, Nick Petalas, Ryanson Jonathan, Jacob Alan Sussman, zxv and the retained scalar, Clifford, precision, compiler and outer contributors retain predecessor credit. The common-chart pre-compensation and exact eight-mode code are the present construction. Local MathProof's Schur block elimination and low-rank composition notes motivated the representation; their source-only inspection is not a fresh Lean/kernel audit or a claim of priority for elementary projection algebra. diff --git a/research/coupled-provider-independent-audit/custody/5402/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/native-center-free-code/SOURCE-WORD.json.gz b/research/coupled-provider-independent-audit/custody/5402/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/native-center-free-code/SOURCE-WORD.json.gz new file mode 100644 index 0000000000..46d929df83 Binary files /dev/null and b/research/coupled-provider-independent-audit/custody/5402/provenance-sources/1ec1119972c9aefe42525172d07b332fcff81cb4/research/native-center-free-code/SOURCE-WORD.json.gz differ diff --git a/research/coupled-provider-independent-audit/custody/5402/registered-driver/152eea4bb046c082e37e916d717d1d0d7f035f88.tree b/research/coupled-provider-independent-audit/custody/5402/registered-driver/152eea4bb046c082e37e916d717d1d0d7f035f88.tree new file mode 100644 index 0000000000..9e75613b17 Binary files /dev/null and b/research/coupled-provider-independent-audit/custody/5402/registered-driver/152eea4bb046c082e37e916d717d1d0d7f035f88.tree differ diff --git a/research/coupled-provider-independent-audit/custody/5402/registered-driver/3348fccea855082786d5f0fc5558b73d4974e745.commit b/research/coupled-provider-independent-audit/custody/5402/registered-driver/3348fccea855082786d5f0fc5558b73d4974e745.commit new file mode 100644 index 0000000000..075b56d7c9 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5402/registered-driver/3348fccea855082786d5f0fc5558b73d4974e745.commit @@ -0,0 +1,6 @@ +tree 152eea4bb046c082e37e916d717d1d0d7f035f88 +parent 1ec1119972c9aefe42525172d07b332fcff81cb4 +author Dillon Amburgey 1792794639 -0400 +committer Dillon Amburgey 1792794639 -0400 + +Retain all native inputs in an eight-mode coupled helper provider diff --git a/research/coupled-provider-independent-audit/custody/5402/registered-driver/681ae2e88caef63561bee40bc1a6916cba335f0b.tree b/research/coupled-provider-independent-audit/custody/5402/registered-driver/681ae2e88caef63561bee40bc1a6916cba335f0b.tree new file mode 100644 index 0000000000..a915e93d59 Binary files /dev/null and b/research/coupled-provider-independent-audit/custody/5402/registered-driver/681ae2e88caef63561bee40bc1a6916cba335f0b.tree differ diff --git a/research/coupled-provider-independent-audit/custody/5402/registered-driver/research_package.py b/research/coupled-provider-independent-audit/custody/5402/registered-driver/research_package.py new file mode 100644 index 0000000000..ef9b52c392 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5402/registered-driver/research_package.py @@ -0,0 +1,1022 @@ +#!/usr/bin/env python3 +"""Validate and replay explicitly registered research packages, never every verify.py. + +Douglas Colkitt, with OpenAI Codex assistance. Apache-2.0. +""" +import argparse +import errno +from contextlib import closing, contextmanager +from itertools import chain +import hashlib +import importlib.metadata +import json +import os +from pathlib import Path, PurePosixPath +import re +import signal +import stat +import subprocess +import sys +import tempfile +import threading + +ROOT = Path(__file__).resolve().parents[1] +GIT_BLOB_RESPONSE_TIMEOUT = 90 + + +def require(ok, message): + if not ok: + raise ValueError(message) + + +def canonical_relative_path(name): + # Git's changed paths use one repository-relative POSIX spelling. Accepting + # aliases here would let a declared input evade the planner's exact match. + require(isinstance(name, str), "canonical relative path must be a string") + path = PurePosixPath(name) + require(bool(path.parts) and not path.is_absolute() and ".." not in path.parts + and "\\" not in name and path.as_posix() == name, + "use a canonical repository-relative POSIX path: " + name) + return path + + +def symlink_free_relative_path(root, name): + """Reject symlink components without requiring a deleted input to exist. + + Git reports changes under the target's path, not a symlink alias declared + by its consumer. Inspect existing components below the repository root; + the checkout must remain stable during planning, validation and replay. + """ + parts = canonical_relative_path(name).parts + current = root + for part in parts: + current = current / part + try: + mode = current.lstat().st_mode + except (FileNotFoundError, NotADirectoryError): + break + require(not stat.S_ISLNK(mode), "symlink in repository-relative path: " + name) + return root / name + + +def relative_file(root, name): + result = symlink_free_relative_path(root, name) + require(result.resolve().is_relative_to(root.resolve()) and result.is_file(), + "missing or external file: " + name) + return result + + +# Adapted from the package-local policy in +# research/t74-2530-source-partner-audit/audit_common.py (Apache-2.0). +# Keep repository configuration and linked-worktree .git discovery intact; +# inherited shell overrides must not choose a different repository or index. +_GIT_REDIRECT_VARS = frozenset(( + "GIT_DIR", "GIT_WORK_TREE", "GIT_INDEX_FILE", "GIT_OBJECT_DIRECTORY", + "GIT_ALTERNATE_OBJECT_DIRECTORIES", "GIT_NAMESPACE", "GIT_CEILING_DIRECTORIES", + "GIT_COMMON_DIR", "GIT_CONFIG_PARAMETERS", "GIT_CONFIG_COUNT", +)) +_GIT_CONFIG_PREFIXES = ("GIT_CONFIG_KEY_", "GIT_CONFIG_VALUE_") + + +def git_source_env(): + """Use cwd's repository and stored objects, without changing the parent. + + Git can ignore cwd when inherited selection variables point elsewhere. + Config-injection variables can also redirect worktree/index operations. + This policy is only for Git metadata/source subprocesses, not verifiers. + """ + env = {name: value for name, value in os.environ.items() + if name not in _GIT_REDIRECT_VARS and not name.startswith(_GIT_CONFIG_PREFIXES)} + # Replacement refs can report an original ID while returning other bytes. + env["GIT_NO_REPLACE_OBJECTS"] = "1" + return env + + +def git(root, *args): + return subprocess.run(["git", *args], cwd=root, env=git_source_env(), + capture_output=True, check=True).stdout + + +def tracked_input_paths(root): + """Use HEAD spelling, never case folding, filesystem resolution or the index. + + Staged/untracked files are not replay inputs until committed. NUL framing + preserves Git filenames containing whitespace, including CR and LF. + """ + raw = subprocess.run( + ["git", "ls-tree", "-r", "--name-only", "-z", "HEAD"], cwd=root, env=git_source_env(), + capture_output=True, check=True, timeout=30).stdout + return frozenset(name.decode("utf-8") for name in raw.split(b"\0") if name) + + +def require_tracked_input(name, paths): + canonical_relative_path(name) + require(name in paths, "use an exact Git-tracked input path from HEAD: " + name) + + +def git_source_rows(root, base, names): + """Read one pinned object at a time through one Git process; no persistent cache. + + Each request is consumed before the next is sent. This avoids pipe deadlocks + and retains the old one-blob memory bound, even for large source archives. + Newline paths and non-blob objects retain the legacy Git-show semantics. + The caller must close this generator if source validation fails mid-stream. + """ + with subprocess.Popen(["git", "cat-file", "--batch"], cwd=root, env=git_source_env(), + stdin=subprocess.PIPE, stdout=subprocess.PIPE, + stderr=subprocess.PIPE) as process: + try: + for name in names: + expression = base + ":" + name + if "\n" in expression or "\r" in expression: + yield git(root, "rev-parse", expression).decode().strip(), git(root, "show", expression) + continue + process.stdin.write(expression.encode("utf-8") + b"\n") + process.stdin.flush() + header = process.stdout.readline().rstrip(b"\n").split(b" ") + require(len(header) == 3 and re.fullmatch(rb"[0-9a-f]{40,64}", header[0]) + and header[2].isdigit(), "missing or invalid Git source: " + name) + size = int(header[2]) + payload = process.stdout.read(size) + require(len(payload) == size and process.stdout.read(1) == b"\n", + "truncated Git source: " + name) + if header[1] != b"blob": + payload = git(root, "show", expression) + yield header[0].decode("ascii"), payload + process.stdin.close() + code = process.wait(timeout=90) + require(code == 0, "Git source reader failed: " + process.stderr.read().decode("utf-8", errors="replace")) + finally: + if not process.stdin.closed: + process.stdin.close() + if process.poll() is None: + try: + process.wait(timeout=5) + except subprocess.TimeoutExpired: + process.kill() + process.wait() + + +class _UnsupportedNulBatch(Exception): + """Git rejected the initial NUL-mode request before yielding any source.""" + + +def _closed_stdin_error(error): + # Windows can report EINVAL instead of EPIPE when a child closes stdin. + # This classifies the pipe error only; the retry still requires exit 129. + return (isinstance(error, BrokenPipeError) + or (os.name == "nt" and error.errno == errno.EINVAL)) + + +def _stop_git_blob_process(process): + """Stop this reader's owned POSIX group even after its leader exits.""" + try: + if os.name == "posix": + # Reap an exited leader first: signaling a group containing only + # its unreaped zombie can report EPERM on macOS. A surviving + # descendant keeps the group alive after the leader is reaped. + process.poll() + os.killpg(process.pid, signal.SIGKILL) + else: + process.kill() + except ProcessLookupError: + pass + + +@contextmanager +def _git_blob_response_deadline(stop): + """Bound one response, excluding time spent by its consumer. + + On POSIX the reader owns a session: ordinary descendants retaining a pipe + are stopped with the leader. Escaped sessions and separate git() calls are + outside this contract; non-POSIX retains the direct-child deadline. + """ + expired = threading.Event() + + def terminate(): + expired.set() + stop() + + timer = threading.Timer(GIT_BLOB_RESPONSE_TIMEOUT, terminate) + timer.start() + try: + yield + finally: + timer.cancel() + timer.join() + if expired.is_set(): + raise subprocess.TimeoutExpired("git cat-file blob response", GIT_BLOB_RESPONSE_TIMEOUT) + + +def _git_blob_batch(root, specs, nul): + argv = ["git", "cat-file", "--batch"] + (["-z"] if nul else []) + # Usage diagnostics from the unsupported-option probe are expected. Avoid + # a second pipe that could block while we consume the framed stdout reply. + with subprocess.Popen(argv, cwd=root, env=git_source_env(), stdin=subprocess.PIPE, + stdout=subprocess.PIPE, stderr=subprocess.DEVNULL, + start_new_session=(os.name == "posix")) as process: + stopped = False + + def stop(): + nonlocal stopped + if not stopped: + _stop_git_blob_process(process) + stopped = True + + try: + for index, spec in enumerate(specs): + require("\0" not in spec, "invalid Git object request") + request = spec + if not nul and ("\n" in spec or "\r" in spec): + # Resolve one literal argument, never split a path into requests. + request = git(root, "rev-parse", "--verify", "--end-of-options", spec).decode("ascii").strip() + require(re.fullmatch(r"[0-9a-f]{40,64}", request), "invalid Git object ID") + with _git_blob_response_deadline(stop): + try: + process.stdin.write(request.encode("utf-8") + (b"\0" if nul else b"\n")) + process.stdin.flush() + except OSError as exc: + if not _closed_stdin_error(exc): + raise + header = b"" + else: + header = process.stdout.readline() + if nul and index == 0 and not header and process.wait(timeout=90) == 129: + raise _UnsupportedNulBatch(spec) + fields = header.rstrip(b"\n").split(b" ") + require(len(fields) == 3 and re.fullmatch(rb"[0-9a-f]{40,64}", fields[0]) + and fields[1] == b"blob" and fields[2].isdigit(), + "missing or non-blob Git source: " + spec) + size = int(fields[2]) + pinned = process.stdout.read(size) + require(len(pinned) == size and process.stdout.read(1) == b"\n", + "incomplete Git blob response: " + spec) + yield fields[0].decode("ascii"), pinned + process.stdin.close() + require(process.wait(timeout=90) == 0, "Git source reader failed") + finally: + # Terminate ordinary descendants before closing buffered pipes. This + # also covers successful leader exit and an early generator close. + if os.name == "posix": + stop() + # Option rejection can close stdin before our first write/flush. + try: + process.stdin.close() + except OSError as exc: + if not _closed_stdin_error(exc): + raise + process.stdout.close() + if process.poll() is None: + try: + process.wait(timeout=5) + except subprocess.TimeoutExpired: + process.kill() + process.wait() + + +def git_blobs(root, specs): + """Stream exact blobs, retaining the one-process NUL protocol on newer Git. + + Git without -z rejects it with usage status 129. Retry only before any + response, replaying the consumed first request through the line protocol. + The fallback resolves CR/LF paths to object IDs before requesting content. + The caller must close this iterator if validation stops before exhaustion. + """ + specs = iter(specs) + sentinel = object() + first = next(specs, sentinel) + if first is sentinel: + return + with closing(_git_blob_batch(root, chain((first,), specs), nul=True)) as rows: + try: + yield from rows + except _UnsupportedNulBatch as exc: + with closing(_git_blob_batch(root, chain((exc.args[0],), specs), nul=False)) as legacy: + yield from legacy + + +def meaningful(value): + return isinstance(value, str) and bool(value.strip()) and not re.search(r"\bTODO\b", value, re.I) + + +def brief(value): + text = json.dumps(value, ensure_ascii=True, sort_keys=True) + return text if len(text) <= 120 else text[:117] + "..." + + +def require_key(mapping, key, where, shape=None): + """Name the missing key and its expected shape instead of a bare KeyError.""" + require(isinstance(mapping, dict), + where + " must be a JSON object; found " + type(mapping).__name__ + ": " + brief(mapping)) + require(key in mapping, where + "." + key + " is missing" + + ("; expected " + shape if shape else "")) + return mapping[key] + + +def require_text(mapping, key, where, shape="a non-empty string without TODO"): + """Name the key and distinguish missing, wrong-shaped and weak values.""" + require(isinstance(mapping, dict), + where + " must be a JSON object; found " + type(mapping).__name__ + ": " + brief(mapping)) + require(key in mapping, where + "." + key + " is missing; expected " + shape) + value = mapping[key] + require(isinstance(value, str) and meaningful(value), + where + "." + key + " must be " + shape + "; found " + type(value).__name__ + ": " + brief(value)) + + +def card_differences(own, pinned): + """Name every key by which a TASK.json original_card differs from its pin.""" + if not isinstance(own, dict): + return "TASK.json original_card is " + type(own).__name__ + ", expected a JSON object" + details = [] + missing = [key for key in pinned if key not in own] + extra = [key for key in own if key not in pinned] + if missing: + details.append("missing keys: " + ", ".join(missing)) + if extra: + details.append("unexpected keys: " + ", ".join(extra)) + for key in (key for key in pinned if key in own and own[key] != pinned[key]): + details.append(key + " differs (TASK.json: " + brief(own[key]) + "; pinned: " + brief(pinned[key]) + ")") + return "; ".join(details) or "cards compare unequal without a key difference" + + +def source_pin(row, base): + """Resolve one SOURCES.json row to its exact Git object expression. + + Rows without an explicit pin keep the historical base_commit: form. + A file vendored from a pull-request head is pinned exactly with + head:<40-hex sha>:, so its bytes resolve at that commit, not at the + package base. An explicit but unparseable pin fails closed. + """ + name = row["path"] + pin = row.get("pin") + if pin is None: + return base + ":" + name + if pin == "base_commit:" + name: + return base + ":" + name + # Git filenames can contain LF; it is part of the exact path, not a delimiter. + match = re.fullmatch(r"head:([0-9a-f]{40}):(.+)", pin, re.DOTALL) if isinstance(pin, str) else None + if match is not None and match.group(2) == name: + return match.group(1) + ":" + name + raise ValueError("SOURCES.json pin for " + name + " is not a supported pin form: " + brief(pin) + + "; accepted pin forms are base_commit: and head:<40-hex sha>:") + + +def validate(root, package, check_pins=True): + parts = PurePosixPath(package).parts + require(len(parts) == 2 and parts[0] == "research" and re.fullmatch(r"[a-z0-9][a-z0-9-]*", parts[1]), + "package must be research/") + data = {} + for name in ("TASK.json", "SOURCES.json", "VERIFY.json"): + data[name] = json.loads(relative_file(root, package + "/" + name).read_text(encoding="utf-8")) + version = require_key(data[name], "schema_version", name) + require(version == 1, name + ".schema_version must be 1; found " + brief(version)) + task, sources, manifest = (data[n] for n in ("TASK.json", "SOURCES.json", "VERIFY.json")) + scope_status = require_key(task, "scope_status", "TASK.json", "unchanged, refined or changed") + require(scope_status in ("unchanged", "refined", "changed"), + "TASK.json.scope_status must be unchanged, refined or changed; found " + brief(scope_status)) + for field in ("actual_scope", "bottleneck_link", "stop_rule", "evidence", "author", "ai_assistance"): + require_text(task, field, "TASK.json") + if scope_status == "unchanged": + question = require_key(require_key(task, "original_card", "TASK.json", + "the pinned catalogue card object"), + "question", "TASK.json.original_card") + require(task["actual_scope"] == question, + "different wording/scope requires refined or changed plus a reason" + + " (TASK.json.actual_scope " + brief(task["actual_scope"]) + + " differs from TASK.json.original_card.question " + brief(question) + ")") + else: + require_text(task, "scope_change_reason", "TASK.json", + "a non-empty string without TODO explaining the scope refinement/change") + outcome = require_key(task, "outcome", "TASK.json", + "partial, completed, blocked or negative-result") + require(outcome in ("partial", "completed", "blocked", "negative-result"), + "TASK.json.outcome must be partial, completed, blocked or negative-result; found " + brief(outcome)) + questions = task.get("open_questions") + require(isinstance(questions, list), + "TASK.json.open_questions must be a list; found " + type(questions).__name__ + ": " + brief(questions)) + if not questions: + require_text(task, "no_open_questions_reason", "TASK.json", + "a non-empty string without TODO explaining an empty next-question list") + for position, question in enumerate(questions): + for field in ("question", "why_it_matters", "first_step", "blocked_by"): + require_text(question, field, "TASK.json.open_questions[" + str(position) + "]") + readme = relative_file(root, package + "/README.md").read_text(encoding="utf-8") + require("## Open next questions" in readme, "README.md needs an \"## Open next questions\" section") + status = require_key(manifest, "status", "VERIFY.json") + require(status == "ready", + "VERIFY.json.status must be \"ready\"; complete the draft before requesting replay; found " + brief(status)) + python = require_key(manifest, "python", "VERIFY.json") + require(python == "3.12", + "VERIFY.json.python must be \"3.12\" (generic replay currently uses Python 3.12); found " + brief(python)) + requirements = manifest.get("requirements", []) + require(isinstance(requirements, list), + "VERIFY.json.requirements must be a list of exact \"name==version\" pins; found " + + type(requirements).__name__ + ": " + brief(requirements)) + require(len(requirements) == len(set(requirements)), "VERIFY.json.requirements must not repeat a pin") + for item in requirements: + require(isinstance(item, str) + and re.fullmatch(r"(?:numpy|sympy|scipy)==[0-9]+(?:\.[0-9]+){1,2}", item), + "generic CI supports exact numpy/sympy/scipy pins; use a dedicated workflow for other environments" + + "; offending entry: " + brief(item)) + names = [item.split("==")[0] for item in requirements] + require(len(names) == len(set(names)), "declare only one version per dependency") + # Validation already treats an omitted list as empty; execution must receive + # that same default without rewriting the contributor's manifest on disk. + manifest["requirements"] = requirements + commands = manifest.get("commands") + require(isinstance(commands, list) and 1 <= len(commands) <= 8, + "VERIFY.json.commands must be a list of 1..8 explicit verification commands; found " + + type(commands).__name__ + ": " + brief(commands)) + total = 0 + for position, command in enumerate(commands): + path = "VERIFY.json.commands[" + str(position) + "]" + require(isinstance(command, dict), + path + " must be a JSON object; found " + type(command).__name__ + ": " + brief(command)) + argv = command.get("argv") + require(isinstance(argv, list) and len(argv) >= 2 and all(isinstance(a, str) for a in argv), + path + ".argv must be a list of at least 2 strings; found " + brief(argv)) + require(argv[0] == "{python}", path + ".argv must explicitly use {python}; no implicit shell") + require_text(command, "checks", path, "a non-empty string without TODO describing command coverage") + seconds = command.get("timeout_seconds") + require(type(seconds) is int, + path + ".timeout_seconds must be an integer number of seconds; found " + + type(seconds).__name__ + ": " + brief(seconds)) + require(1 <= seconds <= 600, + path + ".timeout_seconds " + str(seconds) + + (" exceeds the 600 s per-command cap" if seconds > 600 + else " is below the 1 s per-command minimum")) + total += seconds + require(total <= 1200, "declared replay budget " + str(total) + + " s (sum of timeout_seconds) exceeds the 1200 s total cap" + + "; use a dedicated job for larger checks") + inputs = manifest.get("inputs") + require(isinstance(inputs, list), + "VERIFY.json.inputs must be a list of canonical repository-relative paths; found " + + type(inputs).__name__ + ": " + brief(inputs)) + tracked = tracked_input_paths(root) + for name in inputs: + symlink_free_relative_path(root, name) + require_tracked_input(name, tracked) + relative_file(root, name) + files = require_key(sources, "files", "SOURCES.json") + require(files, "SOURCES.json.files is empty; declare the source inventory") + base = require_key(sources, "base_commit", "SOURCES.json", "a 40-64 hex string pinning an exact base commit") + require(isinstance(base, str) and re.fullmatch(r"[0-9a-f]{40,64}", base), + "SOURCES.json.base_commit must be a 40-64 hex string pinning an exact base commit; found " + brief(base)) + task_base = require_key(task, "base_commit", "TASK.json", + "a 40-64 hex string equal to SOURCES.json.base_commit") + require(task_base == base, "TASK.json.base_commit " + brief(task_base) + + " must equal SOURCES.json.base_commit " + brief(base)) + for row in files: + require(isinstance(row, dict) and isinstance(row.get("path"), str), + "SOURCES.json.files rows must be JSON objects with a string path; offending row: " + brief(row)) + require(row.get("usage") in ("input", "provenance"), + "SOURCES.json.files row " + row["path"] + " must declare usage \"input\" or \"provenance\"; found " + + brief(row.get("usage"))) + undeclared = sorted({r["path"] for r in sources["files"] if r["usage"] == "input"} - set(inputs)) + require(not undeclared, + "every SOURCES.json files row with usage \"input\" must also be declared in VERIFY.json inputs" + + " (they drive CI invalidation); undeclared: " + ", ".join(undeclared)) + if check_pins: + catalog_name = "docs/research/agent-task-catalog.json" + require(catalog_name in {r["path"] for r in sources["files"]}, + "SOURCES.json.files must pin the originating task catalogue " + catalog_name + + " (a provenance row pinned at base_commit)") + names = [r["path"] for r in sources["files"]] + for name in names: + p = PurePosixPath(name) + require(not p.is_absolute() and ".." not in p.parts, "invalid source path") + specs = [source_pin(row, sources["base_commit"]) for row in sources["files"]] + require(all(spec == sources["base_commit"] + ":" + catalog_name + for name, spec in zip(names, specs) if name == catalog_name), + "originating task catalogue must be pinned at base_commit") + with closing(git_blobs(root, specs)) as objects: + for index, (obj, pinned) in enumerate(objects): + row = sources["files"][index] + name = row["path"] + require(obj == row["git_blob"], "source blob provenance mismatch: " + name) + require(hashlib.sha256(pinned).hexdigest() == row["sha256"], "source SHA256 provenance mismatch: " + name) + if row["usage"] == "input": + require(pinned == relative_file(root, name).read_bytes(), "working source drift: " + name) + if name == catalog_name: + catalog = json.loads(pinned) + cards = [t for tr in catalog["tracks"] for t in tr["tasks"] if t["id"] == task["task_id"]] + require(len(cards) == 1, + "TASK.json task_id " + brief(task["task_id"]) + " matches " + str(len(cards)) + + " cards in pinned " + catalog_name + " at base_commit " + sources["base_commit"] + + "; need exactly one") + original_card = require_key(task, "original_card", "TASK.json", + "the pinned catalogue card object (copy --print-card output verbatim)") + if original_card != cards[0]: + raise ValueError("original card in TASK.json must equal the pinned catalogue card object exactly; " + "copy it verbatim from " + catalog_name + " at base_commit " + sources["base_commit"] + + ": " + card_differences(original_card, cards[0])) + return task, manifest + + +def catalogue_card(root, package, task_id): + """The exact original_card object a hand-authored TASK.json must copy. + + Reads the catalogue blob pinned at the package base commit, never the + working tree, because validate() compares original_card against that pin. + """ + sources = json.loads(relative_file(root, package + "/SOURCES.json").read_text(encoding="utf-8")) + name = "docs/research/agent-task-catalog.json" + rows = require_key(sources, "files", "SOURCES.json") + row = next((r for r in rows if isinstance(r, dict) and r.get("path") == name), None) + require(row is not None, "SOURCES.json.files must pin the originating task catalogue " + name) + base = require_key(sources, "base_commit", "SOURCES.json", "a 40-64 hex string pinning an exact base commit") + spec = source_pin(row, base) + require(spec == base + ":" + name, "originating task catalogue must be pinned at base_commit") + catalog = json.loads(git(root, "show", spec)) + cards = [t for tr in catalog["tracks"] for t in tr["tasks"] if t["id"] == task_id] + require(len(cards) == 1, + "task_id " + brief(task_id) + " matches " + str(len(cards)) + + " cards in pinned " + name + " at base_commit " + base + "; need exactly one") + return cards[0] + + +_WINDOWS_GATE = r""" +import ctypes +from ctypes import wintypes +import json +import subprocess +import sys +api = ctypes.WinDLL('kernel32', use_last_error=True) +api.OpenEventW.argtypes = [wintypes.DWORD, wintypes.BOOL, wintypes.LPCWSTR] +api.OpenEventW.restype = wintypes.HANDLE +api.WaitForSingleObject.argtypes = [wintypes.HANDLE, wintypes.DWORD] +api.WaitForSingleObject.restype = wintypes.DWORD +api.CloseHandle.argtypes = [wintypes.HANDLE] +api.CloseHandle.restype = wintypes.BOOL +event = api.OpenEventW(0x00100000, False, sys.argv[1]) +if not event: + raise ctypes.WinError(ctypes.get_last_error()) +try: + if api.WaitForSingleObject(event, 30000) != 0: + raise RuntimeError('replay ownership gate was not released') +finally: + api.CloseHandle(event) +# No verification command or descendant starts until the parent owns this job. +sys.exit(subprocess.call(json.loads(sys.argv[2]))) +""" + +def run_windows_command(argv, cwd, timeout, env): + """Own ordinary verification descendants even after their leader exits. + + The gated launcher joins a kill-on-close Job Object before it may spawn + the requested command. A late taskkill cannot recover an exited leader's + tree. Job handles are not inherited and breakaway is not enabled. + """ + import ctypes + from ctypes import wintypes + import time + import uuid + + class BasicLimits(ctypes.Structure): + _fields_ = [("ProcessTime", ctypes.c_int64), ("JobTime", ctypes.c_int64), + ("Flags", wintypes.DWORD), ("MinWorkingSet", ctypes.c_size_t), + ("MaxWorkingSet", ctypes.c_size_t), ("ActiveProcessLimit", wintypes.DWORD), + ("Affinity", ctypes.c_size_t), ("Priority", wintypes.DWORD), + ("Scheduling", wintypes.DWORD)] + + class IOCounts(ctypes.Structure): + _fields_ = [(name, ctypes.c_uint64) for name in + ("ReadOps", "WriteOps", "OtherOps", "ReadBytes", "WriteBytes", "OtherBytes")] + + class ExtendedLimits(ctypes.Structure): + _fields_ = [("Basic", BasicLimits), ("IO", IOCounts), + ("ProcessMemory", ctypes.c_size_t), ("JobMemory", ctypes.c_size_t), + ("PeakProcessMemory", ctypes.c_size_t), ("PeakJobMemory", ctypes.c_size_t)] + + class Accounting(ctypes.Structure): + _fields_ = [(name, ctypes.c_int64) for name in + ("UserTime", "KernelTime", "PeriodUserTime", "PeriodKernelTime")] + [ + (name, wintypes.DWORD) for name in + ("PageFaults", "TotalProcesses", "ActiveProcesses", "TerminatedProcesses")] + + api = ctypes.WinDLL("kernel32", use_last_error=True) + + def native(name, result, *arguments): + fn = getattr(api, name) + fn.restype, fn.argtypes = result, arguments + return fn + + handle, dword, boolean = wintypes.HANDLE, wintypes.DWORD, wintypes.BOOL + create_job = native("CreateJobObjectW", handle, ctypes.c_void_p, wintypes.LPCWSTR) + set_info = native("SetInformationJobObject", boolean, handle, ctypes.c_int, ctypes.c_void_p, dword) + assign = native("AssignProcessToJobObject", boolean, handle, handle) + terminate = native("TerminateJobObject", boolean, handle, wintypes.UINT) + query = native("QueryInformationJobObject", boolean, handle, ctypes.c_int, + ctypes.c_void_p, dword, ctypes.c_void_p) + create_event = native("CreateEventW", handle, ctypes.c_void_p, boolean, boolean, wintypes.LPCWSTR) + set_event = native("SetEvent", boolean, handle) + close = native("CloseHandle", boolean, handle) + + def checked(ok): + if not ok: + raise ctypes.WinError(ctypes.get_last_error()) + return ok + + job = checked(create_job(None, None)) + event, process, assigned = None, None, False + try: + limits = ExtendedLimits() + limits.Basic.Flags = 0x2000 # JOB_OBJECT_LIMIT_KILL_ON_JOB_CLOSE + checked(set_info(job, 9, ctypes.byref(limits), ctypes.sizeof(limits))) + name = "Local\\research-replay-" + uuid.uuid4().hex + event = checked(create_event(None, True, False, name)) + # A name collision must not attach to an already-signaled event. + if ctypes.get_last_error() == 183: + raise ValueError("replay ownership gate name already exists") + process = subprocess.Popen( + # The gate itself must not run sitecustomize/PYTHONPATH startup + # code before ownership. The requested command retains env/argv. + # Windows accepts Unicode argv directly. ASCII JSON escaping can + # expand an otherwise valid command past its UTF-16 launch limit. + [sys.executable, "-I", "-S", "-c", _WINDOWS_GATE, name, + json.dumps(argv, ensure_ascii=False)], + cwd=cwd, env=env, start_new_session=True) + checked(assign(job, int(process._handle))) + assigned = True + checked(set_event(event)) + try: + return process.wait(timeout=timeout) + except subprocess.TimeoutExpired: + raise ValueError("verification timed out") from None + finally: + try: + if process is not None: + if assigned: + checked(terminate(job, 1)) + # Termination is asynchronous. Require the job to report + # no active processes before releasing its ownership handle. + deadline = time.monotonic() + 10 + while True: + state = Accounting() + checked(query(job, 1, ctypes.byref(state), ctypes.sizeof(state), None)) + if not state.ActiveProcesses: + break + if time.monotonic() >= deadline: + raise ValueError("verification process cleanup timed out") + time.sleep(0.01) + elif process.poll() is None: + # Assignment failed before the gate opened: no command child + # exists, so only this known gated launcher needs stopping. + process.kill() + process.wait(timeout=10) + finally: + try: + if event: + checked(close(event)) + finally: + checked(close(job)) + +def run_command(argv, cwd, timeout): + # Assertion checks must not disappear because of the caller's environment. + # Keep explicit manifest options (including deliberate -O controls) intact. + # PYTHONPATH precedes the standard library on a child's sys.path, so a stray + # same-named module could end a verifier with exit code 0 before any check. + env = os.environ.copy() + env.pop("PYTHONOPTIMIZE", None) + # Ambient inspection can turn a verifier exception into a successful REPL + # exit at terminal EOF. Keep explicit -i and the caller's stdin unchanged. + env.pop("PYTHONINSPECT", None) + env.pop("PYTHONPATH", None) + if os.name == "nt": + code = run_windows_command(argv, cwd, timeout, env) + require(code == 0, f"verification command exited {code}") + return + previous_handler = None + terminating = False + waiting = False + process = None + + def terminate(signum, frame): + nonlocal terminating + if not terminating: + terminating = True + # Only interrupt the protected wait. Launch/assignment and cleanup + # defer delivery; repeated signals cannot interrupt group cleanup. + if waiting: + raise SystemExit(128 + signum) + + # Own a group for POSIX cleanup of this command and its descendants. + try: + if (threading.current_thread() is threading.main_thread() + and signal.getsignal(signal.SIGTERM) == signal.SIG_DFL): + previous_handler = signal.SIG_DFL + signal.signal(signal.SIGTERM, terminate) + if terminating: + raise SystemExit(143) + process = subprocess.Popen(argv, cwd=cwd, env=env, start_new_session=True) + try: + try: + waiting = True + if terminating: + raise SystemExit(143) + code = process.wait(timeout=timeout) + finally: + waiting = False + except subprocess.TimeoutExpired: + raise ValueError("verification timed out") from None + require(code == 0, f"verification command exited {code}") + finally: + try: + if process is not None: + if hasattr(os, "killpg"): + # The leader may have exited while descendants hold its group. + try: + os.killpg(process.pid, signal.SIGKILL) + except ProcessLookupError: + pass + elif process.poll() is None: + subprocess.run(["taskkill", "/F", "/T", "/PID", str(process.pid)], capture_output=True) + process.wait() + finally: + if previous_handler is not None: + signal.signal(signal.SIGTERM, previous_handler) + if terminating: + raise SystemExit(143) + + +def isolated_python_argv(argv, cache_directory): + """Place our cache option after interpreter flags, before the entry point. + + -B prevents writes, not reads of existing .pyc files. A fresh namespace + keeps preexisting source-adjacent and externally configured caches out of + this registered interpreter. It is not inherited by child interpreters. + """ + require(argv and argv[0] == sys.executable, "cache isolation requires the registered Python interpreter") + index = 1 + options = [argv[0]] + while index < len(argv): + option = argv[index] + if option in ("-", "--") or not option.startswith("-"): + break + if option == "--check-hash-based-pycs": + require(index + 1 < len(argv), "missing Python hash-cache option argument") + options.extend(argv[index:index + 2]) + index += 2 + continue + if option.startswith("--"): + options.append(option) + index += 1 + continue + # Python permits combined short flags, attached -c/-m payloads, and + # attached or separate -W/-X arguments. Stop scanning an option once + # its argument begins: letters inside that argument are not flags. + entry = False + consumed = 1 + replace_cache = False + for offset, flag in enumerate(option[1:], start=1): + if flag in "cm": + entry = True + break + if flag in "WX": + if offset == len(option) - 1: + require(index + 1 < len(argv), "missing Python interpreter option argument") + consumed = 2 + value = argv[index + 1] if consumed == 2 else option[offset + 1:] + if flag == "X" and value.split("=", 1)[0] == "pycache_prefix": + replace_cache = True + if offset > 1: + options.append(option[:offset]) + break + if entry: + break + if not replace_cache: + options.extend(argv[index:index + consumed]) + index += consumed + # CPython's effective prefix can use the first duplicate -X value even + # when sys._xoptions shows the last. Remove only earlier cache-prefix + # settings; script arguments remain untouched, even