diff --git a/research/direct-backward-independent-validation/.gitattributes b/research/direct-backward-independent-validation/.gitattributes new file mode 100644 index 0000000000..fa1385d99a --- /dev/null +++ b/research/direct-backward-independent-validation/.gitattributes @@ -0,0 +1 @@ +* -text diff --git a/research/direct-backward-independent-validation/CLAIMS.json b/research/direct-backward-independent-validation/CLAIMS.json new file mode 100644 index 0000000000..de667ed60f --- /dev/null +++ b/research/direct-backward-independent-validation/CLAIMS.json @@ -0,0 +1,61 @@ +{ + "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." + } + ], + "candidates": [ + { + "author": "Ali Romman", + "decimal": ".00302728823", + "head": "174fb211493b43a42210434083e9702b4fb7a2ce", + "kappa": "302728823/100000000000", + "package": "research/kappa-backward-controller-20261023", + "pr": 5398 + } + ], + "canonical_main": "1ec1119972c9aefe42525172d07b332fcff81cb4", + "construction_claim": "No new native construction is claimed by this independent review.", + "fresh_commands": [ + "caller", + "numeric", + "precision" + ], + "gains": { + "PR5387": "122693/200000000000", + "PR5392": "3823/100000000000", + "selected": "551243/100000000000" + }, + "new_unconditional_or_Lean_theorem": false, + "reused_review": { + "head": "787efce72a908f92b8a8b4ebb677a6fdb7729e33", + "pr": 5396 + }, + "review_kind": "Independent direct-backward caller, complete invoice, directed arithmetic and fresh precision; authenticated reuse of unchanged PR5383 supplier reviewed by PR5396", + "review_status": "READY_FOR_COLD_REPLAY", + "same_selected_assumptions_required": true, + "schema_version": 1, + "selected_baseline": ".0030217758", + "selected_kappa": "15108879/5000000000", + "selected_metadata_role": "Frozen historical provenance; future selected-result updates do not invalidate this review.", + "selected_record_changed": false, + "selection_authorized": false, + "uniform_word_materialized": false +} diff --git a/research/direct-backward-independent-validation/COMMANDS.json b/research/direct-backward-independent-validation/COMMANDS.json new file mode 100644 index 0000000000..86df83325a --- /dev/null +++ b/research/direct-backward-independent-validation/COMMANDS.json @@ -0,0 +1,59 @@ +{ + "commands": [ + { + "argv": [ + "agents/caller/check.py", + "--repository", + "repository" + ], + "name": "literal-caller-physical-phase-helper-normalization", + "timeout_seconds": 120 + }, + { + "argv": [ + "agents/numeric/review5398.py", + "--repo", + "repository", + "--prior", + "reuse/5383", + "--output-dir", + "agents/numeric", + "--source-manifest", + "agents/numeric/SOURCE-BINDINGS-v2.json" + ], + "name": "complete-invoice-and-directed-funding", + "timeout_seconds": 120 + }, + { + "argv": [ + "agents/precision/check_precision.py", + "--root", + "repository", + "--prior-word", + "reuse/5383/WORD.json.gz", + "--prior-native", + "reuse/5383/native.py", + "--prior-witness", + "reuse/5383/WITNESS.json", + "--finite-precompilation", + "reuse/framework/FINITE-PRECOMPILATION.md", + "--finite-template-closure", + "reuse/framework/FINITE-TEMPLATE-CLOSURE.md", + "--specialization", + "reuse/framework/SPECIALIZATION.md", + "--framework-proof", + "reuse/framework/PROOF.md", + "--reuse-manifest", + "reuse/5396-REUSE-MANIFEST.json", + "--sources", + "agents/precision/SOURCES.json", + "--out", + "agents/precision/CHECK.json" + ], + "name": "fresh-all-size-precision-stock-compiler", + "timeout_seconds": 30 + } + ], + "schema_version": 1, + "status": "FROZEN" +} diff --git a/research/direct-backward-independent-validation/PROOF.md b/research/direct-backward-independent-validation/PROOF.md new file mode 100644 index 0000000000..99bd0c41f5 --- /dev/null +++ b/research/direct-backward-independent-validation/PROOF.md @@ -0,0 +1,70 @@ +# Direct backward review: proof dependencies and reuse boundary + +The target is Ali Romman's PR5398 head +`174fb211493b43a42210434083e9702b4fb7a2ce`, conditional κ `.00302728823`. +The three independent component reports and their root-run receipts are +frozen inputs. The registered wrapper requires fresh complete caller, numerical +and precision outputs in each normal and optimized replay. + +## Exact source and unchanged supplier + +The canonical framework is `1ec1119972c9aefe42525172d07b332fcff81cb4`. +The native implementation and eight-relation WITNESS in the target are byte +identical to PR5383's `4bd6efa51a495a7c7b7754915cf0244e7e60969e` files. +The source-bound literal supplier payload SHA256 is +`2aee5e997df99726fc763e510d9cb69fbe4f86114dc8d2cd33ad26c6c462a21d`. +The published PR5396 review at +`787efce72a908f92b8a8b4ebb677a6fdb7729e33` supplies its proof and exact +prior coverage under the same physical ABI. Published documents are vendored +with raw Git membership witnesses. Local raw old checker outputs are explicitly +identified as external execution evidence. + +Reuse is limited to the unchanged supplier: sixteen unrestricted relations, +rank-eight simultaneous preparation, 624 retained arbitrary inputs, seventeen +arbitrary owned inputs, retained endpoints and owned zero returns. It includes +source-identical native factors and inherited absolute phases only in their +proved domains. It does not establish the changed caller, helper conversion, +ordinary bill, new compiler endpoint or new precision specialization. + +## Fresh caller and normalization obligations + +The caller engine must prove the literal 32-row Laurent endpoint, both actual +changed wrapper stages, exact phase-bearing contacts and all signed scalar +programs. Productive backward helper outputs require their actual ordered +positive-child factorization and both ordinary monomial normalizers, with no +rank-only shortcut. Scalar signs remain outside tensor substitution. Every +owned bank and productive helper occurrence must be separately named and +charged; borrowed main inputs cannot become destructive scratch. + +## Complete invoice and exact arithmetic + +The numeric engine independently parses the complete caller and unchanged +supplier to derive the paid/productive histograms and ordinary bill. It imports +no submitted evaluator. Its directed rational bounds must establish alpha, +higher paid and target completion tails, reserve and rounding, split/capacity, +strict finite compiler grid, ordinary BIT conversion/stock and all 54 strict +plus four functional outer predicates. The necessary fixed-profile moment root +is distinct from a funded endpoint and from compiler optimality. Fresh outputs +must identify the exact invoice and engine bytes. + +## Fresh all-size specialization + +The precision report instantiates the generic induction with the actual +expanded direct-backward template, including 306 local owned-bank positions, +7200 distinct productive helper owners and simultaneously suspended ancestors. +It must bound full completed/replicated/compiler/matcher/restoration templates, +not merely count raw slots. Its effective integer recurrence defines new +W,P,U,O,R,G,N and E,B,C0,C1, stopping and layout thresholds, Gaussian +chunk/rounding reserve and simultaneous complex/BIT stock. The compiled word is +algorithmically specified rather than materialized. The written induction, +exact integer inequalities and negative controls remain separate from physical +tape execution and a proof-kernel theorem. + +## Invalidation + +Any changed source, native phase, witness, supplier chronology, caller word, +productive profile, helper adapter, owned domain, compiler tuple, reserve, +endpoint or retained assumption invalidates the affected application. Binding +and source guards run before execution; fresh outputs are validated for full +coverage after execution. Historical status strings alone never establish a +changed object. diff --git a/research/direct-backward-independent-validation/README.md b/research/direct-backward-independent-validation/README.md new file mode 100644 index 0000000000..90f4143937 --- /dev/null +++ b/research/direct-backward-independent-validation/README.md @@ -0,0 +1,84 @@ +# Independent validation of the direct backward caller + +This package reviews Ali Romman's PR5398 at exact head +`174fb211493b43a42210434083e9702b4fb7a2ce`, conditional κ +`.00302728823`. The independent scientific acceptance review accepts this fixed object +under the retained five premises. Three independent engines and their written +proofs supply the changed caller, funding and precision coverage; registered +cold replay validates their complete fresh outputs against the frozen review. Final committed/exported +transport, independent acceptance and any maintainer selection are separate +gates. + +The new review concerns the literal direct backward caller, its phase-bearing +wrapper and positive helper normalization, the complete recursive and ordinary +bill, directed funding and outer arithmetic, and a fresh all-size precision and +stock specialization. The unchanged eight-relation PR5383 supplier is reused +through its exact native source, witness and literal payload, together with the +published PR5396 proof. Those old scientific engines are not rerun by this +package. PR5392's different caller is outside this review target. + +The canonical selected baseline remains `.0030217758` at +`1ec1119972c9aefe42525172d07b332fcff81cb4`. The five retained premises are +literal statements in `CLAIMS.json`: native all-column realization and phase; +owned allocation/erasure; finite compiler closure; precision and tape; analytic +and exact-recovery transfer. This package changes no selected record and makes +no unconditional multiplication theorem, formal-kernel acceptance or practical +speedup claim. + +## Reproduction + +From the repository root, with standard-library Python 3.12: + +```sh +python3 -B scripts/research_package.py --package research/direct-backward-independent-validation +``` + +The registered manifest runs both normal and optimized modes. For explicit +receipt destinations: + +```sh +python3 -I -B research/direct-backward-independent-validation/verify.py --output /tmp/direct-backward-normal.json +python3 -I -O -B research/direct-backward-independent-validation/verify.py --output /tmp/direct-backward-optimized.json +``` + +The verifier begins with a builtin-only isolated-Python bootstrap so local +standard-library shadows cannot execute. It authenticates both helpers before +executing either, and the complete input +manifest before any engine executes. It rejects changed bytes, undeclared files, +symlink or hardlink input aliases, stale bytecode caches, wrong source heads and +Git membership proofs. Raw Git commit/tree data establishes file membership +offline; replay needs neither Git nor a private object store nor a network. +The independent scientific engines are preserved byte for byte at their final +review freezes. + +Replay copies the capsule to a new private scratch tree, sets only its newly +created directories to `0700`, and gives every subprocess a fresh bytecode-cache +prefix. Frozen `0444` files and `0555` directories remain untouched. The three +engines run serially, with explicit `-O` propagation; fresh JSON is checked for +complete semantic coverage and source/claim identity. Exit status alone cannot +satisfy the review. Outputs and raw logs stay outside the frozen package. + +`SOURCE-BINDINGS.json` lists every package-local input; its exact bytes and the +command schedule are pinned by the committed verifier. `SOURCES.json` records +canonical provenance. Published PR5396 proof documents have offline Git +membership proofs. The separately labelled old raw algebra/ownership receipts +were frozen external execution evidence; they were **not** files in PR5396's +published tree. Their reuse does not assert a fresh historical replay. + +## Open next questions + +The retained five premises require independent closure beyond this scoped +conditional review. A successor must supply a complete changed caller, every +productive-output loss, ordinary helper/phase normalization charges, fresh +expanded precision/stock constants and a funded strict endpoint. `TASK.json` +gives feasible first steps and invalidation rules. + +## Credit and license + +Ali Romman retains PR5383 and PR5398 construction credit. Cao Yifan supplied the +selected PR4610 framework/source word. Chris R / Clear1nsight supplied the +independent PR5241 and PR5396 reviews and this review, with substantial OpenAI +Codex assistance. Retained source credits include Cinna Davis, zxv, Jacob Alan +Sussman, Dugongue, ToikY and native, Clifford, BIT, compiler, precision and +analytic contributors. Exact source notices remain in vendored inputs. 