when spelled -X. + return [*options, "-X", "pycache_prefix=" + str(cache_directory), *argv[index:]] + + +def run_python_replay(argv, cwd, timeout): + with tempfile.TemporaryDirectory(prefix="research-replay-pycache-") as cache: + run_command(isolated_python_argv(argv, cache), cwd, timeout) + + +def run_package(root, package, install=False): + task, manifest = validate(root, package) + require(sys.version_info[:2] == (3, 12), "run replay with Python 3.12 (metadata check is version-independent)") + if install and manifest["requirements"]: + run_command([sys.executable, "-m", "pip", "install", "--disable-pip-version-check", *manifest["requirements"]], root, 300) + for requirement in manifest["requirements"]: + name, version = requirement.split("==") + require(importlib.metadata.version(name) == version, "dependency version mismatch: " + requirement) + # Coverage labels are UTF-8 metadata but a redirected Windows stdout may + # use cp1252. Escape unrepresentable display characters instead of aborting + # before replay. This changes only our stream, not child encoding or env. + if hasattr(sys.stdout, "reconfigure"): + sys.stdout.reconfigure(errors="backslashreplace") + for command in manifest["commands"]: + argv = [sys.executable if item == "{python}" else item.replace("{package}", package) for item in command["argv"]] + print("CHECK " + command["checks"], flush=True) + run_python_replay(argv, root, command["timeout_seconds"]) + print("PASS_REGISTERED_RESEARCH_PACKAGE " + package + " outcome=" + task["outcome"]) + + +def planning_manifests(root, tracked): + """Include deliberate sparse omissions without disguising deletions or drift. + + The fallback follows the chooser's PR3102 contract: one stage-zero regular + skip-worktree index entry must match the exact HEAD mode and blob. This is + declaration discovery only, not permission to replay absent package code. + """ + committed = {name for name in tracked + if name.startswith("research/") and name.count("/") == 2 + and name.endswith("/VERIFY.json")} + # Explicit scandir retains error detection; only an absent directory is OK. + try: + with os.scandir(root / "research") as entries: + local = {Path(entry.path) / "VERIFY.json" for entry in entries} + except FileNotFoundError: + local = set() + present, missing = {}, set() + for path in sorted(local | {root / name for name in committed}): + name = path.relative_to(root).as_posix() + symlink_free_relative_path(root, name) + try: + mode = path.lstat().st_mode + except (FileNotFoundError, NotADirectoryError): + if name in committed: + missing.add(name) + continue + require(stat.S_ISREG(mode), "non-regular replay manifest: " + name) + present[name] = path + fallback = {} + if missing: + indexed, objects = {}, {} + for record in git(root, "ls-files", "-t", "--stage", "-z", "--", "research").split(b"\0"): + if not record: + continue + header, raw_name = record.split(b"\t", 1) + name = raw_name.decode("utf-8") + if name in missing: + indexed.setdefault(name, []).append(header.split()) + for record in git(root, "ls-tree", "-r", "-z", "HEAD", "--", "research").split(b"\0"): + if not record: + continue + header, raw_name = record.split(b"\t", 1) + name = raw_name.decode("utf-8") + if name in missing: + objects[name] = header.split() + for name in sorted(missing): + metadata = objects.get(name, []) + require(len(metadata) == 3 and metadata[0] in (b"100644", b"100755") + and metadata[1] == b"blob" + and indexed.get(name) == [[b"S", metadata[0], metadata[2], b"0"]], + "missing replay manifest is not an unchanged sparse HEAD input: " + name + + "; materialize it or commit its intended deletion") + # A regular file occupying the package directory is not an omission. + require(not (root / name).parent.exists() or (root / name).parent.is_dir(), + "non-directory replay package: " + name) + names = sorted(missing) + with closing(git_blobs(root, [objects[n][2].decode("ascii") for n in names])) as rows: + for (oid, raw), name in zip(rows, names): + require(oid.encode("ascii") == objects[name][2], "sparse manifest blob mismatch: " + name) + fallback[name] = raw + # Preserve Path's component ordering: package "a" precedes "a-extra". + for name in sorted(present.keys() | fallback.keys(), key=lambda name: PurePosixPath(name).parts): + yield root / name, fallback[name] if name in fallback else present[name].read_bytes(), name in fallback + + +def plan_details(root, changed): + """One selection pass with exact causes; no replay or acceptance decision.""" + changed = set(changed) + # A removed input is absent from HEAD, including an old case-only rename + # spelling on case-insensitive filesystems. Git's exact changed paths remain + # eligible so its consumer is selected, rather than rejected or skipped. + head_tracked = tracked_input_paths(root) + tracked = head_tracked | changed + replay_changed = sorted(changed.intersection({ + "scripts/research_package.py", ".github/workflows/research-packages.yml", + ".github/workflows/research-package-batch.yml"})) + # Group literal Git paths once. Keep removed paths and exact spellings. + changed_packages = {} + for name in sorted(changed): + parts = name.split("/", 2) + if len(parts) == 3 and parts[0] == "research": + changed_packages.setdefault("/".join(parts[:2]), []).append(name) + packages = [] + sparse_count = 0 + for path, raw, sparse in planning_manifests(root, head_tracked): + sparse_count += sparse + package = path.parent.relative_to(root).as_posix() + manifest = json.loads(raw.decode("utf-8")) + # Parse only for selection; validate fully in the isolated replay job. + inputs = manifest.get("inputs", []) + require(isinstance(inputs, list), "declare input paths for CI invalidation") + for name in inputs: + # Do not require existence: a deleted input must still trigger replay. + symlink_free_relative_path(root, name) + require_tracked_input(name, tracked) + causes = { + "declared_inputs": sorted(changed.intersection(inputs)), + "package_files": changed_packages.get(package, []), + "shared_controls": replay_changed, + } + if any(causes.values()): + packages.append({"package": package, "causes": causes, + "manifest_sha256": hashlib.sha256(raw).hexdigest()}) + if sparse_count: + print(f"Planning includes {sparse_count} unchanged sparse manifests from HEAD; " + "materialize packages and inputs before replay.", file=sys.stderr) + return packages + + +def plan(root, changed): + return [row["package"] for row in plan_details(root, changed)] + + +def write_plan_explanation(path, base, head, changed, details): + """Publish a complete sidecar before stdout/GitHub matrix publication.""" + matched = {name for row in details for names in row["causes"].values() for name in names} + report = { + "schema_version": 1, "base": base, "head": head, + "mode": "all-tracked" if base is None else "commit-diff", + "scope": "Selection from working or authenticated sparse HEAD manifests, not replay or mathematical acceptance. " + "Manifest hashes bind the declarations read; checkout must remain stable.", + "changed_paths": sorted(set(changed) - {""}), "selected": details, + "unmatched_paths": sorted(set(changed) - matched - {""}), + } + fd, temporary = tempfile.mkstemp(prefix=".replay-plan-", dir=path.parent) + try: + with os.fdopen(fd, "w", encoding="utf-8") as stream: + json.dump(report, stream, indent=2) + stream.write("\n") + os.replace(temporary, path) + finally: + Path(temporary).unlink(missing_ok=True) + + +def replay_matrix(packages, batch_size=None): + """Retain the flat CLI format, or group complete coverage into bounded matrices.""" + if batch_size is None: + return {"include": [{"package": p} for p in packages]} + require(type(batch_size) is int and 1 <= batch_size <= 256, + "matrix batch size must be 1..256") + batches = [packages[i:i + batch_size] for i in range(0, len(packages), batch_size)] + require(len(batches) <= 256, + "more than 256 matrix batches required; no packages were truncated") + return {"include": [{"packages": batch} for batch in batches]} + + +def main(): + ap = argparse.ArgumentParser(description=__doc__) + ap.add_argument("--package") + ap.add_argument("--check-only", action="store_true") + ap.add_argument("--print-card", metavar="TASK_ID", + help="print the exact pinned catalogue card object to copy into TASK.json original_card") + ap.add_argument("--install-deps", action="store_true", help="explicit opt-in to install manifest's allowed pinned dependencies") + ap.add_argument("--changed-since", help="plan affected opt-in packages relative to this Git commit") + ap.add_argument("--github-output", type=Path) + ap.add_argument("--explain-plan", type=Path, + help="write exact replay-selection causes to JSON; matrix output stays unchanged") + ap.add_argument("--matrix-batch-size", type=int, + help="group planned packages for bounded reusable-workflow matrices (1..256)") + args = ap.parse_args() + if args.explain_plan and (not args.changed_since or args.package or args.print_card): + ap.error("--explain-plan requires --changed-since without --package or --print-card") + if args.explain_plan and args.github_output and args.explain_plan.resolve() == args.github_output.resolve(): + ap.error("--explain-plan and --github-output must use different files") + try: + if args.print_card: + require(args.package, + "--print-card needs --package research/ to resolve its pinned catalogue") + sys.stdout.write(json.dumps(catalogue_card(ROOT, args.package, args.print_card), indent=2) + "\n") + elif args.changed_since: + if set(args.changed_since) == {"0"}: + base = None + changed = git(ROOT, "ls-files", "-z").decode().split("\0") + else: + base = git(ROOT, "rev-parse", "--verify", args.changed_since + "^{commit}").decode().strip() + # A rename must invalidate both the removed input and its new path. + changed = git(ROOT, "diff", "--no-renames", "--name-only", "-z", base, "HEAD").decode().split("\0") + details = plan_details(ROOT, changed) + packages = [row["package"] for row in details] + matrix = json.dumps(replay_matrix(packages, args.matrix_batch_size)) + if args.explain_plan: + head = git(ROOT, "rev-parse", "--verify", "HEAD^{commit}").decode().strip() + write_plan_explanation(args.explain_plan, base, head, changed, details) + print(matrix) + if args.github_output: + with args.github_output.open("a", encoding="utf-8") as out: + out.write(f"matrix={matrix}\ncount={len(packages)}\n") + elif args.package: + if args.check_only: + validate(ROOT, args.package) + print("PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)") + else: + run_package(ROOT, args.package, args.install_deps) + else: + ap.error("use --package, --print-card or --changed-since") + except (OSError, ValueError, KeyError, TypeError, subprocess.SubprocessError, importlib.metadata.PackageNotFoundError) as exc: + ap.exit(1, str(exc) + "\n") + + +if __name__ == "__main__": + main() diff --git a/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/coded-native-caller/NORMALIZERS.json b/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/coded-native-caller/NORMALIZERS.json new file mode 100644 index 0000000000..bca92c222c --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/coded-native-caller/NORMALIZERS.json @@ -0,0 +1,126 @@ +{ + "clifford_sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962", + "code_sha256": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0", + "finite_checks": {"absolute_phase_mutations_rejected":112,"exact_endpoint_factor_identities":896,"gaussian_free_compiled_wrappers":896,"monomial_wrappers":896,"omitted_phase_rejections":112,"ports":112,"scalar_basis_recodings":224,"weight_congruence_addresses":57344}, + "local_gauge_bill": {"added_recursive_calls":0,"backward_extra_monomial_field_maps_upper":448,"main_wrapper_field_maps":448,"owned_fields_reused":8,"recoding_monomial_field_maps":448,"recoding_owned_clears":32,"recoding_scalar_adds":1792,"recodings":2}, + "mode_columns": 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+ ], + "recoding_bill": {"forward_prefix_component_l1_upper":57,"forward_update_coefficient":"-1/4","inverse_output_prefix_component_l1_upper":"69/13","inverse_prefix_component_l1_upper":56,"inverse_update_coefficient":"-1/52","monomial_field_maps":224,"output_scaled_adds":448,"owned_fields":8,"owned_initial_clears":8,"owned_terminal_clears":8,"signed_mode_adds":448}, + "schema": "coded-native-real-normalizers/1", + "scope": "Exact physical central ABI and local gauges; not full-controller or multiplication admission.", + "source_payload_sha256": "cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd", + "status": "PASS_CODED_NATIVE_REAL_NORMALIZERS" +} diff --git a/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/coded-native-caller/PHYSICAL.md b/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/coded-native-caller/PHYSICAL.md new file mode 100644 index 0000000000..da8837ba67 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/coded-native-caller/PHYSICAL.md @@ -0,0 +1,71 @@ +# Real physical normalizers for the coded producer + +This is local constructive research on canonical/pr4929, not a completed supplier or exponent claim. Source code and Gaussian conventions retain the original authors' credit. + +Let n=9 and let q be any of the source's 112 port vectors (weight 3 or 7). Let e0=1. Construct an orthogonal binary matrix G taking e0 to q. If q_0=0, use the orthogonal transvection T_(e0+q). If q_0=1, select j>0 with q_j=0 and use T_(ej+q) T_(e0+ej). Here T_v(x)=x+(v dot x)v; both v have even weight, hence T_v is orthogonal. Such j exists because q is not the all-ones vector. + +For row j of G put z_j=(wt(row_j G)-1)/2 modulo 2. Define K=Z_z P_G. It is a real signed permutation. The full Gaussian R has entries alpha*(-i)^wt(x+y), with alpha=(1+i)^9/2^9. Orthogonality gives + +wt(G^-1 d)-wt(d) = 2 z dot d (mod 4). + +Indeed the degree-two coefficients vanish modulo four because distinct columns of G^-1 have even dot product; the linear coefficient is the weight of that column minus one. Therefore K R K^-1=R exactly, including absolute phase. K also maps the central line to span(q), and its orthogonal complement to q-perp, at the canonical-frame Lagrangian level. All these statements tensor to every positive digit-column count. + +Let Q be the central C gate, D the product of the other eight C gates, so R=DQ. Let E_i and S_i be the actual retained entrance-line and exit-hyperplane frame operators. With the operator convention that rightmost applies first, use + +input X: E_i K_i Q^-1 +input Y: K_i +output X: K_i^-1 +output Y: D K_i^-1 S_i^-1. + +All four wrappers are monomial. Their Lagrangian incidences prove this for every port, and the scratch verifier checks exact tableaus and absolute phases at every one of the 112 source ports. With A from PR4929, define C_ij= A_ij K_i^-1 K_j. Then the full main endpoint is + +F = diag(D,D) [[I,0],[C Q^-1,I]]. + +C is a physically implementable fixed owner recoding: apply K_i to each owner, apply A among the owners at common physical coordinates, and apply K_i^-1. Its inverse uses A^-1=(A+12I)/13. Since each K_i is real orthogonal and A is real symmetric, C^T=C. Since K_i commutes with R, C commutes with R. The polynomial C^2+12C-13I=0 follows by similarity. The 408 independent helper jobs and every paid Gaussian child are unchanged. + +For the actual raw inverse transpose, F^-T=diag(D^-1,D^-1) [[I,-Q^-1 C],[0,I]], since Q,D are symmetric. Multiply both outputs by D^2, then conjugate the physical X bank by Q^2 (input Q^-2 and output Q^2). These are explicit monomial powers. The result is + +B = diag(D,D) [[I,-Q C],[0,I]]. + +The old source convention using Y-only Q^2 conjugation cannot simply be copied for noncommuting C. The X-only convention above is exact. + +For a prior code B0 commuting with the current D, set G(B0)=diag(B0,Q^-1 B0 Q). The following two constructive local identities hold without requiring C and Q to commute: + +(post X C) F (pre Y C) = G(C B0) F_standard G(B0)^-1, +(post X C^-1) B (pre Y C^-1) = G(C^-1 B0) B_standard G(B0)^-1. + +They use [C,DQ]=0 and [B0,D]=0. Every additional operation on the left is physically cheap fixed recoding. For disjoint fresh blocks, codes from earlier stages commute with the current D. These identities do not yet settle interstage ADD/IDLE compatibility, terminal gauges, productive jobs, or the complete moment. + +## Literal recoding and complete local bill + +The source code has an exact factorization A=I-MM^T/4 with M a 112-by-8 matrix having entries 0,+1,-1 and M^T M=56I. Each mode column has 56 nonzero entries, and each owner row has four. The mode columns are emitted in NORMALIZERS.json and all 12,544 entries are checked against the pinned CODE.json. This factorization is used here as a constructive scalar program, without relying on any common physical address chart for separate Gaussian mode transformations. + +To execute A on arbitrary independent owner fields x, allocate eight owned zero fields t. Compute t=M^T x with 448 signed ADDs; update x-=M t/4 with 448 scaled ADDs; clear the eight owned temporaries. Reading x is finished before any x is updated. Hence no input field is overwritten before its last source read. For A^-1 use the same program with coefficient -1/52, since A^-1=I-MM^T/52. Both are exact rational linear programs. The helper fields of the native producer are never used as scratch, copied as free credit, or erased. + +Conjugating this scalar program by the 112 K_i and their inverses implements C or C^-1. This pays 224 monomial field maps, 896 scalar ADDs and 16 owned CLEARs per recoding, with eight owned fields reusable sequentially. The two additional recodings in either local gauge identity therefore cost at most 448 monomial maps, 1,792 scalar ADDs and 32 CLEARs, with no recursive Gaussian child. The four actual port normalizers contribute 448 monomial maps per native invocation. The displayed backward conversion contributes at most 448 further monomial maps (112 input X powers, 112 output X powers and 224 output D-squares); fusing maps can reduce this upper bound but is not assumed. + +These are field-level operation counts. A lifted K_i is an explicit binary map on nine f-bit address blocks together with signs given by block parity. Its constants, indexed movement and phase passes use the retained native monomial implementation. It is therefore a fixed finite O(V polylog p) nonrecursive operation under that caller's precision/address ABI, not a zero-work instruction. Each fixed rational ADD is likewise charged at its actual scalar precision. In particular the inverse denominator 52 must be implemented and rounded; no free exact real-division oracle is assumed. This lemma makes no independent TM tariff or outer-budget claim. + +The maximum exact component-l1 prefix bound for the scalar A program, including its temporaries, is 57. For A^-1 it is 56 (the output-only bound is 69/13). Signed monomial maps preserve component magnitude. A fixed local sequence has a fixed suffix bound obtained by multiplying elementary bounds 1+|coefficient|; owned CLEAR has bound one. This gives a finite bound for local rounding propagation. The number of local uses, compiler precision and complete outer error allocation still belong to the caller theorem. + +The normalized producer still has its exact PR4929 paid profile + + {1:2201, 2:412, 3:510, 4:127, 5:40} + +and independent helper profile + + {4:28, 7:7, 8:47, 9:326}. + +No productive main ranks are asserted merely from the coupled central ABI. Those depend on the completed caller, its initial/final gauges and every paid correction. + +## Universal scope and reproducible evidence + +PR4929 supplies the arbitrary-input logical identity over Q[FreeGroup72] for its emitted center-free word with ground-chart helper pre-compensation. Its normalized main endpoint is L(A), its raw dual is L(A)^-T, and every one of the 408 helper endpoints is autonomous. This proof is an inherited premise with exact source pins, not a consequence of this normalizer checker. The present wrappers and owner recodings act exclusively on the 224 main fields; new scratch is explicitly owned. Thus the helper block remains autonomous and its independent inputs, requested transforms and paid profile remain unchanged. + +For every f>=1, assign the shared native letters their actual consistent invertible lifted operators. Evaluation of the source free-group algebra is a homomorphism and gives the source logical identity. Independently lift each K_i as its f-fold tensor product, retaining spectator coordinates; its signed-permutation word, the two direct frame identities and its commutation with R lift by operator composition. In every compiled monomial word, P and X act columnwise on the f-bit blocks, D sums its Z4 polynomial over the f columns, and a one-column scalar phase i^gamma becomes i^(f*gamma). Reusing the one-column global phase unchanged would be incorrect. Finally form the owner matrix C_f with entries A_ij K_i,f^-1 K_j,f. One does not tensor the whole 224-by-224 owner matrix and does not assert that tensor powers preserve sums. Instead the finite scalar owner program is evaluated directly in the algebra of these lifted address operators. This proves the central ABI and local gauge identities at every positive width. + +Run `python3 -I -B research/coded-native-caller/normalizers.py` or its optimized `-O` form. The checker authenticates the decompressed actual native payload, CODE.json and retained Clifford source before executing the latter. It verifies all 112 real signed normalizers, 57,344 explicit weight-congruence addresses, 896 forward/backward monomial wrappers and eight exact frame/block identities per port, including absolute phase. Each emitted wrapper is separately lowered to a literal P/D/X/phase-only word and checked against its defining expression by exact tableau and absolute-phase state. No C gate remains in an emitted wrapper. The independent incoming-column and outgoing-row identities imply all 5,824 nonzero off-diagonal code blocks, without sampling those pairs. It also executes the eight-mode recoding on all 112 arbitrary-input basis columns in both directions. Omitting the essential signed phase is rejected at every affected port. The default command compares a regenerated mathematical receipt and performs no writes; `--write` is the explicit authoring path. + +Source pins: canonical main 624de9dc66858af0945e5f8a0942488d62280d43, `research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz`, decompressed SHA-256 cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd; PR4929 head 361f5d4100640177d6a983dd2f336021c75bfd5e, `research/native-center-free-code/CODE.json`, SHA-256 8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0; canonical `research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py`, SHA-256 2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962. Gzip container bytes are not substituted for decompressed source identity. + +Credit Dugongue's PR4929 for the coded producer and stable code; Cinna Davis's PR4694/4698 and the original cache/helper construction; Cao Yifan's PR4610 native word; the retained zxv, Jacob Alan Sussman, Cinna Davis and Clifford/native/compiler lineage. The exact canonical-frame implementation and phase conventions are retained source material. The constructive real centralizing normalizers, their explicit lifted words, X-only raw-dual convention and costed local code gauges are the additions here. New work is Apache-2.0 and has substantial OpenAI Codex assistance; no formal-kernel or independent human acceptance is asserted. diff --git a/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/coded-native-caller/clifford_exact.py b/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/coded-native-caller/clifford_exact.py new file mode 100644 index 0000000000..166841a037 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/coded-native-caller/clifford_exact.py @@ -0,0 +1,149 @@ +"""Small exact Gaussian-dyadic Clifford compiler, independent of gx internals. +Paulis use i^p X^x Z^z. State vectors use integer Gaussian numerators / 2^d. +The tableau is supplemented by a literal circuit, so global phases are kept. +""" +from dataclasses import dataclass + +def parity(x):return x.bit_count()&1 +def rank(rows): + p={} + for x in rows: + while x: + b=x.bit_length()-1 + if b not in p:p[b]=x;break + x^=p[b] + return len(p) +def transpose(rows,n):return tuple(sum(((rows[j]>>i)&1)<>j&1);a[j],a[k]=a[k],a[j] + for i in range(n): + if i!=j and a[i]>>j&1:a[i]^=a[j] + assert [r&((1<>n for r in a) +def basis_extend(cols,n): + out=[] + for x in list(cols)+[1<len(out):out.append(x) + assert len(out)==n + return tuple(out) +def nullspace(rows,n): + a=list(rows);p=[];k=0 + for j in range(n): + t=next((i for i in range(k,len(a)) if a[i]>>j&1),None) + if t is None:continue + a[t],a[k]=a[k],a[t] + for i in range(len(a)): + if i!=k and a[i]>>j&1:a[i]^=a[k] + p.append(j);k+=1 + return tuple((1<>j)&1)<>i&1:out=pmul(out,T[i]) + for i in range(n): + if z>>i&1:out=pmul(out,T[n+i]) + return out +def compose(A,B):return tuple(apply(A,p) for p in B) +def inverse(T): + n=len(T)//2;cols=[x|(z<>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4)) + return tuple(out) +def qvalue(Q,alpha,x,n): + return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4 +def mul_i(a,p): + x,y=a;p%=4 + return [(x,y),(-y,x),(-x,-y),(y,-x)][p] +@dataclass +class Op: + n:int + tab:tuple + circuit:list + def then(self,b): + assert self.n==b.n + return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit) + def adjoint(self): + circ=[] + for e in reversed(self.circuit): + if e[0]=='P':circ.append(('P',inv(e[1],self.n))) + elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2]))) + elif e[0]=='C':circ.append(('C',e[1],-e[2])) + elif e[0]=='phase':circ.append(('phase',(-e[1])%4)) + else:circ.append(e) + return Op(self.n,inverse(self.tab),circ) + def zero_state(self,basis=0): + N=1<>i)&1 for i in range(n)) + assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n)) + return Op(n,tuple([(1<>i&1 else 0,1<>i&1 else 0) for i in range(n)]),[('C',q,sgn)]) +def xgate(n,b):return Op(n,tuple([(1<>i)&1)) for i in range(n)]),[('X',b)]) +def fourier(n,axes=None): + out=ident(n) + for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<len(selected):picks.append(j);selected.append(x) + assert len(picks)==r and all(x>>r==0 for x in Bcols) + Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1< (X,Y+X,H)`. Physical entrance and exit charts remain exactly those of the frozen source. + +There is a completely emitted constant dyadic pre-compensation, followed by the source word with every center Gaussian operation replaced by an owned CLEAR, whose exact normalized endpoint is + +`X' = X; Y' = Y + A X; H' = H`. + +All 632 persistent inputs are arbitrary and independent; no helper is initialized, discarded, identified or counted twice. The literal backward construction has exact normalized endpoint + +`X' = X - A^T Y; Y' = Y; H' = H`, + +the raw inverse transpose of the forward endpoint. The paid profile in both directions is + +`{1:2201, 2:412, 3:510, 4:127, 5:40}`. + +The helper profile stays `{4:28,7:7,8:47,9:326}`. Relative to the source, exactly eight rank-eight children are removed and no Gaussian child is added. The pre-compensation adds 6,596 scalar ADDs with a retained scalar allowance of 32,652 primitives; all numerator magnitudes and denominators are at most 4. These finite scalar operations do not establish a better recursive exponent on their own. + +## Constructive proof + +Delete all eight center calls by replacing each with CLEAR of the owned center field in the call's destination chart. Zero has every chart, so this is a valid erasure of owned scratch, not a borrowed input overwrite. Retain every other physical instruction and every endpoint chart. + +The exact sparse replay over the rational free group algebra on the 72 native symbols gives + +`M_0 = I + S + E_X + E_H`. + +Here S is the original transfer X to Y. Both error blocks land only in Y. E_X reads X; E_H reads only 106 particular helpers, each with a ground entrance and full-frame exit. Every helper and every X output remains autonomous. All error terms have EMPTY native word: the errors are ordinary constant dyadic matrices, not uncomputed address-operator oracles. The 12,532 nonzero entries split into 5,936 in E_X and 6,596 in E_H. + +Every pairwise product of S, E_X and E_H is zero, because all three maps land in Y and none reads Y. Before executing the center-cleared word, apply `I-E_H`. Every required source and target is in the actual ground chart: the targets are Y and the sources are those 106 ground-ended helpers. The operation is the explicit list of 6,596 dyadic ADDs. + +Consequently + +`M_0 (I-E_H) = I+S+E_X`. + +Thus `A=I+E_X` on the 112 main port indices gives the claimed offer, with no helper contamination. Scalar operations in one common address chart have their exact owner-space action, so this is a physical fixed-template pre-compensation and not an abstract change of logical coordinates. + +For the backward direction, the separately emitted center-cleared source word is verified to equal `I-S^T-E_X^T-E_H^T`, with the source's distinct inverse-transpose native letters. Prepend `I+E_H^T`, again using only actual ground-chart fields. The product is `I-S^T-E_X^T`. The verifier compares all 632 independent rows in both orientations. The owned center field is empty at termination. + +## Explicit code, inverse and conditioning + +The same exact entries satisfy + +`E_X^T = E_X, E_X^2 = -14 E_X, tr(E_X) = -112`. + +Set `P=-E_X/14`. It is a real symmetric idempotent of trace 8, hence an orthogonal projection of rank 8. Therefore + +`A=I-14P`, + +with eigenvalue -13 on the eight-dimensional image of P and eigenvalue +1 on its 104-dimensional kernel. In particular + +`A^-1 = I + E_X/13`, + +and its Euclidean condition number is exactly 13. The complete main shear is I+N_A with N_A^2=0 and ||N_A||_2=13; both it and its inverse have norm at most 14, so its condition number is at most 196. Helpers are an independent identity block, and the physical boundary charts are unitary, so this same bound applies to the complete physical coded offer. Its inverse uses I-N_A and needs no 1/13 arithmetic; 1/13 appears only when separately inverting the main code A. Every diagonal entry of A is zero; its 5,824 nonzero off-diagonal entries are ±1/2. The exact checker verifies the degree-two polynomial entry by entry over rational arithmetic, so the spectrum and inverse are universal consequences of that identity rather than numerical eigenvalue observations. + +The coefficient 1/13 is part of the mathematical inverse formula. This deliverable does not call it a free dyadic SCALE, assume a division oracle, or insert A^-1 across different physical address charts without paying for the resulting adapters. + +## Arbitrary fiber widths + +The replay identities hold over Q[FreeGroup72]. Every consistently shared invertible assignment of the 72 native operators defines an evaluation homomorphism. Hence the logical word identity holds at every positive column multiplicity under the retained source native implementation. It does not rely on one-column matrix testing, erasure of central phases or tensor powers preserving sums. + +Every physical frame, native monomial and Gaussian child is retained from the authenticated source, except the eight deleted owned-center calls. The new instructions are only constant dyadic scalar operations at an explicitly common ground chart. No fresh nonmonomial address implementation is introduced. + +The exact observed maximum prefix coefficient ℓ1 norms are 457 forward and 258 backward, checked on the fixed free-symbol words. Unitary evaluation bounds intermediate exact states and perturbations at the initial input in the maximum-over-fields Euclidean fiber norm by fixed constants independent of fiber width. For discrepancies inserted at later sites, use a separate suffix bound: assign each scalar ADD or SCALE of coefficient c the bound 1+|c|, and every unitary Gaussian/monomial, owned CLEAR or owned COPY the bound 1. The product of these elementary bounds over the finite word bounds every suffix. Thus the sum of local error magnitudes times this fixed product bounds propagated rounding error; no prefix norm is substituted for a suffix norm. Entrywise infinity-norm statements require the appropriate square-root fiber-volume conversion. There is no precision-dependent epsilon and no recursive border-precision claim. + +## Integration boundary + +The old source wrapper's port-dependent entrance lines and exit hyperplanes remain. A is a constant matrix in the stated normalized logical coordinates. It must not be silently treated as a constant free recoding in every physical main chart or in a different standardized central-Q ABI. Its nonzero off-diagonal entries connect distinct entrance-line charts. A useful next step is an actual coded caller or a paid simultaneous adapter that exploits the eight-mode structure, together with complete moment, raw-dual, compiler, finite precision and outer recovery budgets. This document supplies the exact producer and its bill, not those missing consumers. + +## Predecessor overlap and credit + +Cinna Davis's PR #4694, head `2add42d1edf14a263abe90a3bcde67fc1ba30768`, already emits a center-free kernel with paid profile minus eight rank-eight calls, records its coupled cache ABI, constructs its raw dual, and proves that its 106 observed helpers start at the empty chart. The source CACHE.md was read directly. None of center deletion, the cold-helper observation or the abstract block Schur elimination is claimed here as new. PR #4698, scientific head `9079ab66ba9a1717df478a08eb957c20d84d3e61`, already emits a dyadic helper basis of 379 gates in each direction reducing observations to eight helpers, and a conditional consumer. The present deliberately dense 6,596-ADD pre-compensation is easier to audit, not a claim to a better basis count. Its changed sufficient result is the actual fixed-template helper-independent coded offer, explicit A entries, exact eight-mode spectrum/inverse/conditioning, and unchanged independent helper ABI. + + +Cao Yifan / intqwq supplies the joint-helper/native-map round-three word at canonical `research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz`, commit `624de9dc66858af0945e5f8a0942488d62280d43`. Its predecessor and refreshed public lineage includes PR #4610; the exact source package and bytes, rather than an older PR headline, bind this result. Cinna Davis, the PR #4470 native/helper/controller lineage, Dugongue's exact native and complementary-provider work, DaysSky, Nick Petalas, Ryanson Jonathan, Jacob Alan Sussman, zxv and the retained scalar, Clifford, precision, compiler and outer contributors retain predecessor credit. The common-chart pre-compensation and exact eight-mode code are the present construction. Local MathProof's Schur block elimination and low-rank composition notes motivated the representation; their source-only inspection is not a fresh Lean/kernel audit or a claim of priority for elementary projection algebra. diff --git a/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/native-center-free-code/SOURCE-WORD.json.gz b/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/native-center-free-code/SOURCE-WORD.json.gz new file mode 100644 index 0000000000..46d929df83 Binary files /dev/null and b/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/native-center-free-code/SOURCE-WORD.json.gz differ diff --git a/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/native-rank8-helper-provider/ATTRIBUTION.md b/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/native-rank8-helper-provider/ATTRIBUTION.md new file mode 100644 index 0000000000..efe3acb566 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/native-rank8-helper-provider/ATTRIBUTION.md @@ -0,0 +1,50 @@ +# Predecessors and exact scope + +Ali Romman's [PR5383](https://github.com/CrocSwap/integer-mult-bounds/pull/5383), +head `4bd6efa51a495a7c7b7754915cf0244e7e60969e`, supplies the exact eight +cached-center candidate rows and sites. Its WITNESS is retained verbatim as +package-local candidate data. The byte hash is checked, and all used +relations, chronology and zero-call claims are independently recomputed from +the pinned main native source. The PR head is provenance, not a required Git +object or an assumed accepted theorem. We do not claim priority for the +cached-center relation or for center deletion. + +Cao Yifan / intqwq supplies `kappa-round3-warp-20261022`'s canonical native +helper/map/contact source and the PR4610 lineage. Its exact payload is +retained by main's `native-center-free-code/SOURCE-WORD.json.gz`. +Dugongue / mdumitrean supplies [PR4929](https://github.com/CrocSwap/integer-mult-bounds/pull/4929)'s +center-free code, eight-mode factorization, source construction and analytic +interpretation. Cinna Davis / 1337isnot1337 supplies the +[PR4694](https://github.com/CrocSwap/integer-mult-bounds/pull/4694) retained-center +interface, [PR4698](https://github.com/CrocSwap/integer-mult-bounds/pull/4698) +common-chart helper basis and conditional consumer, and +[PR4470](https://github.com/CrocSwap/integer-mult-bounds/pull/4470) controller. +A retained cache or eight-dimensional defect is not newly discovered here. + +The pinned `coded-native-caller` supplies the physical main normalizers, +corrected conjugated backward convention, compiled wrapper recipes, contact +matrix M, and exact Clifford evaluator. Its Clifford source traces through +`t74-native-fast/vendor/native/new/code/borrow/vendor/clifford`; retain zxv's +native/productive/compiler work and the original license. Retain Jacob Alan +Sussman's mixed-target recursion, Ryanson Jonathan's controller checks, +Dugongue's transported-frame lemma and the cumulative helper/native lineage +identified by the predecessor packages. The exact shared bytes are pinned in +SOURCES.json rather than duplicated under new authorship. + +Within this continuation, coordinated OpenAI Codex agents constructed the +unrestricted retained-cache source, independently replayed all 641 columns, +derived the dual retraction and physical rank-eight normalization, and +reviewed the basis costs. This package combines that work into one fresh +registered replay with an explicit all-owner boundary recipe, verbatim +candidate provenance, local bill and every-positive-width proof. New work is +the fully owned **coupled** provider with all 632 originals preserved and all +nine owned outputs cleared. It is not a caller, an autonomous H8 donor, an +exponent improvement, a formal-kernel proof or independent human review. + +The broader investigation and priority/overlap checkpoints remain in the +campaign's [Discussion4930](https://github.com/CrocSwap/integer-mult-bounds/discussions/4930) +and TASK.json. This package preserves the same frozen native payload while +binding its publication task metadata to main at +`1ec1119972c9aefe42525172d07b332fcff81cb4`. It does not claim an exhaustive +novelty search or alter the selected result. Prepared for Dillon with +substantial OpenAI Codex assistance. Apache-2.0. diff --git a/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/native-rank8-helper-provider/PROOF.md b/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/native-rank8-helper-provider/PROOF.md new file mode 100644 index 0000000000..5cbfc4fd02 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/native-rank8-helper-provider/PROOF.md @@ -0,0 +1,236 @@ +# A source-bound backward provider with eight coupled rank-eight outputs + +The construction has 632 arbitrary original inputs and nine arbitrary owned +inputs. Its paid native profile is +`{1:2193,2:412,3:510,4:127,5:40}`. It returns 400 unchanged native helper jobs +and a coupled block on the 224 main and eight remaining helper owners: + +\[ + X=Dx-Ry+RW h,\qquad Y=Dy,\qquad H=D(h-Zy). \tag{1} +\] + +Here `R=DQ` is the full native rank-nine Gaussian, `D` acts on the eight +noncentral axes, and `Q` acts on the central axis. The eight `H` outputs remain +coupled; they are **not eight autonomous H8 targets**. No complete caller or +new multiplication exponent follows. All nine owned outputs are zero. + +## 1. Exact source and the changed word + +`SOURCES.json` pins the main-branch source, code, normalizers and Clifford +compiler. The native source's decompressed SHA256 is +`cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd`. +`WITNESS.json` retains Ali Romman's PR5383 candidate verbatim, with SHA256 +`24599011da06325e1012619b2b84a4dd3aceb90ab42d3caaf6414879e7d16591`. +It supplies candidate sites and rational rows; it is not a proof oracle or a +pending Git-object dependency. Every used identity is checked again against +the pinned main source. + +For witness row `i`, after the indicated original `cached_event`, CLEAR owned +`C[i+1]` and COPY the indicated persistent row into it at its actual chart. +Every cache precedes every removed center. At the original center event, +replace the H8 call by CLEAR `C0`, then COPY `C[i+1]` into `C0` at that same +rank-eight chart. At the indicated later H1 call, replace the call by a +`zero_retag`: this is physical identity on the **exactly zero** field, with +its bookkeeping chart changed to the old call's output chart. All other +instructions, including inherited physical metadata, remain unchanged. +`WORD.json.gz` emits the complete resulting backward native word; the verifier +regenerates it from the canonical source and compares its parsed content. + +The replay begins with one independent formal column per field, including +all nine owned fields. It tracks exact rational coefficients in the free +group on the source's native warp symbols, their inverses, and actual chart +tags. Every ordinary operation is checked at its true chart. COPY fills only +owned zero; CLEAR acts only on owned fields. Before each of the eight retags, +every one of the 641 input coefficients is zero. All initial owned dirt is +cleared before use and is absent from every endpoint. + +The source's ten `phase` records are named stage annotations, not scalar +Clifford phase gates; its 448 `adapter` records retain the predecessor's +physical entrance/exit bindings (there are no `residual_adapter` records in +this backward word). As in the pinned predecessor normalized-row semantics, +these do not update formal rows. They are preserved in the emitted word, +not deleted or priced away. Their physical interpretation and native cost +are inherited; this package separately verifies every new physical boundary +identity including absolute phase. + +The same interpreter replays the original source, obtaining its full +632-row normalized backward endpoint `(x-y,y,h)` and clean original temporary. +It separately replays center deletion to derive the native coupling below. +The changed word has eight fewer H8 and eight fewer H1 calls than the original +source, with no additional Gaussian call. It has 16 extra COPYs and 16 extra +CLEARs. This is a changed source construction, not a constraint such as +`Delta h=0` on otherwise independent inputs. + +## 2. Source-derived coupling and an ordinary helper basis + +Use the inherited 112-by-8 matrix `M`, stored transposed as `mode_columns`. +The verifier checks all entries of + +\[ + M^T M=56I_8,\qquad A=I-MM^T/4. +\] + +Fresh replay of the center-deleted source gives + +\[ + X=x-A^Ty,\qquad Y=y,\qquad H=h-B^TM^Ty. +\] + +The verifier derives every entry of `B` by projecting the actual 408-by-112 +helper-to-Y coefficient matrix onto `M/56`; it then checks the entire +factorization and all 632 endpoints. The eight candidate rows `Delta` satisfy +`Delta B^T = S`, an exactly checked signed permutation. Put `E=S^-1 Delta`. +Thus `E B^T=I8`. Fresh original-prefix replay also binds the candidate cache +rows, their chronology and their actual rank-eight charts. + +In these coordinates the changed word has normalized endpoint + +\[ + X=x-y+(M/4)Eh,\quad Y=y,\quad H=(I-B^TE)h, \tag{2} +\] + +and its canonical mode-`k` cache is + +\[ + f_i(E_kh-M_k^Ty),\qquad f_i=\texttt{zero_factor}_i\,S_{ik}. \tag{3} +\] + +The registered check composes all changed endpoint rows with the following +basis, rather than accepting (2) or (3) from a saved endpoint registry. + +The union of supports of `B` and `E` comprises 122 actual cold H9 owners: each +has ground entrance chart and full-R exit chart. Choose the eight original +mode owners `[224,225,227,229,240,241,256,257]`. Define `L` on these 122 owners: +its mode columns are `B^T`; its other columns are `(I-B^TE)e_j`. Exact +Gauss-Jordan reduction constructs `L^-1` and verifies both inverse products, +`EL` selecting precisely the eight mode coordinates, and `L^-1B^T` embedding +precisely those coordinates. Every coefficient is dyadic. The emitted +`input_basis_program` and `output_basis_program` execute these two maps in +place, without extra owned basis storage. + +Both bases mix only fields sharing the appropriate physical chart, so scalar +owner operations implement them ordinarily. After entrance `L` and exit +`L^-1`, every one of the 632 persistent rows is checked: the eight selected +helper rows are zero, the other 400 helper rows are unchanged, `Y=y`, and +`X=x-y+(M/4)h_mode`. Each cache is exactly +`f_i(h_mode,k-M_k^T y)`. Thus the cache fills a vacated original direction; +it supplies no additional productive input or job credit. + +## 3. Literal physical boundary maps and ownership + +Backward frames use complex conjugation of the native frames, as in the +pinned source convention; they are not silently replaced by adjoints. Let +`Kp` be the 112 inherited main normalizers. For each actual cache frame `F8`, +the verifier constructs an orthogonal, phase-correct monomial `Km` from its +unique missing odd noncharacteristic line, and compiles a monomial `N` with + +\[ + N\overline{F8}K_m=D,\qquad K_mR=RK_m. +\] + +`PROVIDER.json` contains all eight literal `Km` and `N` words, signed tableaux +and nonzero zero-column phase anchors. The compiler's output is checked +explicitly even under Python `-O`. All `Kp` commute with `R`, including +absolute phase. Every boundary word contains only monomial gates. + +Apply `2Km` to the eight original mode inputs before `L`. At the exit, apply +`N/(2f_i)` to each cache. Use the inherited **fused compiled** backward main +input/output wrappers. The verifier checks 336 main diagonal/shear blocks, +896 nonzero main/helper coupling blocks and eight helper diagonal blocks, +for 1,240 exact physical equations. Comparison includes the signed tableau +and exact zero-state vector, so an undetected global phase is impossible +within this Clifford model. These equations yield (1), with + +\[ + W=\operatorname{diag}(K_p^{-1})M\operatorname{diag}(K_m)/2, + \quad + Z=\operatorname{diag}(K_m^{-1})M^T\operatorname{diag}(K_p)/2. +\] + +The main code is the predecessor's `C=diag(Kp^-1) A diag(Kp)`. Exact word +cancellation and the scalar factorization give +`ZW=14I8`, `WZ=I-C`; `W` and `Z` intertwine `R` on their respective banks. +No commutation with `D` or `Q` is assumed. These are finite ordinary code +maps with exterior scalar coefficients, not additional Gaussian calls. + +After normalization, SWAP each cache's **whole physical field and chart tag** +with its identically zero original mode output. The original owner now holds +the normalized coupled output; the owned slot holds zero and can be CLEARed. +There is no persistent erasure and no attempted free chart conversion of a +nonzero field. `C0` is already zero, so all nine owned outputs are zero. +Ordering the coupled input/output banks as `(y,h,x)` makes (1) triangular +with invertible diagonal `D`. Together with the 400 unchanged native jobs, +this proves preservation of all 632 original input directions. It does not +emit an inverse schedule or establish a same-cost inverse/transpose. + +## 4. Exact local bill + +Relative to the original raw backward source, the selected schedule adds: + +| Ordinary operation | Added field operations | +| --- | ---: | +| ADD | 1,644 | +| SCALE | 40 | +| COPY | 16 | +| CLEAR | 24 | +| Whole-field SWAP, with chart tag | 8 | +| Monomial field map | 464 | + +Each basis direction uses 822 ADD and 12 SCALE: its three elimination swaps +are expanded into three ADDs and one SCALE each. Eight input scalings and +eight cache scalings give the remaining 16 SCALEs. The source rewrite adds +16 COPY and 16 CLEAR; final cache consumption adds eight CLEAR. The 464 +monomial maps are 448 fused inherited main standardizers, eight `Km` and +eight `N`. This counts the newly installed boundary schedule; all unchanged +source warp/phase/adapter traffic and native child implementations remain in +the emitted word and retain their inherited costs. In particular, this table +does not assert that a field monomial map is zero machine work. + +The original source has 16,273 ADD, 1,164 SCALE and 16 CLEAR. Including the +new boundary scalars, the schedule therefore has 17,917 ADD, 1,204 SCALE, +16 COPY, 40 CLEAR and eight whole-field SWAP, plus the explicitly described +monomial boundary maps and inherited native operations. Nine owned fields +suffice: the original center temporary and eight retained caches. Their +initial values are arbitrary; their final values are zero. The autonomous +helper profile is `{4:28,7:7,8:47,9:318}`. The physical implementations of +those unchanged native helper jobs are inherited from the pinned source; +scalar identity rows alone are not a new proof of those implementations. + +For an explicit local stability bound, use the maximum of field Euclidean +norms. ADD by `a` has norm at most `1+|a|`, SCALE has norm at most +`max(1,|a|)`, and unitary Gaussian/monomial maps, COPY, CLEAR and SWAP have +norm at most one. The verifier sums upward-rounded base-two logarithms for +every scalar operation in this finite schedule, obtaining **18,996**. Hence +every suffix amplifies an injected field error by at most `2^18996`; at most +`m` injections of norm `epsilon` give the conservative bound +`m*2^18996*epsilon`. All dyadic constants and word lengths are fixed. This +establishes local bounded amplification, not a complete coordinate rounding, +tape movement, recursive precision or outer multiplier budget. + +## 5. Every positive fiber width and verification boundary + +A free-group identity evaluates in any assignment of invertible native warp +operators. Therefore the exact rational row equalities and zero-retag +premises hold uniformly when native operations act on any positive fiber +width `f`. The scalar owner coefficients and scalar `L/L^-1` programs stay +outside the tensor product; in particular `ZW=14I`, not `14^f I`. Each +compiled monomial word uses the inherited prescription: `P` and `X` act +columnwise, `D` sums its Z4 polynomial over the columns, and a `phase` gate +contributes its phase once per column. Each address-operator identity is lifted +columnwise; an absolute phase `i^gamma` lifts to `i^(f gamma)`, rather than +being confused with an exterior scalar sign. Exact one-column operator +identities, word cancellation and rational matrix identities then prove the +same physical boundary composition for every `f`. The inherited native +uniform implementation hypotheses remain inherited. + +The registered verifier performs complete 641-column native row replay, +exact scalar endpoint composition, and the 1,240 physical boundary checks. +It does not claim a separately flattened 641-column physical-matrix replay, +a formal-kernel proof, independent human approval, hosted CI, or a complete +caller. It rejects a nonzero zero-retag, a single changed basis ADD +coefficient, a changed saved-cache coefficient and a phase-only error with +the correct tableau. Normal and optimized runs use explicit checks for the +new claims. The caller must close all 224 main and eight coupled helper +outputs, preserve the other 400 jobs, charge every added child and ordinary +operation, and discharge precision, storage and outer-budget obligations +before any new target credit or exponent is admitted. diff --git a/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/native-rank8-helper-provider/PROVIDER.json b/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/native-rank8-helper-provider/PROVIDER.json new file mode 100644 index 0000000000..0afd30ed01 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/native-rank8-helper-provider/PROVIDER.json @@ -0,0 +1,13105 @@ +{ + "schema_version": 1, + "source_payload_sha256": "cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd", + "candidate_witness_sha256": "24599011da06325e1012619b2b84a4dd3aceb90ab42d3caaf6414879e7d16591", + "word_payload_sha256": 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+ "paid": { + "1": 2193, + "2": 412, + "3": 510, + "4": 127, + "5": 40 + }, + "autonomous_native_helpers": { + "4": 28, + "7": 7, + "8": 47, + "9": 318 + }, + "owned_fields": { + "count": 9, + "initial_values": "arbitrary", + "final_values": "zero", + "productive_credit": 0 + }, + "added_ordinary_work_vs_original_raw_source": { + "ADD": 1644, + "SCALE": 40, + "COPY": 16, + "CLEAR": 24, + "whole_field_SWAP": 8, + "monomial_field_maps": 464, + "monomial_breakdown": { + "fused_inherited_main_standardizers": 448, + "mode_inputs": 8, + "cache_outputs": 8 + } + }, + "local_error_amplification_power2_bound": 18996, + "source_original_scalar_counts": { + "add": 16273, + "clear": 16, + "scale": 1164 + }, + "source_changed_scalar_counts": { + "add": 16273, + "clear": 32, + "copy": 16, + "scale": 1164 + }, + "physical_phase_bindings": { + "main_diagonal_and_shear": 336, + "two_coupling_directions": 896, + "helper_diagonal": 8 + }, + "exact_zero_retags": [ + [ + 15608, + 92, + 254, + 1 + ], + [ + 15894, + 9, + 624, + 1 + ], + [ + 15900, + 11, + 621, + 1 + ], + [ + 17269, + 240, + 280, + 1 + ], + [ + 17280, + 81, + 619, + 1 + ], + [ + 17288, + 57, + 274, + 1 + ], + [ + 17604, + 288, + 281, + 1 + ], + [ + 17746, + 224, + 279, + 1 + ] + ], + "formula": { + "X": "D x - R y + R W h", + "Y": "D y", + "H": "D (h - Z y)", + "W": "diag(K_port^-1) M diag(K_mode)/2", + "Z": "diag(K_mode^-1) M^T diag(K_port)/2" + }, + "failure_controls": [ + "nonzero zero-retag rejected", + "one altered basis ADD coefficient rejected", + "same-tableau phase-only cache error rejected", + "one altered saved-cache coefficient rejected" + ], + "scope": "Changed coupled backward provider. No autonomous credit for eight coupled outputs; no completed caller, inverse/transpose implementation, new kappa or selected-result change." +} diff --git a/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/native-rank8-helper-provider/README.md b/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/native-rank8-helper-provider/README.md new file mode 100644 index 0000000000..92d0d7e523 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/native-rank8-helper-provider/README.md @@ -0,0 +1,83 @@ +# Eight coupled helper outputs from the retained-center native word + +This package constructs and replays an exact changed backward native provider +on all 632 original owners. It replaces eight rank-eight center calls by +retained earlier same-frame caches; eight later H1 inputs become identically +zero and their calls disappear. The resulting paid profile is +`{1:2193,2:412,3:510,4:127,5:40}`: the center-free profile minus eight H1 calls. + +After explicit ordinary basis and boundary operations, the coupled outputs are + +```text +X = D x - R y + R W h +Y = D y +H = D(h - Z y) +``` + +Here `R=DQ`, `D` is the native rank-eight Gaussian, `ZW=14I8`, and `WZ=I-C` +for the existing physical code `C`. The 400 other original helpers retain +their native jobs, with profile `{4:28,7:7,8:47,9:318}`. All nine owned fields +start arbitrary and finish zero. **The eight H outputs remain coupled; no +new autonomous Gaussian targets, complete caller or improved κ are claimed.** + +[PROOF.md](PROOF.md) gives the every-positive-width argument, ownership rule, +exact local bill and precision boundary. [WORD.json.gz](WORD.json.gz) is the +complete changed native word. [PROVIDER.json](PROVIDER.json) is its ordered +boundary recipe, including explicit dyadic basis programs and phase-bound +monomial words; its references to the pinned source main normalizers are part +of that recipe. The verifier recomputes the word and recipe from authenticated +main inputs, with no scratch paths or network access. + +The new schedule adds 1,644 ADD, 40 SCALE, 16 COPY, 24 CLEAR, eight physical +SWAPs and 464 monomial maps relative to the original raw source. The 464 maps +include 448 fused inherited main wrappers. Unchanged native internal traffic +and implementations remain inherited. These are ordinary work, not free +machine operations. Nine owned fields suffice without basis scratch storage. + +## Reproduce + +From the repository root, using only Python 3.12 and its standard library: + +```sh +python3.12 -B scripts/research_package.py --package research/native-rank8-helper-provider +python3.12 -I -Werror -B research/native-rank8-helper-provider/verify.py +python3.12 -I -Werror -O -B research/native-rank8-helper-provider/verify.py +``` + +The registered normal and optimized commands check all 641 native input +columns, every original endpoint, all nine owned outputs and 1,240 physical +phase bindings. Mutation controls reject a changed basis ADD coefficient, a +changed cache coefficient, nonzero zero-retag input and a same-tableau phase +error. A direct run takes about 13 seconds on the preparation machine; the +registered pair is bounded separately in [VERIFY.json](VERIFY.json). +`--emit` regenerates only the package-local `PROVIDER.json`; normal replay is +read-only. Frozen scientific source inputs are never regenerated or modified. + +[WITNESS.json](WITNESS.json) retains Ali Romman's PR5383 candidate verbatim, +from head `4bd6efa51a495a7c7b7754915cf0244e7e60969e`, SHA256 +`24599011da06325e1012619b2b84a4dd3aceb90ab42d3caaf6414879e7d16591`. +The candidate is package-local data; every used relation is reproved against +main's native source. No pending PR Git object is required. The phase engine, +existing code and native implementation retain their predecessor proof +boundaries; this is author-side exact replay, not formal or human acceptance. + +## Open next questions + +The complete structured obligations are in [TASK.json](TASK.json). A caller +must close the 224 main and eight coupled helper outputs while retaining the +400 autonomous helpers per call, price all additional children and ordinary +work, then prove its final Gaussian ranks, chronology, finite precision and +outer budget. Begin with one fully owned caller identity; a field becoming +available at rank eight is insufficient for autonomous target credit. The +selected frontier is unchanged. + +## Credit + +Ali Romman supplies PR5383's exact cached-center relations. Cao Yifan supplies +the native round-three helper/map word; Dugongue supplies the center-free code +and its factorization; Cinna Davis supplies the earlier retained-center, +helper-basis and controller work. Retain zxv's Clifford/native/compiler work, +Jacob Alan Sussman's recursion, Ryanson Jonathan's controller checks, and the +full source lineage. See [ATTRIBUTION.md](ATTRIBUTION.md). Prepared for Dillon +with substantial OpenAI Codex assistance from coordinated construction, +mechanism and review agents. Apache-2.0. diff --git a/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/native-rank8-helper-provider/SOURCES.json b/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/native-rank8-helper-provider/SOURCES.json new file mode 100644 index 0000000000..dd77397ca5 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/native-rank8-helper-provider/SOURCES.json @@ -0,0 +1,54 @@ +{ + "schema_version": 1, + "base_commit": "1ec1119972c9aefe42525172d07b332fcff81cb4", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "b288ae44032fd84dd5564243422836cbcd29835e", + "sha256": "f9ed52bb642cd1e1486cf2743557ac5fa23cf1514a3277d786a644e39a565038" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602", + "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72" + }, + { + "path": "research/coded-native-caller/NORMALIZERS.json", + "usage": "input", + "git_blob": "bca92c222c395d3d75c047fbb678f3cd0947c60f", + "sha256": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da" + }, + { + "path": "research/coded-native-caller/PHYSICAL.md", + "usage": "input", + "git_blob": "da8837ba67423ef08ef1afb8e8297a8032aafe9f", + "sha256": "4321b159ff8d3fe705419adaaa1beef75606e869e34341bda553f17d598a6078" + }, + { + "path": "research/coded-native-caller/clifford_exact.py", + "usage": "input", + "git_blob": "166841a037f069249f6f7f6dedb89248812f59e2", + "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962" + }, + { + "path": "research/native-center-free-code/CODE.json", + "usage": "input", + "git_blob": "03170f4a31f7a8a3db7228f1cd5a6fdcb32720ae", + "sha256": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0" + }, + { + "path": "research/native-center-free-code/CODED-PROOF.md", + "usage": "input", + "git_blob": "1f28d33884ec99b34f8366d022d8f7b9b7653ae2", + "sha256": "acd904af677718da8cdaf81d205d29866a6855efd393047e7128320a46753b01" + }, + { + "path": "research/native-center-free-code/SOURCE-WORD.json.gz", + "usage": "input", + "git_blob": "46d929df83817b85a5387bcdb9745e0627d6366e", + "sha256": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05" + } + ] +} diff --git a/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/native-rank8-helper-provider/TASK.json b/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/native-rank8-helper-provider/TASK.json new file mode 100644 index 0000000000..e82da0445c --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/native-rank8-helper-provider/TASK.json @@ -0,0 +1,88 @@ +{ + "schema_version": 1, + "task_id": "centre-path-sharing", + "priority_revision": 7, + "base_commit": "1ec1119972c9aefe42525172d07b332fcff81cb4", + "original_card": { + "id": "centre-path-sharing", + "question": "Can the 64-per-call centre path (eight rank-8 COPY/ERASE totals through the private temporary) be shared across calls or shrunk?", + "starting_points": [ + "docs/research/research-family-status.md", + "research/complex-local-word-ceiling/README.md", + "research/split-centres-global/proofs/PR386-BIT-GEOMETRY.txt", + "certificates/selected-result.json" + ], + "methods": [ + "Derive a fully charged favorable relaxation for sharing one centre path across k calls, including restoration, hosting and precision.", + "Prove a lower bound on copied information per call for the selected decoder contract." + ], + "acceptance_gate": "Show the changed centre charge and copy profile per call with every added restoration or hosting cost charged, and its ceiling via ceiling.ceiling(centre=...). A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "research/complex-local-word-ceiling/verify.py" + ], + "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING", + "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.", + "scope": "Positive control and planning budget only; this is not a new construction or full cold replay." + }, + "first_experiment": "Write the per-call centre charge and copy children for sharing across k = 2 calls, charge the sharing overhead, and screen it; stop this route if even the ideal sharing gains under 10%. Ideal budgets: free 2.80x, shared by two 1.90x (levers.py).", + "bottleneck_link": "The centre path consumes 64 of about 99.6 unpaid coordinates per call, i.e. about 64% of the raw deficit.", + "allowed_variations": [ + "One sharing pattern across a fixed number of calls.", + "One reduced copied-total contract for the existing decoder.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "scope_change_triggers": [ + "Removing copies without a replacement contract for the decoder's copied totals.", + "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts." + ], + "overlap_terms": [ + "centre path", + "copied totals", + "private temporary", + "shared centre", + "batching" + ] + }, + "scope_status": "refined", + "actual_scope": "Emit a source-bound backward provider using retained center caches and an invertible cold-helper basis, with eight coupled rank-eight helper outputs, all 632 original owners retained and all 9 owned outputs zero.", + "scope_change_reason": "The user explicitly authorized ambitious changed-source research and removed the hour limit. This focused result replaces the copied-center path using source-proved early observations, while preserving every original direction; it does not claim an autonomous supplier or complete caller.", + "bottleneck_link": "Deletes all eight native H8 center calls and eight later H1 calls. The new bottleneck is closing eight main/helper couplings under a paid, fully owned caller rather than treating them as autonomous H8 targets.", + "budget_minutes": null, + "stop_rule": "Freeze this focused provider once original/changed all-owner replay, explicit ordinary basis programs, exact physical boundaries, owned cleanup, operation counts and every-positive-width proof pass. Further caller work is separate and must close all original outputs before admitting target credit.", + "outcome": "partial", + "evidence": "Registered Python3.12 normal and optimized replay derives B from main source, reproves the verbatim Ali candidate, checks 641 native input columns and 1240 exact physical phase bindings, executes both 122-owner basis programs, clears all 9 owned outputs and rejects coefficient/phase/zero-retag mutations.", + "author": "Dillon / dillona", + "ai_assistance": "Substantial OpenAI Codex assistance from coordinated construction, mechanism, packaging and independent author-side review agents; no independent human or kernel acceptance claimed.", + "open_questions": [ + { + "question": "Can a complete chronological caller close all 224 main and eight coupled helper outputs while retaining 400 autonomous native helper jobs per provider?", + "why_it_matters": "The eight D outputs depend on main inputs and earn no autonomous target credit. The paid savings alone do not imply a recursive multiplier or improved kappa.", + "first_step": "Emit one fully owned caller word using the exact W/Z physical maps; replay every original input and output, price all added Gaussian calls and keep all helper outputs.", + "blocked_by": "No accepted closure with final Gaussian ranks, complete query invoice and owner chronology is supplied by this provider package." + }, + { + "question": "What finite-precision and machine-work budget supports any successful complete caller?", + "why_it_matters": "The local finite schedule has bounded amplification and exact dyadic coefficients, but those facts do not supply recursive rounding, indexed movement or the outer multiplication recurrence.", + "first_step": "Use the emitted ordinary counts and local 2^18996 suffix amplification bound to assign coordinate precision and movement costs to the proposed complete caller.", + "blocked_by": "Depends on a complete caller and its recursion/packing contract; this package claims only the source-bound local primitive." + } + ], + "checkpoint": { + "canonical_main": "1ec1119972c9aefe42525172d07b332fcff81cb4", + "priority_revision": 7, + "selected_kappa": "0.0030217758", + "frozen_source_payload_sha256": "cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd", + "overlap": [ + "Ali Romman PR5383 retained-center candidate at 4bd6efa51a495a7c7b7754915cf0244e7e60969e", + "Cinna Davis PR4694 retained-center and PR4698 common-chart helper basis", + "Dugongue PR4929 center-free code and coded-native-caller physical normalizers", + "PR5397 scoped owned-exchange ceiling, PR5398 direct backward conjugation and independent PR5399/5400 reviews; these do not supply this unrestricted coupled-output contract." + ], + "campaign_thread": "https://github.com/CrocSwap/integer-mult-bounds/discussions/4930", + "frontier_changed": false, + "checked_at_utc": "2026-10-23T22:26:00Z" + } +} diff --git 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} +] diff --git a/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/native-rank8-helper-provider/WORD.json.gz b/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/native-rank8-helper-provider/WORD.json.gz new file mode 100644 index 0000000000..f3111b47e8 Binary files /dev/null and b/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/native-rank8-helper-provider/WORD.json.gz differ diff --git a/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/native-rank8-helper-provider/verify.py b/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/native-rank8-helper-provider/verify.py new file mode 100644 index 0000000000..b62af49c87 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/5402/source-capsule/research/native-rank8-helper-provider/verify.py @@ -0,0 +1,602 @@ +#!