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semantic review coverage; fresh scientific outputs are always generated in private scratch. Old raw prior receipts are local frozen execution evidence, not published PR5396 files.", + "schema_version": 1 +} diff --git a/research/direct-backward-independent-validation/SOURCES.json b/research/direct-backward-independent-validation/SOURCES.json new file mode 100644 index 0000000000..f535ae003e --- /dev/null +++ b/research/direct-backward-independent-validation/SOURCES.json @@ -0,0 +1,24 @@ +{ + "base_commit": "1ec1119972c9aefe42525172d07b332fcff81cb4", + "files": [ + { + "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602", + "path": "docs/research/agent-task-catalog.json", + "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72", + "usage": "provenance" + }, + { + "git_blob": "b288ae44032fd84dd5564243422836cbcd29835e", + "path": "certificates/selected-result.json", + "sha256": "f9ed52bb642cd1e1486cf2743557ac5fa23cf1514a3277d786a644e39a565038", + "usage": "provenance" + } + ], + "review_sources": { + "candidate": "174fb211493b43a42210434083e9702b4fb7a2ce", + "reused_review": "787efce72a908f92b8a8b4ebb677a6fdb7729e33" + }, + "schema_version": 1, + "source_binding_policy": "Every actual runtime input is read from working bytes. Git provenance authenticates history; it never supplies a replacement for missing or mutated working inputs.", + "vendored_source_bindings": "SOURCE-BINDINGS.json" +} diff --git a/research/direct-backward-independent-validation/TASK.json b/research/direct-backward-independent-validation/TASK.json new file mode 100644 index 0000000000..97fba58c16 --- /dev/null +++ b/research/direct-backward-independent-validation/TASK.json @@ -0,0 +1,106 @@ +{ + "actual_scope": "Independent same-premise validation of Ali Romman PR5398 direct backward caller at exact head174fb211493b43a42210434083e9702b4fb7a2ce, with fresh caller/phase/helper normalization, complete funding and precision; source-bound reuse of unchanged PR5383 supplier reviewed by PR5396.", + "ai_assistance": "Substantial OpenAI Codex assistance in independent code, mathematical review, source custody, verification and packaging.", + "author": "Chris R / Clear1nsight", + "base_commit": "1ec1119972c9aefe42525172d07b332fcff81cb4", + "bottleneck_link": "https://github.com/CrocSwap/integer-mult-bounds/pull/5398", + "evidence": "PROOF.md; reports/caller, reports/numeric and reports/precision; exact frozen engines and root component receipts; complete offline SOURCE-BINDINGS. Registered normal/optimized and final transport acceptance remain separate root gates.", + "open_questions": [ + { + "blocked_by": "All-column native realization, owned erasure, finite compiler closure, precision/tape and analytic exact recovery.", + "first_step": "Choose one assumption and bind its exact caller domain, source and effective constants.", + "question": "Can the five retained premises be closed with independently checked all-size physical and analytic constructions?", + "why_it_matters": "Conditional admission does not prove the complete multiplication theorem." + }, + { + "blocked_by": "Physical endpoint, arbitrary helper/owned domains, fresh precision and complete outer funding.", + "first_step": "Publish a complete literal caller and independent all-output bill before a root search.", + "question": "Can another complete caller improve the funded endpoint after every helper loss and ordinary wrapper charge?", + "why_it_matters": "Local identities and equal profiles do not establish complete funding." + } + ], + "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": "completed", + "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": "The donor assigned a complete independent admission of the new author construction in PR5398. The package covers its changed literal caller, full bill, directed endpoint and all-size precision, with authenticated unchanged supplier reuse, beyond the narrower pricing card. This is independent review of Ali Romman construction rather than synthesis of a new helper inventory.", + "scope_status": "changed", + "stop_rule": "Freeze complete evidence and package only after the root scientific and acceptance gates pass; otherwise publish an explicit unresolved scope.", + "task_id": "independent-moment" +} diff --git a/research/direct-backward-independent-validation/VERIFY.json b/research/direct-backward-independent-validation/VERIFY.json new file mode 100644 index 0000000000..42b3e0cc48 --- /dev/null +++ b/research/direct-backward-independent-validation/VERIFY.json @@ -0,0 +1,189 @@ +{ + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-B", + "{package}/verify.py" + ], + "checks": "Fresh independent caller, physical phase/helper normalization, full invoice, exact directed prices, finite compiler/outer predicates and fresh all-size precision specialization; unchanged supplier proof is authenticated reuse under five retained premises.", + "timeout_seconds": 600 + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-B", + "{package}/verify.py" + ], + "checks": "Fresh independent caller, physical phase/helper normalization, full invoice, exact directed prices, finite compiler/outer predicates and fresh all-size precision specialization; unchanged supplier proof is authenticated reuse under five retained premises.", + "timeout_seconds": 600 + } + ], + "input_inventory": "SOURCE-BINDINGS.json authenticates every package-local input before engine execution. 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"3c8efab1f830868c054d33391ee2f8bc74f9bae9c134edf5b455790eb674c1c4", + "research/kappa-backward-controller-20261023/WITNESS.json": "24599011da06325e1012619b2b84a4dd3aceb90ab42d3caaf6414879e7d16591", + "research/joint-helper-lattice/CONTROLLER.json": "1f5d6aa267e4e66048818714b5d3b5eae17a58abe91d15deeaa34574f7391a5f", + "research/joint-helper-lattice/NATIVE.json.gz": "74582cce642c80f0235be7fcbce3716174666326ac6a1d46d02a62a75d7be4c6", + "research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05", + "research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz": "6eae66ed3cfa8a1533e89b9660a57276908e6646640a12f8b1e3489f4ea1354b", + "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa", + "research/final4610-independent-admission/SPECIALIZATION.md": "70430114f744108223bc1d44b98bc25b696c4b408b7b044c2a8bbdfdb434ac5c" + }, + "prior": { + "ownership.json": "63a19a493db991cf16e9c21743854b0d06b0802354bb4646add9800f82d97075", + "algebra.json": "9226f3dafb9ece272607603b925bdbfde32b5267a909962791c1120875da63e3", + "acceptance.json": "c1cf491326df8ed708ad1bb8a80222e18e59d1d500bfe9a1cf79d07a49f4616d", + "WORD.json.gz": "7883ba0faefc96505bb61ca7312d588fa22dfe2164050c817c1718b8fa28693a", + "native.py": "3c8efab1f830868c054d33391ee2f8bc74f9bae9c134edf5b455790eb674c1c4", + "WITNESS.json": "24599011da06325e1012619b2b84a4dd3aceb90ab42d3caaf6414879e7d16591", + "foundation.json": "0b37e1741af786144e1eb78a752bee65424437107c5065181d8a28e05ec30122" + } +} diff --git a/research/direct-backward-independent-validation/capsule/agents/caller/check.py b/research/direct-backward-independent-validation/capsule/agents/caller/check.py new file mode 100644 index 0000000000..39ae0f8425 --- /dev/null +++ b/research/direct-backward-independent-validation/capsule/agents/caller/check.py @@ -0,0 +1,254 @@ +#!/usr/bin/env python3 +"""Independent direct-caller gate; no candidate Python imports or execution. +Reuses the exact previously admitted supplier, by byte binding only. +""" +from pathlib import Path +from fractions import Fraction as F +from collections import Counter +import argparse, copy, gzip, hashlib, json, subprocess, time, resource +HEAD='174fb211493b43a42210434083e9702b4fb7a2ce' +PAYLOAD='2aee5e997df99726fc763e510d9cb69fbe4f86114dc8d2cd33ad26c6c462a21d' +PIVOTS={225,227,229,230,241,245,257,288} +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[2] +PKG='research/kappa-backward-controller-20261023' +def need(v,s): + if not v: raise ValueError(s) +def sha(b):return hashlib.sha256(b).hexdigest() +def load(p): + b=Path(p).read_bytes();return json.loads(gzip.decompress(b) if str(p).endswith('.gz') else b) +def git(repo,path): + b=(repo/path).read_bytes() if not (repo/'.git').exists() else subprocess.check_output(['git','-C',str(repo),'show',HEAD+':'+path]) + need(sha(b)==INPUTS['repository'][path],'exact source hash '+path) + return b +def scale_add(a,b,k): + r=dict(a) + for x,v in b.items(): + r[x]=r.get(x,F(0))+k*v + if not r[x]:del r[x] + return r +def monomial(a,q=0,stages=()): + r={} + for (column,powers),v in a.items(): + ex=list(powers);ex[0]+=q + for s in stages:ex[s+1]+=1 + r[column,tuple(ex)]=v + return r +def scalar_program(rows,program): + r=copy.deepcopy(rows) + for e in program: + k=e[0] + if k=='ADD':r[e[1]]=scale_add(r[e[1]],r[e[2]],F(e[3])) + elif k=='SCALE':r[e[1]]={t:F(e[2])*v for t,v in r[e[1]].items()} + elif k=='SWAP':r[e[1]],r[e[2]]=r[e[2]],r[e[1]] + else:raise ValueError('unlicensed boundary opcode') + return r +def signed_swap(r,x,y): + # Literal three-ADD implementation: (x,y)->(x+y,y)->(x+y,-x)->(y,-x). + r[x]=scale_add(r[x],r[y],1);r[y]=scale_add(r[y],r[x],-1);r[x]=scale_add(r[x],r[y],1) +def literal_replay(word): + zero=(0,)*34 + r=[{(i,zero):F(1)} for i in range(32)] + for side in ['right','left']: + test=scalar_program([{(i,zero):F(1)} for i in range(32)],word['boundaries'][side+'_program']) + want=[{(j,zero):F(v) for j,v in enumerate(row) if F(v)} for row in word['boundaries'][side]] + need(test==want,'literal scalar boundary matrix') + r=scalar_program(r,word['boundaries']['right_program']) + for e in word['physical_events']: + kind=e[0] + if kind in ['LOCAL','QUERY_SHEAR']: + _,stage,pair,back=e;x,y=2*pair,2*pair+1 + if back:r[x]=scale_add(r[x],monomial(r[y],q=1),-1) + else:r[y]=scale_add(r[y],monomial(r[x],q=-1),1) + if kind=='LOCAL': + r[x]=monomial(r[x],stages=[stage]);r[y]=monomial(r[y],stages=[stage]) + elif kind=='IDLE': + for i in [2*e[1],2*e[1]+1]:r[i]=monomial(r[i],stages=e[2]) + elif kind=='ADD':r[e[1]]=scale_add(r[e[1]],r[e[2]],F(e[3])) + elif kind=='Q_POWER': + need(e[2] in [-2,2],'only paid-grammar even central translations');r[e[1]]=monomial(r[e[1]],q=e[2]) + elif kind=='SIGNED_SWAP':signed_swap(r,e[1],e[2]) + elif kind=='SWAP':r[e[1]],r[e[2]]=r[e[2]],r[e[1]] + else:raise ValueError('unknown controller event') + r=scalar_program(r,word['boundaries']['left_program']) + want=[{(i,tuple(v)):F(1)} for i,v in enumerate(word['diagonal'])] + need(r==want,'full independent Laurent caller equality') + return True + +def mv(cols,v): + r=0 + while v: + bit=v&-v;r^=cols[bit.bit_length()-1];v^=bit + return r +def phase(terms,n): + # parity(a.z) = sum a_i z_i - 2 sum_{i>i)&1: + lin[i]=(lin[i]+c)%4 + if c%2:quad[i]^=a&~((1<<(i+1))-1) + return tuple(lin),tuple(quad) +def contact(old,new,route,n): + moved=[(mv(route,a),c) for a,c in old] + p,q=phase(moved,n),phase(new,n) + need(p[1]==q[1],'physical contact quadratic phase') + dif=[(b-a)%4 for a,b in zip(p[0],q[0])] + need(all(c%2==0 for c in dif),'physical contact nonmonomial difference') + shift=sum((c//2)< 0 and d & (d - 1) == 0, 'Nonzero dyadic scalar') + if g[0] == 'scale': + need(n & (n - 1) == 0, 'Dyadic unit SCALE') + return 2 * (abs(n.bit_length() - d.bit_length()) + int(q < 0)) + need(g[0] == 'add', 'Known scalar operation') + return 2 * (3 + n.bit_length() - 1 + n.bit_count() + d.bit_length() - 1) + + +def relation_system(): + """Find exact independent pivots and eliminate all other pivot columns.""" + basis = {} + need(len(WITNESSES) == COUNT, 'Eight declared witnesses') + for witness in WITNESSES: + pairs = witness['relation'] + row = {h: Q(q) for h, q in pairs} + need(len(row) == len(pairs) and all(224 <= h < 632 and q for h, q in row.items()), 'Distinct helper coefficients') + for pivot, prior in sorted(basis.items()): + add(row, prior, -row.get(pivot, Q(0))) + need(row, 'Independent helper relations') + pivot = min(row); scale = row[pivot] + row = {h: q / scale for h, q in row.items()} + for prior in basis.values(): + add(prior, row, -prior.get(pivot, Q(0))) + basis[pivot] = row + need(len(basis) == COUNT, 'Eight paid helper outputs removed') + for pivot, row in basis.items(): + need(all(row.get(h, 0) == int(h == pivot) for h in basis), 'Reduced pivot columns') + return dict(sorted(basis.items())) + + +BASIS = relation_system() + + +def construct(source): + c = source['canonical']; old = source['programs']['backward'] + all_helpers = {h for x in WITNESSES for h, _ in x['relation']} + need(all(c['start'][h] == 0 and c['final'][h] == 1 for h in all_helpers), 'Every relation uses cold full-ended helpers') + snapshots, centers, zeros = {}, {}, {} + for slot, x in enumerate(WITNESSES, 1): + frame, role = x['frame'], x['cached_role'] + need(old[x['event']] == ['center', 0, 0, frame, 8], 'Exact source center') + event = old[x['cached_event']] + need(event[0] == 'climb' and event[2] == role and event[4] == frame, 'Exact snapshot source') + need(old[x['zero_event']] == ['climb', 'warp_retimed', x['zero_role'], frame, 1, 1], 'Exact zero source job') + need(x['cached_event'] < x['event'] < x['zero_event'] and Q(x['copy_factor']) == 1, 'Snapshot chronology and COPY coefficient') + snapshots[x['cached_event']] = (slot, x) + centers[x['event']] = (slot, x) + zeros[x['zero_event']] = x + need(len(snapshots) == len(centers) == len(zeros) == COUNT, 'Distinct replacement sites') + word = [] + for pivot, row in BASIS.items(): + word.append(['scalar', ['clear', ['L', pivot]], 0]) + for h, q in sorted(row.items()): + if h != pivot: + word.append(['scalar', ['add', ['L', pivot], ['L', h], -q.numerator, q.denominator], 0]) + for index, event in enumerate(old): + if index in centers: + slot, x = centers[index]; f = x['frame'] + word += [['scalar', ['clear', ['C', 0]], f], + ['scalar', ['copy', ['C', 0], ['C', slot]], f], + ['scalar', ['clear', ['C', slot]], f]] + elif index in zeros: + x = zeros[index] + word.append(['zero_retag', ['L', x['zero_role']], x['frame'], 1]) + else: + word.append(deepcopy(event)) + if index in snapshots: + slot, x = snapshots[index]; f = x['frame'] + word += [['scalar', ['clear', ['C', slot]], f], + ['scalar', ['copy', ['C', slot], ['L', x['cached_role']]], f]] + word += [['scalar', ['clear', ['L', h]], 1] for h in BASIS] + physical = deepcopy(c); physical.pop('local_profile') + return {'schema': 'joint-helper-relations-word/1', 'canonical': physical, + 'relation_basis': encode(BASIS), + 'paid_profiles': {'forward': OLD_PAID, 'backward': NEW_PAID}, + 'owned': {'forward': [['C', 0]], 'backward': [['C', i] for i in range(COUNT + 1)] + [['L', h] for h in BASIS]}, + 'programs': {'forward': deepcopy(source['programs']['forward']), 'backward': word}} + + +def replay(c, program, backward, specialized): + """Run every event on all independent entry columns and exact frames.""" + owned = {('C', 0)} | ({('C', i) for i in range(1, COUNT + 1)} | {('L', h) for h in BASIS} if specialized else set()) + roles = {('L', i) for i in range(632)} | owned + rows = {r: {(r, ()): Q(1)} for r in roles} + frames = {('L', i): f for i, f in enumerate(c['start'])} + frames.update({r: None for r in owned if r[0] == 'C'}) + spaces = [span(b) for b in c['frames']] + paid = Counter() + cost, max_l1, denominator, zero_count = 0, Q(1), 1, 0 + for e in program: + kind, touched = e[0], None + if kind == 'scalar': + g, frame = e[1:] + dst = tuple(g[1]); touched = dst + need(dst in rows and 0 <= frame < len(spaces), 'Declared scalar destination and frame') + cost += allowance(g) + if g[0] == 'clear': + need(dst in owned, 'Only owned fields can be erased') + rows[dst] = {}; frames[dst] = frame + else: + need(frames[dst] == frame, 'Exact scalar destination frame') + if g[0] in ('add', 'copy'): + src = tuple(g[2]) + need(src in rows and frames[src] == frame and dst != src, 'Exact scalar source frame') + if g[0] == 'copy': + need(dst in owned and not rows[dst], 'COPY into cleared owned storage') + rows[dst] = dict(rows[src]) + else: + add(rows[dst], rows[src], Q(g[3], g[4])) + else: + need(g[0] == 'scale', 'Known scalar operation') + rows[dst] = {k: Q(g[2], g[3]) * v for k, v in rows[dst].items()} + elif kind == 'warp': + _, role, op, old, new = e + dst = tuple(role); touched = dst + need(frames[dst] == old and 1 <= abs(op) <= len(c['warps']), 'Exact warp input') + symbol = (1 if op > 0 else -1) * (abs(op) + (10**6 if backward else 0)) + rows[dst] = {(r, w[1:] if w and w[0] == -symbol else (symbol,) + w): q + for (r, w), q in rows[dst].items()} + frames[dst] = new + elif kind in ('climb', 'center'): + if kind == 'climb': + _, _, i, old, new, rank = e + dst = ('L', i) + need(spaces[old] < spaces[new], 'Ascending paid climb') + else: + _, i, old, new, rank = e + dst = ('C', i) + need(spaces[old] < spaces[new] or spaces[new] < spaces[old], 'Nested paid center') + need(frames[dst] == old and rank == abs(len(c['frames'][new]) - len(c['frames'][old])), 'Exact paid rank and frame') + frames[dst] = new; paid[rank] += 1 + elif kind == 'zero_retag': + _, role, old, new = e + dst = tuple(role) + need(specialized and backward and any(dst == ('L', x['zero_role']) and (old, new) == (x['frame'], 1) for x in WITNESSES), 'Declared zero identity') + need(frames[dst] == old and not rows[dst], 'Zero identity requires an identically zero full row') + frames[dst] = new; zero_count += 1 + else: + need(kind in ('phase', 'adapter'), 'Known inert source marker') + if touched is not None: + max_l1 = max(max_l1, sum(map(abs, rows[touched].values()), Q(0))) + denominator = max(denominator, max((q.denominator for q in rows[touched].values()), default=1)) + need([frames['L', i] for i in range(632)] == c['final'], 'Every final native frame') + for i in range(632): + r = ('L', i) + if r in owned: + continue + expected = {(r, ()): Q(1)} + if i < 112 if backward else 112 <= i < 224: + expected[(('L', i + 112 if backward else i - 112), ())] = Q(-1 if backward else 1) + need(rows[r] == expected, 'Every independent main/helper endpoint: ' + str(i)) + need(all(not rows[r] for r in owned), 'Every owned entry column is erased at return') + need(zero_count == COUNT * int(specialized), 'All eight zero identities checked') + helpers = Counter() + for i in range(224, 632): + if ('L', i) in owned: + continue + a, b = c['start'][i], c['final'][i] + need(spaces[a] < spaces[b], 'Strict independent productive helper') + helpers[len(c['frames'][b]) - len(c['frames'][a])] += 1 + return {'paid': dict(sorted(paid.items())), 'helpers': dict(sorted(helpers.items())), + 'independent_persistent_columns': 632 - COUNT if specialized else 632, + 'independent_owned_entry_columns': len(owned), 'owned_outputs_zero': True, + 'real_scalar_allowance': cost, 'max_formal_prefix_l1': str(max_l1), + 'max_denominator': denominator, 'zero_identities': zero_count} + + +def independent_source_identities(source): + """Check unrestricted source identities with the predecessor row engine.""" + v = load('research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py', 'joint_relation_source_rows') + rows = {('L', i): v.identity(('L', i)) for i in range(632)} + rows['C', 0] = v.identity(('C', 0)); saved = {}; checked = [] + for index, e in enumerate(source['programs']['backward']): + if e[0] == 'scalar': + g = e[1]; dst = tuple(g[1]) + if g[0] == 'clear': rows[dst] = {} + elif g[0] == 'copy': rows[dst] = dict(rows[tuple(g[2])]) + elif g[0] == 'scale': rows[dst] = {k: Q(g[2], g[3]) * a for k, a in rows[dst].items()} + else: v.add(rows[dst], rows[tuple(g[2])], Q(g[3], g[4])) + elif e[0] == 'warp': + dst = tuple(e[1]); rows[dst] = v.warp(rows[dst], e[2], True) + for x in WITNESSES: + delta = {(('L', h), ()): Q(q) for h, q in x['relation']} + if index == x['cached_event']: + saved[index] = dict(rows['L', x['cached_role']]) + if index == x['event']: + diff = dict(rows['C', 0]); v.add(diff, saved[x['cached_event']], -Q(x['copy_factor'])) + need(diff == {k: Q(x['difference_factor']) * q for k, q in delta.items()}, 'Independent exact center minus snapshot identity') + checked.append(('center', index)) + if index == x['zero_event']: + need(rows['L', x['zero_role']] == {k: Q(x['zero_factor']) * q for k, q in delta.items()}, 'Independent exact zero-site row identity') + checked.append(('zero', index)) + need(len(checked) == 2 * COUNT, 'Sixteen unrestricted source identities') + need(all(rows['L', i] == v.expected(('L', i), [], True, False) for i in range(632)), 'Independent unrestricted source endpoints') + return {'source_event_indices_are_zero_based': True, 'witnesses': WITNESSES, + 'relation_rank': COUNT, 'owned_pivots': list(BASIS), 'reduced_basis': BASIS, + 'snapshot_terms_before_substitution': {i: len(row) for i, row in saved.items()}, + 'checked': checked} + + +def phase_inheritance(source, candidate): + receipt = read(ROOT / PHASE) + need(receipt['status'] == 'PASS_JOINT_HELPER_MAPS_ALL_ACTUAL_ABSOLUTE_PHASES' and + receipt['actual_word_canonical_sha256'] == PAYLOAD, 'Authenticated source absolute-phase receipt') + physical = deepcopy(source['canonical']); physical.pop('local_profile') + need(candidate['canonical'] == physical, 'Every frame, native map and main adapter unchanged') + for direction, program in candidate['programs'].items(): + old = source['programs'][direction] + for kind in ('warp', 'adapter', 'phase'): + need([e for e in program if e[0] == kind] == [e for e in old if e[0] == kind], 'Exact inherited ' + kind + ' sequence') + old_paid = Counter(tuple(e) for e in old if e[0] in ('climb', 'center')) + new_paid = Counter(tuple(e) for e in program if e[0] in ('climb', 'center')) + expected = Counter() if direction == 'forward' else Counter(tuple(old[i]) for x in WITNESSES for i in (x['event'], x['zero_event'])) + need(old_paid - new_paid == expected and not new_paid - old_paid, 'Only the sixteen proved jobs are removed') + return {'new_gaussian_operators': 0, 'new_native_maps': 0, + 'all_retained_paid_events_and_warps_from_source': True, + 'absolute_phase_receipt_reused': PHASE, + 'source_amplitudes_and_phase_lowering_freshly_replayed': False, + 'new_operations': 'Same-frame COPY, owned CLEAR/ADD, and physical identity on a proved zero row.'} + + +def controls(c, candidate): + controls = {} + base = candidate['programs']['backward'] + variants = {} + bad = deepcopy(base); bad[1][1][3] *= -1; variants['wrong_relation_sign'] = bad + variants['missing_owned_input_clear'] = deepcopy(base[1:]) + bad = deepcopy(base) + next(e for e in bad if e[0] == 'scalar' and e[1][:2] == ['copy', ['C', 1]])[1][2] = ['L', 63] + variants['wrong_snapshot_source'] = bad + bad = deepcopy(base); next(e for e in bad if e[0] == 'zero_retag')[2] = 0 + variants['wrong_zero_input_frame'] = bad + bad = deepcopy(base); next(e for e in bad if e[0] == 'climb')[5] += 1 + variants['under_or_overstated_paid_rank'] = bad + bad = deepcopy(base) + next(e for e in bad if e[0] == 'scalar' and e[1][:2] == ['copy', ['C', 0]])[2] = 0 + variants['wrong_copy_gauge'] = bad + variants['uncleared_owned_output'] = deepcopy(base[:-1]) + for name, program in variants.items(): + try: + replay(c, program, True, True) + except ValueError as err: + controls[name] = str(err) + else: + raise ValueError('Control accepted: ' + name) + return controls diff --git a/research/direct-backward-independent-validation/capsule/agents/caller/inputs/prior/ownership.json b/research/direct-backward-independent-validation/capsule/agents/caller/inputs/prior/ownership.json new file mode 100644 index 0000000000..9bf4ce85bf --- /dev/null +++ b/research/direct-backward-independent-validation/capsule/agents/caller/inputs/prior/ownership.json @@ -0,0 +1,661 @@ +{ + "candidate_head": "4bd6efa51a495a7c7b7754915cf0244e7e60969e", + "candidate_word": "/home/d3lerium/.codex/.chatgpt-projects/g-p-6ad5817fd84881918865926b6fd51453/swarm-execution-sol-high-20261024/repository/research/kappa-joint-relations-20261023/WORD.json.gz", + "candidate_word_sha256": "7883ba0faefc96505bb61ca7312d588fa22dfe2164050c817c1718b8fa28693a", + "canonical_main": "1ec1119972c9aefe42525172d07b332fcff81cb4", + "mutation_controls": { + "alias_owned_snapshot_bank": "17 distinct owned roles required", + "borrowed_clear": "Preparation owner/frame", + "changed_phase_marker": "Source start marker missing", + "missing_initial_pivot_clear": "Pivot read before initial clear", + "missing_owner_return": "Every owned pivot must be returned zero at exact full frame", + "missing_retained_output_operation": "Unlicensed change at source event 110, candidate event 172", + "reused_live_snapshot_bank": "Reused live snapshot bank", + "undeclared_storage_alias": "Snapshot requires immediate same-frame COPY", + "wrong_center_copy_gauge": "Center replacement must clear/COPY C0 in exact output frame", + "wrong_final_owned_frame": "Every owned pivot must be returned zero at exact full frame", + "wrong_snapshot_frame": "Snapshot requires immediate same-frame COPY", + "wrong_snapshot_source": "Snapshot must read source data role" + }, + "result": { + "backward": { + "all_exact_endpoints_checked": true, + "all_owned_last_writes_are_clears": true, + "initial_columns": 641, + "owned_arbitrary_columns": 17, + "owned_def_use": [ + 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arithmetic; no candidate/project modules imported. + +Directed atanh60/Taylor32 rational engine derived from our independent #5377 +review, with a separately transcribed selected #5241 outer ledger. Candidate +histograms must come from a separately authenticated independent census. +#5398 retains the #5392 profile through a distinct direct backward caller. +Only the source-bound saving/reserve inputs change; enclosure formulas are +unchanged. The literal caller, phases and fresh precision are separate gates. +Predecessors: Ali Romman (construction); Cao Yifan; Cinna Davis; zxv; +Jacob Alan Sussman; Chris R/Clear1nsight. Substantial OpenAI Codex assistance. +""" +from fractions import Fraction as Q +from functools import lru_cache +from hashlib import sha256 +from pathlib import Path +import json, time +UNIT=10**55 +MODEL='selected-mixed-target-p16-completion1024-v1' +ASSUMPTIONS=['native_all_columns','owned_erasure','compiler','precision_tape','analytic_recovery'] +def need(v, why): + if not v: raise ValueError(why) +def down(x): return Q(x.numerator*UNIT//x.denominator,UNIT) +def up(x): return -down(-x) +def mul(a,b): + p=[x*y for x in a for y in b]; return down(min(p)),up(max(p)) +def divide(a,b): + need(b[0]>0,'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 scalar required') + if g[0]=='scale': + need(n&(n-1)==0,'dyadic unit SCALE required') + return 2*(abs(n.bit_length()-d.bit_length())+int(q<0)) + need(g[0]=='add','scalar alphabet') + return 2*(3+n.bit_length()-1+n.bit_count()+d.bit_length()-1) + +def authenticate(): + if MANIFEST is None: + need(subprocess.check_output(['git','rev-parse','HEAD'],cwd=REPO,text=True).strip()==HEAD,'wrong source checkout') + rows=[] + tree=subprocess.check_output(['git','ls-tree','-rz',HEAD,'--',PKG],cwd=REPO) + for line in tree.split(b'\0'): + if not line: continue + meta,path=line.split(b'\t'); mode,kind,gitblob=meta.decode().split();path=path.decode() + need(mode=='100644' and kind=='blob','package regular source file required') + b=(REPO/path).read_bytes();need(blob(b)==gitblob,'candidate source differs from exact Git blob: '+path) + rows.append({'path':path,'sha256':sha256(b).hexdigest(),'git_blob':gitblob}) + else: + frozen=read(MANIFEST);need(frozen['head']==HEAD,'frozen source manifest head') + rows=frozen['package_rows'] + for row in rows: + b=(REPO/row['path']).read_bytes() + need(sha256(b).hexdigest()==row['sha256'] and blob(b)==row['git_blob'],'source manifest row differs') + need(len(rows)==11,'new package census changed') + source=read(REPO/PKG/'SOURCES.json');need(source['base_commit']==BASE,'canonical base changed') + inputs=[] + verify=read(REPO/PKG/'VERIFY.json');expected=set(verify['inputs']) + for row in source['files']: + if row['usage']!