/usr/bin/env python3 +"""Source-bound coupled provider, exact rational rows and absolute phases. + +No scratch registry, pending Git object, network access or third-party package. +The authenticated predecessor Clifford evaluator is the only imported module. +""" +from collections import Counter +from fractions import Fraction as F +from functools import lru_cache +from hashlib import sha256 +from pathlib import Path +import argparse +import gzip +import importlib.util +import json +import sys +import time + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parent.parent +SOURCE_HASH = 'cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd' +WITNESS_HASH = '24599011da06325e1012619b2b84a4dd3aceb90ab42d3caaf6414879e7d16591' +MODE = [224, 225, 227, 229, 240, 241, 256, 257] +PAID = Counter({1: 2193, 2: 412, 3: 510, 4: 127, 5: 40}) + + +def need(condition, message): + if not condition: + raise ValueError(message) + + +def enc(row): + return [[j, str(a)] for j, a in sorted(row.items()) if a] + + +def add(target, source, factor=1): + for key, value in tuple(source.items()): + value = target.get(key, F(0)) + factor * value + if value: + target[key] = value + else: + target.pop(key, None) + + +def addr(ref): + need(ref[0] in ('L', 'C'), 'unknown field kind') + return ref[1] + (632 if ref[0] == 'C' else 0) + + +def replay(program, c, owners, snapshots=()): + """Every owner is an independent free-group column, including dirty C fields.""" + rows = [{(j, ()): F(1)} for j in range(owners)] + charts = c['start'][:] + [None] * (owners - 632) + paid, scalar = Counter(), Counter() + zeros, dirt_clears, saved = [], [], {} + for event, e in enumerate(program): + kind = e[0] + if kind == 'scalar': + op, chart = e[1:] + dst = addr(op[1]) + scalar[op[0]] += 1 + if op[0] == 'clear': + need(dst >= 632, 'persistent CLEAR forbidden') + dirt = {k: v for k, v in rows[dst].items() if k[0] >= 632} + if dirt: + dirt_clears.append((dst, dirt)) + rows[dst], charts[dst] = {}, chart + else: + need(charts[dst] == chart, 'destination chart') + if op[0] in ('copy', 'add'): + src = addr(op[2]) + need(charts[src] == chart, 'source chart') + if op[0] == 'copy': + need(dst >= 632 and not rows[dst], 'COPY must fill owned zero') + rows[dst] = dict(rows[src]) + else: + need(dst != src, 'ADD self alias') + add(rows[dst], rows[src], F(op[3], op[4])) + else: + need(op[0] == 'scale', 'unknown scalar operation') + factor = F(op[2], op[3]) + rows[dst] = {k: v * factor for k, v in rows[dst].items() if v * factor} + elif kind == 'warp': + _, ref, warp, old, new = e + dst = addr(ref) + need(charts[dst] == old, 'warp chart') + symbol = (1 if warp > 0 else -1) * (abs(warp) + 1000000) + after = {} + for (owner, word), value in rows[dst].items(): + word = word[1:] if word and word[0] == -symbol else (symbol,) + word + add(after, {(owner, word): value}) + rows[dst], charts[dst] = after, new + elif kind in ('climb', 'center'): + if kind == 'climb': + _, _, dst, old, new, rank = e + expected = len(c['frames'][new]) - len(c['frames'][old]) + else: + _, dst, old, new, rank = e + dst += 632 + expected = abs(len(c['frames'][new]) - len(c['frames'][old])) + need(charts[dst] == old and rank == expected and rank > 0, + 'paid child chart/rank') + charts[dst] = new + paid[rank] += 1 + elif kind == 'zero_retag': + _, dst, old, new = e + need(charts[dst] == old and not rows[dst], 'zero retag has nonzero input') + zeros.append([event, dst, old, new]) + charts[dst] = new + else: + # Inherited source annotations / physical boundary bindings. The + # predecessor's normalized-row convention treats these as no row + # update; they remain byte-for-byte records in the emitted word. + # New physical boundaries are checked separately below, with phase. + need(kind in ('phase', 'adapter', 'residual_adapter'), 'unknown source record') + for at, owner in snapshots: + if event == at: + saved[(at, owner)] = (charts[owner], dict(rows[owner])) + return rows, charts, paid, scalar, zeros, dirt_clears, saved + + +def scalar(row): + need(all(not word for _, word in row), 'endpoint has unreduced native word') + return {j: a for (j, _), a in row.items()} + + +def rewrite(source, witness): + centers = {r['event']: i for i, r in enumerate(witness)} + late = {r['zero_event']: i for i, r in enumerate(witness)} + caches = {r['cached_event']: i for i, r in enumerate(witness)} + need(len(centers) == len(late) == len(caches) == 8, 'distinct eight sites') + need(max(caches) < min(centers), 'caches must precede all replacements') + word = [] + for event, op in enumerate(source['programs']['backward']): + if event in centers: + i = centers[event] + frame = witness[i]['frame'] + need(op == ['center', 0, 0, frame, 8], 'center source binding') + word += [['scalar', ['clear', ['C', 0]], frame], + ['scalar', ['copy', ['C', 0], ['C', i + 1]], frame]] + elif event in late: + r = witness[late[event]] + need(op == ['climb', 'warp_retimed', r['zero_role'], r['frame'], 1, 1], + 'late H1 source binding') + word.append(['zero_retag', r['zero_role'], r['frame'], 1]) + else: + word.append(op) + if event in caches: + i = caches[event] + r = witness[i] + word += [['scalar', ['clear', ['C', i + 1]], r['frame']], + ['scalar', ['copy', ['C', i + 1], ['L', r['cached_role']]], r['frame']]] + return {'source_sha256': SOURCE_HASH, 'direction': 'backward', 'word': word} + + +def inverse(matrix): + n = len(matrix) + a, b, ops = [dict(r) for r in matrix], [{j: F(1)} for j in range(n)], [] + for j in range(n): + k = next((i for i in range(j, n) if a[i].get(j)), None) + need(k is not None, 'singular basis') + if k != j: + a[j], a[k], b[j], b[k] = a[k], a[j], b[k], b[j] + ops.append(['swap', j, k]) + factor = 1 / a[j][j] + if factor != 1: + a[j] = {k: factor * v for k, v in a[j].items()} + b[j] = {k: factor * v for k, v in b[j].items()} + ops.append(['scale', j, str(factor)]) + for i in range(n): + if i == j or not a[i].get(j): + continue + factor = -a[i][j] + add(a[i], a[j], factor) + add(b[i], b[j], factor) + ops.append(['add', i, j, str(factor)]) + need(a == [{j: F(1)} for j in range(n)], 'basis reduction') + return b, ops + + +def ordinary(ops, roles, reverse=False): + out = [] + for e in reversed(ops) if reverse else ops: + if e[0] == 'swap': + a, b = roles[e[1]], roles[e[2]] + out += [['add', a, b, '1'], ['add', b, a, '-1'], + ['add', a, b, '1'], ['scale', b, '-1']] + elif e[0] == 'scale': + v = F(e[2]) + out.append(['scale', roles[e[1]], str(1 / v if reverse else v)]) + else: + v = F(e[3]) + out.append(['add', roles[e[1]], roles[e[2]], str(-v if reverse else v)]) + return out + + +def apply_ordinary(program, rows): + rows = [dict(r) for r in rows] + for e in program: + if e[0] == 'add': + need(e[1] != e[2], 'ordinary ADD alias') + add(rows[e[1]], rows[e[2]], F(e[3])) + else: + need(e[0] == 'scale', 'ordinary operation') + rows[e[1]] = {j: a * F(e[2]) for j, a in rows[e[1]].items() if a * F(e[2])} + return rows + + +def authenticate(): + pins = json.loads((HERE / 'SOURCES.json').read_text()) + for r in pins['files']: + if r['usage'] == 'input': + need(sha256((ROOT / r['path']).read_bytes()).hexdigest() == r['sha256'], + 'changed scientific input: ' + r['path']) + raw = gzip.decompress((ROOT / 'research/native-center-free-code/SOURCE-WORD.json.gz').read_bytes()) + need(sha256(raw).hexdigest() == SOURCE_HASH, 'native payload') + need(sha256((HERE / 'WITNESS.json').read_bytes()).hexdigest() == WITNESS_HASH, + 'Ali verbatim candidate provenance') + cp = ROOT / 'research/coded-native-caller/clifford_exact.py' + spec = importlib.util.spec_from_file_location('rank8_provider_clifford', cp) + ce = importlib.util.module_from_spec(spec) + sys.modules[spec.name] = ce + spec.loader.exec_module(ce) + return json.loads(raw), json.loads((HERE / 'WITNESS.json').read_text()), ce + + +def main(emit=False): + started = time.monotonic() + source, witness, ce = authenticate() + c = source['canonical'] + normal = json.loads((ROOT / 'research/coded-native-caller/NORMALIZERS.json').read_text()) + M = normal['mode_columns'] + A = [[F(a) for a in r] for r in json.loads((ROOT / 'research/native-center-free-code/CODE.json').read_text())['A']] + need(c['start'][112:224] == [0] * 112, 'main Y inputs have ground chart') + need(len(M) == 8 and all(len(r) == 112 for r in M), 'M dimensions') + need(all(sum(M[k][i] * M[l][i] for i in range(112)) == 56 * int(k == l) + for k in range(8) for l in range(8)), 'M Gram') + need(all(A[i][j] == F(i == j) - sum(F(M[k][i] * M[k][j], 4) for k in range(8)) + for i in range(112) for j in range(112)), 'A factorization') + original = replay(source['programs']['backward'], c, 633, + [(r['cached_event'], r['cached_role']) for r in witness]) + oldrows, oldcharts, oldpaid, oldscalar = original[:4] + expected = [{(j, ()): F(1)} for j in range(632)] + for j in range(112): + expected[j][(j + 112, ())] = F(-1) + need(oldrows[:632] == expected and not oldrows[632], 'original 632-row endpoint') + need(oldcharts[:632] == c['final'], 'original exit charts') + + centerfree = [['scalar', ['clear', ['C', e[1]]], e[3]] if e[0] == 'center' else e + for e in source['programs']['backward']] + cf = replay(centerfree, c, 633) + cfrows = [scalar(r) for r in cf[0]] + need(cf[1][:632] == c['final'] and not cfrows[632], 'center-free charts/owned') + P = [[-cfrows[j + 224].get(i + 112, F(0)) for i in range(112)] for j in range(408)] + B = [[sum(P[j][i] * M[k][i] for i in range(112)) / 56 for j in range(408)] for k in range(8)] + need(all(P[j][i] == sum(B[k][j] * M[k][i] for k in range(8)) + for j in range(408) for i in range(112)), 'full native coupling factorization') + for j in range(632): + row = {j: F(1)} + if j < 112: + for i in range(112): + if A[i][j]: + row[i + 112] = -A[i][j] + elif j >= 224: + for i, a in enumerate(P[j - 224]): + if a: + row[i + 112] = -a + need(cfrows[j] == row, 'center-free complete scalar endpoint') + + delta = [{j - 224: F(a) for j, a in r['relation']} for r in witness] + coupling = [[sum(a * B[k][j] for j, a in d.items()) for k in range(8)] for d in delta] + need(all(sum(bool(a) for a in r) == 1 and set(r) <= {F(0), F(1), F(-1)} + for r in coupling), 'candidate is not a signed retraction') + perm = [next(k for k, a in enumerate(r) if a) for r in coupling] + sign = [coupling[i][perm[i]] for i in range(8)] + need(sorted(perm) == list(range(8)), 'retraction permutation') + E = [{} for _ in range(8)] + for i, k in enumerate(perm): + E[k] = {j: sign[i] * a for j, a in delta[i].items()} + row = {(j + 224, ()): F(witness[i]['zero_factor']) * a for j, a in delta[i].items()} + for j in range(112): + a = -F(witness[i]['zero_factor']) * sign[i] * M[k][j] + if a: + row[(j + 112, ())] = a + need(original[6][(witness[i]['cached_event'], witness[i]['cached_role'])] + == (witness[i]['frame'], row), 'fresh original cached row binding') + need(all(sum(a * B[l][j] for j, a in E[k].items()) == int(k == l) + for k in range(8) for l in range(8)), 'E B^T identity') + active = sorted(set(j for r in B for j, a in enumerate(r) if a) | set(j for r in E for j in r)) + roles, index = [224 + j for j in active], {j: i for i, j in enumerate(active)} + need(len(active) == 122 and all(c['start'][j] == 0 and c['final'][j] == 1 for j in roles), + 'basis requires 122 actual cold H9 owners') + J = [j - 224 for j in MODE] + L = [{} for _ in active] + for k, j in enumerate(J): + for r in active: + if B[k][r]: + L[index[r]][index[j]] = B[k][r] + for j in active: + if j in J: + continue + for r in active: + a = F(r == j) - sum(B[k][r] * E[k].get(j, F(0)) for k in range(8)) + if a: + L[index[r]][index[j]] = a + Li, ops = inverse(L) + for left, right in ((L, Li), (Li, L)): + for i, row in enumerate(left): + product = {} + for j, a in row.items(): + add(product, right[j], a) + need(product == {i: F(1)}, 'two-sided basis inverse') + for k, row in enumerate(E): + product = {} + for j, a in row.items(): + add(product, L[index[j]], a) + need(product == {index[J[k]]: F(1)}, 'E L mode selection') + need(all(sum(a * B[k][active[j]] for j, a in row.items()) == int(i == index[J[k]]) + for i, row in enumerate(Li) for k in range(8)), 'Li B mode embedding') + need(all(a.denominator & (a.denominator - 1) == 0 + for matrix in (L, Li) for row in matrix for a in row.values()), 'dyadic basis') + entrance, exitword = ordinary(ops, roles, True), ordinary(ops, roles) + identity = [{j: F(1)} for j in range(632)] + entered = apply_ordinary(entrance, identity) + def check_basis(rows): + for i, j in enumerate(roles): + need(rows[j] == {roles[k]: a for k, a in L[i].items()}, 'literal L program') + check_basis(entered) + need(apply_ordinary(exitword, entered) == identity, 'literal Li program') + need(Counter(e[0] for e in entrance) == Counter(add=822, scale=12), 'basis program bill') + need(Counter(e[0] for e in exitword) == Counter(add=822, scale=12), 'inverse program bill') + + changed = rewrite(source, witness) + frozen_word = json.loads(gzip.decompress((HERE / 'WORD.json.gz').read_bytes())) + need(changed == frozen_word, 'committed exact word differs from source rewrite') + result = replay(changed['word'], c, 641) + rawrows, charts, paid, scalars, zeros, dirt = result[:6] + need(charts[:632] == c['final'] and not rawrows[632], 'changed persistent charts/C0') + need(paid == PAID and oldpaid == paid + Counter({1: 8, 8: 8}), 'paid children') + need(scalars == oldscalar + Counter(clear=16, copy=16), 'source ordinary delta') + need(len(zeros) == 8, 'eight exact zero retags') + need(len(dirt) == 9 and {j for j, _ in dirt} == set(range(632, 641)) + and all(d == {(j, ()): F(1)} for j, d in dirt), 'all arbitrary owned dirt cleared') + need(not any(j >= 632 for row in rawrows for j, _ in row), 'owned dirt leaked') + need(sum(rawrows[j] != oldrows[j] for j in range(632)) == 218, 'changed endpoint count') + endpoint = [] + for row in rawrows: + out = {} + for j, a in scalar(row).items(): + add(out, entered[j], a) + endpoint.append(out) + endpoint = apply_ordinary(exitword, endpoint) + for j in range(632): + expected = {} if j in MODE else {j: F(1)} + if j < 112: + expected[j + 112] = F(-1) + for k in range(8): + if M[k][j]: + expected[MODE[k]] = F(M[k][j], 4) + need(endpoint[j] == expected, 'composed all-owner endpoint at ' + str(j)) + def check_cache(i, row): + r, k = witness[i], perm[i] + factor = F(r['zero_factor']) * sign[i] + expected = {MODE[k]: factor} + for j in range(112): + if M[k][j]: + expected[j + 112] = -factor * M[k][j] + need(row == expected and charts[633 + i] == r['frame'], 'composed retained cache') + for i in range(8): + check_cache(i, endpoint[633 + i]) + first_cache = dict(endpoint[633]) + + def conjugate(op): + circuit = [] + for e in op.circuit: + if e[0] == 'D': + circuit.append(('D', e[1], tuple((-x) % 4 for x in e[2]))) + elif e[0] == 'C': + circuit.append(('C', e[1], -e[2])) + elif e[0] == 'phase': + circuit.append(('phase', (-e[1]) % 4)) + else: + circuit.append(e) + return ce.Op(9, tuple((x, z, -p % 4) for x, z, p in op.tab), circuit) + + @lru_cache(None) + def frame(j, back=False): + op = ce.canonical_frame(9, c['frames'][j]) + return conjugate(op) if back else op + + def literal(word): + op = ce.ident(9) + for e in word: + if e[0] == 'P': + part = ce.perm(9, tuple(e[1])) + elif e[0] == 'D': + part = ce.diag(9, tuple(e[1]), tuple(e[2])) + elif e[0] == 'X': + part = ce.xgate(9, e[1]) + elif e[0] == 'phase': + part = ce.Op(9, ce.identity(9), [('phase', e[1])]) + else: + raise ValueError('boundary contains a Gaussian gate') + op = op.then(part) + return op + + def equal(a, b): + return a.tab == b.tab and a.zero_state() == b.zero_state() + + def rank(op): + return ce.rank([x for x, _, _ in op.tab[9:]]) + + def receipt(op): + vec, den = op.zero_state() + j = next(j for j, a in enumerate(vec) if a != (0, 0)) + return {'literal_word': op.circuit, 'signed_tableau': op.tab, + 'zero_column_anchor': {'index': j, 'gaussian_numerator': vec[j], + 'denominator_power2': den}} + + def compile_monomial(op): + need(rank(op) == 0, 'nonmonomial boundary map') + compiled, _ = ce.monomial(op) + need(equal(compiled, op) and equal(literal(compiled.circuit), op), + 'literal phase-correct monomial compilation') + return compiled + + R, D = frame(1), ce.fourier(9, range(1, 9)) + Km, N = [None] * 8, [None] * 8 + records = [None] * 8 + for i, r in enumerate(witness): + k = perm[i] + candidates = [q for q in range(1, 512) + if all(ce.parity(q & v) == 0 for v in c['frames'][r['frame']])] + need(len(candidates) == 1, 'rank-eight missing line') + q = candidates[0] + need(q.bit_count() % 2 == 1 and q != 511, 'odd noncharacteristic line') + if not q & 1: + transvections = [1 ^ q] + else: + j = next(j for j in range(1, 9) if not q >> j & 1) + transvections = [1 ^ (1 << j), (1 << j) ^ q] + cols = [] + for j in range(9): + x = 1 << j + for v in transvections: + x ^= v if ce.parity(x & v) else 0 + cols.append(x) + G = ce.transpose(cols, 9) + z = sum((((row.bit_count() - 1) // 2) & 1) << j for j, row in enumerate(G)) + K = ce.perm(9, G).then(ce.diag(9, (0,) * 9, tuple(2 * ((z >> j) & 1) for j in range(9)))) + need(equal(K.then(R), R.then(K)), 'mode K/R absolute phase') + need(all((ce.mv(ce.transpose(G, 9), x).bit_count() - x.bit_count() + - 2 * ce.parity(z & x)) % 4 == 0 for x in range(512)), 'K weight congruence') + F8 = frame(r['frame'], True) + need(rank(F8) == 8, 'actual cache rank') + Km[k] = compile_monomial(K) + N[k] = compile_monomial(K.then(F8).adjoint().then(D)) + records[k] = {'mode': k, 'owner': MODE[k], 'cache_slot': 633 + i, + 'witness_row': i, 'frame': r['frame'], 'missing_line': q, + 'cache_scalar': str(1 / (2 * F(r['zero_factor']) * sign[i])), + 'input_K': receipt(Km[k]), 'output_N': receipt(N[k])} + Kp = [literal(r['K_word']) for r in normal['ports']] + checks = Counter() + for j, port in enumerate(normal['ports']): + need(port['port'] == j and rank(Kp[j]) == 0 and equal(Kp[j].then(R), R.then(Kp[j])), + 'port K binding and R commutation') + wrappers = port['compiled_wrappers'] + BX, BY, OX, OY = [literal(wrappers[key]['word']) for key in + ('backward_input_X', 'backward_input_Y', 'backward_output_X', 'backward_output_Y')] + birth, final, finalY = frame(c['start'][j], True), frame(c['final'][j], True), frame(c['final'][112 + j], True) + need(equal(BX.then(birth.adjoint()).then(final).then(OX), D), 'X diagonal physical block') + need(equal(BY.then(finalY).then(OY), D), 'Y diagonal physical block') + need(equal(BY.then(final).then(OX), R), 'main shear physical block') + checks['main_diagonal_and_shear'] += 3 + for k in range(8): + if not M[k][j]: + continue + need(equal(Km[k].then(final).then(OX), Km[k].then(Kp[j].adjoint()).then(R)), + 'helper-to-main physical coupling') + F8 = frame(records[k]['frame'], True) + need(equal(BY.then(F8).then(N[k]), Kp[j].then(Km[k].adjoint()).then(D)), + 'main-to-helper physical coupling') + checks['two_coupling_directions'] += 2 + for k in range(8): + need(equal(Km[k].then(frame(records[k]['frame'], True)).then(N[k]), D), + 'helper diagonal physical block') + checks['helper_diagonal'] += 1 + need(dict(checks) == {'main_diagonal_and_shear': 336, 'two_coupling_directions': 896, + 'helper_diagonal': 8}, '1,240 physical bindings') + autonomous = Counter(len(c['frames'][c['final'][j]]) - len(c['frames'][c['start'][j]]) + for j in range(224, 632) if j not in MODE) + need(autonomous == Counter({4: 28, 7: 7, 8: 47, 9: 318}), '400 retained native helper jobs') + # Physical normalization precedes a complete-field SWAP, including chart tags. + for r in records: + owner, cache = r['owner'], r['cache_slot'] + need(not endpoint[owner], 'SWAP destination must be identically zero') + endpoint[owner], endpoint[cache] = endpoint[cache], endpoint[owner] + need(all(not endpoint[j] for j in range(632, 641)), 'all owned outputs clean') + + # Failure controls invoke the same predicates as the construction. + controls = [] + bad_c = dict(c) + bad_c['start'] = c['start'][:] + bad_c['start'][0] = 0 + try: + replay([['zero_retag', 0, 0, 1]], bad_c, 641) + except ValueError as e: + need(str(e) == 'zero retag has nonzero input', 'wrong rejection') + controls.append('nonzero zero-retag rejected') + need(len(controls) == 1, 'zero-retag control accepted') + corrupted = [e[:] for e in entrance] + mutated = next(e for e in corrupted if e[0] == 'add') + mutated[3] = str(F(mutated[3]) + 1) + try: + check_basis(apply_ordinary(corrupted, identity)) + except ValueError as e: + need(str(e) == 'literal L program', 'wrong basis rejection') + controls.append('one altered basis ADD coefficient rejected') + need(len(controls) == 2, 'basis coefficient mutation accepted') + badN = ce.Op(9, N[0].tab, N[0].circuit + [('phase', 1)]) + need(badN.tab == N[0].tab and not equal(Km[0].then(frame(records[0]['frame'], True)).then(badN), D), + 'phase-only error escaped') + controls.append('same-tableau phase-only cache error rejected') + wrong = dict(first_cache) + add(wrong, {MODE[perm[0]]: F(1)}) + try: + check_cache(0, wrong) + except ValueError as e: + need(str(e) == 'composed retained cache', 'wrong cache rejection') + controls.append('one altered saved-cache coefficient rejected') + need(len(controls) == 4, 'saved-cache coefficient mutation accepted') + + # An explicit, conservative local error-amplification bound for this finite + # schedule. Gaussian and monomial field maps have Euclidean norm one. + def log2_bound(a): + a, exponent = max(F(1), a), 0 + while a > 1: + a /= 2 + exponent += 1 + return exponent + amplification = 0 + for e in changed['word']: + if e[0] == 'scalar': + op = e[1] + if op[0] == 'add': + amplification += log2_bound(1 + abs(F(op[3], op[4]))) + elif op[0] == 'scale': + amplification += log2_bound(abs(F(op[2], op[3]))) + for e in entrance + exitword: + amplification += log2_bound(1 + abs(F(e[3]))) if e[0] == 'add' else log2_bound(abs(F(e[2]))) + amplification += 8 * log2_bound(F(2)) + amplification += sum(log2_bound(abs(F(r['cache_scalar']))) for r in records) + + artifact = { + 'schema_version': 1, 'source_payload_sha256': SOURCE_HASH, + 'candidate_witness_sha256': WITNESS_HASH, + 'word_payload_sha256': sha256(gzip.decompress((HERE / 'WORD.json.gz').read_bytes())).hexdigest(), + 'basis_roles': roles, 'mode_owners': MODE, + 'candidate_mode_permutation': perm, 'candidate_mode_signs': list(map(str, sign)), + 'canonical_retraction_E': [enc(row) for row in E], + 'input_basis_program': entrance, 'output_basis_program': exitword, + 'mode_boundaries': records, + 'ordered_schedule': [ + 'Main input wrappers: NORMALIZERS.ports[j].compiled_wrappers.backward_input_X/Y.', + 'On each mode owner apply input_K and scalar 2; run input_basis_program.', + 'Run every instruction of WORD.json.gz; C0..C8 initially arbitrary.', + 'Run output_basis_program on the 122 persistent common-chart helpers.', + 'For each mode apply cache_scalar and output_N to its owned cache; SWAP the whole field and chart with its zero original owner; CLEAR the owned zero.', + 'Main output wrappers: NORMALIZERS.ports[j].compiled_wrappers.backward_output_X/Y.' + ], + 'paid': dict(sorted(paid.items())), 'autonomous_native_helpers': dict(sorted(autonomous.items())), + 'owned_fields': {'count': 9, 'initial_values': 'arbitrary', 'final_values': 'zero', 'productive_credit': 0}, + 'added_ordinary_work_vs_original_raw_source': { + 'ADD': 1644, 'SCALE': 40, 'COPY': 16, 'CLEAR': 24, 'whole_field_SWAP': 8, + 'monomial_field_maps': 464, + 'monomial_breakdown': {'fused_inherited_main_standardizers': 448, 'mode_inputs': 8, 'cache_outputs': 8}}, + 'local_error_amplification_power2_bound': amplification, + 'source_original_scalar_counts': dict(sorted(oldscalar.items())), + 'source_changed_scalar_counts': dict(sorted(scalars.items())), + 'physical_phase_bindings': dict(checks), 'exact_zero_retags': zeros, + 'formula': {'X': 'D x - R y + R W h', 'Y': 'D y', 'H': 'D (h - Z y)', + 'W': 'diag(K_port^-1) M diag(K_mode)/2', + 'Z': 'diag(K_mode^-1) M^T diag(K_port)/2'}, + 'failure_controls': controls, + 'scope': 'Changed coupled backward provider. No autonomous credit for eight coupled outputs; no completed caller, inverse/transpose implementation, new kappa or selected-result change.' + } + artifact = json.loads(json.dumps(artifact)) + path = HERE / 'PROVIDER.json' + if emit: + path.write_text(json.dumps(artifact, indent=2) + '\n') + else: + need(json.loads(path.read_text()) == artifact, 'committed boundary recipe differs from replay') + print('PASS_NATIVE_RANK8_HELPER_PROVIDER ' + json.dumps({ + 'original_inputs': 632, 'arbitrary_owned_inputs': 9, 'owned_outputs_zero': 9, + 'autonomous_helpers': 400, 'coupled_helpers': 8, 'paid': dict(sorted(paid.items())), + 'phase_bindings': sum(checks.values()), 'seconds': round(time.monotonic() - started, 3)})) + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--emit', action='store_true', help='regenerate the package-local boundary recipe') + main(parser.parse_args().emit) diff --git a/research/coupled-provider-independent-audit/custody/verify_custody.py b/research/coupled-provider-independent-audit/custody/verify_custody.py new file mode 100644 index 0000000000..ab91c961d7 --- /dev/null +++ b/research/coupled-provider-independent-audit/custody/verify_custody.py @@ -0,0 +1,67 @@ +#!/usr/bin/env python3 +"""Verify source-capsule SHA256 and Git origin bindings without Git or scientific imports.""" +from pathlib import Path +import hashlib +import json + +HERE=Path(__file__).resolve().parent + +def require(condition, message): + if not condition: raise ValueError(message) + +def verify(number): + root=HERE/number + report=json.loads((root/'SOURCE-CUSTODY.json').read_text()) + inventory=json.loads((root/'PRE-EXECUTION-HASHES.json').read_text()) + for row in inventory['files']: + path=root/row['path'] + data=path.read_bytes() + require(not path.is_symlink(),'symlink') + require(len(data)==row['bytes'] and hashlib.sha256(data).hexdigest()==row['sha256'],'changed inventory file '+row['path']) + require(path.stat().st_mode & 0o222 == 0,'source file writable') + def object_bytes(oid,kind): + row=report['raw_git_origin_objects'][oid] + data=(root/row['path']).read_bytes() + require(row['kind']==kind,'wrong object kind') + require(hashlib.sha1(kind.encode()+b' '+str(len(data)).encode()+b'\0'+data).hexdigest()==oid,'wrong Git identity') + return data + def tree_entries(data): + entries={} + while data: + split=data.index(b'\0') + mode,name=data[:split].split(b' ',1) + oid=data[split+1:split+21].hex() + entries[name.decode()]=(mode.decode(),oid) + data=data[split+21:] + return entries + def origin(binding,data): + commit=object_bytes(binding['commit'],'commit') + tree=commit.splitlines()[0].split()[1].decode() + parts=Path(binding['path']).parts + for part in parts: + mode,oid=tree_entries(object_bytes(tree,'tree'))[part] + tree=oid + require(oid==binding['git_blob'] and mode==binding['git_mode'],'tree path binding') + require(hashlib.sha1(b'blob '+str(len(data)).encode()+b'\0'+data).hexdigest()==oid,'blob bytes binding') + for row in report['runtime_files']: + data=(root/'source-capsule'/row['path']).read_bytes() + require(hashlib.sha256(data).hexdigest()==row['sha256'],'runtime SHA') + origin(row['origin'],data) + for row in report['source_rows']: + data=(root/row['stored_source']).read_bytes() + origin(row['origin'],data) + require(hashlib.sha256(data).hexdigest()==row['declared']['sha256'],'SOURCES SHA') + require(row['origin']['git_blob']==row['declared']['git_blob'],'SOURCES blob') + if row['declared'].get('retained_copy'): + retained=root/'source-capsule'/report['package']/row['declared']['retained_copy'] + require(retained.read_bytes()==data,'retained source copy') + result={'status':'PASS_OFFLINE_SOURCE_CUSTODY','source_pr':int(number),'head':report['head'], + 'inventory_files_checked':len(inventory['files']),'runtime_files_bound':len(report['runtime_files']), + 'source_rows_bound':len(report['source_rows']),'all_source_bytes_unchanged':True, + 'raw_commit_tree_blob_chain_verified':True,'git_invocations':0,'scientific_executions':0} + (root/'OFFLINE-CUSTODY-VERIFICATION.json').write_text(json.dumps(result,indent=2)+'\n') + print(json.dumps(result)) + +if __name__=='__main__': + for number in ['5402','5376']: + verify(number) diff --git a/research/coupled-provider-independent-audit/engine_adapter.py b/research/coupled-provider-independent-audit/engine_adapter.py new file mode 100644 index 0000000000..e0a448e61c --- /dev/null +++ b/research/coupled-provider-independent-audit/engine_adapter.py @@ -0,0 +1,30 @@ +#!/usr/bin/env python3 +"""Execute authenticated unchanged engines without loading bytecode or stripping asserts.""" +import sys +if not sys.flags.isolated: + import posix + posix.execv(sys.executable,[sys.executable,'-I',*(['-O']*sys.flags.optimize),'-B',*sys.argv]) +import importlib.abc +import importlib.machinery +from pathlib import Path +import os +sys.dont_write_bytecode=True +root=Path(sys.argv[1]).resolve() +engine=(root/sys.argv[2]).resolve() +if not engine.is_relative_to(root):raise ValueError('Engine outside private scratch') +class SourceOnly(importlib.machinery.SourceFileLoader): + def get_code(self, fullname): + raw=self.get_data(self.path) + return compile(raw,self.path,'exec',dont_inherit=True,optimize=0) +class LocalFinder(importlib.abc.MetaPathFinder): + def find_spec(self,fullname,path=None,target=None): + spec=importlib.machinery.PathFinder.find_spec(fullname,path,target) + if spec and spec.origin and spec.origin.endswith('.py') and Path(spec.origin).resolve().is_relative_to(root): + spec.loader=SourceOnly(fullname,spec.origin) + return spec +sys.meta_path.insert(0,LocalFinder()) +sys.path.insert(0,str(engine.parent)) +sys.argv=[str(engine),*sys.argv[3:]] +os.chdir(root) +raw=engine.read_bytes() +exec(compile(raw,str(engine),'exec',dont_inherit=True,optimize=0),{'__name__':'__main__','__file__':str(engine)}) diff --git a/research/coupled-provider-independent-audit/receipt_guard.py b/research/coupled-provider-independent-audit/receipt_guard.py new file mode 100644 index 0000000000..0ff64c1cbd --- /dev/null +++ b/research/coupled-provider-independent-audit/receipt_guard.py @@ -0,0 +1,29 @@ +"""Compare all stable mathematical result fields, with exact frozen evidence bindings.""" +import hashlib,json +from pathlib import Path +def require(ok,message): + if not ok:raise ValueError(message) +def read(root,path):return json.loads((root/path).read_bytes()) +def stable(value,drop): + result=dict(value) + for name in drop:result.pop(name,None) + return result +def validate(root,scratch,commands): + summaries={} + for command in commands: + actual=read(scratch,command['result']);expected=read(root,command['expected']) + require(stable(actual,command['drop'])==stable(expected,command['drop']),'Changed mathematical receipt: '+command['name']) + summaries[command['name']]={'all_stable_fields_equal':True,'ignored_only':command['drop'],'fresh_sha256':hashlib.sha256((scratch/command['result']).read_bytes()).hexdigest()} + a=read(scratch,'agents/algebra/FRESH.json') + require(a['status']=='PASS_INDEPENDENT_COUPLED_PROVIDER_COMPONENT' and a['coupled_helpers_without_target_credit']==8 and a['owned_outputs_zero']==9,'Wrong provider scope') + b=read(scratch,'agents/budget/FRESH.json') + require(b['coupled']['autonomous_credit']==0,'Unearned coupled helper credit') + require(b['full_profile']['hypothetical_added_target_profile']=={'8':144},'Wrong conditional profile') + require(b['full_profile']['eight_paid_H8_per_provider']['signed_profile_equals_reference'] is True,'Rankwise cancellation failed') + require(b['conditional_screen']['new_kappa'] is None,'Unexpected kappa claim') + require(b['executed_checker_sha256']==hashlib.sha256((root/'capsule/agents/budget/screen_v3.py').read_bytes()).hexdigest(),'Wrong freshly executed final budget source') + require(b['boundary_scalar_units']==42 and b['scalar_tariff_units_including_swaps']==175022,'Wrong literal boundary tariff') + e=read(scratch,'agents/budget/FRESH-ENVELOPE.json') + require(e['total_max_field_l2_exponent']==18996 and e['total_joint_field_l2_exponent']==19012 and e['copy_count']==16,'Wrong local norm bounds') + require(e['executed_checker_sha256']==hashlib.sha256((root/'capsule/agents/budget/independent_local_envelope.py').read_bytes()).hexdigest(),'Wrong freshly executed envelope source') + return summaries diff --git a/research/coupled-provider-independent-audit/reports/acceptance/BINDINGS.json b/research/coupled-provider-independent-audit/reports/acceptance/BINDINGS.json new file mode 100644 index 0000000000..b6973dcbe5 --- /dev/null +++ b/research/coupled-provider-independent-audit/reports/acceptance/BINDINGS.json @@ -0,0 +1,57 @@ +{ + "artifact_sha256": { + "swarm-price-plane-20261023T112711Z/runs/clifford5376-independent-pilot/RECEIPT.json": "ee289f8b74d9ff760d5e1b45e327b8ce3b431ca302ec91f6f86213f84cde3ab3", + "swarm-price-plane-20261023T112711Z/runs/clifford5376-independent-pilot/stdout.log": "a63cacee6186866837d237a5dceb09ef90578653fd3b6f46dd987fd57ea45c0c", + "swarm-price-plane-20261023T112711Z/runs/provider5402-author-registered/RECEIPT.json": "f08ff9410f5b9908ed76ca4191945cb75acd945d23070c1862d141bf28bf364b", + "swarm-price-plane-20261023T112711Z/runs/provider5402-author-registered/stdout.log": "55ab1283e19d6f304b9f5a69b8509674bdf7eb79948cd785cbf92061cb411163", + "swarm-price-plane-20261023T112711Z/runs/provider5402-independent-algebra/RECEIPT.json": "e79403fc2d7e71a9a4aecaf492757bb3ac89fd5ca1765c8da1bd261f11767ad4", + "swarm-price-plane-20261023T112711Z/runs/provider5402-independent-algebra/stdout.log": "690b1a619233a55701d5e06997ef4c61e5fbcbab5519c317276853a4d42b61ec", + "swarm-price-plane-20261023T112711Z/runs/provider5402-independent-budget-fixed/RECEIPT.json": "5804c78debcb3af5094aec94f66e99b03d275357d31d83258fd1b3677cd9e006", + "swarm-price-plane-20261023T112711Z/runs/provider5402-independent-budget-fixed/stdout.log": "79b9b8bd80c146518d16f58cefb7e701226e09ce5ef86b98ed3ff0e68634a349", + "swarm-price-plane-20261023T112711Z/runs/provider5402-independent-budget/RECEIPT.json": "369d48d7096cb494358da43d01333492cb1cf0b6aecace6ab33e10dfa13dd659", + "swarm-price-plane-20261023T112711Z/runs/provider5402-independent-budget/stdout.log": "95c8284304f2bfe5d7cf080b3d6e3fc4197edc0b9c7868fa35ff84bd05c37846", + "swarm-provider-audit-sol-high-20261024/agents/algebra/RESULT.json": "e5b325235eeb6c976a8dc568df838f609fcca0f52945f00bb6b2e9a973a1a11b", + "swarm-provider-audit-sol-high-20261024/agents/algebra/RUN-REQUEST.json": "de7a2168effb21ce77508ad0046b26bc53753fb17137fab76d5500d655d686bc", + "swarm-provider-audit-sol-high-20261024/agents/budget/RESULT-v1.json": "62842778ec9467579c04280182c7c591c1c73abe38034231c40cf5e00238861c", + "swarm-provider-audit-sol-high-20261024/agents/budget/screen.failed-v1.py": "080803a22fc1545c95e97da0937887e711dcdee6089091ad3d2a9c4ec6759833", + "swarm-provider-audit-sol-high-20261024/agents/budget/screen.py": "1046234495045ffc83226d698af0f26bbe061dba9c3059c7a1124b7ce8e86e46", + "swarm-provider-audit-sol-high-20261024/agents/clifford-proof/RESULT.json": "a63cacee6186866837d237a5dceb09ef90578653fd3b6f46dd987fd57ea45c0c", + "swarm-provider-audit-sol-high-20261024/agents/clifford-proof/SOURCE-MANIFEST.json": "59f2bebd1ac5f49523ff01ee82e7ed01f786089683cf0f238a812e2777351def", + "swarm-provider-audit-sol-high-20261024/agents/provenance/RESULT.json": "718995cfd673ee36dfca1d397ae0ddb64150e9e5dc743860d026d4c728dfd241" + }, + "limitations": [ + "Static review authenticates completed evidence; it does not rerun scientific checks.", + "Run receipts bind stdout; algebra result hashes self-bind code/inputs. The root guard does not itself hash every independent checker.", + "The all-n conclusion is written proof review, not the finite oracle result.", + "No completed #5402 caller, autonomous coupled-H credit or new kappa is accepted." + ], + "run_receipts": { + "clifford5376-independent-pilot": { + "elapsed_seconds": 2.1140065640211105, + "exit_code": 0, + "sampled_peak_descendant_rss_bytes": 20733952 + }, + "provider5402-author-registered": { + "elapsed_seconds": 51.350174140010495, + "exit_code": 0, + "sampled_peak_descendant_rss_bytes": 108593152 + }, + "provider5402-independent-algebra": { + "elapsed_seconds": 33.09615578700323, + "exit_code": 0, + "sampled_peak_descendant_rss_bytes": 181915648 + }, + "provider5402-independent-budget": { + "elapsed_seconds": 0.5033487160108052, + "exit_code": 1, + "sampled_peak_descendant_rss_bytes": 68902912 + }, + "provider5402-independent-budget-fixed": { + "elapsed_seconds": 0.80603354802588, + "exit_code": 0, + "sampled_peak_descendant_rss_bytes": 57536512 + } + }, + "scientific_executions": 0, + "status": "PASS_STATIC_ARTIFACT_BINDINGS" +} diff --git a/research/coupled-provider-independent-audit/reports/acceptance/FINAL-BUDGET-ENVELOPE-REVIEW.md b/research/coupled-provider-independent-audit/reports/acceptance/FINAL-BUDGET-ENVELOPE-REVIEW.md new file mode 100644 index 0000000000..1688469d58 --- /dev/null +++ b/research/coupled-provider-independent-audit/reports/acceptance/FINAL-BUDGET-ENVELOPE-REVIEW.md @@ -0,0 +1,62 @@ +# Acceptance addendum: corrected literal tariff and independent local envelope + +This addendum **supersedes two version-specific statements in the frozen `REVIEW.md`**: the exact scalar tariff is 175,022, not 175,038; and the provider's maximum-field local exponent 18,996 now has an independent literal recomputation and proof review. The partial-provider acceptance scope is unchanged. There is still no completed consumer, autonomous credit for coupled H, complete precision/funding theorem or new kappa. + +The authoritative new scientific outputs are `agents/budget/RESULT-v3.json` and `agents/budget/LOCAL-ENVELOPE-v1.json`, produced by root's guarded runs. I inspected both scripts, the written `LOCAL-ENVELOPE-PROOF.md`, semantic results and root guard receipts/stdout. A separate static check authenticated the script/result hashes, all fourteen norm-source pins and both log hashes. It also compared the complete stored recursive profile and conditional moment screen against v1 and found exact equality. No scientific execution occurred in this acceptance lane. Original acceptance and scientific artifacts remain untouched. + +## Literal scalar-tariff correction + +The emitted `PROVIDER.json` field `cache_scalar` already means the final output coefficient `1/(2 f_i)`. The earlier independent checker treated it as f_i and applied the reciprocal formula again. That misread affected its exact boundary scalar tariff. It did not change the emitted source, physical equations, operation counts, paid/productive profiles, moment intervals, cleanup budgets or no-credit boundary. + +The new `screen_v3.py` uses the emitted `cache_scalar` directly. Its diff changes that interpretation, checks the resulting totals, and records its own executed SHA256. The actual boundary scalar tariff is 42 rather than 58; the full inherited tariff including eight SWAP allowances is **175,022**, or **16,854 above the original raw-source 158,168**. The prior 175,038 was a conservative overestimate, but calling it an exact literal bill was incorrect. Earlier code/results and their preserved execution history remain version-scoped evidence of the independent checker's correction, not a provider construction failure. + +The root v3 run passed with exit zero, no termination, 0.908223 seconds guard elapsed and sampled peak descendant RSS 57,507,840 bytes. The complete recursive comparison and the hypothetical eight-H8-per-provider necessary screen are byte-for-byte equal as JSON objects to the previously reviewed result. No numeric moment conclusion is strengthened by this sixteen-unit ordinary-tariff reduction. + +## Independent envelope and its geometry + +The new checker constructs the entire finite provider schedule from the current literal changed word, both basis programs, all actual mode input/output scalings, cache swaps/clears and boundary words. It recomputes exact upward power-of-two factors without executing submitted Python. Only after summing them does it compare the maximum-field exponent with the author's declaration. + +For fields in the same square ambient Hilbert space at one fixed fiber width, use either + +``` +||v||max = max_j ||v_j||2 +||v||joint = (sum_j ||v_j||2^2)^(1/2). +``` + +ADD has norm at most `1+|q|` in either geometry; SCALE has whole-bank norm at most `max(1,|q|)`. CLEAR, whole-field SWAP and square unitary maps have norm at most one. COPY has maximum-field norm at most one, but joint-field norm at most `sqrt(2)`, conservatively enclosed by two. This COPY bound applies to arbitrary destination perturbations, because COPY discards the old destination and duplicates the source. It does not assume a numerically clean destination. + +The exact logarithm ceilings produce + +| Geometry | Independent exponent L | Bound | +| --- | ---: | --- | +| Maximum of field Euclidean norms | 18,996 | `2^18996` | +| Joint field Euclidean norm | 19,012 | `2^19012` | + +The difference is exactly the sixteen COPY operations. It is a change of norm geometry, not a contradiction of the author's maximum-field statement. The exact rational-logarithm, COPY-geometry and direct emitted output-scaling controls passed. + +All elementary assigned exponents are nonnegative, so the sum over any contiguous subinterval, prefix or suffix is at most the complete L. Submultiplicativity gives its operator bound `2^L`. Expanding propagated initial error and local residuals through suffixes then gives, in the selected same geometry, + +``` +||e_out|| <= 2^L (||e_in|| + sum_j ||local_residual_j||). +``` + +These are whole-field residual norms at one fixed width. With zero initial error and m residuals of norm at most epsilon this gives `m*2^L*epsilon`. It is not a dimension-independent conversion from coordinatewise error, nor a choice of machine precision. + +The all-width premise is substantive: mere free-group invertibility would not suffice for the unitary bound. The written proof uses the normalized square native gate `C_q=((1+i)/2)I+((1-i)/2)X_q`, where the translation X_q is a self-adjoint involution; cross terms cancel, so C_q and its inverse are unitary. Invertible address permutations and unit-modulus diagonal/phase factors are unitary. Canonical frames, their complex conjugates and chart transitions preserve this property. The checker verifies the actual frame/warp rank conditions and invertibility of each literal boundary P. Columnwise tensor lifts preserve unitarity at every positive width, while scalar owner coefficients stay exterior. Therefore the finite exponent bound is uniform over widths under the stated normalized square realization. + +The source's adapter and phase annotations retain the pinned physical interpretation. This new checker does not reconstruct every inherited native physical implementation or prove the absence of hidden rescalings independently of that retained contract. The already reviewed source/physical audit and explicit square-unitary premise remain necessary. Complete caller precision, routing, storage, movement, recursive primitive implementation, compiler and outer funding remain outside the local envelope. + +The root envelope run passed with exit zero, no termination, 0.504455 seconds guard elapsed and sampled peak descendant RSS 59,138,048 bytes. The result records the complete grouped exponent contributions and abstract scalar/unitary transcript hash. + +## Static bindings + +| Artifact | SHA256 | +| --- | --- | +| `screen_v3.py` | `9805fb55fe2888ae7e10a96c5f91e032fc9e6ac95a7831fed987d502e4814c2e` | +| `RESULT-v3.json` | `3918ce76fabf77199f18756249b13067c3d2319b67dfbab86d922de463320def` | +| v3 stdout, matching root receipt | `32fde6ed6a8a21cbcd27c1b95fcb3cd2e91d9222d7773cb5124b0c50c0631d98` | +| `independent_local_envelope.py` | `11d8b361adacac9ae44985ffa8a83ff0e9de47e94571e486427baa7201da7715` | +| `LOCAL-ENVELOPE-v1.json` | `f99bc2dd5f60b38d6ee9617fac9fb1f03ce9c5f10455650ccf2f7acc54bb490f` | +| Envelope stdout, matching root receipt | `1a27db01ba466c1ea58cf2bc1e8c6909b10ab6cb5144354f5fc4747fc3ef0350` | + +The fourteen source pins in the envelope result match the files read during this static review. The result's executed-checker hashes match the current scripts. The written envelope proof was reviewed for the mathematical implications described above; subsequent publication prose should identify these outputs as executed and the v3 tariff as authoritative. Construction and predecessor credit remain as preserved in the source and other audit lanes. diff --git a/research/coupled-provider-independent-audit/reports/acceptance/GATE-MAP.md b/research/coupled-provider-independent-audit/reports/acceptance/GATE-MAP.md new file mode 100644 index 0000000000..b42a0318e7 --- /dev/null +++ b/research/coupled-provider-independent-audit/reports/acceptance/GATE-MAP.md @@ -0,0 +1,41 @@ +# Independent acceptance gate map + +Frozen review targets: provider #5402 at `3348fccea855082786d5f0fc5558b73d4974e745`; Clifford proof #5376 at `848cdce9003262c4b6e02ec4558f302e4fae56ad`. Canonical source reference is `1ec1119972c9aefe42525172d07b332fcff81cb4`. The latter is a source-custody reference, not an asserted ancestor of the older-base #5376 branch. + +This lane is read-only with respect to source packages, other auditors and scientific execution. Root owns guarded execution and publication. The map distinguishes a useful partial provider audit from completion of a multiplication construction. + +| Gate | Required implication and evidence | What passing does not establish | +| --- | --- | --- | +| Custody | Raw consumed bytes bind to frozen Git objects; capsule closure and registered driver have origin evidence; before/after hashes agree. Each independent checker binds its own source and code bytes. | Canonical ancestry where it is false; correctness merely from a hash or author receipt. | +| Author reproduction | Registered #5402 normal and optimized runs pass, with exact head/code/runtime receipts. | Independence, full caller admission or new kappa. | +| Unrestricted algebra | Separate original and center-free source replay; every one of 632 original and nine owned entry directions remains independent. Derive cache rows, E, B and their full factorizations from the current source. | A clean-subspace or quotient-domain result does not suffice. | +| Chronology and ownership | Literal zipper preserves every unchanged record, binds eight cache births and eight center/H1 replacements; no borrowed erasure; complete zero at every retag; all nine owned outputs zero after actual boundary/swap composition. | A nonzero field may not receive a free chart conversion. | +| Ordinary basis | Literal in-place entrance and exit agree with the derived 122-role map and both inverse products; complete endpoint comparison includes arbitrary helpers. | Endpoint invertibility is not an emitted same-cost inverse/transpose schedule. | +| Physical phase | Independent literal elementary-gate interpreter checks all 1,240 current boundary equations using full signed Pauli action plus the complete zero-state image. Include exact global phase and actual order. | The unchanged 400 helper physical implementations, source adapters/warps, generic tape implementation and precision are inherited premises. | +| All-width lift | Free-group identities use only adjacent inverse cancellation; the scalar basis/field coefficients stay exterior. Exact one-column operator equalities lift columnwise. | Tensor powers do not distribute over scalar sums; 14 remains 14 in `ZW=14I`. | +| Negative controls | Mutations of actual source/cache/basis data, borrowed erasure, global phase, order, nonzero retag and false helper credit fail the relevant semantic predicate. | A list of mutations without actual rejection and its frozen run receipt is not executed coverage. | +| Literal bill | Independent counts retain the complete native profile, source traffic, all ordinary scalars, eight swaps, 464 monomial maps and nine owned fields. Scalar tariff is bound to the raw source, not a different #5383 subtotal. | Ordinary scalar/monomial work is not zero and is not recursive target credit. | +| Closure interface | Explicitly hypothetical eight autonomous H8 per provider under the same #5398 p16 comparator; reconstruct all 18 provider occurrences, query costs, idles, main targets and existing helpers. Added paid jobs, lost targets and ordinary overhead remain explicit unknowns. | The current coupled H outputs have zero autonomous credit; the conditional screen is not a physical closure theorem or universal ceiling. | +| #5376 written mathematics | Independently follow discrete phase/trace alphabet, exact matrix grouping, polynomial Gram separation, eight-copy invariant descent, stability induction and n=0/1 exceptions for all n. | Finite tested n values do not establish any of those universal implications. | +| #5376 implementation evidence | Independently constructed exact small matrix oracle challenges submitted code as the device under test. Record finite widths, phase/order/dirty-input cases, literal witness mutants, modular rank and Reynolds calibration. | No replay of every recipe/provider/fusion search; no proof-assistant or arbitrary-program implementation theorem. | +| Checker contract | Existing literal witness checker proves a negative discrepancy; compact positive equality depends on its expander/arithmetic/trace/merge execution. Native and matrix witness schemas need explicit conversion/binding. | A negative-only checker need not reject a forged unused energy field if it validates a real nonzero entry. Compact positive receipts are not independently accepted by that negative checker. | +| Scientific admission | Require a complete consumer schedule and its paid/productive invoice, restored standard main contract, coupled-mode closure, movement/storage/precision/compiler/recursive/outer funding. | This round has no complete provider/consumer admission and no new kappa. | + +## Provisional review observations + +The current algebra implementation imports the retained independent #5383 dyadic arithmetic engine with explicit reuse credit. It does not import author/native/Clifford evaluators as its oracle. Its new phase interpreter derives literal gate action. The #5376 oracle imports submitted modules only as the tested implementation and builds its own matrices and arithmetic. These are distinct claims from an assertion that every line is newly invented. + +The algebra controls include real current cache-source, native ADD and basis ADD changes, not only metadata edits. Full replay is required before they count. Exact signed Pauli action determines a Clifford operator only up to scalar; comparing the complete zero-state image supplies that scalar. Both halves are necessary, and the phase mutation tests that distinction. + +The proposed budget statement is a necessary incremental screen for a fully specified hypothetical comparator: eight additional H8 credits are exactly canceled by eight paid H8 jobs; any further positive paid job makes that incremental delta negative when every other term stays fixed. This does not rule out changed main targets, idle profiles, provider count, lost helpers, productive graph or compiler headroom. The #5405 fixed-owned-profile ceiling remains separately scoped and is not rerun here. + +The private continuation and an undefined A/S identity do not supply accepted evidence. Only source-bound released statements can support this audit's conclusions. Preserve author and predecessor credits and describe independent checking as an audit contribution. + +## Receipt state at map creation + +- Author #5402 normal/optimized passes were reported by root; final binding review is pending. +- Algebra independent run is pending. `RUN-REQUEST.json` is preparation, not a pass. +- Budget `RESULT-v1.json` exists after a failed first tariff binding; final guarded receipt and failure preservation remain to be checked. +- #5376 `RESULT.json` and written review exist; final guarded receipt/source binding review remains to be checked. + +Missing evidence will remain explicit in the final acceptance report. No pending gate is promoted merely because a useful scoped PR is possible. diff --git a/research/coupled-provider-independent-audit/reports/acceptance/README.md b/research/coupled-provider-independent-audit/reports/acceptance/README.md new file mode 100644 index 0000000000..87d62e0bbc --- /dev/null +++ b/research/coupled-provider-independent-audit/reports/acceptance/README.md @@ -0,0 +1,5 @@ +# Acceptance record versions + +Read `FINAL-BUDGET-ENVELOPE-REVIEW.md` and `SAME-CHART-REVIEW.md` alongside `REVIEW.md`. The final budget addendum supersedes the old 175,038 exact-tariff statement with the emitted-scale tariff 175,022 and independently validates the local two-norm envelope. The cache addendum supplies a legal same-chart content mutation beyond the original frame rejection. + +`REVIEW.md`, `BINDINGS.json` and `GATE-MAP.md` are preserved original artifacts. Their creation-time pending rows and original v1 budget values are historical states, not the final package schedule. The final scoped acceptance remains a partial coupled provider, conditional closure budget and bounded Clifford proof/certificate review. No completed caller, autonomous credit for coupled H, new κ or full #5376 provider/fusion admission follows. diff --git a/research/coupled-provider-independent-audit/reports/acceptance/REVIEW.md b/research/coupled-provider-independent-audit/reports/acceptance/REVIEW.md new file mode 100644 index 0000000000..c0aa4a2399 --- /dev/null +++ b/research/coupled-provider-independent-audit/reports/acceptance/REVIEW.md @@ -0,0 +1,71 @@ +# Independent final challenge and scoped acceptance + +Decision: **accept the source-bound #5402 partial-provider audit, literal invoice and conditional closure-budget screen, and accept the bounded #5376 theorem/checker review with the explicit limits below.** No reviewed evidence supplies a completed #5402 consumer, autonomous credit for the eight coupled H outputs, a new kappa, a proof-assistant theorem or a selected-result change. I found no concrete mathematical or implementation defect that blocks this scoped audit contribution. + +The review targets remain #5402 `3348fccea855082786d5f0fc5558b73d4974e745` and #5376 `848cdce9003262c4b6e02ec4558f302e4fae56ad`. `GATE-MAP.md` records the acceptance implications and their exclusions. This lane inspected source and checker implementations and authenticated existing receipts; it ran no scientific check and changed no other lane's files. `verify_bindings.py` and `BINDINGS.json` supply its read-only static check, which passed. + +## Completed evidence + +| Root-owned run | Result | Guard elapsed | Sampled peak descendant RSS | +| --- | --- | ---: | ---: | +| #5402 registered author normal/optimized pair | PASS, outcome partial | 51.350 s | 108,593,152 bytes | +| #5402 independent algebra/physical boundary audit | PASS | 33.096 s | 181,915,648 bytes | +| Budget first checker version | FAIL, scalar-tariff source binding | 0.503 s | 68,902,912 bytes | +| Budget corrected checker | PASS | 0.806 s | 57,536,512 bytes | +| #5376 independent exact-matrix pilot | PASS | 2.114 s | 20,733,952 bytes | + +Each stored stdout SHA256 matches its guard receipt. The registered author log contains two scientific pass records and the driver's explicit `outcome=partial`. The independent algebra's code SHA256 values agree with the frozen run request and its result. All five consumed scientific files agree with the corresponding #5402 custody capsule bytes. The proof oracle and nine reviewed source hashes agree with its source manifest, and those source bytes agree with the #5376 capsule. Every budget input agrees with its frozen manifest and the corrected checker has its declared SHA256. `BINDINGS.json` records hashes of the reviewed results and receipts. + +These bindings do not upgrade the guard into a proof kernel: it authenticates stdout and observed process outcome. The scientific implications still depend on the reviewed checker, mathematical derivations and pinned inherited premises. The #5402 independent result also records its own code and consumed input hashes. The source-custody lane's commit/tree/blob authentication supplies the separate origin chain. I inspected that lane's completed report/result and capsule cross-bindings; I did not rerun its offline verifier. + +The failed budget checker used the #5383 retained-owned-body subtotal 158,744 as a precondition for the original raw source. The original raw-source subtotal is 158,168. The first source version and failure log remain present; the corrected checker binds the right source before computing its output. This is a checker binding error with preserved evidence, not a detected #5402 construction error. + +## #5402 algebra, ownership and phase + +The checker carries 632 independent original symbols and nine independent owned symbols. Its old source replay, center-free replay and current changed-word replay are separate. B is derived by projection from the current full helper-to-Y matrix and then checked against every actual row. E is derived from current original-prefix cache rows and checked through `EB^T=I`. A literal source/candidate zipper binds every deletion, cache birth and unchanged record. It checks all 632 original endpoints, both literal basis inverse products, the complete transformed endpoints and the nine final zero outputs. + +I checked that persistent CLEAR is forbidden, COPY requires a zero owned destination, the initial owned fields are arbitrary rather than clean assumptions, and every zero retag requires a complete zero formal row. The zero retags are not accepted merely because one selected entry or a clean-input evaluation vanishes. Every cache exists before any deleted center; the result records simultaneous retention with the center temporary. Basis changes mix only the common physical charts and use dyadic ADDs and signed-power-of-two SCALEs. Transferring a normalized cache into the vacated original owner is a whole-field/chart swap with an exactly zero recipient. This supplies the intended nine-owned-field boundary without erasing a persistent direction. + +The independent phase implementation derives action from elementary P, X, D, C and literal phase gates. Complete signed Pauli action determines a Clifford up to scalar; the complete zero-state vector fixes that scalar. Both are compared, with exact integer/dyadic arithmetic. The fresh result covers 336 main diagonal/shear identities, 896 actual nonzero coupling directions and eight helper diagonals, totaling 1,240. The compared formulas respect word order; the implementation introduces no D/K or Q/K commutation. The rational M identities give `ZW=14I` and `WZ=I-C` after adjacent inverse cancellation. Exterior rational coefficients remain exterior at every fiber width. + +Nine controls rejected. They challenge a current native ADD, current basis ADD, borrowed erasure, a global phase invisible to a tableau alone, noncommuting boundary order, a nonzero original-field retag, false autonomous H credit, and inappropriate commutation of distinct free generators. The current cache-source mutation rejects at the **source-frame gate**. That is meaningful chart-contract coverage; it is not additional evidence that a same-chart altered cache algebra passes that gate and then fails an endpoint identity. The full positive cache algebra is independently checked, and the native ADD control supplies actual current endpoint sensitivity. This coverage nuance does not block scoped acceptance. + +The accepted physical result is exactly the coupled block + +``` +X = D x - R y + R W h +Y = D y +H = D(h - Z y). +``` + +The independent Y terms in H prohibit autonomous H8 target credit. Ordering the banks as `(y,h,x)` gives an invertible triangular map, hence preservation of all original information. It does not provide an emitted inverse or same-cost transpose schedule. The 400 retained helper implementations and unchanged source native/adapter realization are inherited premises. This audit does not independently reimplement their tape-level realization or flatten the entire physical 641-column operator. + +## Budget and closure boundary + +The accepted literal paid profile is `{1:2193,2:412,3:510,4:127,5:40}` and the autonomous helper profile is `{4:28,7:7,8:47,9:318}`. Those local profiles already match the #5398 comparator body. Removing eight H8 and eight H1 jobs relative to the raw native source cannot be counted a second time as extra savings against #5398. + +The literal boundary-inclusive inventory is 17,917 ADD, 1,204 SCALE, 16 COPY, 40 CLEAR, eight whole-field swaps and 464 monomial field maps per provider. The budget checker also reconstructs all eighteen provider occurrences, fifteen query shears, retained whole idles and main targets from the actual p16 controller and requires equality with the separately validated #5400 invoice. It retains ordinary caller/boundary work separately. The inherited scalar tariff yields 175,038 units per provider, 16,870 above the raw-source scalar subtotal; the physical cost of monomial maps and other retained realization work remains an explicit unknown. + +The optimistic interface grants eight **hypothetical new autonomous H8 jobs per provider** while preserving all standard main outputs and 400 existing helpers. Across eighteen providers this grants 144 targets. It has not been constructed. For a fixed saving, added paid jobs, lost productive jobs and other changed main/idle terms enter the exact signed moment comparison separately. The moment table is therefore a necessary incremental budget, not an actual #5402 ledger or a complete obstruction. + +If every other signed term is held fixed, 144 paid H8 jobs cancel the hypothetical 144 H8 targets identically rank by rank. An additional positive paid job then worsens the incremental moment. This is a valid conditional statement for every `0=2. + +The finite independent pilot supplies 25 native-entry checks, four traces, seven conditional inners, 24 programs, 64 small dense tensor-width instances, seventeen literal witnesses and 68 rejected witness mutations. It independently constructs the 96 one-axis matrices and obtains modular Gram rank 96 and Reynolds ranks zero through seven then fifteen at eight. Its own matrix/arithmetic/endpoint compiler forms the oracle; submitted modules are the device under test. This supports the implementation on those finite inputs. It does not establish arbitrary-program correctness or replace any all-n implication above. + +The literal checker accepts a **negative nonzero-entry witness**. It is not a positive equality checker. A forged unused energy field beside a valid nonzero entry is outside that negative acceptance contract. Compact native receipts also require explicit conversion and schema/digest rebinding before the matrix witness checker accepts them. Compact positive equality still trusts the expander, exact trace arithmetic and merge loop. The compact producer shares word expansion helpers with the negative checker; the stronger producer/checker compiler separation of the original dense path cannot be attributed to every compact component. + +I did not independently replay all 7,000 recipe classes, complete provider programs, the six registered #5376 science commands or the 30,328 fusion census. No current hosted CI result follows from the latest timeout-only metadata change. The candidate's older base and missing non-runtime contributor document remain visible in provenance; authenticated explicit later source pins do not imply current canonical main is its ancestor. + +## Publication boundary + +This is a useful, reviewable independent audit package with preserved author/predecessor credit and substantial OpenAI Codex assistance. Its accepted positive outcomes are a partial source-bound provider, explicit missing consumer obligations, a conditional closure-budget interface and a bounded written-proof/executable review. Completion of the whole multiplication construction and any frontier claim remain unaccepted. diff --git a/research/coupled-provider-independent-audit/reports/acceptance/SAME-CHART-REVIEW.md b/research/coupled-provider-independent-audit/reports/acceptance/SAME-CHART-REVIEW.md new file mode 100644 index 0000000000..58d403f47f --- /dev/null +++ b/research/coupled-provider-independent-audit/reports/acceptance/SAME-CHART-REVIEW.md @@ -0,0 +1,28 @@ +# Acceptance addendum: same-chart cache-content control + +The new independent control **closes the cache-content mutation coverage gap identified in `REVIEW.md`**. The original source-frame rejection remains accurate for the original control; it is now supplemented by a legally charted content mutation that reaches and fails the zero-row algebra predicate. The scoped acceptance decision is unchanged. + +I read `agents/algebra/check_same_chart_cache_mutant.py`, its `SAME-CHART-CACHE-MUTANT.json`, and the root-owned `provider5402-same-chart-cache-control` receipt/stdout. No scientific execution was performed in this acceptance lane. The original acceptance review, binding receipt and scientific checker files were left unchanged. + +The script selects the actual first COPY into C1 at event 11207, checks its preceding owned CLEAR at the same chart, and inserts precisely one event: + +``` +['scalar', ['scale', ['C', 1], -1, 1], 254] +``` + +This is a permitted signed-power-of-two SCALE on the retained cache's current chart. It preserves the existing source and destination identities, owned CLEAR/COPY rules, persistent-owner protections and chronology. It changes the copied content rather than choosing another-chart source. Prefix/suffix comparisons require every other event to remain identical. + +The control deliberately bypasses the source zipper, which would reject the extra instruction before any row-content check. It calls the same frozen independent native interpreter directly. Success requires exactly the exception `zero retag requires complete exact zero row`; a chart/ownership rejection or a different exception does not satisfy the control. The observed result has precisely that exception. Thus a wrong same-chart cache value makes a later asserted zero retag nonzero and is rejected by algebra rather than by frame metadata. + +The root guard reports exit zero, no termination, 0.705130 seconds elapsed and sampled peak descendant RSS 48,652,288 bytes. The semantic result records 0.575157 seconds internal execution and status `PASS_SAME_CHART_CACHE_CONTENT_MUTANT_REJECTED`. + +Static SHA256 checks confirm: + +| Artifact | SHA256 | +| --- | --- | +| Additional checker | `4bf90d4656e03e6716448026ba120c172585c9aced067d35d6ca1a75250d9aad` | +| Semantic result | `c8224338d3143f36ba5668908064971f11e2e684a80d9097b1bbd922cf152b15` | +| Root stdout, matching receipt log hash | `afc4e5719c0e7cf1b2c8c1770d6d5f5f3c8b9411df6b7644419cc138b9be9261` | +| Root guard receipt | `15ff49f21e110782ea6dcbbe2196e22790241f42c3eb823a5a7211a2b2ed2a4e` | + +The recorded SHA256 values of `check_provider.py`, `provider_rows.py`, `phase_exact.py` and `prior_dyadic_engine.py` match the current files and the original independent run's frozen values. The result also retains the same previously authenticated source/candidate raw hashes. This addendum adds one narrow successful semantic control; it does not rerun or broaden the full provider's admitted physical implementation, consumer closure, target credit, precision or kappa boundary. diff --git a/research/coupled-provider-independent-audit/reports/algebra/REPLAY-EXPECTED-PROVENANCE.json b/research/coupled-provider-independent-audit/reports/algebra/REPLAY-EXPECTED-PROVENANCE.json new file mode 100644 index 0000000000..2937a6d720 --- /dev/null +++ b/research/coupled-provider-independent-audit/reports/algebra/REPLAY-EXPECTED-PROVENANCE.json @@ -0,0 +1,13 @@ +{ + "added_value": "4bf90d4656e03e6716448026ba120c172585c9aced067d35d6ca1a75250d9aad", + "authenticated_file": "capsule/agents/algebra/check_same_chart_cache_mutant.py", + "derived_expectation": "reports/algebra/REPLAY-EXPECTED.json", + "derived_from_fresh_output": false, + "mathematical_result_fields_changed": false, + "only_added_json_field": "checker_files_sha256.check_same_chart_cache_mutant.py", + "original_receipt": "reports/algebra/RESULT.json", + "original_receipt_changed": false, + "original_receipt_sha256": "e5b325235eeb6c976a8dc568df838f609fcca0f52945f00bb6b2e9a973a1a11b", + "reason": "Original main root result predates the separately added same-chart control. The unchanged main checker inventories every adjacent Python file, including this unused helper, during fresh replay. The helper is separately scheduled as its own control.", + "status": "EXPLICIT_ADJACENT_CODE_INVENTORY_ADDITION_ONLY" +} diff --git a/research/coupled-provider-independent-audit/reports/algebra/REPLAY-EXPECTED.json b/research/coupled-provider-independent-audit/reports/algebra/REPLAY-EXPECTED.json new file mode 100644 index 0000000000..3be9defb56 --- /dev/null +++ b/research/coupled-provider-independent-audit/reports/algebra/REPLAY-EXPECTED.json @@ -0,0 +1,556 @@ +{ + "all_original_inputs": 632, + "arbitrary_owned_inputs": 9, + "autonomous_helpers": 400, + "basis_roles": [ + 224, + 225, + 227, + 229, + 230, + 231, + 232, + 233, + 234, + 235, + 236, + 237, + 238, + 239, + 240, + 241, + 242, + 243, + 245, + 246, + 247, + 250, + 252, + 253, + 254, + 255, + 256, + 257, + 258, + 259, + 261, + 262, + 263, + 266, + 268, + 269, + 270, + 271, + 272, + 276, + 280, + 283, + 286, + 287, + 288, + 294, + 296, + 297, + 300, + 302, + 303, + 306, + 308, + 312, + 315, + 318, + 319, + 324, + 326, + 328, + 332, + 333, + 334, + 335, + 336, + 340, + 347, + 350, + 351, + 352, + 356, + 366, + 367, + 368, + 372, + 379, + 382, + 383, + 384, + 388, + 390, + 391, + 392, + 397, + 398, + 399, + 400, + 401, + 402, + 403, + 405, + 406, + 409, + 410, + 411, + 413, + 414, + 415, + 416, + 417, + 418, + 419, + 421, + 422, + 425, + 426, + 427, + 429, + 430, + 431, + 432, + 433, + 434, + 435, + 437, + 438, + 441, + 442, + 443, + 445, + 446, + 447 + ], + "candidate_head": "3348fccea855082786d5f0fc5558b73d4974e745", + "checker_files_sha256": { + "check_provider.py": "3774c5742b565ea9007af90d10e43d38a3e675c2074583c8c365799fc256baaf", + "check_same_chart_cache_mutant.py": "4bf90d4656e03e6716448026ba120c172585c9aced067d35d6ca1a75250d9aad", + "phase_exact.py": "15e90b63c5659090f02902cb38951ec4ab252352fb0b967b411ed547c501e2ba", + "prior_dyadic_engine.py": "3ee4ae79a55188d5abf2306f678179f4aafb799602ffb970fc1bc8f76cb061d9", + "provider_rows.py": "c7e579939d89709d72457d5fa213173b3b492c3cc3de7546afc3ed6a6fb32f0c" + }, + "claims": [ + "X=D x-R y+R W h", + "Y=D y", + "H=D(h-Z y)", + "ZW=14 I8", + "WZ=I-C" + ], + "consumed_sha256": { + "research/coded-native-caller/NORMALIZERS.json": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da", + "research/native-center-free-code/CODE.json": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0", + "research/native-center-free-code/SOURCE-WORD.json.gz": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05", + "research/native-rank8-helper-provider/PROVIDER.json": "676de7551d3364598f4a7e29ae97cae0e4364348786bbe70435b84294ba7dd65", + "research/native-rank8-helper-provider/WORD.json.gz": "7dc356001ed597ad6fc9fd3e0bc6ff7e3ec3a580a579a956827aa17fccfdd2dc" + }, + "controls": { + "actual_basis_ADD_changed": "derived basis matrix changed", + "actual_borrowed_erasure": "borrowed erasure", + "actual_cache_source_changed": "source scalar frame", + "actual_native_ADD_changed": "actual source ADD changes complete endpoint", + "false_autonomous_H8_credit": "H contains nonzero independent Y columns", + "false_zero_retag_original_input": "zero retag requires complete exact zero row", + "free_generators_do_not_commute": "distinct native generators retain order", + "same_tableau_wrong_global_phase": "global phase mismatch", + "wrong_operator_order": "reversed noncommuting factors" + }, + "coupled_helpers_without_target_credit": 8, + "limitations": [ + "No autonomous target credit for coupled H.", + "No caller, kappa, inverse/transpose schedule or outer budget.", + "Native realization and unchanged helper physical implementations inherited from pinned source.", + "Phase proof is exact Pauli action plus full zero-column anchor, not flattened all-column physical tape." + ], + "native_replay": { + "arbitrary_owned_inputs": 9, + "event_counts": { + "adapter": 448, + "climb": 3282, + "phase": 10, + "scalar": 17485, + "warp": 240, + "zero_retag": 8 + }, + "events": 21473, + "max_live_owned_rows": 9, + "original_inputs": 632, + "owner_lifetimes": { + "('C', 0)": { + "first_write": [ + 11325, + "clear" + ], + "last_read": 11539, + "last_write": [ + 11540, + "clear" + ] + }, + "('C', 1)": { + "first_write": [ + 11206, + "clear" + ], + "last_read": 11349, + "last_write": [ + 11207, + "copy" + ] + }, + "('C', 2)": { + "first_write": [ + 11221, + "clear" + ], + "last_read": 11376, + "last_write": [ + 11222, + "copy" + ] + }, + "('C', 3)": { + "first_write": [ + 11236, + "clear" + ], + "last_read": 11403, + "last_write": [ + 11237, + "copy" + ] + }, + "('C', 4)": { + "first_write": [ + 11251, + "clear" + ], + "last_read": 11430, + "last_write": [ + 11252, + "copy" + ] + }, + "('C', 5)": { + "first_write": [ + 11266, + "clear" + ], + "last_read": 11457, + "last_write": [ + 11267, + "copy" + ] + }, + "('C', 6)": { + "first_write": [ + 11281, + "clear" + ], + "last_read": 11484, + "last_write": [ + 11282, + "copy" + ] + }, + "('C', 7)": { + "first_write": [ + 11296, + "clear" + ], + "last_read": 11511, + "last_write": [ + 11297, + "copy" + ] + }, + "('C', 8)": { + "first_write": [ + 11321, + "clear" + ], + "last_read": 11538, + "last_write": [ + 11322, + "copy" + ] + } + }, + "paid": { + "1": 2193, + "2": 412, + "3": 510, + "4": 127, + "5": 40 + } + }, + "ordinary_basis_counts": { + "input": { + "add": 822, + "scale": 12 + }, + "output": { + "add": 822, + "scale": 12 + } + }, + "owned_outputs_zero": 9, + "paid": { + "1": 2193, + "2": 412, + "3": 510, + "4": 127, + "5": 40 + }, + "physical_phase_bindings": { + "helper_diagonal": 8, + "main_diagonal_and_shear": 336, + "two_coupling_directions": 896 + }, + "runtime_seconds": 32.940536, + "source_16_identities": [ + { + "cache_source_event": 11205, + "center_source_event": 11332, + "frame": 254, + "scalar_relation": { + "230": "1/4", + "324": "-1/4", + "326": "1/4", + "328": "1/4", + "333": "-1/4" + } + }, + { + "cache_source_event": 11218, + "center_source_event": 11358, + "frame": 274, + "scalar_relation": { + "225": "1/4", + "384": "-1/4", + "388": "-1/4", + "390": "1/4", + "391": "1/4", + "392": "1/4", + "397": "-1/4" + } + }, + { + "cache_source_event": 11231, + "center_source_event": 11384, + "frame": 619, + "scalar_relation": { + "225": "1/4", + "227": "-1/4", + "229": "1/4", + "231": "-1/2", + "232": "1/4", + "234": "-1/4", + "235": "-1/4", + "236": "-1/4", + "237": "-1/4", + "238": "1/2", + "239": "1/4", + "384": "-1/4", + "388": "-1/4", + "390": "1/4", + "391": "1/4", + "392": "1/4", + "397": "-1/4" + } + }, + { + "cache_source_event": 11244, + "center_source_event": 11410, + "frame": 279, + "scalar_relation": { + "227": "-1/4", + "229": "-1/4", + "232": "1/4", + "234": "-1/4", + "235": "-1/4", + "236": "1/4", + "237": "-1/4", + "239": "1/4", + "324": "1/4", + "326": "-1/4", + "328": "-1/4", + "333": "1/4" + } + }, + { + "cache_source_event": 11257, + "center_source_event": 11436, + "frame": 621, + "scalar_relation": { + "241": "1/4", + "243": "-1/4", + "245": "1/4", + "247": "-1/4", + "252": "-1/4", + "253": "-1/4", + "254": "1/4", + "255": "1/4" + } + }, + { + "cache_source_event": 11270, + "center_source_event": 11462, + "frame": 280, + "scalar_relation": { + "225": "-1/4", + "241": "1/4", + "243": "-1/4", + "245": "-1/4", + "247": "1/4", + "252": "1/4", + "253": "-1/4", + "254": "-1/4", + "255": "1/4", + "324": "1/4", + "326": "-1/4", + "328": "-1/4", + "333": "1/4", + "384": "1/4", + "388": "1/4", + "390": "-1/4", + "391": "-1/4", + "392": "-1/4", + "397": "1/4" + } + }, + { + "cache_source_event": 11283, + "center_source_event": 11488, + "frame": 624, + "scalar_relation": { + "257": "1/4", + "259": "-1/4", + "261": "1/4", + "263": "-1/4", + "268": "-1/4", + "269": "-1/4", + "270": "1/4", + "271": "1/4" + } + }, + { + "cache_source_event": 11306, + "center_source_event": 11514, + "frame": 281, + "scalar_relation": { + "288": "1/4", + "294": "-1/4", + "296": "-1/4", + "297": "-1/4", + "300": "1/4", + "303": "1/4" + } + } + ], + "source_derived_E": [ + { + "225": "1", + "384": "-1", + "388": "-1", + "390": "1", + "391": "1", + "392": "1", + "397": "-1" + }, + { + "225": "1", + "227": "-1", + "229": "1", + "231": "-2", + "232": "1", + "234": "-1", + "235": "-1", + "236": "-1", + "237": "-1", + "238": "2", + "239": "1", + "384": "-1", + "388": "-1", + "390": "1", + "391": "1", + "392": "1", + "397": "-1" + }, + { + "230": "1", + "324": "-1", + "326": "1", + "328": "1", + "333": "-1" + }, + { + "227": "-1", + "229": "-1", + "232": "1", + "234": "-1", + "235": "-1", + "236": "1", + "237": "-1", + "239": "1", + "324": "1", + "326": "-1", + "328": "-1", + "333": "1" + }, + { + "288": "-1", + "294": "1", + "296": "1", + "297": "1", + "300": "-1", + "303": "-1" + }, + { + "241": "-1", + "243": "1", + "245": "-1", + "247": "1", + "252": "1", + "253": "1", + "254": "-1", + "255": "-1" + }, + { + "257": "1", + "259": "-1", + "261": "1", + "263": "-1", + "268": "-1", + "269": "-1", + "270": "1", + "271": "1" + }, + { + "225": "1", + "241": "-1", + "243": "1", + "245": "1", + "247": "-1", + "252": "-1", + "253": "1", + "254": "1", + "255": "-1", + "324": "-1", + "326": "1", + "328": "1", + "333": "-1", + "384": "-1", + "388": "-1", + "390": "1", + "391": "1", + "392": "1", + "397": "-1" + } + ], + "status": "PASS_INDEPENDENT_COUPLED_PROVIDER_COMPONENT" +} diff --git a/research/coupled-provider-independent-audit/reports/algebra/REPORT.md b/research/coupled-provider-independent-audit/reports/algebra/REPORT.md new file mode 100644 index 0000000000..ea5d404cae --- /dev/null +++ b/research/coupled-provider-independent-audit/reports/algebra/REPORT.md @@ -0,0 +1,53 @@ +# Independent coupled-provider algebra and physical-boundary audit + +Scope: Dillon's PR5402 exact head `3348fccea855082786d5f0fc5558b73d4974e745`, package `research/native-rank8-helper-provider`. Construction credit remains with Dillon and the package's explicitly attributed predecessors, including Ali Romman's cached-center identities, Cao Yifan's native source, Dugongue's center-free code/factorization, Cinna Davis's helper/controller work and the other retained contributors. This is an independent component audit with substantial OpenAI Codex assistance. It supplies no competing caller and no publication. + +**The independent component passed root's bounded serial run.