='input':continue + p=REPO/row['path'];b=p.read_bytes() + need(sha256(b).hexdigest()==row['sha256'] and blob(b)==row['git_blob'],'source input changed: '+row['path']) + inputs.append(dict(row)) + need({r['path'] for r in inputs}==expected and len(inputs)==11,'complete source input inventory') + reuse=[] + for name,digest in [('native.py','3c8efab1f830868c054d33391ee2f8bc74f9bae9c134edf5b455790eb674c1c4'),('WITNESS.json','24599011da06325e1012619b2b84a4dd3aceb90ab42d3caaf6414879e7d16591')]: + p=REPO/PKG/name;old=PREVIOUS/name + need(sha(p)==digest and p.read_bytes()==old.read_bytes(),'unchanged admitted backward supplier differs') + reuse.append({'candidate_path':PKG+'/'+name,'prior_path':'research/kappa-joint-relations-20261023/'+name,'sha256':digest}) + oldword=PREVIOUS/'WORD.json.gz';need(sha(oldword)==WORD_SHA,'prior admitted literal word changed') + need(sha256(gzip.decompress(oldword.read_bytes())).hexdigest()==PAYLOAD_SHA,'prior word payload changed') + return {'head':HEAD,'canonical_base':BASE,'package_rows':rows,'input_rows':inputs,'unchanged_supplier':reuse,'prior_word':{'path':'research/kappa-joint-relations-20261023/WORD.json.gz','sha256':WORD_SHA,'payload_sha256':PAYLOAD_SHA}} + +def source_keys(): + p=REPO/'research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py' + node=next(n for n in ast.parse(p.read_bytes()).body if isinstance(n,ast.FunctionDef) and n.name=='ledger');keys={} + for n in node.body: + if isinstance(n,ast.Assign) and len(n.targets)==1 and isinstance(n.targets[0],ast.Name) and isinstance(n.value,ast.Dict): keys[n.targets[0].id]=[k.value for k in n.value.keys] + return {'path':str(p.relative_to(REPO)),'sha256':sha(p),'strict':sorted(set(keys['checks'])|{k+'_above_kappa' for k in keys['margins']}),'functional':sorted(set(keys['functional'])|{'actual_new_BIT_stock_sublinear'})} + +def invoice(): + auth=authenticate() + controller=read(REPO/'research/joint-helper-lattice/CONTROLLER.json') + changed=copy.deepcopy(controller);events=[];sites=[] + for i,e in enumerate(controller['physical_events']): + if e[0]=='LOCAL' and e[3] is False: + _,stage,pair,_=e;x,y=2*pair,2*pair+1 + sites.append({'source_index':i,'stage':stage,'pair':pair}) + events.extend([['SIGNED_SWAP',y,x],['Q_POWER',x,2],['LOCAL',stage,pair,True],['SIGNED_SWAP',x,y],['Q_POWER',y,-2]]) + else:events.append(copy.deepcopy(e)) + changed['physical_events']=events;changed['wrapper_sites']=sites;del changed['invoice'] + def check_caller(payload): need(changed==payload,'literal caller differs from independent wrapper reconstruction') + candidate=read(REPO/PKG/'CONTROLLER.json');check_caller(candidate) + need([s['stage'] for s in sites]==[0,32] and len(sites)==2,'actual boundary replacement stages') + old=read(PREVIOUS/'WORD.json.gz');base=read(REPO/'research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz');c=base['canonical'] + need(all(c[k]==v for k,v in old['canonical'].items()) and set(c)-set(old['canonical'])=={'local_profile'},'source frame inventory changed') + owned=set(map(tuple,old['owned']['backward']));need(len(owned)==17,'raw backward owner count') + def derive_local(program): + local=Counter();allowance=0;kinds=Counter();ops=Counter() + for e in program: + kinds[e[0]]+=1 + if e[0] in ('climb','center'): + a,b=e[-3:-1];rank=e[-1] + need(type(rank)is int and rank>0 and abs(len(c['frames'][a])-len(c['frames'][b]))==rank,'paid frame delta mismatch') + local[rank]+=1 + elif e[0]=='scalar':allowance+=scalar(e[1]);ops[e[1][0]]+=1 + return local,allowance,kinds,ops + local,allowance,kinds,ops=derive_local(old['programs']['backward']) + helpers=Counter(len(c['frames'][c['final'][r]])-len(c['frames'][c['start'][r]]) for r in range(224,len(c['start'])) if ('L',r) not in owned) + P=Counter();T=Counter();counts=Counter();chron=[];main=Counter();idles=Counter() + stages={e[1] for e in events if e[0]=='LOCAL'} + for i,e in enumerate(events): + counts[e[0]]+=1;paid=Counter();productive=Counter() + if e[0]=='LOCAL':need(e[3] is True,'unfunded forward source used');paid.update(local);productive.update(helpers) + elif e[0]=='QUERY_SHEAR':paid[1]+=112 + elif e[0]=='IDLE': + need(len(set(e[2]))==len(e[2]) and all(type(s)is int and s in stages for s in e[2]),'idle stage set mismatch') + paid[8*len(e[2])]+=224;idles.update(paid) + else:need(e[0] in ('ADD','SIGNED_SWAP','Q_POWER'),'unknown caller charge') + P.update(paid);T.update(productive);chron.append({'index':i,'event':e,'paid':hist(paid),'productive':hist(productive)}) + for term in changed['diagonal']: + need(abs(term[0])==1 and all(x in (0,1) for x in term[1:]),'main rank term') + main[1+8*sum(term[1:])]+=112 + T.update(main) + need((counts['LOCAL'],counts['QUERY_SHEAR'],sum(P.values()),sum(T.values()))==(18,15,64116,10784),'complete invoice changed') + need(sum(r*n for r,n in T.items())-sum(r*n for r,n in P.items())==752,'rank surplus changed') + need((local,helpers,allowance)==(Counter({1:2193,2:412,3:510,4:127,5:40}),Counter({4:28,7:7,8:47,9:318}),158744),'literal supplier counts differ') + routes={'source_paid':sum(local.values()),'two_helper_wrappers':2*408,'warps':kinds['warp'],'adapters':kinds['adapter'],'phases':kinds['phase'],'two_per_added_owned':2*(len(owned)-1)} + route_units=1000*sum(routes.values());need(route_units+allowance<10**7,'source ordinary local cap fails') + # Both scalar boundary programs and ordinary caller records fit32/port. + boundary={} + for side in ['left','right']: + cost=0;prog=changed['boundaries'][side+'_program'] + for e in prog: + if e[0]=='SWAP':units=26 + elif e[0]=='SCALE':q=Q(e[2]);units=scalar(['scale',['L',0],q.numerator,q.denominator]) + else:need(e[0]=='ADD','boundary alphabet');q=Q(e[3]);units=scalar(['add',['L',0],['L',1],q.numerator,q.denominator]) + need(units<=32,'boundary tariff exceeded');cost+=112*units + boundary[side]={'events':len(prog),'explicit_scalar_units':cost} + newcounts=Counter(e[0] for e in events)-Counter(e[0] for e in controller['physical_events']) + need(newcounts==Counter({'SIGNED_SWAP':4,'Q_POWER':4}),'new wrapper count mismatch') + # A signed swap is three ADDs (24units); reserve26, also covering an + # ordinary swap. Its intermediate row l1 norm is at most2, never omitted. + x,y=[Q(1),Q(0)],[Q(0),Q(1)] + x=[a+b for a,b in zip(x,y)];y=[b-a for a,b in zip(x,y)];x=[a+b for a,b in zip(x,y)] + need((x,y)==([Q(0),Q(1)],[Q(-1),Q(0)]),'signed swap scalar recipe') + wrapper=112*(newcounts['SIGNED_SWAP']*26+newcounts['Q_POWER']*1000) + ctlreserve=32*112*(len(events)+sum(v['events'] for v in boundary.values())) + raw=18*10**7+counts['QUERY_SHEAR']*1792+ctlreserve+wrapper + need(raw==181586816 and wrapper==459648 and raw<10**9,'complete ordinary raw allowance differs') + controls={} + for label,kind in [('omitted_native_wrapper','Q_POWER'),('omitted_idle_job','IDLE'),('omitted_query_shear','QUERY_SHEAR'),('omitted_scalar_sign_swap','SIGNED_SWAP')]: + bad=copy.deepcopy(changed) + bad['physical_events'].pop(next(i for i,e in enumerate(events) if e[0]==kind)) + try:check_caller(bad) + except ValueError as exc:controls[label]=str(exc) + else:raise ValueError('accepted missing charged record: '+label) + # Normalizer records are source-derived role/frame pairs, not the + # author's helper counters. Both sides of every productive helper exist. + normalizers=[{'role':r,'entry_frame':c['start'][r],'exit_frame':c['final'][r],'rank':len(c['frames'][c['final'][r]])-len(c['frames'][c['start'][r]]),'sides':2} for r in range(224,len(c['start'])) if ('L',r) not in owned] + def validate_invoice_payload(payload): + need(payload['histograms']=={'paid':hist(P),'productive':hist(T)},'claimed recursive invoice differs from literal source/caller census') + need(payload['helper_normalizers']==normalizers,'missing/wrong source helper normalizer role/frame/side') + need(payload['local_paid']==hist(derive_local(payload['local_program'])[0]),'paid program invoice mismatch') + need(payload['local_paid']==hist(local),'claimed local profile differs from unchanged complete backward supplier') + need(payload['wrapper_allowance']>=112*(newcounts['SIGNED_SWAP']*26+newcounts['Q_POWER']*1000),'unfunded actual wrapper ordinary bill') + payload={'histograms':{'paid':hist(P),'productive':hist(T)},'helper_normalizers':normalizers,'local_program':old['programs']['backward'],'local_paid':hist(local),'wrapper_allowance':wrapper} + validate_invoice_payload(payload) + mutations={} + bad=copy.deepcopy(payload);bad['histograms']['productive']['9']+=16;mutations['unearned16rank9_targets']=bad + bad=copy.deepcopy(payload);bad['histograms']['productive']['9']-=16;mutations['lost16rank9_targets']=bad + bad=copy.deepcopy(payload);bad['helper_normalizers'].pop();mutations['missing_helper_normalizer']=bad + bad=copy.deepcopy(payload);bad['helper_normalizers'][0]['sides']=1;mutations['one_sided_helper_normalizer']=bad + bad=copy.deepcopy(payload);bad['wrapper_allowance']=0;mutations['unfunded_wrapper_bill']=bad + bad=copy.deepcopy(payload);next(e for e in bad['local_program'] if e[0] in ('climb','center'))[-1]+=1;mutations['wrong_paid_job_rank']=bad + for label,bad in mutations.items(): + # Re-serialize each private mutant as valid JSON: rejection is in the + # same validator used for the valid scientific payload, not its hash. + bad=json.loads(json.dumps(bad)) + try:validate_invoice_payload(bad) + except ValueError as exc:controls[label]=str(exc) + else:raise ValueError('accepted invoice mutation: '+label) + return {'schema':'independent5398-literal-invoice/1','candidate':{'head':HEAD,'package':PKG},'authentication':auth,'histograms':{'paid':hist(P),'productive':hist(T)},'totals':{'paid':sum(P.values()),'productive':sum(T.values()),'paid_mass':sum(r*n for r,n in P.items()),'productive_mass':sum(r*n for r,n in T.items()),'rank_surplus':752},'local':{'paid':hist(local),'helpers':hist(helpers),'scalar_units':allowance,'kinds':dict(kinds),'scalar_ops':dict(ops),'owned':len(owned)},'controller':{'events':len(events),'counts':dict(counts),'sites':sites,'new_wrapper_counts':dict(newcounts),'main':hist(main),'idle':hist(idles),'raw_owned':18*len(owned)},'ordinary':{'source_route_terms':routes,'source_route_units_upper':route_units,'local_units_upper':route_units+allowance,'local_budget':10**7,'wrapper_allowance':wrapper,'boundary':boundary,'boundary_controller_reserve':ctlreserve,'raw_upper':raw,'raw_budget':10**9,'signed_swap_intermediate_norm_factor':2,'tariff_scope':'Retained primitive allowances, not literal tape-step counts. Common1000/group reserved for source9axis recipes only; compiler matchers need their own finite fold.'},'chronology':chron,'helper_normalizers':normalizers,'controls':controls,'source_keys':source_keys(),'no_candidate_code_imported':True,'external_gates':['full Laurent caller and native wrapper-contact phase','authenticated unchanged all641 source columns/17owned returns','fresh complete306bank precision/compiler/stock/tape including signed-swap intermediate factor2']} + +def save(name,data): + p=OUT/name;need(not p.exists(),'immutable receipt already exists: '+name) + p.write_text(json.dumps(enc(data),indent=2,sort_keys=True)+'\n');p.chmod(0o444) + return sha(p) + +def main(): + global REPO,PREVIOUS,OUT,MANIFEST + parser=argparse.ArgumentParser() + parser.add_argument('--repo',type=Path,default=REPO) + parser.add_argument('--prior',type=Path,default=PREVIOUS) + parser.add_argument('--output-dir',type=Path,default=HERE) + parser.add_argument('--source-manifest',type=Path) + parser.add_argument('--static-only',action='store_true') + args=parser.parse_args();REPO=args.repo.resolve();PREVIOUS=args.prior.resolve();OUT=args.output_dir.resolve();MANIFEST=args.source_manifest + OUT.mkdir(parents=True,exist_ok=True) + resource.setrlimit(resource.RLIMIT_AS,(500*1024*1024,500*1024*1024)) + start=time.monotonic();inv=invoice() + if args.static_only: + save('SOURCE-BINDINGS-v2.json',{'head':HEAD,'package_rows':inv['authentication']['package_rows']}) + digest=save('INVOICE-v2.json',inv) + print(json.dumps({'status':'PASS_STATIC_LITERAL_INVOICE','sha256':digest,'totals':inv['totals'],'ordinary':inv['ordinary'],'seconds':time.monotonic()-start}));return + if not (OUT/'INVOICE-v2.json').exists():save('INVOICE-v2.json',inv) + old=read(OUT/'INVOICE-v2.json');need(inv==old,'fresh literal invoice differs from frozen preflight') + constants={} + for n in ast.parse((REPO/PKG/'price.py').read_bytes()).body: + if isinstance(n,ast.Assign) and len(n.targets)==1 and isinstance(n.targets[0],ast.Name) and isinstance(n.value,ast.Call) and isinstance(n.value.func,ast.Name) and n.value.func.id=='Q' and len(n.value.args)==1 and isinstance(n.value.args[0],ast.Constant):constants[n.targets[0].id]=n.value.args[0].value + need(constants['KAPPA']=='.00302728823' and constants['TESTED']=='.00302728824','candidate typed endpoints differ') + bit=read(REPO/'research/query-thinned-controllers/RESULT.json')['ordinary_BIT'] + config={'model':MODEL,'tuple':{'power':1024,'cutoff':20,'floor':21,'tail_offset':'1/5','theta':'63/64','logarithm_power':1000},'kappa':constants['KAPPA'],'tested':constants['TESTED'],'reserve':'1/1000000000000','root_bracket':['.00302728824993','.00302728824994'],'ordinary_BIT':bit} + result=evaluate(inv['histograms']['productive'],inv['histograms']['paid'],config) + need(set(result['outer']['strict_checks'])==set(inv['source_keys']['strict']) and set(result['outer']['functional_checks'])==set(inv['source_keys']['functional']),'uncovered