** `RESULT.json` records `PASS_INDEPENDENT_COUPLED_PROVIDER_COMPONENT`, 32.940536 seconds of internal elapsed runtime, all 1,240 actual physical phase bindings and nine rejecting controls. Root's separate guard measured **33.096155 seconds and 181,915,648 bytes sampled peak descendant RSS**, under a 300-second/1-GiB guard. Its receipt and stdout are retained at `swarm-price-plane-20261023T112711Z/runs/provider5402-independent-algebra/`. The RSS measurement is sampled rather than a cgroup hard-memory guarantee. Every checker-file SHA256 in the result matches `RUN-REQUEST.json`: main `3774c5742b565ea9007af90d10e43d38a3e675c2074583c8c365799fc256baaf`, phase evaluator `15e90b63c5659090f02902cb38951ec4ab252352fb0b967b411ed547c501e2ba`, native interpreter `c7e579939d89709d72457d5fa213173b3b492c3cc3de7546afc3ed6a6fb32f0c`, prior dyadic arithmetic `3ee4ae79a55188d5abf2306f678179f4aafb799602ffb970fc1bc8f76cb061d9`. This is a provider component result, with the complete-caller and budget boundaries below. + +## Independent implementation and exact source boundary + +`check_provider.py` imports no candidate verifier, native evaluator, Clifford evaluator or expected endpoint registry. `provider_rows.py` is a newly written chronological interpreter with a complete owner/frame contract. Its dyadic sparse arithmetic explicitly reuses our frozen independent PR5383 engine, copied without modification as `prior_dyadic_engine.py`, SHA256 `3ee4ae79a55188d5abf2306f678179f4aafb799602ffb970fc1bc8f76cb061d9`. This is the old audit's arithmetic implementation, not its old quotient word or old owned-pivot input domain. Every actual current word is interpreted afresh. + +`phase_exact.py` is a separately written nine-bit operator evaluator. It derives all eighteen signed Pauli images from literal elementary operations and propagates the complete zero-address state using pairs of integers and a power-of-two denominator. Equality requires both the entire signed Pauli action and the full zero-column vector. The former determines a Clifford unitary up to scalar; the latter fixes its absolute phase. It imports no author or predecessor evaluator and does not use a stored signed tableau as an oracle. + +The checker pins the original native payload to SHA256 `cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd`. It consumes the actual emitted coupled word, the actual boundary recipe, the source M/code and main normalizers. Each consumed raw file is hashed in the fresh result; the separate provenance lane establishes their Git/source custody. Source `phase` records are stage annotations, and `adapter` records retain inherited physical entrance/exit bindings. They remain byte-for-byte in place through the chronological zipper. Their full physical implementation remains a retained source premise. + +## All 632 original directions, not a quotient domain + +The original source replay seeds L0..L631 and C0 with separate arbitrary basis symbols and checks all 632 exact source endpoints. The center-free replay separately derives the complete helper-to-Y matrix and projects it against M/56 to derive B. Every center-free row must equal the full reconstructed formula; the rank-eight factorization is checked entrywise rather than accepted from metadata. + +The coupled replay seeds **all 632 original fields plus all nine C owners independently**. There are no owned L pivots and no imposed relation on the original helper inputs. The literal source/candidate zipper identifies all eight saved rows, all eight center replacements and all eight later H1 replacements, preserving the exact order and contents of every other record. Every cache is born after its actual source producer and all eight caches are retained simultaneously before the first removed center. COPY acts only on cleared C owners. Persistent CLEAR is forbidden. + +E is freshly derived from complete unrestricted source cache rows. The checker projects their helper components against B and checks their complete main/helper coefficients, obtaining eight independent canonical modes. It proves EB^T=I entrywise. Separately, eight source center-minus-cache differences must contain only scalar helper columns, and the eight later source rows must equal their negatives. The current changed word is then replayed, and every zero retag must encounter a complete zero row across all 641 arbitrary entry directions. Arbitrary owned dirt may not survive in any endpoint. + +Free-word operators retain exact order. Only adjacent generator/inverse pairs cancel. Scalar coefficients remain outside operator evaluation. Thus these formal identities evaluate at every positive fiber multiplicity, without assuming any source generator commutation or distributing tensor powers over sums. + +## Ordinary helper basis and coupled physical output + +The checker derives the 122-owner common-chart matrix L from its freshly computed B and E. It runs the literal submitted entrance program and requires exact equality with L on all 632 original input columns. It executes both products of the submitted entrance/exit programs and requires the identity. Every ADD is dyadic, every SCALE is a signed power of two, all mixed fields share the actual entrance or exit physical chart, and no basis instruction may erase a field or borrow hidden scratch. + +It substitutes the resulting entrance rows into every changed native endpoint and runs the actual exit program. All 632 persistent outputs and eight saved-cache rows are compared with their complete exact formulas. Exactly eight original mode outputs are zero before the cache transfer. Every other helper row is restored, and all 224 main rows have the specified coupling. Whole physical fields, together with their chart tags, may then be swapped from the normalized owned caches into these identically zero original directions. The owned slots receive zero; C0 was already zero. This proves the nine-owner final zero condition for arbitrary original owner dirt, rather than presuming entry cleanliness. + +For the new physical boundaries, the independent phase evaluator checks the submitted literal monomial words, their stored signed-tableau/anchor records, their actual saved frames and their scalar factors. It checks all 336 actual main diagonal/shear blocks, all 896 nonzero main/helper coupling blocks and all eight helper diagonals: 1,240 equations with absolute phase. In operator product notation, the order is exactly + +``` +X = D x - R y + R W h +Y = D y +H = D (h - Z y) +W = diag(Kp^-1) M diag(Km) / 2 +Z = diag(Km^-1) M^T diag(Kp) / 2. +``` + +The main and mode K maps commute with R with exact phase. No K/D or K/Q commutation is introduced. In ZW, the adjacent Kp/Kp^-1 factors cancel before M^TM/4=14I is used. In WZ, adjacent Km/Km^-1 factors cancel before MM^T/4=I-A is used. The source code is C=diag(Kp^-1)A diag(Kp), so WZ=I-C. These are ordinary code maps with exterior scalar coefficients; the factor 14 remains 14 at every fiber width. + +Ordering banks as (y,h,x) makes the coupled map triangular with invertible diagonal D. Together with the other 400 restored helpers this retains every one of the 632 original input directions. This is an information-preservation proof, not a same-cost emitted inverse or transpose schedule. + +## Credits, bill and controls + +The checker independently counts the native paid profile and checks exactly eight H8 plus eight H1 deletions. The target grammar permits only the 400 autonomous helper outputs, profile `{4:28,7:7,8:47,9:318}`. The eight H outputs contain nonzero independent Y columns and remain coupled. They have no autonomous H8 target credit. The separate budget lane owns the complete added ordinary work, amplification and caller obligations. + +All nine full-run controls rejected. They alter actual current cache-source data (rejected at the source-chart predicate), an actual native ADD coefficient (rejected by a changed complete endpoint), an actual basis ADD coefficient (rejected against the source-derived L), and an actual CLEAR into borrowed erasure. Other controls inject a same-tableau global phase, reverse noncommuting boundary order, attempt a retag on a nonzero original field, falsely credit the coupled H outputs as autonomous, and test that distinct free generators do not commute. Each fails the same semantic predicate used for the accepted instance. Both executed basis programs contain exactly 822 ADD and 12 SCALE operations. + +The separate `check_same_chart_cache_mutant.py`, frozen SHA256 `4bf90d4656e03e6716448026ba120c172585c9aced067d35d6ca1a75250d9aad`, adds a tenth control without changing any frozen full-run engine. Immediately after the actual C1 CLEAR/COPY at chart 254, it inserts one legal SCALE -1 on C1 in that same chart. This preserves ownership, all COPY preconditions and every chart binding. The mutated actual native word is then replayed through the same frozen independent interpreter. `SAME-CHART-CACHE-MUTANT.json` records rejection specifically at **the complete nonzero row before a zero retag**, rather than a chart or ownership mismatch. Its internal runtime was 0.575157 seconds. This separately proves sensitivity to actual saved-cache algebraic content; the full run's wrong-source control by itself establishes only source-chart sensitivity. The separate root guard receipt is retained under `swarm-price-plane-20261023T112711Z/runs/provider5402-same-chart-cache-control/`. + +This component does not emit or fund a complete caller, claim a new kappa, change selection, prove generic native/tape/compiler assumptions, or rerun the 400 inherited helper implementations. One-column exact phase identities lift columnwise; rational field coefficients remain exterior. The native realization and generic precision/storage/recursive outer obligations retain their explicit source boundaries. diff --git a/research/coupled-provider-independent-audit/reports/algebra/RESULT.json b/research/coupled-provider-independent-audit/reports/algebra/RESULT.json new file mode 100644 index 0000000000..3ccee4f764 --- /dev/null +++ b/research/coupled-provider-independent-audit/reports/algebra/RESULT.json @@ -0,0 +1,555 @@ +{ + "all_original_inputs": 632, + "arbitrary_owned_inputs": 9, + "autonomous_helpers": 400, + "basis_roles": [ + 224, + 225, + 227, + 229, + 230, + 231, + 232, + 233, + 234, + 235, + 236, + 237, + 238, + 239, + 240, + 241, + 242, + 243, + 245, + 246, + 247, + 250, + 252, + 253, + 254, + 255, + 256, + 257, + 258, + 259, + 261, + 262, + 263, + 266, + 268, + 269, + 270, + 271, + 272, + 276, + 280, + 283, + 286, + 287, + 288, + 294, + 296, + 297, + 300, + 302, + 303, + 306, + 308, + 312, + 315, + 318, + 319, + 324, + 326, + 328, + 332, + 333, + 334, + 335, + 336, + 340, + 347, + 350, + 351, + 352, + 356, + 366, + 367, + 368, + 372, + 379, + 382, + 383, + 384, + 388, + 390, + 391, + 392, + 397, + 398, + 399, + 400, + 401, + 402, + 403, + 405, + 406, + 409, + 410, + 411, + 413, + 414, + 415, + 416, + 417, + 418, + 419, + 421, + 422, + 425, + 426, + 427, + 429, + 430, + 431, + 432, + 433, + 434, + 435, + 437, + 438, + 441, + 442, + 443, + 445, + 446, + 447 + ], + "candidate_head": "3348fccea855082786d5f0fc5558b73d4974e745", + "checker_files_sha256": { + "check_provider.py": "3774c5742b565ea9007af90d10e43d38a3e675c2074583c8c365799fc256baaf", + "phase_exact.py": "15e90b63c5659090f02902cb38951ec4ab252352fb0b967b411ed547c501e2ba", + "prior_dyadic_engine.py": "3ee4ae79a55188d5abf2306f678179f4aafb799602ffb970fc1bc8f76cb061d9", + "provider_rows.py": "c7e579939d89709d72457d5fa213173b3b492c3cc3de7546afc3ed6a6fb32f0c" + }, + "claims": [ + "X=D x-R y+R W h", + "Y=D y", + "H=D(h-Z y)", + "ZW=14 I8", + "WZ=I-C" + ], + "consumed_sha256": { + "research/coded-native-caller/NORMALIZERS.json": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da", + "research/native-center-free-code/CODE.json": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0", + "research/native-center-free-code/SOURCE-WORD.json.gz": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05", + "research/native-rank8-helper-provider/PROVIDER.json": "676de7551d3364598f4a7e29ae97cae0e4364348786bbe70435b84294ba7dd65", + "research/native-rank8-helper-provider/WORD.json.gz": "7dc356001ed597ad6fc9fd3e0bc6ff7e3ec3a580a579a956827aa17fccfdd2dc" + }, + "controls": { + "actual_basis_ADD_changed": "derived basis matrix changed", + "actual_borrowed_erasure": "borrowed erasure", + "actual_cache_source_changed": "source scalar frame", + "actual_native_ADD_changed": "actual source ADD changes complete endpoint", + "false_autonomous_H8_credit": "H contains nonzero independent Y columns", + "false_zero_retag_original_input": "zero retag requires complete exact zero row", + "free_generators_do_not_commute": "distinct native generators retain order", + "same_tableau_wrong_global_phase": "global phase mismatch", + "wrong_operator_order": "reversed noncommuting factors" + }, + "coupled_helpers_without_target_credit": 8, + "limitations": [ + "No autonomous target credit for coupled H.", + "No caller, kappa, inverse/transpose schedule or outer budget.", + "Native realization and unchanged helper physical implementations inherited from pinned source.", + "Phase proof is exact Pauli action plus full zero-column anchor, not flattened all-column physical tape." + ], + "native_replay": { + "arbitrary_owned_inputs": 9, + "event_counts": { + "adapter": 448, + "climb": 3282, + "phase": 10, + "scalar": 17485, + "warp": 240, + "zero_retag": 8 + }, + "events": 21473, + "max_live_owned_rows": 9, + "original_inputs": 632, + "owner_lifetimes": { + "('C', 0)": { + "first_write": [ + 11325, + "clear" + ], + "last_read": 11539, + 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"3774c5742b565ea9007af90d10e43d38a3e675c2074583c8c365799fc256baaf", + "phase_exact.py": "15e90b63c5659090f02902cb38951ec4ab252352fb0b967b411ed547c501e2ba", + "prior_dyadic_engine.py": "3ee4ae79a55188d5abf2306f678179f4aafb799602ffb970fc1bc8f76cb061d9", + "provider_rows.py": "c7e579939d89709d72457d5fa213173b3b492c3cc3de7546afc3ed6a6fb32f0c" + }, + "dependencies": "Python3 standard library only; no candidate/source evaluator import. Explicit reuse of our independent 5383 dyadic engine." +} diff --git a/research/coupled-provider-independent-audit/reports/algebra/RUNTIME.json b/research/coupled-provider-independent-audit/reports/algebra/RUNTIME.json new file mode 100644 index 0000000000..bd02549f94 --- /dev/null +++ b/research/coupled-provider-independent-audit/reports/algebra/RUNTIME.json @@ -0,0 +1,54 @@ +{ + "guard_receipt_path": "/home/d3lerium/.codex/.chatgpt-projects/g-p-6ad5817fd84881918865926b6fd51453/swarm-price-plane-20261023T112711Z/runs/provider5402-independent-algebra/RECEIPT.json", + "guard_receipt_sha256": "e79403fc2d7e71a9a4aecaf492757bb3ac89fd5ca1765c8da1bd261f11767ad4", + "stdout_sha256": "690b1a619233a55701d5e06997ef4c61e5fbcbab5519c317276853a4d42b61ec", + "guard": { + "schema": "serial-research-run/v1", + "command": [ + "/usr/bin/python3", + "-B", + "check_provider.py", + "--out", + "RESULT.json" + ], + "cwd": "/home/d3lerium/.codex/.chatgpt-projects/g-p-6ad5817fd84881918865926b6fd51453/swarm-provider-audit-sol-high-20261024/agents/algebra", + "exit_code": 0, + "termination": null, + "elapsed_seconds": 33.09615578700323, + "sampled_peak_descendant_rss_bytes": 181915648, + "rss_samples": 329, + "memory_limit_mib": 1024, + "timeout_seconds": 300.0, + "python": "3.12.3 (main, Aug 31 2026, 10:18:26) [GCC 13.3.0]", + "log_sha256": "690b1a619233a55701d5e06997ef4c61e5fbcbab5519c317276853a4d42b61ec", + "scope": "Fresh command execution only; scientific claim determined by reviewed output." + }, + "result_sha256": "e5b325235eeb6c976a8dc568df838f609fcca0f52945f00bb6b2e9a973a1a11b", + "source_byte_policy": "No source file edited; source custody is separately reviewed.", + "same_chart_cache_control": { + "guard_receipt_path": "/home/d3lerium/.codex/.chatgpt-projects/g-p-6ad5817fd84881918865926b6fd51453/swarm-price-plane-20261023T112711Z/runs/provider5402-same-chart-cache-control/RECEIPT.json", + "guard_receipt_sha256": "15ff49f21e110782ea6dcbbe2196e22790241f42c3eb823a5a7211a2b2ed2a4e", + "guard": { + "schema": "serial-research-run/v1", + "command": [ + "/usr/bin/python3", + "-B", + "check_same_chart_cache_mutant.py", + "--out", + "SAME-CHART-CACHE-MUTANT.json" + ], + "cwd": "/home/d3lerium/.codex/.chatgpt-projects/g-p-6ad5817fd84881918865926b6fd51453/swarm-provider-audit-sol-high-20261024/agents/algebra", + "exit_code": 0, + "termination": null, + "elapsed_seconds": 0.7051301799947396, + "sampled_peak_descendant_rss_bytes": 48652288, + "rss_samples": 7, + "memory_limit_mib": 256, + "timeout_seconds": 30.0, + "python": "3.12.3 (main, Aug 31 2026, 10:18:26) [GCC 13.3.0]", + "log_sha256": "afc4e5719c0e7cf1b2c8c1770d6d5f5f3c8b9411df6b7644419cc138b9be9261", + "scope": "Fresh command execution only; scientific claim determined by reviewed output." + }, + "result_sha256": "c8224338d3143f36ba5668908064971f11e2e684a80d9097b1bbd922cf152b15" + } +} diff --git a/research/coupled-provider-independent-audit/reports/algebra/SAME-CHART-CACHE-MUTANT.json b/research/coupled-provider-independent-audit/reports/algebra/SAME-CHART-CACHE-MUTANT.json new file mode 100644 index 0000000000..d16ae63422 --- /dev/null +++ b/research/coupled-provider-independent-audit/reports/algebra/SAME-CHART-CACHE-MUTANT.json @@ -0,0 +1,29 @@ +{ + "candidate_raw_sha256": "7dc356001ed597ad6fc9fd3e0bc6ff7e3ec3a580a579a956827aa17fccfdd2dc", + "checker_sha256": "4bf90d4656e03e6716448026ba120c172585c9aced067d35d6ca1a75250d9aad", + "frozen_engine_sha256": { + "check_provider.py": "3774c5742b565ea9007af90d10e43d38a3e675c2074583c8c365799fc256baaf", + "phase_exact.py": "15e90b63c5659090f02902cb38951ec4ab252352fb0b967b411ed547c501e2ba", + "prior_dyadic_engine.py": "3ee4ae79a55188d5abf2306f678179f4aafb799602ffb970fc1bc8f76cb061d9", + "provider_rows.py": "c7e579939d89709d72457d5fa213173b3b492c3cc3de7546afc3ed6a6fb32f0c" + }, + "inserted_event": [ + "scalar", + [ + "scale", + [ + "C", + 1 + ], + -1, + 1 + ], + 254 + ], + "mutation_source_event": 11207, + "preserved": "same chart, all owned CLEAR/COPY rules, no borrowed erasure; one legal SCALE -1 on retained C1 only", + "rejection": "zero retag requires complete exact zero row", + "runtime_seconds": 0.575157, + "source_raw_sha256": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05", + "status": "PASS_SAME_CHART_CACHE_CONTENT_MUTANT_REJECTED" +} diff --git a/research/coupled-provider-independent-audit/reports/budget/LIVE-5405-INTAKE.json b/research/coupled-provider-independent-audit/reports/budget/LIVE-5405-INTAKE.json new file mode 100644 index 0000000000..c9dc5a00af --- /dev/null +++ b/research/coupled-provider-independent-audit/reports/budget/LIVE-5405-INTAKE.json @@ -0,0 +1,7 @@ +{ + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5405", + "title": "Prove an unbounded FULL/QUERY controller ceiling (no κ gain)", + "head": "314b56a6c0056c2358538f072c6fde9d365be44d", + "base": "1ec1119972c9aefe42525172d07b332fcff81cb4", + "body": "This scoped proof puts a ceiling on the entire prefix/suffix FULL/QUERY invoice family with the current owned local profile: **no pair count, split or stage mask can fund `0.00302728825 <= κ < 1` through its strict moment test. No higher κ is claimed.** This removes the pair-count and stage-neighborhood limits of the earlier checks.\n\nThe [proof](https://github.com/aliromman/integer-mult-bounds/blob/314b56a6c0056c2358538f072c6fde9d365be44d/research/global-query-controller-ceiling/PROOF.md), [exact receipt](https://github.com/aliromman/integer-mult-bounds/blob/314b56a6c0056c2358538f072c6fde9d365be44d/research/global-query-controller-ceiling/RESULT.json), [verifier](https://github.com/aliromman/integer-mult-bounds/blob/314b56a6c0056c2358538f072c6fde9d365be44d/research/global-query-controller-ceiling/verify.py) and [source pins](https://github.com/aliromman/integer-mult-bounds/blob/314b56a6c0056c2358538f072c6fde9d365be44d/research/global-query-controller-ceiling/SOURCES.json) define the review object. The current complete conditional comparison is **κ = 0.00302728823**, from [PR #5398](https://github.com/CrocSwap/integer-mult-bounds/pull/5398), with [independent validation in PR #5400](https://github.com/CrocSwap/integer-mult-bounds/pull/5400). Its remaining room in this family is less than `2e-11`; this package does not rerun that positive admission.\n\nThe proof fixes the local paid/helper profiles, 112 ports, rank-eight stage blocks, rank-one query price and prefix/suffix idle law. A concavity bound rejects every allocation with at least 96 FULL stages. Deleting pairs of QUERY stages reduces the remaining unbounded family to at most 96 pairs. An integer dynamic program checks all **10,290,000** remaining state combinations. The minimum certified paid-minus-target margin is greater than **0.000000014914967918767741908079**, at the current p16/a7 invoice. A separate monotonicity argument extends the sign from the tested saving to the full stated interval.\n\nThis covers all masks and all pair counts, unlike the at-most-two-stage screen in [PR #5393](https://github.com/CrocSwap/integer-mult-bounds/pull/5393). [PR #5397](https://github.com/CrocSwap/integer-mult-bounds/pull/5397) supplies the related fixed 144-exchange invoice ceiling. It does not exclude another native profile, connection graph, idle law or recursive contract. In particular, the coupled outputs of [PR #5402](https://github.com/CrocSwap/integer-mult-bounds/pull/5402) require a different completed caller and are outside this theorem.\n\nBase: canonical main `1ec1119972c9aefe42525172d07b332fcff81cb4`, priority 7. The exact [PR #5392](https://github.com/CrocSwap/integer-mult-bounds/pull/5392) result at `329b2ff35d2994b11abbb59f770d12da75c494ac` is retained byte for byte in this branch's ancestor `6919161525e69b687630cb6468aa32b9414d7206`. Replay needs no pending predecessor checkout. The selected frontier is unchanged.\n\nPython 3.12 and the standard library:\n\n```sh\npython3 -B scripts/research_package.py --package research/global-query-controller-ceiling\n```\n\nExpected result in both registered modes:\n\n```text\nPASS_GLOBAL_QUERY_CONTROLLER_CEILING_NO_KAPPA_GAIN\n```\n\nNormal and optimized registered replays pass. Checks include source authentication, exact outward rational arithmetic, the infinite-tail inequalities, the complete dynamic program, 15 exact Laurent factorizations and all 12,744 masks through five pairs. The literal invoices and exhaustive minima agree with the new formula and dynamic program. Controls detect an omitted idle that falsely funds the moment, unearned helper credit and the middle-idle charge at an even FULL stage. All 16 committed-file bindings and official export integrity pass. An optimized read-only replay with Git absent passes; all 17 exported files remain unchanged. The optional full-history check is unavailable in this shallow checkout; direct base and retained-source ancestry checks pass. Hosted CI is pending at publication.\n\nThe native phase suite, complete compiler/outer and selected cold replays, physical tape execution and formal kernel were not run. The cited positive bounds retain the five selected framework assumptions. This is an author-checked mathematical ceiling for the stated invoices, not a global circuit optimum or a new multiplication theorem.\n\nCredit: Cinna Davis (@1337isnot1337) for the controller, Ali Romman (@aliromman) for the owned/transposed profile, Cao Yifan (@intqwq) for the native source, @zxv for the reused interval engine and invoice preflight, Chris R (@Clear1nsight) for the earlier stage screen and independent admission, and @Dugongue for the frame and compiler lineage. The [retained source notice](https://github.com/aliromman/integer-mult-bounds/blob/314b56a6c0056c2358538f072c6fde9d365be44d/research/global-query-controller-ceiling/source/NOTICE.md) preserves Jacob Alan Sussman and the earlier native, compiler and analytic credit. New proof and dynamic program by Ali Romman with substantial OpenAI Codex assistance; no subagents; Apache-2.0.\n" +} diff --git a/research/coupled-provider-independent-audit/reports/budget/LOCAL-ENVELOPE-PROOF.md b/research/coupled-provider-independent-audit/reports/budget/LOCAL-ENVELOPE-PROOF.md new file mode 100644 index 0000000000..e16f3c18f3 --- /dev/null +++ b/research/coupled-provider-independent-audit/reports/budget/LOCAL-ENVELOPE-PROOF.md @@ -0,0 +1,60 @@ +# One-provider local envelopes in two norm geometries + +This is a local bound for the complete #5402 provider schedule at exact head `3348fccea855082786d5f0fc5558b73d4974e745`. It covers arbitrary positive fiber width under the retained square normalized native/Clifford realization. It is not a full caller rounding, recursion, coordinate, storage, movement, tape or outer-funding theorem. + +Let each of the 641 fields be a vector in the same physical Hilbert space H_f, with its field Euclidean norm. Define + +``` +||v||max = max_j ||v_j||2 +||v||joint = (sum_j ||v_j||2^2)^(1/2). +``` + +The first is the maximum-field geometry explicitly declared by the provider's proof. The second measures joint field Euclidean error. Their elementary COPY bounds differ; a different exponent in the second geometry is not a discrepancy in the author's first-geometry claim. + +## Square unitary native contract + +The pinned `clifford_exact.py` defines a normalized square Gaussian gate on a binary translation X_q by + +``` +C_q = ((1+i)/2) I + ((1-i)/2) X_q. +``` + +Here X_q is a self-adjoint unitary involution. The two coefficient squared magnitudes sum to one, and their cross terms cancel, so C_q is unitary; its inverse conjugates the coefficients and is also unitary. Address permutations, X shifts and D/phase gates are unitary. The canonical frame constructor consists of these gates and unitary conjugations. Complex conjugation of a frame preserves unitarity. A relative chart/frame transition and each normalized signed Gaussian child therefore act on a square field space by a unitary map. This does not follow merely from formal free-group invertibility. + +The emitted source's 72 warp address matrices are independently checked for full binary rank nine, and every canonical frame row list is checked to be an independent subspace basis. Every literal P in the 464 boundary monomial words is checked to be invertible. Their D and phase factors have unit modulus. Tensoring/lifting these primitive address operations columnwise preserves unitarity at every positive width; exterior scalar owner coefficients remain scalar coefficients and are not tensor powered. Thus the unitary bound does not grow with the width. + +The native source phase/adapter records preserve the predecessor's physical bindings; they are not newly reconstructed in this norm checker. The separate independent source/physical audit binds that inherited realization. The envelope's premise is that those records are realized by the stated square canonical Clifford maps, with no hidden nonunitary scalar rescaling. It does not newly discharge the native implementation foundation. This norm audit never executes submitted Python. + +## Elementary bounds + +For either geometry, ADD `v_d += q v_s` with distinct fields has norm at most `1+|q|`. In joint geometry, write the map as `I+q E_ds`, where the block matrix E_ds has operator norm one. In maximum-field geometry, use the triangle inequality for the changed destination. SCALE has bound `max(1,|q|)` on the whole bank. CLEAR and whole-field SWAP have norm at most one. A single-field unitary map, including each Gaussian/monomial/chart operation above, has norm one. + +COPY overwrites one destination with its source. Its maximum-field norm is at most one. In joint geometry its norm is at most sqrt(2), since the old destination is discarded and the source contributes to two output fields. The integer power-of-two enclosure uses 2. The COPY bound applies to arbitrary perturbations; it does not rely on silently restricting the destination's error to zero. Exact zero-retag is physical identity and has norm one; correctness of its exact-zero prerequisite belongs to the separate source replay. + +For each elementary operation assign exponent zero for a nonexpanding map; assign + +``` +ceil(log2(1+|q|)) for ADD, +ceil(log2(max(1,|q|))) for SCALE, +0 / 1 for COPY in max / joint geometry. +``` + +All ceiling decisions are exact rational comparisons against powers of two. The checker parses the actual changed WORD, both emitted basis programs, all eight input scalings, all eight emitted output scalings, all final consumption clears/swaps and the literal monomial boundaries. It counts the normalized output `cache_scalar` directly: that field already stores `1/(2 f_i)`. + +If L is the sum of these nonnegative exponents, every contiguous subinterval, prefix and suffix has operator norm at most 2^L. Indeed its exponent sum is no larger than the complete sum. This is a deliberately coarse upper bound; it does not assert an optimal norm or exponent. + +For residuals inserted after any local operation, the standard telescoping error expansion and the suffix bound give, in the selected same geometry, + +``` +||e_out|| <= 2^L (||e_in|| + sum_j ||residual_j||). +``` + +With m residuals each bounded by epsilon and zero initial error, this is at most `m*2^L*epsilon`. The residual bounds are whole-field norm bounds at a fixed width. There is no implicit dimension-independent conversion from coordinate error to whole-field error, and no machine precision or tape budget is inferred. + +## Execution and separate scalar-invoice correction + +`independent_local_envelope.py` independently reconstructs both exponents and compares the first with the author's declared maximum-field bound only after completing the literal calculation. It also checks exact rational ceiling, COPY-geometry and direct-output-SCALE controls. Its output is `LOCAL-ENVELOPE-v1.json`; root performs the guarded execution. The guarded run passed. The exact stage exponents (max / joint geometry) are: mode inputs 8/8, input basis 844/844, changed native word 17,282/17,298, output basis 854/854, and cache output normalizers 8/8; fused main wrappers contribute zero. Their sums are **18,996 / 19,012**. Thus the author's declared maximum-field bound is independently reproduced. Root's external guard recorded 0.504455 seconds and 59,138,048 sampled descendant bytes. The checker recorded 0.413036 seconds internally and 57,752 KiB maximum RSS. Checker SHA256 is `11d8b361adacac9ae44985ffa8a83ff0e9de47e94571e486427baa7201da7715`; receipt SHA256 is `f99bc2dd5f60b38d6ee9617fac9fb1f03ce9c5f10455650ccf2f7acc54bb490f`. + +The original budget checker misread the emitted `cache_scalar` as the unnormalized cache coefficient and applied its reciprocal formula a second time. All eight actual output magnitudes are two. The field operation counts and all recursive profiles/moments were unaffected. The old scalar tariff of 175,038 remains a conservative overestimate but is not the exact literal scalar tariff. The fresh `screen_v3.py` uses the emitted coefficient directly and checks boundary scalar tariff 42 rather than 58, giving exact total 175,022 rather than 175,038. Its authoritative output is `RESULT-v3.json`; earlier checker/result files are retained as version-scoped history. This correction concerns this independent checker, not the provider. + +Credit remains with the native, provider, Clifford, controller, compiler and other contributors retained in the pinned source. Independent derivation: Chris R/Clear1nsight with substantial OpenAI Codex assistance. No human or formal-kernel acceptance is claimed. diff --git a/research/coupled-provider-independent-audit/reports/budget/LOCAL-ENVELOPE-v1.json b/research/coupled-provider-independent-audit/reports/budget/LOCAL-ENVELOPE-v1.json new file mode 100644 index 0000000000..bd4cbcf367 --- /dev/null +++ b/research/coupled-provider-independent-audit/reports/budget/LOCAL-ENVELOPE-v1.json @@ -0,0 +1,174 @@ +{ + "abstract_scalar_unitary_transcript_sha256": "8c96a283c2fe5523456ea898254199c6bf633cf9e7c3033b65151a6f5b9bd50a", + "author_declared_geometry": "maximum over fields of field Euclidean norms", + "author_stated_max_field_exponent": 18996, + "controls": [ + "upward_rational_logarithm", + "COPY_norm_geometry", + "emitted_output_scale_used_directly" + ], + "copy_count": 16, + "error_inequality": "For either stated norm and its exponent L: ||e_out|| <= 2^L (||e_in|| + sum_j ||local_residual_j||). Residuals use that same whole-field geometry, at one fixed width. No implicit coordinatewise-to-field or width-independent injection conversion is claimed.", + "executed_checker_sha256": "11d8b361adacac9ae44985ffa8a83ff0e9de47e94571e486427baa7201da7715", + "groups": [ + { + "counts": { + "unitary": 224 + }, + "gate_count": 224, + "group": "224_fused_main_input_wrappers", + "joint_field_l2_exponent": 0, + "max_field_l2_exponent": 0 + }, + { + "counts": { + "scale": 8, + "unitary": 8 + }, + "gate_count": 16, + "group": "eight_mode_inputs", + "joint_field_l2_exponent": 8, + "max_field_l2_exponent": 8 + }, + { + "counts": { + "add": 822, + "scale": 12 + }, + "gate_count": 834, + "group": "input_basis", + "joint_field_l2_exponent": 844, + "max_field_l2_exponent": 844 + }, + { + "counts": { + "add": 16273, + "annotation": 458, + "clear": 32, + "copy": 16, + "scale": 1164, + "unitary": 3522, + "zero_retag": 8 + }, + "gate_count": 21473, + "group": "changed_native_word", + "joint_field_l2_exponent": 17298, + "max_field_l2_exponent": 17282 + }, + { + "counts": { + "add": 822, + "scale": 12 + }, + "gate_count": 834, + "group": "output_basis", + "joint_field_l2_exponent": 854, + "max_field_l2_exponent": 854 + }, + { + "counts": { + "clear": 8, + "scale": 8, + "swap": 8, + "unitary": 8 + }, + "gate_count": 32, + "group": "eight_cache_output_normalizers_and_consumption", + "joint_field_l2_exponent": 8, + "max_field_l2_exponent": 8 + }, + { + "counts": { + "unitary": 224 + }, + "gate_count": 224, + "group": "224_fused_main_output_wrappers", + "joint_field_l2_exponent": 0, + "max_field_l2_exponent": 0 + } + ], + "head": "3348fccea855082786d5f0fc5558b73d4974e745", + "native_records": { + "adapter": 448, + "climb": 3282, + "phase": 10, + "scalar": 17485, + "warp": 240, + "zero_retag": 8 + }, + "runtime": { + "maxrss_kib": 57752, + "seconds": 0.4130356339737773 + }, + "scope": "One raw provider only. Not recursive precision, caller error allocation, tape routing/movement, machine storage, compiler or outer funding.", + "source_files": [ + { + "local": "inputs/NORMALIZERS.json", + "sha256": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da" + }, + { + "local": "inputs/PROOF.md", + "sha256": "2d59282f3b5e9fb848d0099ce91729fa433162e6975f877a441e2ab4f57a29c5" + }, + { + "local": "inputs/PROVIDER.json", + "sha256": "676de7551d3364598f4a7e29ae97cae0e4364348786bbe70435b84294ba7dd65" + }, + { + "local": "inputs/README.md", + "sha256": "0d86590c471a498f3b735397d42bbaf4d5e89c33b75ddbd48dbf972192ab351f" + }, + { + "local": "inputs/REFERENCE-5398-CONTROLLER.json", + "sha256": "60cc512b39cdb9ea2c2ac6c6634c8d3f9627d96ace08ffa659a9d9472444122b" + }, + { + "local": "inputs/REFERENCE-5400-INVOICE.json", + "sha256": "a53bdbc009830f83b91233cf7cc2c8e9a03d76cff93c73bdd4f52fceb742e73f" + }, + { + "local": "inputs/SOURCE-PINS.json", + "sha256": "fc2e447a0043f74b133a24b67b2a87e4ff87232dd8a003253d19dbf2390a9092" + }, + { + "local": "inputs/SOURCE-WORD.json.gz", + "sha256": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05" + }, + { + "local": "inputs/SOURCES.json", + "sha256": "f16756004bd3100e4993b250181c4c8d15c31b0a1478b627091dd900e1103888" + }, + { + "local": "inputs/WORD.json.gz", + "sha256": "7dc356001ed597ad6fc9fd3e0bc6ff7e3ec3a580a579a956827aa17fccfdd2dc" + }, + { + "local": "independent_price_engine.py", + "sha256": "9ef7ee4082631566eb7903c3e21e517ef58039dca2a47104a2279c459589eb47" + }, + { + "head": "3348fccea855082786d5f0fc5558b73d4974e745", + "local": "envelope-inputs/clifford_exact.py", + "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962", + "source_path": "research/coded-native-caller/clifford_exact.py" + }, + { + "head": "3348fccea855082786d5f0fc5558b73d4974e745", + "local": "envelope-inputs/PHYSICAL.md", + "sha256": "4321b159ff8d3fe705419adaaa1beef75606e869e34341bda553f17d598a6078", + "source_path": "research/coded-native-caller/PHYSICAL.md" + }, + { + "head": "3348fccea855082786d5f0fc5558b73d4974e745", + "local": "envelope-inputs/verify.py", + "sha256": "121d87787c0f76bd530b6e1682704a311e96dfb33d787bea2ba29a1d0e5ee23e", + "source_path": "research/native-rank8-helper-provider/verify.py" + } + ], + "square_clifford_contract": "All fields are square ambient2^(9f) address arrays. Normalized signed C gates, canonical frames/conjugates, invertible address warps and literal monomial wrappers are unitary for every positive width f. Physical phase/adapter binding is inherited/audited separately; free-group invertibility alone would not establish this premise.", + "status": "PASS_INDEPENDENT_ONE_PROVIDER_TWO_NORM_ENVELOPE", + "total_joint_field_l2_exponent": 19012, + "total_max_field_l2_exponent": 18996, + "uniform_contiguous_intervals": true, + "uniform_suffixes": true +} diff --git a/research/coupled-provider-independent-audit/reports/budget/REPORT-v3.md b/research/coupled-provider-independent-audit/reports/budget/REPORT-v3.md new file mode 100644 index 0000000000..c420bed962 --- /dev/null +++ b/research/coupled-provider-independent-audit/reports/budget/REPORT-v3.md @@ -0,0 +1,91 @@ +# Independent provider closure budget + +This lane supplies a typed necessary-condition screen and a literal ordinary inventory for #5402 at `3348fccea855082786d5f0fc5558b73d4974e745`. It supplies no completed caller and no new kappa. Its favorable comparison deliberately grants a target contract that has not been constructed: each of the eighteen provider instances closes to the same standard B main interface used by #5398, preserves its 400 autonomous helpers, and earns eight additional autonomous H8 jobs. The actual eight coupled H outputs have zero autonomous credit. + +## Exact source and complete comparison invoice + +`inputs/ALL-PINS.json` binds the literal original and changed words, PROVIDER basis programs, canonical NORMALIZERS, the independently validated #5400 invoice and the exact #5398 controller. The standalone price engine is copied without modification from our prior independent numeric lane; no submitted provider/native/price/verifier module is executed. The checker reconstructs the complete old invoice using all eighteen local bodies, fifteen 112-job H1 queries, every retained whole idle, and every main diagonal term. It requires literal equality with the independent #5400 invoice. + +The local paid profile is `{1:2193,2:412,3:510,4:127,5:40}`. Removing the eight selected mode owners from the original source's helper-frame census leaves `{4:28,7:7,8:47,9:318}`: 400 jobs. Both profiles already equal the comparison's local profiles. The advertised deletion of eight H8 plus eight H1 jobs is relative to the original raw source; those are not additional savings over #5398. + +The complete paid comparison is: + +``` +{1:41154,2:7416,3:9180,4:2286,5:720, + 16:448,24:448,32:448,40:448,48:448,56:448,64:448,72:224} +``` + +Its productive profile is: + +``` +{4:504,7:126,8:846,9:5724,17:448,25:448,33:448, + 41:448,49:448,57:448,65:448,73:224,145:224} +``` + +There are 64,116 paid calls and 10,784 productive jobs, with paid/productive rank masses 237,838/238,590 and surplus 752. The optimistic closure contract adds exactly `{8:144}` to the productive profile. It therefore has 10,928 productive jobs and surplus 1,904 before charging any closure Gaussian, lost target, changed idle or main output. This favorable profile is an upper relaxation under the named contract, not an attained caller profile. + +For aggregate closure paid histogram K, lost productive histogram L and other signed caller-profile change Delta, define `t=1-kappa` and `M(J)=sum_r J[r] r^t`. The exact required comparison is + +``` +margin_new = margin_5398 + 144*8^t - M(K) - M(L) + M(Delta). +``` + +Every unproved term remains unknown. In particular, `Delta=0` requires the actual eighteen closed interfaces, all original queries/idles and the main diagonal to be preserved. Ordinary scalar and monomial work does not enter this recursive moment identity; its separate funding remains mandatory. + +If K is exactly 144 H8 calls and L and Delta vanish, the entire signed profile equals #5398 at every rank. It has exactly the same moment for every saving. If any further paid job is added with no compensating productive change, its moment is worse. This gives no strict recursive-profile improvement. It does not exclude improvements to compiler headroom or a different productive contract, coupling graph or idle law. + +At the reference saving `.00302728823`, the exact directed intervals give reference target-minus-paid moment approximately `0.00000492044809504` and the hypothetical credit `63.59838102597` per provider, or `1144.77085846746` across eighteen. The following are strict *incremental* moment budgets with no lost targets and no other caller change; each column assumes all closure jobs have the single displayed rank. Mixed-rank closure must use the weighted inequality above. + +| Paid closure rank | Maximum per provider | Maximum across eighteen providers | +|---:|---:|---:| +|1|63|1144| +|2|31|573| +|3|21|382| +|4|15|287| +|5|12|230| +|8|7|143| +|9|7|128| +|16|4|72| +|32|2|36| +|64|1|18| +|145|0|8| + +The per-provider column assumes identical independent cleanup allowances; the aggregate column permits the caller to share cleanup across providers. `TOTAL-BUDGET-v3.json` derives the aggregate column from the exact intervals already produced by the guarded run, including exact equality at rank eight. The actual reference's tiny positive margin is separate from strict incremental gain; no table entry by itself proves full compiler funding. + +## Ordinary inventory and explicit unknown costs + +The checker parses all scalar operations of the changed literal source, both emitted basis programs, all exterior mode scalings and final consumption clears. Per provider, the complete boundary-inclusive scalar schedule has 17,917 ADD, 1,204 SCALE, 16 COPY, 40 CLEAR and eight whole-field SWAP operations. The 464 monomial maps comprise 448 inherited fused main standardizers and sixteen mode/cache maps. Their literal gate words are counted separately. Every unchanged warp, adapter and phase annotation remains in the census. The eight zero retags receive no paid Gaussian charge because their required exact-zero premise belongs to the independent source replay gate. + +Across eighteen providers, the known subtotal is 322,506 ADD, 21,672 SCALE, 288 COPY, 720 CLEAR, 144 whole-field SWAP and 8,352 monomial maps, before consumer closure and the separate outer caller records. The exact controller has 90 ADD, 20 SIGNED_SWAP and four Q_POWER records on 112-field banks, plus the complete left/right scalar boundary programs; its LOCAL, QUERY_SHEAR and IDLE records are already included in the recursive invoice. These are literal finite field-operation counts, not physical tape-step counts. + +The inherited dyadic scalar tariff is the prior independent tariff: COPY/CLEAR two units, dyadic unit SCALE twice its shift/sign count, ADD twice `3+floor(log2 numerator)+popcount(numerator)+log2 denominator`, SWAP reserved at 26. The original raw source scalar total is **158,168**, not 158,744: the latter belongs to the distinct prior retained-owned source body. The first frozen checker used that wrong precondition and failed before numerical work. Its source is retained as `screen.failed-v1.py`; the root's failure log is preserved. This was a checker binding failure, not a #5402 construction failure. + +Unknown costs remain explicit: physical machine/tape realization of monomial maps and retained native primitives; the closure's Gaussian and ordinary operations; productive targets lost through closure; caller-specific finite precision, growth constants, routing, storage and movement; the complete compiler and outer ledger. The local source amplification bound does not discharge these full caller obligations. + +## Independently derived local suffix and subinterval envelopes + +The fresh [LOCAL-ENVELOPE-PROOF.md](LOCAL-ENVELOPE-PROOF.md) and guarded `LOCAL-ENVELOPE-v1.json` independently reconstruct the full one-provider schedule's elementary norm product. In the author's explicitly declared maximum-over-fields Euclidean geometry, the derived exponent is **18,996**, agreeing with the author. In joint-field Euclidean geometry, sixteen COPYs each receive the safe power-of-two factor two, giving exponent **19,012**. This difference is a geometry change, not a defect in the author's maximum-field bound. + +The stage exponents in maximum-field geometry are: input wrappers zero; eight input scalings eight; input basis 844; changed native word 17,282; output basis 854; eight output scalings eight; output wrappers zero. Joint geometry changes only the native-word subtotal to 17,298. The proof uses normalized square Clifford/Gaussian/monomial unitarity and independently checks source-frame and address-permutation ranks. It explicitly retains the audited native physical interpretation premise, rather than inferring unitarity from free-group invertibility alone. + +For either geometry and its L, every contiguous subinterval and suffix has norm at most `2^L`. At one fixed width, `||e_out|| <= 2^L (||e_in|| + sum_j ||local_residual_j||)`. No coordinatewise-to-field error conversion, recursive caller error allocation, tape movement or machine precision is hidden in this statement. Root's envelope guard passed in 0.504455 seconds with 59,138,048 bytes sampled descendant RSS; its own process reports 0.413036 seconds and 57,752 KiB maximum RSS. + +The followup also found and corrected an interpretation error in the independent budget checker: `mode_boundaries.cache_scalar` already stores the final output factor. The old checker applied a reciprocal formula twice. Its 175,038 scalar tariff remains conservative, but its claim to an exact literal tariff was wrong. `screen_v3.py` uses the emitted coefficient directly, yielding exact boundary tariff 42 and total 175,022. Field operation counts, complete recursive profiles, moments and conditional budgets are unchanged. Earlier `screen.py`, `RESULT-v1.json`, `TOTAL-BUDGET-v1.json` and the text now preserved as `REPORT-v1.md` are historical, version-scoped evidence; `screen_v3.py`, `RESULT-v3.json`, `TOTAL-BUDGET-v3.json` and this v3 report are authoritative. + +## Scope relative to #5405 and the latest caller handoff + +Live [#5405](https://github.com/CrocSwap/integer-mult-bounds/pull/5405), head `314b56a6c0056c2358538f072c6fde9d365be44d`, fixes the existing paid/helper profiles, 112 ports, rank-eight stage blocks, rank-one query price and prefix/suffix idle law. Its unbounded FULL/QUERY ceiling excludes `.00302728825 <= kappa < 1` inside that exact invoice family. Its body explicitly excludes #5402's unfinished coupled caller. This lane does not rerun or extend that theorem. Any attempt to gain only by changing old FULL/QUERY pair counts or masks should consume that public ceiling; an earned new target contract changes its premises. + +Root's live intake of [Dillon's latest #4930 handoff](https://github.com/CrocSwap/integer-mult-bounds/discussions/4930#discussioncomment-19155935) reports that the caller claim has been released. The stated local-only snapshot and its execution counts are not independently validated here. The proposed next bounded control is an uncoded eight-owner identity written `A S A = Q S`, with helper-tail updates from retained original inputs. No portable exact A/S definitions, ordered physical words, charts and helper-tail implementation are supplied by the inputs reviewed in this lane. Substituting a guessed scalar code or commuting D/Q through W/Z would invent a different control. The alternative p2 pivot similarly requires its ordered eight-field right-hand side. Therefore this lane reports a missing typed next-test input, not a failed control and not an implemented coded closure. + +## Execution and reproducibility + +Final checker is `screen_v3.py`; frozen SHA256 `9805fb55fe2888ae7e10a96c5f91e032fc9e6ac95a7831fed987d502e4814c2e`. Input manifest SHA256 `a37fa9735bbb2697811de72a706b243842d1303243f6e6a0300bd5046d4f3d66`. Root alone runs the exact moment screen with a ten-second external guard and 128 MiB address-space bound: + +``` +python3 -B agents/budget/screen_v3.py --moments --output agents/budget/RESULT-v3.json +``` + +Root's final v3 guarded execution passed in 0.908223 seconds with 57,507,840 bytes sampled peak descendant RSS. `RESULT-v3.json` records 0.822612 seconds internally and 56,160 KiB process maximum RSS. The exact receipt derives scalar tariff 175,022 units per provider (16,854 above the original raw source), including both 8,262-unit basis programs, 42 units of exterior mode scalings, final consumption clears and 26-unit SWAP allowances. The 464 monomial maps contain 464 each of D/P/X/phase gates (1,856 monomial primitive gates). These remain a separate physical cost term. The complete left/right caller boundary programs have respectively 56/25 ADD, 4/3 SCALE and 30/27 SWAP records. The checker authenticates all frozen inputs before deriving the inventory and conditional moments. Acceptance does not admit any actual #5402 consumer. Native identities, ownership/phase checks, full caller precision and complete funding remain distinct gates. + +Construction credit remains with Ali Romman and the native/provider/controller/Clifford/compiler predecessors named in the pinned source; the independent price engine and #5400 receipt retain their prior attribution. This budget audit is Chris R/Clear1nsight with substantial OpenAI Codex assistance. No independent human or formal-kernel acceptance is claimed. diff --git a/research/coupled-provider-independent-audit/reports/budget/REPORT.md b/research/coupled-provider-independent-audit/reports/budget/REPORT.md new file mode 100644 index 0000000000..c420bed962 --- /dev/null +++ b/research/coupled-provider-independent-audit/reports/budget/REPORT.md @@ -0,0 +1,91 @@ +# Independent provider closure budget + +This lane supplies a typed necessary-condition screen and a literal ordinary inventory for #5402 at `3348fccea855082786d5f0fc5558b73d4974e745`. It supplies no completed caller and no new kappa. Its favorable comparison deliberately grants a target contract that has not been constructed: each of the eighteen provider instances closes to the same standard B main interface used by #5398, preserves its 400 autonomous helpers, and earns eight additional autonomous H8 jobs. The actual eight coupled H outputs have zero autonomous credit. + +## Exact source and complete comparison invoice + +`inputs/ALL-PINS.json` binds the literal original and changed words, PROVIDER basis programs, canonical NORMALIZERS, the independently validated #5400 invoice and the exact #5398 controller. The standalone price engine is copied without modification from our prior independent numeric lane; no submitted provider/native/price/verifier module is executed. The checker reconstructs the complete old invoice using all eighteen local bodies, fifteen 112-job H1 queries, every retained whole idle, and every main diagonal term. It requires literal equality with the independent #5400 invoice. + +The local paid profile is `{1:2193,2:412,3:510,4:127,5:40}`. Removing the eight selected mode owners from the original source's helper-frame census leaves `{4:28,7:7,8:47,9:318}`: 400 jobs. Both profiles already equal the comparison's local profiles. The advertised deletion of eight H8 plus eight H1 jobs is relative to the original raw source; those are not additional savings over #5398. + +The complete paid comparison is: + +``` +{1:41154,2:7416,3:9180,4:2286,5:720, + 16:448,24:448,32:448,40:448,48:448,56:448,64:448,72:224} +``` + +Its productive profile is: + +``` +{4:504,7:126,8:846,9:5724,17:448,25:448,33:448, + 41:448,49:448,57:448,65:448,73:224,145:224} +``` + +There are 64,116 paid calls and 10,784 productive jobs, with paid/productive rank masses 237,838/238,590 and surplus 752. The optimistic closure contract adds exactly `{8:144}` to the productive profile. It therefore has 10,928 productive jobs and surplus 1,904 before charging any closure Gaussian, lost target, changed idle or main output. This favorable profile is an upper relaxation under the named contract, not an attained caller profile. + +For aggregate closure paid histogram K, lost productive histogram L and other signed caller-profile change Delta, define `t=1-kappa` and `M(J)=sum_r J[r] r^t`. The exact required comparison is + +``` +margin_new = margin_5398 + 144*8^t - M(K) - M(L) + M(Delta). +``` + +Every unproved term remains unknown. In particular, `Delta=0` requires the actual eighteen closed interfaces, all original queries/idles and the main diagonal to be preserved. Ordinary scalar and monomial work does not enter this recursive moment identity; its separate funding remains mandatory. + +If K is exactly 144 H8 calls and L and Delta vanish, the entire signed profile equals #5398 at every rank. It has exactly the same moment for every saving. If any further paid job is added with no compensating productive change, its moment is worse. This gives no strict recursive-profile improvement. It does not exclude improvements to compiler headroom or a different productive contract, coupling graph or idle law. + +At the reference saving `.00302728823`, the exact directed intervals give reference target-minus-paid moment approximately `0.00000492044809504` and the hypothetical credit `63.59838102597` per provider, or `1144.77085846746` across eighteen. The following are strict *incremental* moment budgets with no lost targets and no other caller change; each column assumes all closure jobs have the single displayed rank. Mixed-rank closure must use the weighted inequality above. + +| Paid closure rank | Maximum per provider | Maximum across eighteen providers | +|---:|---:|---:| +|1|63|1144| +|2|31|573| +|3|21|382| +|4|15|287| +|5|12|230| +|8|7|143| +|9|7|128| +|16|4|72| +|32|2|36| +|64|1|18| +|145|0|8| + +The per-provider column assumes identical independent cleanup allowances; the aggregate column permits the caller to share cleanup across providers. `TOTAL-BUDGET-v3.json` derives the aggregate column from the exact intervals already produced by the guarded run, including exact equality at rank eight. The actual reference's tiny positive margin is separate from strict incremental gain; no table entry by itself proves full compiler funding. + +## Ordinary inventory and explicit unknown costs + +The checker parses all scalar operations of the changed literal source, both emitted basis programs, all exterior mode scalings and final consumption clears. Per provider, the complete boundary-inclusive scalar schedule has 17,917 ADD, 1,204 SCALE, 16 COPY, 40 CLEAR and eight whole-field SWAP operations. The 464 monomial maps comprise 448 inherited fused main standardizers and sixteen mode/cache maps. Their literal gate words are counted separately. Every unchanged warp, adapter and phase annotation remains in the census. The eight zero retags receive no paid Gaussian charge because their required exact-zero premise belongs to the independent source replay gate. + +Across eighteen providers, the known subtotal is 322,506 ADD, 21,672 SCALE, 288 COPY, 720 CLEAR, 144 whole-field SWAP and 8,352 monomial maps, before consumer closure and the separate outer caller records. The exact controller has 90 ADD, 20 SIGNED_SWAP and four Q_POWER records on 112-field banks, plus the complete left/right scalar boundary programs; its LOCAL, QUERY_SHEAR and IDLE records are already included in the recursive invoice. These are literal finite field-operation counts, not physical tape-step counts. + +The inherited dyadic scalar tariff is the prior independent tariff: COPY/CLEAR two units, dyadic unit SCALE twice its shift/sign count, ADD twice `3+floor(log2 numerator)+popcount(numerator)+log2 denominator`, SWAP reserved at 26. The original raw source scalar total is **158,168**, not 158,744: the latter belongs to the distinct prior retained-owned source body. The first frozen checker used that wrong precondition and failed before numerical work. Its source is retained as `screen.failed-v1.py`; the root's failure log is preserved. This was a checker binding failure, not a #5402 construction failure. + +Unknown costs remain explicit: physical machine/tape realization of monomial maps and retained native primitives; the closure's Gaussian and ordinary operations; productive targets lost through closure; caller-specific finite precision, growth constants, routing, storage and movement; the complete compiler and outer ledger. The local source amplification bound does not discharge these full caller obligations. + +## Independently derived local suffix and subinterval envelopes + +The fresh [LOCAL-ENVELOPE-PROOF.md](LOCAL-ENVELOPE-PROOF.md) and guarded `LOCAL-ENVELOPE-v1.json` independently reconstruct the full one-provider schedule's elementary norm product. In the author's explicitly declared maximum-over-fields Euclidean geometry, the derived exponent is **18,996**, agreeing with the author. In joint-field Euclidean geometry, sixteen COPYs each receive the safe power-of-two factor two, giving exponent **19,012**. This difference is a geometry change, not a defect in the author's maximum-field bound. + +The stage exponents in maximum-field geometry are: input wrappers zero; eight input scalings eight; input basis 844; changed native word 17,282; output basis 854; eight output scalings eight; output wrappers zero. Joint geometry changes only the native-word subtotal to 17,298. The proof uses normalized square Clifford/Gaussian/monomial unitarity and independently checks source-frame and address-permutation ranks. It explicitly retains the audited native physical interpretation premise, rather than inferring unitarity from free-group invertibility alone. + +For either geometry and its L, every contiguous subinterval and suffix has norm at most `2^L`. At one fixed width, `||e_out|| <= 2^L (||e_in|| + sum_j ||local_residual_j||)`. No coordinatewise-to-field error conversion, recursive caller error allocation, tape movement or machine precision is hidden in this statement. Root's envelope guard passed in 0.504455 seconds with 59,138,048 bytes sampled descendant RSS; its own process reports 0.413036 seconds and 57,752 KiB maximum RSS. + +The followup also found and corrected an interpretation error in the independent budget checker: `mode_boundaries.cache_scalar` already stores the final output factor. The old checker applied a reciprocal formula twice. Its 175,038 scalar tariff remains conservative, but its claim to an exact literal tariff was wrong. `screen_v3.py` uses the emitted coefficient directly, yielding exact boundary tariff 42 and total 175,022. Field operation counts, complete recursive profiles, moments and conditional budgets are unchanged. Earlier `screen.py`, `RESULT-v1.json`, `TOTAL-BUDGET-v1.json` and the text now preserved as `REPORT-v1.md` are historical, version-scoped evidence; `screen_v3.py`, `RESULT-v3.json`, `TOTAL-BUDGET-v3.json` and this v3 report are authoritative. + +## Scope relative to #5405 and the latest caller handoff + +Live [#5405](https://github.com/CrocSwap/integer-mult-bounds/pull/5405), head `314b56a6c0056c2358538f072c6fde9d365be44d`, fixes the existing paid/helper profiles, 112 ports, rank-eight stage blocks, rank-one query price and prefix/suffix idle law. Its unbounded FULL/QUERY ceiling excludes `.00302728825 <= kappa < 1` inside that exact invoice family. Its body explicitly excludes #5402's unfinished coupled caller. This lane does not rerun or extend that theorem. Any attempt to gain only by changing old FULL/QUERY pair counts or masks should consume that public ceiling; an earned new target contract changes its premises. + +Root's live intake of [Dillon's latest #4930 handoff](https://github.com/CrocSwap/integer-mult-bounds/discussions/4930#discussioncomment-19155935) reports that the caller claim has been released. The stated local-only snapshot and its execution counts are not independently validated here. The proposed next bounded control is an uncoded eight-owner identity written `A S A = Q S`, with helper-tail updates from retained original inputs. No portable exact A/S definitions, ordered physical words, charts and helper-tail implementation are supplied by the inputs reviewed in this lane. Substituting a guessed scalar code or commuting D/Q through W/Z would invent a different control. The alternative p2 pivot similarly requires its ordered eight-field right-hand side. Therefore this lane reports a missing typed next-test input, not a failed control and not an implemented coded closure. + +## Execution and reproducibility + +Final checker is `screen_v3.py`; frozen SHA256 `9805fb55fe2888ae7e10a96c5f91e032fc9e6ac95a7831fed987d502e4814c2e`. Input manifest SHA256 `a37fa9735bbb2697811de72a706b243842d1303243f6e6a0300bd5046d4f3d66`. Root alone runs the exact moment screen with a ten-second external guard and 128 MiB address-space bound: + +``` +python3 -B agents/budget/screen_v3.py --moments --output agents/budget/RESULT-v3.json +``` + +Root's final v3 guarded execution passed in 0.908223 seconds with 57,507,840 bytes sampled peak descendant RSS. `RESULT-v3.json` records 0.822612 seconds internally and 56,160 KiB process maximum RSS. The exact receipt derives scalar tariff 175,022 units per provider (16,854 above the original raw source), including both 8,262-unit basis programs, 42 units of exterior mode scalings, final consumption clears and 26-unit SWAP allowances. The 464 monomial maps contain 464 each of D/P/X/phase gates (1,856 monomial primitive gates). These remain a separate physical cost term. The complete left/right caller boundary programs have respectively 56/25 ADD, 4/3 SCALE and 30/27 SWAP records. The checker authenticates all frozen inputs before deriving the inventory and conditional moments. Acceptance does not admit any actual #5402 consumer. Native identities, ownership/phase checks, full caller precision and complete funding remain distinct gates. + +Construction credit remains with Ali Romman and the native/provider/controller/Clifford/compiler predecessors named in the pinned source; the independent price engine and #5400 receipt retain their prior attribution. This budget audit is Chris R/Clear1nsight with substantial OpenAI Codex assistance. No independent human or formal-kernel acceptance is claimed. diff --git a/research/coupled-provider-independent-audit/reports/budget/RESULT-v3.json b/research/coupled-provider-independent-audit/reports/budget/RESULT-v3.json new file mode 100644 index 0000000000..5c7e1ed2dd --- /dev/null +++ b/research/coupled-provider-independent-audit/reports/budget/RESULT-v3.json @@ -0,0 +1,558 @@ +{ + "added_scalar": { + "add": 1644, + "clear": 24, + "copy": 16, + "scale": 40 + }, + "autonomous_count": 400, + "autonomous_helpers": { + "4": 28, + "7": 7, + "8": 47, + "9": 318 + }, + "autonomous_rank_mass": 3399, + "basis_counts": [ + { + "add": 822, + "scale": 12 + }, + { + "add": 822, + "scale": 12 + } + ], + "basis_scalar_units": [ + 8262, + 8262 + ], + "boundary_scalar_units": 42, + "changed_word_scalar": { + "add": 16273, + "clear": 32, + "copy": 16, + "scale": 1164 + }, + "complete_scalar": { + "add": 17917, + "clear": 40, + "copy": 16, + "scale": 1204 + }, + "conditional_screen": { + "contract": "For any completed comparator at t=1-kappa: margin_new=margin_reference+sum(extra_target_count[r]*r^t)-sum(closure_paid_count[r]*r^t)-sum(lost_target_count[r]*r^t)+main_idle_other_delta. Unknown terms never default to zero.", + "new_kappa": null, + "ordinary_warning": "Field operation/monomial counts are ordinary work, never recursive moment terms.", + "relaxation": "Reference p16 invoice plus n times eight autonomous H8, all other paid/productive jobs unchanged. 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"-18643709898459677385098849972810657856153076087/1250000000000000000000000000000000000000000000000000000" + ] + } + ], + "status": "PASS_CONDITIONAL_CLOSURE_NECESSARY_SCREEN_NO_CALLER_NO_KAPPA", + "stop_test": "If all other changes vanish and per-provider closure costs eight H8 plus any positive paid job, its incremental margin is strictly negative for every 0=1 shell, while taking value one at z=1. For a unitary, trace D forces the exact identity, so it selects equality of full phase-bearing operators. +3. **Grouping exact matrices is essential.** Expand each endpoint entry as `sum c_g g^tensor f` with coefficients independent of f, and first add the coefficients of equal exact matrices. Expanding Hilbert-Schmidt norms gives `E_f=sum conjugate(c_g)c_h z_gh^f`. The filter identity then yields `sum b_f E_f=sum |c_g|^2`. This is valid for arbitrary complex coefficients in the theorem, even though the executable uses Q(i). If all tested energies are zero, every grouped coefficient vanishes. No rational-nullspace argument or floating-point rank test is being silently substituted. Merely projectively equal matrices must remain distinct because their phases are raised to f. +4. **The finite maximum 8n+4 follows for every n.** The filter has zero constant coefficient and degree 8n+4. Thus zero at all widths 1 through 8n+4 implies zero grouped coefficients and hence zero at every positive width. This holds separately for every input/output role and needs independent arbitrary inputs. It does not justify testing only a clean subspace. +5. **The eight selected widths follow for every n>=2, not just tested n.** The length-eight code has 16 words, is self-dual, and every weight is divisible by four. The vector obtained by selecting a codeword independently on every axis is fixed by S, CNOT, native H, and iI. For native H, `((1+i)/2)^8=1/16`, and the code Fourier sum contributes exactly 16; the absolute phase is essential. These generators produce the whole dyadic normalizer: reduce the image of Z1 to Z1; while preserving it, remove the other-axis X/Z components of the image of X1 with CNOT/CZ, then remove its Z1 component and sign. Commutation with both X1 and Z1 leaves `I tensor V`. Iterate, leaving only a dyadic scalar unit. Native H has the ordinary H Pauli action, with its scalar absorbed in that final allowed unit. Consequently every g fixes the eighth-copy code vector. The nonzero injection `v -> v tensor tau` intertwines the f and f+8 residuals. Zero at f+8 therefore implies zero at f. Every width 1..8n+4 ascends into `[8n-3,8n+4]` in steps of eight. Combining with item 4 proves the claim. This descent does not preserve the same stability constant on the eight selected widths. +6. **The stability improvement has an all-n argument.** The four coefficient residue classes of `q_n` are disjoint, so its coefficient L1 norm equals that of P_(2n). The elementary-symmetric-product formula has positive real product factors even for r=-1/4, giving descending signs ++--. When the roots -a,b are added, the sign pattern gives the displayed recurrence for L_new-L. The first odd-index coefficient gives `U_odd/L >= (3/16)/(3/2)=1/8`; meanwhile `ab/(a-b)<=1/192`. Hence the L1 norms strictly decrease for n>=1. At n=1 the norm is 77/75, and at n=0 it is one. Because q_n(1)=1, positive coefficient mass is at most 76/75. Removing negative multiples of nonnegative E_f gives `max E_f >= (75/76) sum |c_g|^2`, for the full range 1..8n+4. Finite polynomial checks in the oracle corroborate this derivation; they do not replace induction. +7. **The n=0 and n=1 exceptions are correctly separated.** C0 consists of the four scalar units; the four positive residues 1,2,3,4 give the Fourier separation. In one axis, exact closure of C and S has 96 matrices; there are at most 24 signed anticommuting Pauli-image pairs and four scalar lifts, so this is the full group. A nonsingular sum of Gram matrices for widths 5..8 implies zero joint kernel over characteristic zero. Modular nonsingularity is legitimate because the entries lie in Z[i,1/2] and odd-prime reduction maps i to a square root of -1. The Reynolds average is an orthogonal projection; traces zero at widths 1..7 imply the zero operator, while rank 15 at width 8 proves a counterexample to every test whose maximum is <=7. Scalar Fourier residuals force at least one width in each residue modulo four, establishing minimum count four. Neither argument proves sharpness for n>=2. + +## Compact implementation and trust boundary + +`compact.py:80-100` expands literal signed words, interprets gate order by reversing the stored prepend order, and merges full matrices only when their normalized exact Hilbert-Schmidt inner product is one. For unitaries, `||g-h||_HS^2=2D-2Re tr(g*h)` makes that equality criterion exact. The gate grammar contains unitary gates with dyadic entries, so the required hypothesis is maintained by construction. + +`compact.certify` sets its positive all-width result from the absence of grouped residual coefficients. A positive result is therefore trusted execution of the word expander, quadratic-sum trace implementation, exact arithmetic, and merge loop. It does **not** emit a separate small independently replayable proof of positive equality. This is a substantiation boundary, not an unsound implication in the stated algorithm. + +The existing `check_witness.py` is explicitly a **negative-only** literal witness checker (`:123-136`). It recomputes a single nonzero discrepancy, which suffices to disprove all-width equality without trusting the filter or Gram energies. It does not validate a positive equality receipt or every displayed energy. Moreover, the compact producer imports `word_endpoint` and `add_term` from that checker, so the word expansion is shared in this compact path. The original dense producer and the literal checker have separate compilers; that stronger separation should not be read as applying to every compact component. + +There is also an interface distinction: compact emits schema `clifford-tensor-gram/native-v1` with gate circuits; `check_witness.check` accepts `clifford-tensor-gram/v1` with explicit base matrices. A compact JSON receipt is not directly accepted by the existing checker. The author's advance verifier converts through its dense test problem and invokes the discrepancy evaluator. The independent audit does the conversion from separately constructed exact matrices and explicitly rebinds schema/digest. This conversion is part of the audit, not a hidden claim that the CLI already accepts native receipts. + +No flaw follows from a checker ignoring a forged energy field while confirming a real nonzero literal entry: that field is outside this negative checker's acceptance statement. A malformed witness value/digest/width, or a purported positive receipt, must be rejected; the bounded tests exercise those distinctions. + +## Independent oracle and bounded evidence + +`independent_audit.py` owns its arithmetic (pairs of stdlib Fractions), gate matrices, matrix multiplication/adjoint, literal gate composition, tensor products, direct role-block interpreter, exact matrix-key endpoint expansion, one-axis group closure, modular rank elimination, and filter construction. It imports submitted quadratic/compact/checker code only as the device under test. It does not import the submitted arithmetic, compiler, kernel, traces, or path engine as ground truth. No source module is edited. + +The discriminating cases include: phase inside a tensor versus an outer scalar; C inverse and q=0; query sign; a self query requiring snapshot semantics; noncommuting gate order; loss of an arbitrary dirty role; role swap and rational scaling; and exact coefficient grouping. Direct small tensor matrices bind the oracle's expansion on widths <=3 (n=2 restricted to width<=2). Witnesses at larger selected widths are evaluated by products of independently constructed base entries, without allocating tensor matrices. The independent 96-matrix one-axis closure is also used for a fresh modular Gram rank and Reynolds ranks; it does not read the submitted inverse as an oracle. + +`RESULT.json` records successful execution only after the root resource guard runs the frozen checker. This scope is finite implementation evidence, not exhaustive correctness of arbitrary circuits or arbitrary n. The all-n conclusion comes from the written proof above. + +## Complexity and admissibility boundaries + +The compact quadratic representation and bitwise conditional norm splitting avoid arrays indexed by all 2^n base states or 2^(nf) tensor states. This is compatible with polynomial arithmetic cost in expanded support and literal path size. The support can grow exponentially in register-program length, and every pair of surviving terms is compared. Integer/Fraction operation counts are not bit complexity bounds; they still depend on operand sizes. The selected provider support measurements are case-specific and cannot establish a general support bound. The small dense matrices in this independent oracle intentionally do not claim the compact implementation's scaling. + +No statement here proves physical tape layout, precision/rounding, stock, analytic recovery, a new complete supplier, or a smaller complete kappa. The five framework assumptions remain. I have not independently replayed all 7,000 recipe classes, the two complete selected-provider programs, or the 30,328 fusion obstructions in this assignment. + +## Executed result + +The root-run frozen pilot completed successfully. `RESULT.json` records 24 independently interpreted programs and 64 direct tensor-width comparisons; 17 literal nonzero witness values matched the independent base-entry evaluator, and 68 altered witness receipts were rejected (wrong value, digest, positive flag, or width). Gate checks covered 25 entries, four traces, and seven conditional inner products. The fresh one-axis closure had 96 matrices, the independently reconstructed K had modular rank 96, and Reynolds ranks at widths 1..8 were `0,0,0,0,0,0,0,15`. Separately constructed filter coefficient norms for n=0..8 respected 77/75. The measured checker runtime was 1.996 seconds. These bounded passes support the written-proof review and exposed no discrepancy in the tested implementation implications. + +Final conclusion: **PASS within the declared theorem/checker scope**, with the positive-receipt and native-interface substantiation boundaries above. No complete-provider/fusion-census conclusion is inferred from this pilot. diff --git a/research/coupled-provider-independent-audit/reports/clifford-proof/SOURCE-MANIFEST.json b/research/coupled-provider-independent-audit/reports/clifford-proof/SOURCE-MANIFEST.json new file mode 100644 index 0000000000..fae64f400a --- /dev/null +++ b/research/coupled-provider-independent-audit/reports/clifford-proof/SOURCE-MANIFEST.json @@ -0,0 +1,15 @@ +{ + "head": "848cdce9003262c4b6e02ec4558f302e4fae56ad", + "sources": { + "PROOF.md": "f79c723a869a480c9959038f59db206359e4b6768e9839aff25b3921beaec84a", + "ADVANCES.md": "f3fb828fa04cf35b94e2199e51955e36dec26fb04e5be781feb9c84f3278f700", + "PROVIDER.md": "148852913905af606848601bf1a22b9149d9d422cdf2539b98e19dc6c42e13ce", + "compact.py": "ddd6c245f8e66a02071e3475a6f8c1fecc21e0ad5de00ac0d0fe5d9244ff0497", + "quadratic.py": "e10a809ab78b93340072a1b57d7158e1bf75fa8d1ddfda546b9262861883938b", + "certify.py": "a0dcd5a8551179305a993b1f9c034aa7c3898e08cd2344fd63f5ea9449dbb8bd", + "check_witness.py": "f3b811928a44301bb87b619bcedefa0a5dccb6ecc3fcaa9e69c21e7decf8ef3c", + "vendor/fields.py": "0829ad6ed3775ba6e3d11cf04cfb3513ac763549b730aaed74958b1238e660d7", + "ONE-AXIS-RANK.json": "cb6c030faf71d14685d237acbbf659a22b7e9fc8b3e848b7711c46c5ecc5ac70" + }, + "checker_sha256": "d7045d7e09291e7a38ff15431b17e6ef4b869a6e80414edc0d31c951c835c43e" +} diff --git a/research/coupled-provider-independent-audit/reports/diagnostics/REPORT-before-literal-scale-correction.md b/research/coupled-provider-independent-audit/reports/diagnostics/REPORT-before-literal-scale-correction.md new file mode 100644 index 0000000000..eaff66deed --- /dev/null +++ b/research/coupled-provider-independent-audit/reports/diagnostics/REPORT-before-literal-scale-correction.md @@ -0,0 +1,81 @@ +# Independent provider closure budget + +This lane supplies a typed necessary-condition screen and a literal ordinary inventory for #5402 at `3348fccea855082786d5f0fc5558b73d4974e745`. It supplies no completed caller and no new kappa. Its favorable comparison deliberately grants a target contract that has not been constructed: each of the eighteen provider instances closes to the same standard B main interface used by #5398, preserves its 400 autonomous helpers, and earns eight additional autonomous H8 jobs. The actual eight coupled H outputs have zero autonomous credit. + +## Exact source and complete comparison invoice + +`inputs/ALL-PINS.json` binds the literal original and changed words, PROVIDER basis programs, canonical NORMALIZERS, the independently validated #5400 invoice and the exact #5398 controller. The standalone price engine is copied without modification from our prior independent numeric lane; no submitted provider/native/price/verifier module is executed. The checker reconstructs the complete old invoice using all eighteen local bodies, fifteen 112-job H1 queries, every retained whole idle, and every main diagonal term. It requires literal equality with the independent #5400 invoice. + +The local paid profile is `{1:2193,2:412,3:510,4:127,5:40}`. Removing the eight selected mode owners from the original source's helper-frame census leaves `{4:28,7:7,8:47,9:318}`: 400 jobs. Both profiles already equal the comparison's local profiles. The advertised deletion of eight H8 plus eight H1 jobs is relative to the original raw source; those are not additional savings over #5398. + +The complete paid comparison is: + +``` +{1:41154,2:7416,3:9180,4:2286,5:720, + 16:448,24:448,32:448,40:448,48:448,56:448,64:448,72:224} +``` + +Its productive profile is: + +``` +{4:504,7:126,8:846,9:5724,17:448,25:448,33:448, + 41:448,49:448,57:448,65:448,73:224,145:224} +``` + +There are 64,116 paid calls and 10,784 productive jobs, with paid/productive rank masses 237,838/238,590 and surplus 752. The optimistic closure contract adds exactly `{8:144}` to the productive profile. It therefore has 10,928 productive jobs and surplus 1,904 before charging any closure Gaussian, lost target, changed idle or main output. This favorable profile is an upper relaxation under the named contract, not an attained caller profile. + +For aggregate closure paid histogram K, lost productive histogram L and other signed caller-profile change Delta, define `t=1-kappa` and `M(J)=sum_r J[r] r^t`. The exact required comparison is + +``` +margin_new = margin_5398 + 144*8^t - M(K) - M(L) + M(Delta). +``` + +Every unproved term remains unknown. In particular, `Delta=0` requires the actual eighteen closed interfaces, all original queries/idles and the main diagonal to be preserved. Ordinary scalar and monomial work does not enter this recursive moment identity; its separate funding remains mandatory. + +If K is exactly 144 H8 calls and L and Delta vanish, the entire signed profile equals #5398 at every rank. It has exactly the same moment for every saving. If any further paid job is added with no compensating productive change, its moment is worse. This gives no strict recursive-profile improvement. It does not exclude improvements to compiler headroom or a different productive contract, coupling graph or idle law. + +At the reference saving `.00302728823`, the exact directed intervals give reference target-minus-paid moment approximately `0.00000492044809504` and the hypothetical credit `63.59838102597` per provider, or `1144.77085846746` across eighteen. The following are strict *incremental* moment budgets with no lost targets and no other caller change; each column assumes all closure jobs have the single displayed rank. Mixed-rank closure must use the weighted inequality above. + +| Paid closure rank | Maximum per provider | Maximum across eighteen providers | +|---:|---:|---:| +|1|63|1144| +|2|31|573| +|3|21|382| +|4|15|287| +|5|12|230| +|8|7|143| +|9|7|128| +|16|4|72| +|32|2|36| +|64|1|18| +|145|0|8| + +The per-provider column assumes identical independent cleanup allowances; the aggregate column permits the caller to share cleanup across providers. `TOTAL-BUDGET-v1.json` derives the aggregate column from the exact intervals already produced by the guarded run, including exact equality at rank eight. The actual reference's tiny positive margin is separate from strict incremental gain; no table entry by itself proves full compiler funding. + +## Ordinary inventory and explicit unknown costs + +The checker parses all scalar operations of the changed literal source, both emitted basis programs, all exterior mode scalings and final consumption clears. Per provider, the complete boundary-inclusive scalar schedule has 17,917 ADD, 1,204 SCALE, 16 COPY, 40 CLEAR and eight whole-field SWAP operations. The 464 monomial maps comprise 448 inherited fused main standardizers and sixteen mode/cache maps. Their literal gate words are counted separately. Every unchanged warp, adapter and phase annotation remains in the census. The eight zero retags receive no paid Gaussian charge because their required exact-zero premise belongs to the independent source replay gate. + +Across eighteen providers, the known subtotal is 322,506 ADD, 21,672 SCALE, 288 COPY, 720 CLEAR, 144 whole-field SWAP and 8,352 monomial maps, before consumer closure and the separate outer caller records. The exact controller has 90 ADD, 20 SIGNED_SWAP and four Q_POWER records on 112-field banks, plus the complete left/right scalar boundary programs; its LOCAL, QUERY_SHEAR and IDLE records are already included in the recursive invoice. These are literal finite field-operation counts, not physical tape-step counts. + +The inherited dyadic scalar tariff is the prior independent tariff: COPY/CLEAR two units, dyadic unit SCALE twice its shift/sign count, ADD twice `3+floor(log2 numerator)+popcount(numerator)+log2 denominator`, SWAP reserved at 26. The original raw source scalar total is **158,168**, not 158,744: the latter belongs to the distinct prior retained-owned source body. The first frozen checker used that wrong precondition and failed before numerical work. Its source is retained as `screen.failed-v1.py`; the root's failure log is preserved. This was a checker binding failure, not a #5402 construction failure. + +Unknown costs remain explicit: physical machine/tape realization of monomial maps and retained native primitives; the closure's Gaussian and ordinary operations; productive targets lost through closure; caller-specific finite precision, growth constants, routing, storage and movement; the complete compiler and outer ledger. The local source amplification bound does not discharge these full caller obligations. + +## Scope relative to #5405 and the latest caller handoff + +Live [#5405](https://github.com/CrocSwap/integer-mult-bounds/pull/5405), head `314b56a6c0056c2358538f072c6fde9d365be44d`, fixes the existing paid/helper profiles, 112 ports, rank-eight stage blocks, rank-one query price and prefix/suffix idle law. Its unbounded FULL/QUERY ceiling excludes `.00302728825 <= kappa < 1` inside that exact invoice family. Its body explicitly excludes #5402's unfinished coupled caller. This lane does not rerun or extend that theorem. Any attempt to gain only by changing old FULL/QUERY pair counts or masks should consume that public ceiling; an earned new target contract changes its premises. + +Root's live intake of [Dillon's latest #4930 handoff](https://github.com/CrocSwap/integer-mult-bounds/discussions/4930#discussioncomment-19155935) reports that the caller claim has been released. The stated local-only snapshot and its execution counts are not independently validated here. The proposed next bounded control is an uncoded eight-owner identity written `A S A = Q S`, with helper-tail updates from retained original inputs. No portable exact A/S definitions, ordered physical words, charts and helper-tail implementation are supplied by the inputs reviewed in this lane. Substituting a guessed scalar code or commuting D/Q through W/Z would invent a different control. The alternative p2 pivot similarly requires its ordered eight-field right-hand side. Therefore this lane reports a missing typed next-test input, not a failed control and not an implemented coded closure. + +## Execution and reproducibility + +Final checker is `screen.py`; frozen SHA256 `1046234495045ffc83226d698af0f26bbe061dba9c3059c7a1124b7ce8e86e46`. Input manifest SHA256 `a37fa9735bbb2697811de72a706b243842d1303243f6e6a0300bd5046d4f3d66`. Root alone runs the exact moment screen with a ten-second external guard and 128 MiB address-space bound: + +``` +python3 -B agents/budget/screen.py --moments --output agents/budget/RESULT-v1.json +``` + +Root's guarded second execution passed: `RESULT-v1.json` records 0.706799 seconds of internal execution and 56,316 KiB maximum RSS. The exact receipt derives scalar tariff 175,038 units per provider (16,870 above the original raw source), including both 8,262-unit basis programs, 58 units of exterior mode scalings, final consumption clears and 26-unit SWAP allowances. The 464 monomial maps contain 464 each of D/P/X/phase gates (1,856 monomial primitive gates). These remain a separate physical cost term. The complete left/right caller boundary programs have respectively 56/25 ADD, 4/3 SCALE and 30/27 SWAP records. The checker authenticates all frozen inputs before deriving the inventory and conditional moments. Acceptance does not admit any actual #5402 consumer. Native identities, ownership/phase checks, full caller precision and complete funding remain distinct gates. + +Construction credit remains with Ali Romman and the native/provider/controller/Clifford/compiler predecessors named in the pinned source; the independent price engine and #5400 receipt retain their prior attribution. This budget audit is Chris R/Clear1nsight with substantial OpenAI Codex assistance. No independent human or formal-kernel acceptance is claimed. diff --git a/research/coupled-provider-independent-audit/reports/diagnostics/RESULT-conservative-v1.json b/research/coupled-provider-independent-audit/reports/diagnostics/RESULT-conservative-v1.json new file mode 100644 index 0000000000..79eae1fd09 --- /dev/null +++ b/research/coupled-provider-independent-audit/reports/diagnostics/RESULT-conservative-v1.json @@ -0,0 +1,557 @@ +{ + "added_scalar": { + "add": 1644, + "clear": 24, + "copy": 16, + "scale": 40 + }, + "autonomous_count": 400, + "autonomous_helpers": { + "4": 28, + "7": 7, + "8": 47, + "9": 318 + }, + "autonomous_rank_mass": 3399, + "basis_counts": [ + { + "add": 822, + "scale": 12 + }, + { + "add": 822, + "scale": 12 + } + ], + "basis_scalar_units": [ + 8262, + 8262 + ], + "boundary_scalar_units": 58, + "changed_word_scalar": { + "add": 16273, + "clear": 32, + "copy": 16, + "scale": 1164 + }, + "complete_scalar": { + "add": 17917, + "clear": 40, + "copy": 16, + "scale": 1204 + }, + "conditional_screen": { + "contract": "For any completed comparator at t=1-kappa: margin_new=margin_reference+sum(extra_target_count[r]*r^t)-sum(closure_paid_count[r]*r^t)-sum(lost_target_count[r]*r^t)+main_idle_other_delta. Unknown terms never default to zero.", + "new_kappa": null, + "ordinary_warning": "Field operation/monomial counts are ordinary work, never recursive moment terms.", + "relaxation": "Reference p16 invoice plus n times eight autonomous H8, all other paid/productive jobs unchanged. Coupled5402 H fields do NOT supply this credit; physical reachability is unproved.", + "rows": [ + { + "hypothetical_credit_per_provider": [ + "39748988141231362883988648454174576952193700984584469411/625000000000000000000000000000000000000000000000000000", + "19874494070615681441994324227087288476096850492292235161/312500000000000000000000000000000000000000000000000000" + ], + "hypothetical_p16_credit": [ + "357740893271082265955897836087571192569743308861260224699/312500000000000000000000000000000000000000000000000000", + "178870446635541132977948918043785596284871654430630116449/156250000000000000000000000000000000000000000000000000" + ], + "identical_paid_jobs": { + "1": { + "max_identical_paid_jobs_for_strict_incremental_gain": 63, + "ratio_interval": [ + "39748988141231362883988648454174576952193700984584469411/625000000000000000000000000000000000000000000000000000", + "19874494070615681441994324227087288476096850492292235161/312500000000000000000000000000000000000000000000000000" + ] + }, + "145": { + "max_identical_paid_jobs_for_strict_incremental_gain": 0, + "ratio_interval": [ + "158995952564925451535954593816698307808774803938337877644/357079507408942003365184750854259754927379596777781842805", + "19874494070615681441994324227087288476096850492292235161/44634938426117750420648093856782469365922449597222728289" + ] + }, + "16": { + "max_identical_paid_jobs_for_strict_incremental_gain": 4, + "ratio_interval": [ + "37410812368217753302577551486281954778535247985491265328/9333098364631538005119628123997789588712161960987413767", + "105997301709950301023969729211132205205849869292225254192/26443778699789357681172279684660403834684458889464338369" + ] + }, + "2": { + "max_identical_paid_jobs_for_strict_incremental_gain": 31, + "ratio_interval": [ + 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"317991905123238447297528685819699991205151785638908851236/44701669845604494974692207412521341742024808454340698447" + ] + } + }, + "kappa": "37841103/12500000000", + "reference_full_calls": 18, + "reference_target_minus_paid": [ + "12263832817543735274523503727444271472723812779617/5000000000000000000000000000000000000000000000000000000", + "2452766563508747054904700745488854294544775959081/1000000000000000000000000000000000000000000000000000000" + ] + }, + { + "hypothetical_credit_per_provider": [ + "39748988139578248940410710769787451549316055132618118917/625000000000000000000000000000000000000000000000000000", + "79497976279156497880821421539574903098632110265236239719/1250000000000000000000000000000000000000000000000000000" + ], + "hypothetical_p16_credit": [ + "357740893256204240463696396928087063943844496193563070253/312500000000000000000000000000000000000000000000000000", + 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"-18643709898459677385098849972810657856153076087/1250000000000000000000000000000000000000000000000000000" + ] + } + ], + "status": "PASS_CONDITIONAL_CLOSURE_NECESSARY_SCREEN_NO_CALLER_NO_KAPPA", + "stop_test": "If all other changes vanish and per-provider closure costs eight H8 plus any positive paid job, its incremental margin is strictly negative for every 00 and d&(d-1)==0,'nonzero dyadic tariff') + if g[0]=='scale': + need(n&(n-1)==0,'scale is dyadic unit') + return 2*(abs(n.bit_length()-d.bit_length())+int(q<0)) + need(g[0]=='add','scalar tariff alphabet') + return 2*(3+n.bit_length()-1+n.bit_count()+d.bit_length()-1) +def basis_gate(g): + q=Q(g[-1]);return [g[0],g[1],g[2],q.numerator,q.denominator]if g[0]=='add'else[g[0],g[1],q.numerator,q.denominator] +def static(): + pins=read('ALL-PINS.json') + for p in pins: + need(sha256((HERE/p['local']).read_bytes()).hexdigest()==p['sha256'],'changed input: '+p['local']) + a,w,s,n=read('PROVIDER.json'),read('WORD.json.gz')['word'],read('SOURCE-WORD.json.gz'),read('NORMALIZERS.json') + original=s['programs']['backward'];c=s['canonical']; paid=Counter(e[-1]for e in w if e[0]in('climb','center')) + raw_orig=Counter(e[-1]for e in original if e[0]in('climb','center')) + mode=set(a['mode_owners']);need(len(mode)==8,'eight distinct mode owners') + helpers=Counter(len(c['frames'][c['final'][r]])-len(c['frames'][c['start'][r]])for r in range(224,632)if r not in mode) + need(paid==Counter({1:2193,2:412,3:510,4:127,5:40}),'literal paid census') + need(helpers==Counter({4:28,7:7,8:47,9:318}),'autonomous remainder frame census') + scalars=[e[1]for e in w if e[0]=='scalar']; old=[e[1]for e in original if e[0]=='scalar'] + bp=[a['input_basis_program'],a['output_basis_program']] + basis=[basis_gate(g)for p in bp for g in p] + # Boundary exterior scalar factors: input 2; output 1/(2*f_i), where f_i=cache_scalar. + boundary=[] + for m in a['mode_boundaries']: + for q in [Q(2),1/(2*Q(m['cache_scalar']))]:boundary.append(['scale',m['owner'],q.numerator,q.denominator]) + full=scalars+basis+boundary+[['clear',['C',i]]for i in range(1,9)] + counts=Counter(g[0]for g in full);need(counts==Counter(add=17917,scale=1204,copy=16,clear=40),'complete field operation census') + oldcounts=Counter(g[0]for g in old);delta=counts-oldcounts + # Read all monomial words literally; native physical validation belongs to another lane. + wrappers=[p['compiled_wrappers'][k]['word']for p in n['ports']for k in ['backward_input_X','backward_input_Y','backward_output_X','backward_output_Y']] + words=wrappers+[m[k]['literal_word']for m in a['mode_boundaries']for k in ['input_K','output_N']] + need(len(words)==464,'complete boundary monomial count') + gates=Counter(g[0]for w0 in words for g in w0);need(set(gates)<=set(['D','P','X','phase']),'monomial word alphabet') + kinds=Counter(e[0]for e in w);need(kinds['zero_retag']==8,'retag census') + units=sum(tariff(g)for g in full)+8*26 + need(sum(tariff(g)for g in old)==158168,'original raw source scalar tariff binding') + return dict(status='PASS_STATIC_LITERAL_BUDGET_INVENTORY',head=HEAD,paid=paid,autonomous_helpers=helpers,paid_calls=sum(paid.values()),paid_rank_mass=sum(r*v for r,v in paid.items()),autonomous_count=sum(helpers.values()),autonomous_rank_mass=sum(r*v for r,v in helpers.items()),coupled=dict(owners=8,diagonal_rank=8,autonomous_credit=0),original_paid=raw_orig,removed_paid=raw_orig-paid,original_scalar=oldcounts,changed_word_scalar=Counter(g[0]for g in scalars),basis_counts=[Counter(g[0]for g in p)for p in bp],basis_scalar_units=[sum(tariff(basis_gate(g))for g in p)for p in bp],boundary_scalar_units=sum(tariff(g)for g in boundary),complete_scalar=counts,added_scalar=delta,whole_field_swaps=8,monomial_maps=len(words),monomial_primitive_gates=gates,scalar_tariff_units_including_swaps=units,scalar_tariff_units_added=units-158168,retained_native_word_records=kinds,owned_fields=9,owned_credit=0,unknown_costs=['ordinary monomial maps at machine/tape level','retained native warps/adapters/phase annotations and recursive primitive internals','consumer closure recursive invoice and changed/lost targets','caller query/idles/boundaries/main diagonal','full caller finite precision/movement/storage/compiler/outer funding'],scope='Static literal census and inherited scalar tariff only; source equation, endpoint and physical admission are separate gates') +def full_profile(paid,helpers): + ref=read('REFERENCE-5400-INVOICE.json');ctl=read('REFERENCE-5398-CONTROLLER.json');P,T=Counter(),Counter();events=Counter();idles=Counter() + for e in ctl['physical_events']: + events[e[0]]+=1 + if e[0]=='LOCAL':need(e[3] is True,'all comparison providers backward');P.update(paid);T.update(helpers) + elif e[0]=='QUERY_SHEAR':P[1]+=112 + elif e[0]=='IDLE':need(len(set(e[2]))==len(e[2]),'distinct idle stage incidence');r=8*len(e[2]);P[r]+=224;idles[r]+=224 + else:need(e[0]in('ADD','SIGNED_SWAP','Q_POWER'),'comparison caller ordinary alphabet') + main=Counter() + for term in ctl['diagonal']: + need(abs(term[0])==1 and all(x in(0,1)for x in term[1:]),'comparison main diagonal');main[1+8*sum(term[1:])]+=112 + T.update(main) + need((P,T)==tuple(Counter({int(k):v for k,v in ref['histograms'][name].items()})for name in ['paid','productive']),'reconstructed complete comparison invoice differs') + need(events['LOCAL']==18 and sum(P.values())==64116 and sum(T.values())==10784,'full comparison census') + optimistic=T.copy();optimistic[8]+=8*18 + equal_paid=P.copy();equal_paid[8]+=8*18 + bct={side:Counter(g[0]for g in ctl['boundaries'][side+'_program'])for side in ['left','right']} + return dict(reference_head='174fb211493b43a42210434083e9702b4fb7a2ce',reference_paid=P,reference_targets=T,main_targets=main,whole_idles=idles,caller_events=events,boundary_program_events=bct,hypothetical_paid=P,hypothetical_targets=optimistic,hypothetical_paid_count=sum(P.values()),hypothetical_target_count=sum(optimistic.values()),hypothetical_rank_mass_surplus=sum(r*v for r,v in optimistic.items())-sum(r*v for r,v in P.items()),hypothetical_added_target_profile={8:144},eight_paid_H8_per_provider=dict(paid=equal_paid,targets=optimistic,signed_profile_equals_reference={r:optimistic[r]-equal_paid[r]for r in optimistic.keys()|equal_paid.keys()}=={r:T[r]-P[r]for r in T.keys()|P.keys()}),unproved_contract='All 18 providers must close to standard B main outputs, preserve400 ordinary helpers each, and supply8 new autonomous H8 each; no source proves this contract. Closure paid jobs/lost targets and ordinary overhead are unknown, not zero.',ordinary_provider_subtotal_for_18={k:18*v for k,v in dict(ADD=17917,SCALE=1204,COPY=16,CLEAR=40,SWAP=8,monomial_field_map=464).items()},ordinary_caller_scope='The literal caller and left/right boundary record counts are retained; ADD, SIGNED_SWAP and Q_POWER each act on112 fields. QUERY_SHEAR recursive costs are included in P. Consumer closure operations and their finite movement/storage/precision costs remain unknown.') +def screen(): + from independent_price_engine import power,moment,difference + ref=read('REFERENCE-5400-INVOICE.json')['histograms'];P={int(r):v for r,v in ref['paid'].items()};T={int(r):v for r,v in ref['productive'].items()} + rows=[] + for k in [Q('.00302728823'),Q('.00302728824'),Q('.00302728825')]: + t=1-k;base=difference(moment(T,t),moment(P,t));u=power(8,t);credit=(8*u[0],8*u[1]);ratios={} + for r in [1,2,3,4,5,8,9,16,32,64,145]: + v=power(r,t);lo,hi=(Q(8),Q(8)) if r==8 else (credit[0]/v[1],credit[1]/v[0]) + # Strict incremental budget requires m < ratio; equality is not gain. + maximum=(lo.numerator-1)//lo.denominator + need(maximum < lo and maximum+1>=hi,'integer budget separated') + ratios[r]=dict(ratio_interval=(lo,hi),max_identical_paid_jobs_for_strict_incremental_gain=maximum) + rows.append(dict(kappa=k,reference_target_minus_paid=base,hypothetical_credit_per_provider=credit,identical_paid_jobs=ratios,reference_full_calls=18,hypothetical_p16_credit=(18*credit[0],18*credit[1]))) + return dict(status='PASS_CONDITIONAL_CLOSURE_NECESSARY_SCREEN_NO_CALLER_NO_KAPPA',new_kappa=None,rows=rows,contract='For any completed comparator at t=1-kappa: margin_new=margin_reference+sum(extra_target_count[r]*r^t)-sum(closure_paid_count[r]*r^t)-sum(lost_target_count[r]*r^t)+main_idle_other_delta. Unknown terms never default to zero.',relaxation='Reference p16 invoice plus n times eight autonomous H8, all other paid/productive jobs unchanged. Coupled5402 H fields do NOT supply this credit; physical reachability is unproved.',stop_test='If all other changes vanish and per-provider closure costs eight H8 plus any positive paid job, its incremental margin is strictly negative for every 0 + if __name__=='__main__':main() + ^^^^^^ + File "/home/d3lerium/.codex/.chatgpt-projects/g-p-6ad5817fd84881918865926b6fd51453/swarm-provider-audit-sol-high-20261024/agents/budget/screen.py", line 99, in main + resource.setrlimit(resource.RLIMIT_AS,(128*1024*1024,128*1024*1024));start=time.monotonic();result=static() + ^^^^^^^^ + File "/home/d3lerium/.codex/.chatgpt-projects/g-p-6ad5817fd84881918865926b6fd51453/swarm-provider-audit-sol-high-20261024/agents/budget/screen.py", line 63, in static + need(sum(tariff(g)for g in old)==158744,'prior source scalar tariff binding') + File "/home/d3lerium/.codex/.chatgpt-projects/g-p-6ad5817fd84881918865926b6fd51453/swarm-provider-audit-sol-high-20261024/agents/budget/screen.py", line 16, in need + if not v: raise ValueError(s) + ^^^^^^^^^^^^^^^^^^^ +ValueError: prior source scalar tariff binding diff --git a/research/coupled-provider-independent-audit/reports/root-runs/provider5402-local-envelope/RECEIPT.json b/research/coupled-provider-independent-audit/reports/root-runs/provider5402-local-envelope/RECEIPT.json new file mode 100644 index 0000000000..8ec6e26291 --- /dev/null +++ b/research/coupled-provider-independent-audit/reports/root-runs/provider5402-local-envelope/RECEIPT.json @@ -0,0 +1,21 @@ +{ + "schema": "serial-research-run/v1", + "command": [ + "/usr/bin/python3", + "-B", + "agents/budget/independent_local_envelope.py", + "--output", + "agents/budget/LOCAL-ENVELOPE-v1.json" + ], + "cwd": "/home/d3lerium/.codex/.chatgpt-projects/g-p-6ad5817fd84881918865926b6fd51453/swarm-provider-audit-sol-high-20261024", + "exit_code": 0, + "termination": null, + "elapsed_seconds": 0.5044546050485224, + "sampled_peak_descendant_rss_bytes": 59138048, + "rss_samples": 5, + "memory_limit_mib": 128, + "timeout_seconds": 10.0, + "python": "3.12.3 (main, Aug 31 2026, 10:18:26) [GCC 13.3.0]", + "log_sha256": "1a27db01ba466c1ea58cf2bc1e8c6909b10ab6cb5144354f5fc4747fc3ef0350", + "scope": "Fresh command execution only; scientific claim determined by reviewed output." +} diff --git a/research/coupled-provider-independent-audit/reports/root-runs/provider5402-local-envelope/stdout.log b/research/coupled-provider-independent-audit/reports/root-runs/provider5402-local-envelope/stdout.log new file mode 100644 index 0000000000..e869112877 --- /dev/null +++ b/research/coupled-provider-independent-audit/reports/root-runs/provider5402-local-envelope/stdout.log @@ -0,0 +1 @@ +{"status": "PASS_INDEPENDENT_ONE_PROVIDER_TWO_NORM_ENVELOPE", "max_field_exponent": 18996, "joint_field_exponent": 19012, "runtime": {"seconds": 0.4130356339737773, "maxrss_kib": 57752}} diff --git a/research/coupled-provider-independent-audit/reports/root-runs/provider5402-same-chart-cache-control/RECEIPT.json b/research/coupled-provider-independent-audit/reports/root-runs/provider5402-same-chart-cache-control/RECEIPT.json new file mode 100644 index 0000000000..8941bc3b34 --- /dev/null +++ b/research/coupled-provider-independent-audit/reports/root-runs/provider5402-same-chart-cache-control/RECEIPT.json @@ -0,0 +1,21 @@ +{ + "schema": "serial-research-run/v1", + "command": [ + "/usr/bin/python3", + "-B", + "check_same_chart_cache_mutant.py", + "--out", + "SAME-CHART-CACHE-MUTANT.json" + ], + "cwd": "/home/d3lerium/.codex/.chatgpt-projects/g-p-6ad5817fd84881918865926b6fd51453/swarm-provider-audit-sol-high-20261024/agents/algebra", + "exit_code": 0, + "termination": null, + "elapsed_seconds": 0.7051301799947396, + "sampled_peak_descendant_rss_bytes": 48652288, + "rss_samples": 7, + "memory_limit_mib": 256, + "timeout_seconds": 30.0, + "python": "3.12.3 (main, Aug 31 2026, 10:18:26) [GCC 13.3.0]", + "log_sha256": "afc4e5719c0e7cf1b2c8c1770d6d5f5f3c8b9411df6b7644419cc138b9be9261", + "scope": "Fresh command execution only; scientific claim determined by reviewed output." +} diff --git a/research/coupled-provider-independent-audit/reports/root-runs/provider5402-same-chart-cache-control/stdout.log b/research/coupled-provider-independent-audit/reports/root-runs/provider5402-same-chart-cache-control/stdout.log new file mode 100644 index 0000000000..09b29082bf --- /dev/null +++ b/research/coupled-provider-independent-audit/reports/root-runs/provider5402-same-chart-cache-control/stdout.log @@ -0,0 +1 @@ +{"status": "PASS_SAME_CHART_CACHE_CONTENT_MUTANT_REJECTED", "mutation_source_event": 11207, "inserted_event": ["scalar", ["scale", ["C", 1], -1, 1], 254], "preserved": "same chart, all owned CLEAR/COPY rules, no borrowed erasure; one legal SCALE -1 on retained C1 only", "rejection": "zero retag requires complete exact zero row", "runtime_seconds": 0.575157, "source_raw_sha256": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05", "candidate_raw_sha256": "7dc356001ed597ad6fc9fd3e0bc6ff7e3ec3a580a579a956827aa17fccfdd2dc", "frozen_engine_sha256": {"check_provider.py": "3774c5742b565ea9007af90d10e43d38a3e675c2074583c8c365799fc256baaf", "phase_exact.py": "15e90b63c5659090f02902cb38951ec4ab252352fb0b967b411ed547c501e2ba", "provider_rows.py": "c7e579939d89709d72457d5fa213173b3b492c3cc3de7546afc3ed6a6fb32f0c", "prior_dyadic_engine.py": "3ee4ae79a55188d5abf2306f678179f4aafb799602ffb970fc1bc8f76cb061d9"}, "checker_sha256": "4bf90d4656e03e6716448026ba120c172585c9aced067d35d6ca1a75250d9aad"} diff --git a/research/coupled-provider-independent-audit/source_guard.py b/research/coupled-provider-independent-audit/source_guard.py new file mode 100644 index 0000000000..c072708fe9 --- /dev/null +++ b/research/coupled-provider-independent-audit/source_guard.py @@ -0,0 +1,143 @@ +"""Actual bytes, source origin and scoped claims; no scientific evaluator imports.""" +import gzip,hashlib,json +from pathlib import Path,PurePosixPath +MAIN='1ec1119972c9aefe42525172d07b332fcff81cb4' +HEAD='3348fccea855082786d5f0fc5558b73d4974e745' +CLIFFORD='848cdce9003262c4b6e02ec4558f302e4fae56ad' +CLAIMS_EXPECTED={'admitted_kappa': None, 'canonical_main': '1ec1119972c9aefe42525172d07b332fcff81cb4', 'clifford': {'finite_oracle': 'bounded implementation evidence only', 'full_provider_replay': False, 'fusion_census_replayed': False, 'head': '848cdce9003262c4b6e02ec4558f302e4fae56ad', 'positive_compact_equality_independent_certificate': False, 'pr': 5376, 'written_all_n_criterion': 'sound under fixed-coefficient exact dyadic-Clifford hypotheses'}, 'closure_budget': {'actual_extra_autonomous_H8_admitted': 0, 'closure_constructed': False, 'hypothetical_unearned_extra_H8': 144, 'paid_144_H8_cancels_hypothetical_credit': True, 'providers': 18, 'status': 'conditional necessary comparison only', 'unpriced_terms': ['closure paid calls', 'lost targets', 'changed main/idle profile', 'physical ordinary work', 'full caller precision and compiler/outer funding']}, 'completed_caller': False, 'new_unconditional_or_formal_kernel_theorem': False, 'provider': {'admission': 'independent partial coupled component', 'arbitrary_owned_inputs': 9, 'autonomous_credit_from_coupled_helpers': 0, 'autonomous_helpers': 400, 'coupled_helpers': 8, 'head': '3348fccea855082786d5f0fc5558b73d4974e745', 'original_inputs': 632, 'owned_outputs_zero': 9, 'paid': {'1': 2193, '2': 412, '3': 510, '4': 127, '5': 40}, 'phase_bindings': 1240, 'pr': 5402}, 'review_status': 'READY_FOR_COLD_REPLAY', 'schema_version': 1, 'selected_record_changed': False, 'local_envelope': {'head': '3348fccea855082786d5f0fc5558b73d4974e745', 'max_field_l2_exponent': 18996, 'joint_field_l2_exponent': 19012, 'copy_count': 16, 'scope': 'one-provider abstract scalar/unitary transcript; arbitrary contiguous intervals and suffixes; local residuals measured in the same stated field norm', 'full_caller_precision_admitted': False}} +def require(ok,message): + if not ok:raise ValueError(message) + +def regular(root,relative): + parts=PurePosixPath(relative).parts + require(parts and not relative.startswith('/') and all(p not in ('','.','..') for p in parts) and str(PurePosixPath(relative))==relative,'Noncanonical input path: '+relative) + here=root + for part in parts: + here=here/part + require(not here.is_symlink(),'Symlink input component: '+str(here)) + require(here.is_file(),'Missing regular input: '+relative) + require(here.stat().st_nlink==1,'Hardlinked input alias: '+relative) + return here + +def oid(kind,raw): + return hashlib.sha1(kind.encode()+b' '+str(len(raw)).encode()+b'\0'+raw).hexdigest() + +def tree_entries(raw): + entries={};i=0 + while i