current-source outer predicate') + scientific_controls={} + for label,change in [('unearned16rank9_targets',16),('lost16rank9_targets',-16)]: + mutant=copy.deepcopy(inv['histograms']['productive']);mutant['9']+=change + try:evaluate(mutant,inv['histograms']['paid'],config) + except ValueError as exc:scientific_controls[label]=str(exc) + else:raise ValueError('accepted changed complete target profile: '+label) + for label,patch in [('unsupported_source_tuple',{'tuple':dict(config['tuple'],cutoff=22)}),('former_reserve_1e9',{'reserve':'1/1000000000'}),('insufficient_rounding_reserve_1e13',{'reserve':'1/10000000000000'})]: + try:evaluate(inv['histograms']['productive'],inv['histograms']['paid'],dict(config,**patch)) + except ValueError as exc:scientific_controls[label]=str(exc) + else:raise ValueError('accepted unsupported/unfunded numerical mutation: '+label) + result['changed_profile_controls']=scientific_controls + # j and H are computed by exact integer bisection in evaluate(), never + # read from the candidate RESULT or prior funding receipts. + result.update(schema='independent5398-exact-funding/1',candidate=inv['candidate'],config=config,invoice_sha256=sha(OUT/'INVOICE-v2.json'),invoice_source_bindings=inv['authentication'],ordinary=inv['ordinary'],source_predicates=inv['source_keys'],typed_endpoints=constants,engine_sha256=sha(HERE/'exact_engine.py'),reviewer_sha256=sha(Path(__file__)),gain_over_5387=str(Q(result['kappa'])-Q('.003026674765')),gain_over_5392=str(Q(result['kappa'])-Q('.00302725')),endpoint_funded=False,scientific_scope='Independent exact funding arithmetic and literal bill only. New direct caller/native-contact correctness and fresh expanded306bank precision remain separate prerequisite gates. Existing5392 profile equality does not admit the new caller. No unconditional theorem, selected promotion or proof-kernel acceptance.') + digest=save('FUNDING-v1.json',result) + print(json.dumps({'status':result['status'],'sha256':digest,'kappa':result['kappa'],'H':result['H'],'j':result['j'],'seconds':time.monotonic()-start,'endpoint_funded':False})) + +if __name__=='__main__':main() diff --git a/research/direct-backward-independent-validation/capsule/agents/precision/SOURCES.json b/research/direct-backward-independent-validation/capsule/agents/precision/SOURCES.json new file mode 100644 index 0000000000..282314216f --- /dev/null +++ b/research/direct-backward-independent-validation/capsule/agents/precision/SOURCES.json @@ -0,0 +1,194 @@ +{ + "candidate_head": "174fb211493b43a42210434083e9702b4fb7a2ce", + "framework_main": "1ec1119972c9aefe42525172d07b332fcff81cb4", + "rows": [ + { + "path": "swarm-next-gain-sol-high-20261024/repository/research/kappa-backward-controller-20261023/controller.py", + "sha256": 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preceding review/foundation, not candidate runtime import" + } + ] +} diff --git a/research/direct-backward-independent-validation/capsule/agents/precision/check_precision.py b/research/direct-backward-independent-validation/capsule/agents/precision/check_precision.py new file mode 100644 index 0000000000..3f6f389bbc --- /dev/null +++ b/research/direct-backward-independent-validation/capsule/agents/precision/check_precision.py @@ -0,0 +1,245 @@ +#!/usr/bin/env python3 +"""Independent bounded literal/precision/compiler screen for PR5398. + +No submitted Python is imported or executed. The all-n result is the written +induction in REPORT.md; finite checks below corroborate its inequalities. +Apache-2.0. Chris R/Clear1nsight with substantial OpenAI Codex assistance. +""" +from argparse import ArgumentParser +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha1, sha256 +from pathlib import Path +import gzip +import json +import resource +import time + +HERE = Path(__file__).resolve().parent +HEAD = '174fb211493b43a42210434083e9702b4fb7a2ce' +PACKAGE = 'research/kappa-backward-controller-20261023' + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def read(path): + b = path.read_bytes() + return json.loads(gzip.decompress(b) if path.suffix == '.gz' else b) + + +def scalar_allowance(g): + if g[0] in ('copy', 'clear'): + return 2 + q = Q(*g[3:]) if g[0] == 'add' else Q(*g[2:]) + a, b = abs(q.numerator), q.denominator + need(a and b & (b - 1) == 0, 'nonzero dyadic scalar') + if g[0] == 'scale': + need(a & (a - 1) == 0, 'dyadic unit SCALE') + return 2 * (abs(a.bit_length() - b.bit_length()) + int(q < 0)) + need(g[0] == 'add', 'known scalar opcode') + return 2 * (2 + a.bit_length() + a.bit_count() + b.bit_length() - 1) + + +def scalar_height(g): + if g[0] in ('copy', 'clear'): + return 0 + q = Q(*g[3:]) if g[0] == 'add' else Q(*g[2:]) + v = 1 + abs(q) if g[0] == 'add' else max(Q(1), abs(q)) + k = 0 + while v > 1: + v /= 2 + k += 1 + return k + q.denominator.bit_length() - 1 + + +def signed_swap(): + # a+=b; b-=a; a+=b implements (a,b) -> (b,-a). + a, b = [1, 0], [0, 1] + norms = [] + a = [x + y for x, y in zip(a, b)] + norms.append(max(sum(map(abs, a)), sum(map(abs, b)))) + b = [y - x for x, y in zip(a, b)] + norms.append(max(sum(map(abs, a)), sum(map(abs, b)))) + a = [x + y for x, y in zip(a, b)] + norms.append(max(sum(map(abs, a)), sum(map(abs, b)))) + need(a == [0, 1] and b == [-1, 0], 'exact signed rotation') + need(norms == [2, 2, 1], 'three-ADD transient amplification') + return norms + + +def gaussian_multiply(a, b): + return (a[0]*b[0]-a[1]*b[1], a[0]*b[1]+a[1]*b[0]) + + +def rejects(action, label): + try: + action() + except ValueError: + return label + raise ValueError('mutant accepted: '+label) + + +def main(): + start = time.monotonic() + resource.setrlimit(resource.RLIMIT_CPU, (15, 15)) + resource.setrlimit(resource.RLIMIT_AS, (128*1024**2, 128*1024**2)) + p = ArgumentParser() + p.add_argument('--root', '--repo', dest='repo', type=Path, default=HERE.parents[1]/'repository') + p.add_argument('--prior-root', type=Path, default=HERE.parents[2]/'swarm-execution-sol-high-20261024') + p.add_argument('--prior-word', type=Path) + p.add_argument('--prior-native', type=Path) + p.add_argument('--prior-witness', type=Path) + p.add_argument('--finite-precompilation', type=Path) + p.add_argument('--finite-template-closure', type=Path) + p.add_argument('--specialization', type=Path) + p.add_argument('--framework-proof', type=Path) + p.add_argument('--reuse-manifest', type=Path, default=HERE.parent/'provenance/5396-REUSE-MANIFEST.json') + p.add_argument('--sources', type=Path, default=HERE/'SOURCES.json') + p.add_argument('--out', type=Path, default=HERE/'CHECK.json') + args = p.parse_args() + manifest = read(args.sources) + need(manifest['candidate_head'] == HEAD, 'exact candidate pin') + overrides = { + 'repository/research/kappa-joint-relations-20261023/WORD.json.gz': args.prior_word, + 'repository/research/kappa-joint-relations-20261023/native.py': args.prior_native, + 'repository/research/kappa-joint-relations-20261023/WITNESS.json': args.prior_witness, + 'agents/applicability/FINITE-PRECOMPILATION.md': args.finite_precompilation, + 'agents/applicability/FINITE-TEMPLATE-CLOSURE.md': args.finite_template_closure, + 'agents/sources/pr5241/research/final4610-independent-admission/SPECIALIZATION.md': args.specialization, + 'agents/sources/pr5241/research/final4610-independent-admission/PROOF.md': args.framework_proof, + } + resolved = [] + for row in manifest['rows']: + rel = row['path'] + prefix = 'swarm-next-gain-sol-high-20261024/repository/' + oldprefix = 'swarm-execution-sol-high-20261024/' + if rel.startswith(prefix): + file = args.repo/rel[len(prefix):] + elif rel.startswith(oldprefix): + oldrel = rel[len(oldprefix):] + file = overrides.get(oldrel) or args.prior_root/oldrel + else: + need(rel.endswith('/provenance/5396-REUSE-MANIFEST.json'), 'known provenance mapping') + file = args.reuse_manifest + b = file.read_bytes() + need(sha256(b).hexdigest() == row['sha256'], 'source SHA256 '+rel) + need(sha1(b'blob '+str(len(b)).encode()+b'\0'+b).hexdigest() == row['git_blob'], 'source Git blob '+rel) + resolved.append(dict(path=rel, sha256=row['sha256'])) + pkg = args.repo/PACKAGE + priorpkg = args.prior_root/'repository/research/kappa-joint-relations-20261023' + for name in ('native.py', 'WITNESS.json'): + priorfile = (args.prior_native if name == 'native.py' else args.prior_witness) or priorpkg/name + need((pkg/name).read_bytes() == priorfile.read_bytes(), 'unchanged independently validated5383 '+name) + priorword = args.prior_word or priorpkg/'WORD.json.gz' + word = read(priorword) + need(sha256(gzip.decompress(priorword.read_bytes())).hexdigest() == + '2aee5e997df99726fc763e510d9cb69fbe4f86114dc8d2cd33ad26c6c462a21d', 'source word payload') + back = word['programs']['backward'] + owned = {tuple(r) for r in word['owned']['backward']} + need(len(owned) == 17 and ('L', 0) not in owned, 'seventeen owners, borrowed main remains borrowed') + for e in back: + if e[0] == 'scalar' and e[1][0] in ('clear', 'copy'): + need(tuple(e[1][1]) in owned, 'only owned destructive targets') + local_scalar = sum(scalar_allowance(e[1]) for e in back if e[0] == 'scalar') + height = sum(scalar_height(e[1]) for e in back if e[0] == 'scalar') + need(local_scalar == 158744 and height == 29183, 'fresh local scalar allowance and height') + ctl = read(pkg/'CONTROLLER.json') + source_ctl = read(args.repo/'research/joint-helper-lattice/CONTROLLER.json') + expected, sites = [], [] + for i, e in enumerate(source_ctl['physical_events']): + if e[0] == 'LOCAL' and e[3] is False: + _, stage, pair, _ = e + x, y = 2*pair, 2*pair+1 + sites.append(dict(source_index=i, stage=stage, pair=pair)) + expected += [['SIGNED_SWAP', y, x], ['Q_POWER', x, 2], ['LOCAL', stage, pair, True], + ['SIGNED_SWAP', x, y], ['Q_POWER', y, -2]] + else: + expected.append(e) + need(ctl['physical_events'] == expected and ctl['wrapper_sites'] == sites, 'fresh literal direct caller wrappers') + need([s['stage'] for s in sites] == [0, 32], 'both actual wrapper stages') + count = Counter(e[0] for e in expected) + need(count['LOCAL'] == 18 and all(e[3] is True for e in expected if e[0] == 'LOCAL'), 'eighteen unchanged backward suppliers') + source_count = Counter(e[0] for e in source_ctl['physical_events']) + need(count['SIGNED_SWAP']-source_count['SIGNED_SWAP'] == count['Q_POWER'] == 4 and + count['QUERY_SHEAR'] == 15, 'four new wrappers plus sixteen retained signed swaps') + # Q=aI+bX, X^2=I. Exact Gaussian arithmetic proves Q^2=X with phase+1. + a, b = (Q(1, 2), Q(1, 2)), (Q(1, 2), Q(-1, 2)) + aa, bb, ab = gaussian_multiply(a, a), gaussian_multiply(b, b), gaussian_multiply(a, b) + need(tuple(x+y for x,y in zip(aa,bb)) == (0,0) and tuple(2*x for x in ab) == (1,0), 'Q squared is phase+1 translation') + # conjugate(Q)=XQ: the coefficients of I and X are exchanged. + need((a[0],-a[1]) == b and (b[0],-b[1]) == a, 'signed helper conjugation absorbed in monomial adapter') + norms = signed_swap() + raw_local_banks = count['LOCAL']*len(owned) + need(raw_local_banks == 306, 'new complete simultaneous LOCAL banks') + rho, k, tested = Q(1,10**12), Q('.00302728823'), Q('.00302728824') + gap = (tested-k)/7 + j, H = 55099, 38569300000000000 + need(gap == Q(1,700000000000) and H == j*gap.denominator, 'fresh exact compiler grid') + need((H+1)**1000 < 2**j, 'fresh winning compiler comparison') + need((gap.denominator*(j-1)+1)**1000 >= 2**(j-1), 'fresh preceding compiler grid fails') + normalized = 1/(1+1024*rho)+Q(4,2**32) + need(normalized < 1 and 1/(1+1024*Q(1,10**13))+Q(4,2**32) > 1, 'funded reserve and rejecting control') + need(20**64 < 21**63 and Q(97,100)**128 < Q(1,16), 'strict split and tail-block guards') + need(4*Q(97,100)**1024 < Q(4,2**32), 'both conservative tail powers') + need(2*20**(1024*64) <= 145**(1024*63), 'shifted-exit rank capacity') + need(H > 8*1024 and 1000*gap > Q(1,H+1), 'initial rank and eventual logarithmic derivative') + # The all-n proof is algebraic. These exact checks are sanity controls, + # with no astronomical F(n) or N instantiated. + strictified_log_bound = 2*(82*1024+10+2*8192)+6+3*8193 + need(strictified_log_bound == 225309 and strictified_log_bound < 262144, 'fresh strictified unit majorant') + for n in range(1,1001): + need(16*(n+1)**2 >= 9*n+20, 'universal exponent inequality probe') + proof_polynomial = [16,23,-4] + need(sum(proof_polynomial) == 35 and proof_polynomial[0] > 0 and proof_polynomial[1] > 0, + 'positive increasing induction polynomial on n>=1') + arithmetic = read(pkg/'RESULT.json')['arithmetic'] + need(arithmetic['compiler']['H'] == H and arithmetic['compiler']['integer_test_exponent'] == j, + 'independent result compared to submitted receipt only after computation') + need(Q(arithmetic['strictification']['normalized_paid_upper']) == normalized, 'normalized receipt comparison') + need(arithmetic['nonrecursive']['raw_scalar_upper'] == 181586816, 'separate invoice raw cap binding') + rejected = [ + rejects(lambda: need(('L',0) in owned, 'borrowed erase'), 'borrowed_erase'), + rejects(lambda: need(18 >= raw_local_banks, 'missing live banks'), 'one_bank_per_depth'), + rejects(lambda: need(274 >= raw_local_banks, 'stale LOCAL banks'), 'unchanged_274_bank_cap'), + rejects(lambda: need(1 >= max(norms), 'swap prefix underfunded'), 'completed_swap_norm_for_prefix'), + rejects(lambda: need(30 >= 262144, 'raw cap is not expanded stock'), 'raw_1e9_expanded_cap'), + rejects(lambda: need(1/(1+1024*Q(1,10**13))+Q(4,2**32) < 1, 'rounding reserve underfunded'), 'insufficient_reserve'), + rejects(lambda: need((gap.denominator*(j-1)+1)**1000 < 2**(j-1), 'preceding grid insufficient'), 'preceding_compiler_grid'), + ] + result = dict(schema='5398-precision/1', status='PASS_SCOPED_DIRECT_CALLER_PRECISION_STOCK_COMPILER', + candidate_head=HEAD, source_bindings=len(resolved), + source_manifest_sha256=sha256(args.sources.read_bytes()).hexdigest(), + retained_5383_supplier=True, source_word_payload_sha256='2aee5e997df99726fc763e510d9cb69fbe4f86114dc8d2cd33ad26c6c462a21d', + backward_scalar_allowance=local_scalar, backward_scalar_height=height, + full_backward_calls=18, local_owned_banks=17, raw_LOCAL_owned_banks=raw_local_banks, + signed_swap_three_ADD_prefix_sup_norms=norms, signed_swap_total=count['SIGNED_SWAP'], + signed_swap_new=count['SIGNED_SWAP']-source_count['SIGNED_SWAP'], translation_phase=1, + conjugate_gaussian_is_monomial_times_positive_gaussian=True, + helper_full_signed_two_sided_factorization_required=True, + compiler=dict(H=H,j=j,gap=str(gap),tested=str(tested),kappa=str(k),reserve=str(rho), + normalized_paid_upper=str(normalized),remaining_rounding_margin=str(1-normalized)), + expanded=dict(unit_bound='D0=2^262144',unit_log_bound=225309, + recursion='F(0)=D0; X_n=(n+1)*(D0+1)*(F(n-1)+1); F(n)=X_n^(16*(n+1)^2)', + bound='M=F(2^38569300000000000)',counts=['W','P','U','O','R','G'], + all_n_proof='REPORT.md; strong induction, not the finite probes', + numerical_majorant_materialized=False,raw_cap_used_as_expanded_stock=False), + precision=dict(C1=1,constants='Zbar=2M; Ebar=64*(Zbar+N+2M+1)^3; Bbar=M+Ebar; C0bar=32*N*Bbar^2', + arbitrary_interval_recurrence='Jamp(e)<=2*Jamp(floor(e/N))+Pbar*floor(e/N)+Ebar', + intermediate_swap_factor_paid=True), + stock=dict(complex='[W*(O+1)]^Dord(d)',simultaneous='S_complex*S_BIT*every additional independent stock', + all_suspended_owners_distinct=True,owned_productive_credit=False,BIT_atom='1/250'), + controls=dict(kind='algebraic_underfunding_and_grammar_sentinels_not_mutated_circuit_semantic_replays', + rejected=rejected, count=len(rejected)), + assumptions=['native_all_columns','owned_erasure','compiler','precision_tape','analytic_recovery'], + complete_conditional_admission=False, independent_interval_or_native_replay=False, + seconds=time.monotonic()-start, max_rss_kib=resource.getrusage(resource.RUSAGE_SELF).ru_maxrss, + scope='Fresh literal/scalar/guard checks plus written constructive all-n closure; independent caller physical/phase/invoice and numerical moment/outer gates remain separate.') + args.out.write_text(json.dumps(result,indent=2)+'\n') + print(json.dumps(dict(status=result['status'],seconds=result['seconds'],raw_LOCAL_owned_banks=raw_local_banks))) + + +if __name__ == '__main__': + main() diff --git a/research/direct-backward-independent-validation/capsule/expected/FUNDING-v1.json b/research/direct-backward-independent-validation/capsule/expected/FUNDING-v1.json new file mode 100644 index 0000000000..1b7c9bf70c --- /dev/null +++ b/research/direct-backward-independent-validation/capsule/expected/FUNDING-v1.json @@ -0,0 +1,557 @@ +{ + "H": 38569300000000000, + "N": "2^38569300000000000", + "assumptions": [ + "native_all_columns", + "owned_erasure", + "compiler", + "precision_tape", + "analytic_recovery" + ], + "candidate": { + "head": "174fb211493b43a42210434083e9702b4fb7a2ce", + "package": "research/kappa-backward-controller-20261023" + }, + "capacity": { + "eta": true, + "height_domain": true, + "height_success": true, + "initial_range": true, + "normalized_paid_upper": true, + "preceding_grid_fails": true, + "shifted_exits": true, + "split": true, + "tail_block": true, + "total_tails": true + }, + "changed_profile_controls": { + "former_reserve_1e9": "unfunded reserve", + "insufficient_rounding_reserve_1e13": "compiler capacity failure", + "lost16rank9_targets": "strict root bracket fails", + "unearned16rank9_targets": "strict root bracket fails", + "unsupported_source_tuple": "OUTSIDE_PROVED_DOMAIN: tuple" + }, + "completion_strict_slack": "97179323/1048576001073741824", + "config": { + "kappa": ".00302728823", + "model": "selected-mixed-target-p16-completion1024-v1", + "ordinary_BIT": { + "admitted": "17/5000", + "after_cover": "69/20000", + "atom": "1/250", + "before_cover": "3459/1000000", + "ordinary_saving": "8590884599/2500000000000", + "prime_rule": "odd q > 2^26*N^5 avoiding all fixed denominators and rank witnesses" + }, + "reserve": "1/1000000000000", + "root_bracket": [ + ".00302728824993", + ".00302728824994" + ], + "tested": ".00302728824", + "tuple": { + "cutoff": 20, + "floor": 21, + "logarithm_power": 1000, + "power": 1024, + "tail_offset": "1/5", + "theta": "63/64" + } + }, + "controls": { + "closed_epsilon": [ + "epsilon_below_one", + "global_gamma_power_slack", + "actual_logarithmic_gamma_guard", + "source_axis_superpolynomial", + "gaussian_above_main", + "new_semantic_guard_with_C1_one" + ], + "closed_uniform": [ + "new_complex_uniform_saving_above_b" + ], + "excess_reserve": true, + "group_full_dimension": [ + "group_below_dimension", + "group_key_fits_record", + "membership_arithmetic_fits_record" + ], + "insufficient_reserve_completion": true, + "missing_layout": [ + "positive_layout_slack" + ], + "old_BIT": [ + "actual_bit_above_effective" + ], + "power128_tail_envelope": true, + "preceding_grid_rejected": true, + "raw_upper_has_negative_moment": true, + "tested_as_final_endpoint": [ + "main_transform_above_kappa", + "global_coordinate_router_above_kappa", + "fused_gaussian_above_kappa", + "group_bit_router_above_kappa", + "boundary_algebraic_matrix_above_kappa" + ] + }, + "endpoint_funded": false, + "engine_sha256": "9ef7ee4082631566eb7903c3e21e517ef58039dca2a47104a2279c459589eb47", + "eta": [ + "1988681901856543954159310389635307633654907355163/10000000000000000000000000000000000000000000000000000000", + "397736380371308790831862077927061526730981471033/2000000000000000000000000000000000000000000000000000000" + ], + "external_gate_requirements": [ + "independent literal physical gate", + "independent complete census/ordinary invoice", + "fresh finite-template precision/stock applicability", + "source provenance/capsule", + "registered cold replay before public admission" + ], + "gain_over_5387": "122693/200000000000", + "gain_over_5392": "3823/100000000000", + "gain_over_independent_5377": "493823/100000000000", + 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Common1000/group reserved for source9axis recipes only; compiler matchers need their own finite fold.", + "wrapper_allowance": 459648 + }, + "ordinary_BIT": { + "admitted": "17/5000", + "admitted_above_tested": "4658897/12500000000", + "after_cover": "69/20000", + "atom": "1/250", + "conversion_slack": "90884599/2500000000000", + "ordinary_saving": "8590884599/2500000000000", + "stock_slack": "2481409115401/2500000000000" + }, + "outer": { + "functional_checks": { + "actual_new_BIT_stock_sublinear": "174299999999253/175000000000000", + "fixed_halo_explicit_metadata_branch": "13475000000001/175000000000", + "new_BIT_row_stock_sublinear_in_active_group": "697899999997009/700000000000000", + "new_semantic_group_guard": "3/700000000000" + }, + "functional_count": 4, + "margins": { + "boundary_algebraic_matrix": "370842808874470224559/122500000000000000000000", + "fused_gaussian": "370842808873410673677/122500000000000000000000", + "global_coordinate_router": "423820353/140000000000", + "group_bit_router": "296674247238728538941/98000000000000000000000", + "group_scans": "349999999999/350000000000", + "main_transform": "370842808699470224559/122500000000000000000000", + "microbox_face_corrections": "13475000000001/175000000000", + "polynomial_products": "699999999999/700000000000", + "sparse_union_movement": "50136467808874470224559/122500000000000000000000" + }, + "minimum_functional_slack": "3/700000000000", + "minimum_strict_slack": "1/7000000000000", + "parameters": { + "a": "423820353/140000000000", + "b": "1059550883/350000000000", + "beta": "699999999997/700000000000", + "bit_atom": "1/250", + "bit_saving": "17/5000", + "complex_uniform_saving": "2119101767/700000000000", + "d": "1/700000000000", + "epsilon": "699999999999/700000000000", + "kappa": "302728823/100000000000", + "layout": "1/700000000000", + "q": "529775441/175000000000", + "r0": "1/7000000000000", + "stop": "1/700000000000", + "tested_saving": "37841103/12500000000" + }, + "strict_checks": { + "actual_bit_above_effective": "52179647/140000000000", + "actual_logarithmic_gamma_guard": "1/700000000000", + "actual_logarithmic_group_guard": "11113532191563029775441/61250000000000000000000", + "alpha_logarithm_absorption": "1/7000000000000", + "boundary_algebraic_matrix_above_kappa": "699470224559/122500000000000000000000", + "cap_above_band": "50136467808699470224559/122500000000000000000000", + "cap_below_cell": "11113532191125529775441/122500000000000000000000", + "cap_below_phase_cell_power": "133613532191300529775441/122500000000000000000000", + "complex_above_effective": "1/700000000000", + "complex_below_one_over_32": "9877949117/350000000000", + "complex_endpoint": "1/350000000000", + "epsilon_below_one": "1/700000000000", + "epsilon_positive": "699999999999/700000000000", + "fine_prime_halo_umbrella": "7/2", + "fused_gaussian_above_kappa": "698410673677/122500000000000000000000", + "gaussian_above_main": "86970224559/61250000000000000000000", + "global_coordinate_router_above_kappa": "1/175000000000", + "global_gamma_power_slack": "9/7000000000000", + "group_below_dimension": "1/350000000000", + "group_bit_router_above_kappa": "698728538941/98000000000000000000000", + "group_gauge_power_slack": "11113532191554279775441/61250000000000000000000", + "group_key_fits_record": "1/350000000000", + "group_positive": "699999999997/700000000000", + "group_scans_above_kappa": "697880898237/700000000000", + "halo_covers_generic_inverse_radius": "5", + "improvement_over_user_baseline": "648158905400418148631/500000000000000000000000", + "lambda_above_internal": "1/1400000000000", + "lambda_above_sigma": "3/1400000000000", + "lambda_above_tau": "1/1400000000000", + "lambda_prime_above_lambda": "1/1400000000000", + "lambda_prime_above_leaf": "698940449117/245000000000000000000000", + "leaf_saving_above_effective": "348940449117/245000000000000000000000", + "main_transform_above_kappa": "524470224559/122500000000000000000000", + "membership_arithmetic_fits_record": "1/700000000000", + "microbox_face_corrections_above_kappa": "53897880898243/700000000000", + "microbox_halo_volume": "55300000000003/700000000000", + "new_complex_uniform_saving_above_b": "1/700000000000", + "new_semantic_guard_with_C1_one": "1/700000000000", + "polynomial_products_above_kappa": "348940449119/350000000000", + "positive_layout_slack": "1/700000000000", + "q_below_effective": "1/700000000000", + "q_below_internal": "1/700000000000", + "q_below_leaf": "698940449117/245000000000000000000000", + "q_positive": "529775441/175000000000", + "short_record_fallback": "348940449117/350000000000", + "source_axis_superpolynomial": "1/700000000000", + "sparse_union_movement_above_kappa": "49765625000699470224559/122500000000000000000000", + "stop_below_one": "699999999999/700000000000", + "stop_positive": "1/700000000000", + "strassen_integer_power_gap": "1951441519231", + "support_router_span": "3/700000000000", + "theta_positive_polynomial_power": "2", + "union_header_fits_record": "3/700000000000", + "union_tag_work_per_visit_fits_record": "3/700000000000" + }, + "strict_count": 54 + }, + "paid": { + "1": 41154, + "16": 448, + "2": 7416, + "24": 448, + "3": 9180, + "32": 448, + "4": 2286, + "40": 448, + "48": 448, + "5": 720, + "56": 448, + "64": 448, + "72": 224 + }, + "paid_count": 64116, + "productive_count": 10784, + "rank_mass_surplus": 752, + "ratios": { + "alpha": [ + "9999999999896081368455975420121411368034585745108937549/10000000000000000000000000000000000000000000000000000000", + "4999999999948040684227987710060705684017292872554469059/5000000000000000000000000000000000000000000000000000000" + ], + "delta": [ + "297130890612779792166888219295221641686408682444154693/312500000000000000000000000000000000000000000000000000", + "9508188499608953349340423017447092533965077838212950501/10000000000000000000000000000000000000000000000000000000" + ], + "gamma": [ + "1914125922687898432775397589046349650890572450248263387/2000000000000000000000000000000000000000000000000000000", + "239265740335987304096924698630793706361321556281032941/250000000000000000000000000000000000000000000000000000" + ] + }, + "reserve": "1/1000000000000", + "reserve_strict_slack": "46959315772012289939294315982707127445530941/5000000000000000000000000000000000000000000000000000000", + "reviewer_sha256": "38a9143de82ec504b8dd8f1050e9e99bdec56e8af1a3b3c881ed0e86360cd837", + "root": { + "bracket": [ + "302728824993/100000000000000", + "151364412497/50000000000000" + ], + "decreasing_domain": [ + "0", + "1/20" + ], + "derivative_upper": "-488574633873797629325887094057628159044930722792328443378489/2500000000000000000000000000000000000000000000000000000", + "remaining_domain": [ + "1/20", + "1" + ], + "remaining_moment_upper": "-34089066070491587384150451659819727093287680864599145503219/5000000000000000000000000000000000000000000000000000000", + "scope": "necessary fixed-profile moment ceiling on 0 -> i^(a+q(x)) |A*x xor b>, +q(x) = sum_i alpha_i*x_i + 2*sum_(i A*x_j xor b for every j, +phase = a*f + sum_(j=1..f) q(x_j) (mod4). +``` + +Apply the finite row-addition list to the corresponding pair of complete f-axis slots, and use the pointwise residue above. Each selected slot is a full range; arbitrary intervening, preceding and following spectator fields remain present. The temporary complete compact fields are returned by each addition. Thus the lift is exactly m tensor-powered f, acting as identity on the other address fields. It uses one fixed list of primitive **types/operations**, rather than f separately allocated tapes. Its per-record descriptor arithmetic is polynomial in the same selected address bound, and the number of work tapes stays fixed for the template. + +For a recorded positive-rank recipe, source equality is the ordered product `right.then(C_r).then(left)`. Tensoring this product gives `right_f.then(C_(r*f)).then(left_f)` after the fixed coordinate reordering. This is one ordinary positive rank-r*f child on the actual owner's full stream, with its input and output monomials independently retained. Inverse orientation and Pauli corrections are included by the actual signed recipes. No identity distributes a tensor power over a matrix sum. + +For the scalar word itself, use selected #4359's free-word substitution theorem: replace each warp generator by its f-column lift while leaving ADD/SCALE coefficients and chronology unchanged. This is an algebra homomorphism from the noncommuting free-word algebra; hence the already checked arbitrary-input word identity survives. The scalar program is not itself tensor-powered. Keeping a single constant phase a instead of a*f would violate the lift; a negative control explicitly distinguishes that mutation at f=2. + +The ideal algebraic lift holds for every positive f. Its physical tariff applies only in the selected source domain: f<=p, A=O(p), K/log p tending to infinity, and a superpolynomial record fiber. In the actual layer f<=e<=floor(b_in^epsilon) and p=6*b_in eventually. No tariff is extrapolated to arbitrary independent f,p/geometry. The compact-control parameter hypotheses are unchanged: f slots, complete dirty reservations, `A=O(p)`, record fiber beyond fixed powers, and the same selected movement exponent. The final uniform template may have much larger fixed dimensions and operation counts. That changes constants and thresholds through section6 below, rather than changing these quantifiers or creating a new tape per coordinate. + +## 4. Exhaustive family/owner specialization + +The executable source census is over the actual final payload, not its proposed histogram. It classifies every event in both21449-record orientations, and checks exact scalar coefficients/opcodes/chronology against the selected THREE-base word. Main charts on all224 persistent main owners are exact retained records. Every scalar target/source belongs to the632 declared persistent owners or the one declared owned C0. Clear and overwrite COPY target only C0; ADD arguments are distinct owners; no new borrowed owner, alias or productive C0 is introduced. + +| Actual family | Membership/coverage | Selected physical interpretation | +| --- | --- | --- | +| 180 signed warp classes,240 occurrences | Each actual G is invertible; both signed recipes have rank0;800new monomial records cover this and the changed families below | Fixed affine binary permutation and unit quadratic phase from section2; same all-f native generator | +| 3290 borrowed climbs per orientation | Actual source/target bases strictly nested, correct current owner/frame and rank | The selected arbitrary-U-subset-V factorization: two rank-zero adapters and one positive rank-r*f child | +| Eight center calls per orientation | Actual nested comparable bases, owned C0 only, all eight rank8 jobs billed | Same positive child plus signed adapters; no productive credit, no allocation of a new arbitrary input | +| 408 helper endpoints | Actual strict nested entrance/exit, profile `{4:28,7:7,8:47,9:326}` | Complete two-sided normal form on each distinct arbitrary input field; no internal scalar reframing shortcut | +| 448 main entrance/exit charts | Exact event equality with retained base main charts | Source-identical selected chart/axis interface, with its retained charge | +| 17453 scalar records per orientation | Exact old opcode/coefficient sequence, dyadic grammar and current-frame checks | Retained ADD, dyadic unit SCALE, owned COPY/CLEAR; identical scalar tariff | +| Ten phase labels | Fixed annotations, no new physical instruction | Existing scalar-word scope boundaries; not extra outputs or uncharged operators | + +Exact factorization equality and arbitrary-input endpoints are independently established by the admission dossier's native/phase replays, not by a syntactic schema. This module supplies the missing **physical class implication** for those exact factors. The new phase receipt covers180signedwarp classes,105newpaid pairs and5changedhelper pairs. The382 unchanged helpers are bound to the selected #4470 phase receipt through gain_acceptance's exact ordered-basis/owner lineage;26changed helpers use the new five-pair receipt. The independently replayed all2855paid-pair factorization module supplies the full actual paid-pair coverage. These coverage claims remain separate from this module's fresh class/census checks. + +For owned return, the local word retains one physical C0 and ends its C0 updates with a permitted erase. The existing arbitrary-input native proof establishes completed main/helper endpoints and C0 clearance. During product/compiler substitution, each suspended local occurrence receives its own center bank; all child inputs are distinct actual fields, even when values are correlated or one input is a parent's center. The child finishes and its adapters/role ordering return **before** the parent resumes. The parent clears only its own bank after its last use. Every such bank is excluded from productive W and included in full O. This is exactly the selected compiler ownership rule; no one-bank-per-depth reuse or undeclared initialized input is used. + +## 5. Finite raw tariffs in the selected unit + +The tariff unit here is a retained elementary scalar/movement/phase **record**, each realized with the selected physical primitive's asymptotic bound. It is not one literal tape instruction and does not suppress the f-dependent movement bound. Choose the same common upper unit for the fixed primitive alphabet as in the selected finite-word accounting. Each new two-sided nine-axis recipe has at most342 elementary records, below the retained conservative1000-per-group allowance. Unchanged main charts retain their selected count/unit. The selected primitive implementation constants, record-paid setup, scans and repair remain paid in that common physical unit. Changing the finite catalogue does not require a new asymptotic movement assumption. + +The actual local route groups are + +``` +3298 paid jobs + 2*408 helper wrappers + 240 warps + 448 main charts + = 4802 groups, +4802*1000 = 4,802,000. +``` + +The source scalar allowance formula, reimplemented directly without importing its evaluator, gives158120 forward and158168 backward. Therefore + +``` +158168 + 4802000 = 4960168 < 10^7. +``` + +This is an instantiation of the selected raw-unit bound with a smaller changed paid count, not reuse of an old expanded compiler cap. The controller remains18full calls and15thin queries, with the exact retained physical-event and boundary programs. The complete source raw bound is + +``` +18*10^7 + 15*1792 + + 32*112*(#physical_events + #left_boundary_program + #right_boundary_program) + = 181098496 < 10^9. +``` + +Each thin query's paid rank-one request, owned copy/add/erase and inverse orientation remain in the source invoice. Idle jobs, main normalizations, inherited controller geometry and actual exact phase bills remain charged. No local or controller charge is credited as a new productive output. These numerical bounds concern **raw** supplier records only; they are not the expanded uniform word's operation count, storage or literal physical runtime. + +## 6. Expanded compiler, precision and tape constants + +Apply the selected chronological product, same-owner paid completion, disjoint splitting and integer finite compiler to this now-specialized raw program. The algorithms are finite and only instantiate the same grammar. Their matching uses complete job endpoints and restores adapters, and their owner allocation is the rule just proved applicable. No new movement species occurs when a fixed matcher has a larger fixed rank: binary basis/coordinate permutations have the same finite elimination construction, now with a larger fixed list. + +Let W,P,O be the actual final productive width, paid rank-one count and full owned-bank allocation; let R count the full native/movement/normalizer records, including product, completion, split and compiler routes. Let G be their fresh dyadic coefficient/phase allowance, computed by summing the actual scalar allowances (plus the source's conservative non-scalar charge). These are finite computable integers of the new expanded template. They are fixed before multiplication input size varies. A record-count overestimate and one owned bank per relevant occurrence suffice; no practical materialization or old p3 numerical count is needed. + +Use the **new** values in the selected semantic prescription: + +``` +Z=W+O, +E=64*(Z+N+P+G+1)^3, +B=P+E, +C0=32*N*B^2. +``` + +The selected completed-child argument gives `A(e)<=A(floor(e/N))+P*floor(e/N)+E`, hence `A(e)<=2B*e`. Monomial permutations/unit phases add no coefficient height but do retain their execution/descriptor costs. The new C0 determines a new eventual fine-grid threshold. The compact row reserve, full simultaneous stock products, depth-first parking, fixed tape inventory and polynomial setup degrees also use the new W,P,O,R,N and selected formulas. Fixed enlarged degrees/counts are absorbed by the same retained superpolynomial record fiber and strict outer epsilon<1 after increasing the threshold. In particular, neither raw10^9 nor selected p3/p16 reserve constants stand in for these expanded values. + +Thus P2–P4 can consume a genuine new finite instance of H_selected's grammar and precision/stock/tape prescriptions. This note does not independently prove the historical native movement/repair or outer analytic/recovery stack. Those are exactly the assumptions already retained by selected #4470, with no additional candidate-specific implementation assumption. + +## 7. Conclusion and exact limits + +Given H_selected and the source-bound exact semantic/phase endpoints supplied by the independent native dossier, the final catalogue has permitted explicit all-f realizations, legal actual-owner return, finite raw tariffs and the selected expanded-constant substitution. No extra primitive or changed movement exponent is required. P1 is therefore a **consequence** of H_selected for this instance. It need not be restated as a new hypothesis “the new recipes implement.” + +`checks/specialization.py` runs through the master verifier and its source-authenticated `--repo` working-byte loader; it never substitutes clean Git blobs for dirty inputs. Its new actual catalogue has800monomials with at most83 elementary records each, compared with the uniform171 bound. It also checks1692selected monomial records by the identical schema, exhaustive event/role/rank/scalar census in both orientations, helper geometry, retained main charts, the4802route grouping and raw bounds. Controls reject singular maps, non-Z4 absolute phases, borrowed clear, unpaid rank changes, non-dyadic scalars and an unlifted f=2 global phase. Exact phase/operator equality is intentionally supplied by the separate phase/native verification rather than inferred from membership. + +Credits remain with Cao Yifan/intqwq (#4610), Cinna Davis (#4470/#4416/controller/helper lineage), zxv (#4359/native/compiler/semantic precision), icekylinx and Dugongue (general Clifford/transported frames), Jacob Alan Sussman (mixed integer compiler), and all retained physical/BIT/geometry/analytic contributors. This new specialization/proof/check uses substantial OpenAI assistance. It is a scoped conditional AI verification contribution, not an unconditional multiplication theorem or independent human/kernel acceptance. diff --git a/research/direct-backward-independent-validation/capsule/repository/research/higher-moment-strictification/verify.py b/research/direct-backward-independent-validation/capsule/repository/research/higher-moment-strictification/verify.py new file mode 100644 index 0000000000..4b24a50961 --- /dev/null +++ b/research/direct-backward-independent-validation/capsule/repository/research/higher-moment-strictification/verify.py @@ -0,0 +1,421 @@ +#!/usr/bin/env python3 +"""Higher-moment strictification and a polynomial-logarithm compiler bound. + +New arithmetic is independent of predecessor interval code. The unchanged +invoice replay and two outer ledgers are credited, byte-pinned oracles. +zxv with substantial OpenAI Codex assistance. Apache-2.0. +""" +import argparse +import ast +from collections import Counter +from contextlib import redirect_stdout +from fractions import Fraction as Q +from functools import lru_cache +from hashlib import sha256, sha1 +import io +import json +from pathlib import Path + +HERE = Path(__file__).resolve().parent +GRID = 2**192 +C = Q('0.00268648') +KAPPA = Q('0.00268647') +T = {5:420, 6:270, 7:840, 8:1395, 9:3195, + 25:448, 41:448, 57:448, 121:224} +P = {1:37305, 2:10695, 3:3360, 4:1530, 5:300, + 8:1464, 16:448, 32:448, 48:448} + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def down(x): + return Q((x*GRID).__floor__(), GRID) + + +def up(x): + return Q(-((-x*GRID).__floor__()), GRID) + + +def rounded(lo, hi): + return down(lo), up(hi) + + +def mul(a, b): + products = [x*y for x in a for y in b] + return rounded(min(products), max(products)) + + +def scale(a, x): + return mul(a, (x, x)) + + +def divide(a, b): + need(b[0] > 0, 'positive interval denominator') + return mul(a, rounded(1/b[1], 1/b[0])) + + +@lru_cache(None) +def log_bounds(n): + """Exact atanh series, binary reduction; round only the final interval.""" + need(isinstance(n, int) and n >= 1, 'positive integer logarithm') + + def series(x): + u = (x-1)/(x+1) + term, total = u, Q(0) + for j in range(80): + total += 2*term/(2*j+1) + term *= u*u + tail = 2*term/(161*(1-u*u)) + return total, total+tail + + k = n.bit_length()-1 + a, b = series(Q(2)) + c, d = series(Q(n, 2**k)) + return rounded(k*a+c, k*b+d) + + +def exp_point(x): + """Outward fixed-point Taylor enclosure, with binary scaling/squaring.""" + need(abs(x) < 16, 'bounded exponential argument') + if x < 0: + a, b = exp_point(-x) + return rounded(1/b, 1/a) + divisions = 0 + while x > Q(1, 2): + x /= 2 + divisions += 1 + term = total = (Q(1), Q(1)) + for j in range(1, 65): + term = scale(term, x/j) + total = rounded(total[0]+term[0], total[1]+term[1]) + following = scale(term, x/65) + # Every remaining ratio is <= 1/132. Twice the next term is safe. + result = rounded(total[0], total[1]+2*following[1]) + for _ in range(divisions): + result = mul(result, result) + return result + + +def exp_interval(a): + return exp_point(a[0])[0], exp_point(a[1])[1] + + +@lru_cache(None) +def power(n, exponent): + return exp_interval(scale(log_bounds(n), exponent)) + + +def moment(histogram, exponent): + low = high = Q(0) + for n, count in histogram.items(): + a, b = power(n, exponent) + low += count*a + high += count*b + return rounded(low, high) + + +def display(a): + unit = 10**30 + + def fixed(n): + sign = '-' if n < 0 else '' + s = str(abs(n)).rjust(31, '0') + return sign+s[:-30]+'.'+s[-30:] + + return {'lower': fixed((a[0]*unit).__floor__()), + 'upper': fixed(-((-a[1]*unit).__floor__()))} + + +def encoded(x): + if isinstance(x, Q): + return str(x) + if isinstance(x, dict): + return {str(k): encoded(v) for k, v in x.items()} + if isinstance(x, (list, tuple)): + return [encoded(v) for v in x] + return x + + +def source_environment(path): + env = {'__file__': str(path), '__name__': 'pinned_source_oracle'} + exec(compile(path.read_bytes(), str(path), 'exec'), env) + return env + + +def authenticate(): + result = {} + for row in json.loads((HERE/'VENDOR.json').read_text())['files']: + path = HERE/'vendor'/Path(row['path']).relative_to( + 'research/higher-moment-strictification/vendor') + digest = sha256(path.read_bytes()).hexdigest() + need(digest == row['sha256'], 'changed source: '+row['path']) + raw = path.read_bytes() + need(sha1(b'blob '+str(len(raw)).encode()+b'\0'+raw).hexdigest() + == row['git_blob'], 'changed Git source blob') + result[row['path']] = digest + return result + + +def invoice_oracle(): + """Run #4426 unchanged, rebinding only its two file-location globals.""" + path = HERE/'vendor/invoice-review/verify.py' + env = source_environment(path) + env.update(ROOT=path.parent, PHASES='DATA-PHASES.json') + output = io.StringIO() + with redirect_stdout(output): + env['main']() + result = json.loads(output.getvalue()) + need(result['status'] == 'PASS_PR4416_INVOICE_REBUILD', 'source invoice oracle') + need({int(k): v for k, v in result['targets'].items()} == T + and {int(k): v for k, v in result['paid'].items()} == P, + 'exact literal-word invoice') + return result + + +def tail_certificate(v=150, cutoff=10, floor=15, u=Q(3, 10)): + t = 1-C + need(v >= 1 and 1 < cutoff < floor < 121, 'strict finite ranks') + need(t+u >= 1, 'tail moment exponent at least one') + target, paid = moment(T, t), moment(P, t) + alpha = divide(paid, target) + gamma = divide(moment(P, t+u), mul(power(cutoff, u), target)) + delta = divide((Q(sum(T.values())*floor),)*2, + mul(power(cutoff, C), target)) + limits = (1-Q(1, 10**8), Q(181, 200), Q(439, 500)) + for name, bounds, limit in zip(('alpha', 'gamma', 'delta'), + (alpha, gamma, delta), limits): + need(0 < bounds[0] <= bounds[1] < limit < 1, name+' certified limit') + a, g, d = limits + bound = 1/(1+v*(1-a))+2*g**v+2*d**v + need(bound < 1, 'complete charged normalized moment') + old_gamma = divide((Q(sum(k*n for k, n in P.items())),)*2, + mul(power(cutoff, C), target)) + old_lower = alpha[0]**v+2*old_gamma[0]**v + need(old_lower > 1, 'rank-one-tail estimate fails at this tensor power') + return {'tensor_power': v, 'cutoff_base': cutoff, 'floor_base': floor, + 'paid_moment_exponent': t+u, 'tail_offset_u': u, + 'tested_saving': C, 'alpha': display(alpha), 'gamma': display(gamma), + 'delta': display(delta), 'rational_upper_limits': limits, + 'normalized_paid_upper': bound, 'strict_moment_gap': display((1-bound,)*2), + 'old_rank_one_gamma': display(old_gamma), + 'old_rank_one_bound_lower': display((old_lower, old_lower)), + 'ambient': '121^'+str(v), 'minimum_target': str(floor)+'^'+str(v), + 'maximum_paid': str(cutoff)+'^'+str(v), + 'productive_fields_before_uniform_compiler': '7688^'+str(v), + 'rank_one_surplus': '131723^'+str(v)+'-131115^'+str(v), + 'materialized_product_or_uniform_word': False} + + +def uniform_rank(v): + t, p, theta = 1-C, 13, Q(6, 7) + gap = (C-KAPPA)/7 + uniform_saving = C-gap + need(10**7 < 15**6, 'theta upper bound') + need(2*(10**v)**7 <= (121**v)**6, 'shifted logarithm inequality') + eta = scale(exp_interval(scale(log_bounds(121), -v*C)), t) + need(eta[0] > theta**p, 'exit contraction below complement capacity') + base = exp_interval(scale(log_bounds(121), v*C)) + need(base[1] < 2**p, 'entire ordinary base range fits') + # Integer grid: gap*H is integral, avoiding enormous rational powers. + step = gap.denominator + need(gap.numerator == 1, 'chosen rational gap grid') + + def passes(j): + H = step*j + return (H+1)**p < 2**j + + lo, hi = 1, 2 + while not passes(hi): + lo, hi = hi, 2*hi + while hi-lo > 1: + mid = (lo+hi)//2 + if passes(mid): + hi = mid + else: + lo = mid + H = step*hi + need(H > 7*v and passes(hi) and not passes(hi-1), 'final integer comparison') + need(eta[1] < theta**(p-1), 'one smaller logarithmic power fails') + return {'t': t, 'uniform_saving': uniform_saving, 'gap': gap, + 'logarithm_power': p, 'theta_upper': theta, 'eta': display(eta), + 'eta_minus_theta_to_p': display((eta[0]-theta**p, eta[1]-theta**p)), + 'm_to_saving': display(base), 'H': H, 'N': '2^'+str(H), + 'integer_test': {'left_base': H+1, 'left_exponent': p, + 'right_base': 2, 'right_exponent': hi}, + 'grid_step': step, 'previous_grid_point_rejected': True, + 'smaller_logarithmic_power_rejected': True} + + +def power_majorant_comparison(v, uniform_saving): + """Retain #4416's older power proof, changing only the new unit's ranks.""" + t, z, h = 1-C, 1-uniform_saving, Q(1, 7) + z0 = (t+z)/2 + delta = z0-t + B, debt = (4+7*h)*v, 1+7*v*(1-z0) + ratio = (delta*B+debt)/(h*delta) + H0 = -((-ratio.numerator)//ratio.denominator) + ratio = H0*(1-z0)/(z-z0) + H1 = ratio.numerator//ratio.denominator+1 + need(H0 >= 7*v and H0*h*delta >= delta*B+debt, 'power majorant threshold') + need((H0-1)*h*delta < delta*B+debt, 'previous power threshold rejected') + need(H1*(z-z0) > H0*(1-z0) >= (H1-1)*(z-z0), + 'strict power-majorant comparison and previous-rank control') + return {'H0': H0, 'H1': H1, 'N': '2^'+str(H1), 'theta_upper': 1-h, + 'scope': 'Tail transformation alone, retaining the older power majorant.'} + + +def outer_ledger(uniform_saving): + d = (C-KAPPA)/7 + params = {'kappa': KAPPA, 'tested_saving': C, + 'complex_uniform_saving': uniform_saving, 'b': KAPPA+5*d, + 'a': KAPPA+4*d, 'q': KAPPA+3*d, 'bit_saving': Q('0.0027'), + 'epsilon': 1-d, 'beta': 1-3*d, 'r0': d/10, + 'stop': d, 'layout': d, 'd': d} + env = source_environment(HERE/'vendor/outer_endpoint.py') + row = env['ledger'](params) + need(len(row['strict_checks']) == 54 and len(row['functional_checks']) == 3, + 'complete first outer ledger') + need(all(v > 0 for group in ('strict_checks', 'functional_checks') + for v in row[group].values()), 'all outer predicates') + frozen = json.loads((HERE/'vendor/p7-RESULT.json').read_text())['endpoint']['outer'] + need(encoded(row) == frozen, 'unchanged full p7 endpoint ledger') + parsed = ast.parse((HERE/'vendor/check_ledger.py').read_bytes()) + function = next(n for n in parsed.body + if isinstance(n, ast.FunctionDef) and n.name == 'ledger') + constants = [n for n in parsed.body if isinstance(n, ast.Assign) + and any(isinstance(t, ast.Name) and t.id.startswith('KAPPA_') + for t in n.targets)] + eps, beta, q, a = (params[k] for k in ('epsilon', 'beta', 'q', 'a')) + grid = 10**10 + backoff = Q((eps*q*grid).__floor__(), grid)-KAPPA + need(backoff > 0, 'strict derived oracle grid backoff') + oracle = {'Q': Q, 'R0': params['r0'], 'ZETA': Q(1, 10**8), + 'SLACK': d, 'STOP': d, 'FLOOR': grid, 'BACKOFF': backoff, + 'EPS': eps, 'BETA': beta, 'THETA_POWER': Q(2), + 'HALO_POWER': 48, 'CORE_POWER': 128, 'STRASSEN_TAU': Q(45, 16), + 'b': params['b'], 'q': q, 'a': a, 'bit': params['bit_saving'], + 'online': Q('0.001730970419199163702738'), + 'old': Q('0.001730970419199163702738')} + code = ast.fix_missing_locations(ast.Module(body=constants+[function], type_ignores=[])) + exec(compile(code, 'pinned 63-predicate ledger', 'exec'), oracle) + second = oracle['ledger']('higher_moment_smaller_ranks') + need(second['kappa'] == KAPPA and second['margins'] == row['margins'], + 'all nine rows match both ledgers') + need(len(second['strict_checks']) == 63 and + all(v > 0 for v in second['strict_checks'].values()), 'all 63 legacy predicates') + controls = {} + for name, updates in [('closed_epsilon', {'epsilon': Q(1)}), + ('missing_layout', {'layout': Q(0)}), + ('unfunded_kappa', {'kappa': C}), + ('closed_uniform_gap', {'complex_uniform_saving': params['b']}), + ('insufficient_BIT', {'bit_saving': Q('0.0023')})]: + bad = env['ledger'](dict(params, **updates)) + failed = sorted(k for k, v in bad['strict_checks'].items() if v <= 0) + need(failed, 'outer control rejected: '+name) + controls[name] = failed + for name, options in [('old_per_axis_scan', {'old_scan': True}), + ('group_equals_dimension', {'beta_': eps})]: + bad = oracle['ledger']('reject_'+name, **options) + failed = sorted(k for k, v in bad['strict_checks'].items() if v <= 0) + need(failed, 'legacy control rejected: '+name) + controls[name] = failed + return {'ledger': row, 'legacy_63_checks': second['strict_checks'], + 'legacy_grid': grid, 'legacy_backoff': backoff, + 'minimum_margin_minus_kappa': min(row['margins'].values())-KAPPA, + 'rejected_controls': controls} + + +def finite_controls(): + def tensor(histogram): + out = Counter() + for k, n in histogram.items(): + for h, b in histogram.items(): + out[k*h] += n*b + return out + + def split(histogram, cutoff): + out = Counter() + for k, n in histogram.items(): + q, r = divmod(k, cutoff) + out[cutoff] += q*n + if r: + out[r] += n + return +out + + target, paid = tensor({2:1, 5:1}), tensor({1:2, 4:1}) + padded, completion = Counter(), Counter() + for k, n in target.items(): + padded[max(k, 9)] += n + if k < 9: + completion[9-k] += n + final = split(paid+completion, 4) + mass = lambda x: sum(k*n for k, n in x.items()) + need(mass(padded)-mass(final) == 7**2-6**2 == 13, 'exact paid padding mass') + need(min(padded) > max(final), 'exact toy separation') + need(final == Counter({1:5, 4:9}), 'literal toy expanded inventory') + # t=1/2, sigma=3/4, R=100, J=1 refutes a sublinear tail extension. + invalid = power(100, Q(1, 2))[1]+2*power(100, Q(3, 4))[1] + need(invalid < 100, 'sublinear upper-tail moment cannot bound splitting') + return {'toy_targets': padded, 'toy_paid': final, 'rank_one_surplus': 13, + 'sublinear_tail_counterexample': {'R': 100, 'J': 1, 't': '1/2', + 'sigma': '3/4', 'actual_charge': 100, + 'invalid_upper': display((invalid, invalid))}} + + +def verify(): + sources = authenticate() + invoice = invoice_oracle() + tail = tail_certificate() + rank = uniform_rank(tail['tensor_power']) + endpoint = outer_ledger(rank['uniform_saving']) + controls = finite_controls() + rejected = [] + for name, updates, expected in [ + ('too_short_product', {'v': 100}, 'complete charged normalized moment'), + ('sublinear_tail', {'u': C/2}, 'tail moment exponent at least one'), + ('lost_separation', {'floor': 10}, 'strict finite ranks'), + ]: + try: + tail_certificate(**updates) + except ValueError as error: + need(str(error) == expected, 'wrong rejection: '+name) + rejected.append({'mutation': name, 'failed_at': str(error)}) + else: + raise ValueError('accepted mutation: '+name) + old = json.loads((HERE/'vendor/p7-RESULT.json').read_text())['endpoint']['compiler'] + return encoded({'schema': 'higher-moment-native-strictification/1', + 'status': 'PASS_HIGHER_MOMENT_STRICTIFICATION', 'kappa': KAPPA, + 'invoice_oracle': invoice, 'strictification': tail, + 'uniform_rank': rank, 'outer': endpoint, + 'tail_only_power_majorant': power_majorant_comparison( + tail['tensor_power'], rank['uniform_saving']), + 'finite_controls': controls, 'rejected_mutations': rejected, + 'predecessor_H': old['H1'], + 'rank_exponent_reduction_factor': Q(old['H1'], rank['H']), + 'tensor_power_reduction_factor': Q(6240, tail['tensor_power']), + 'source_sha256': sources, + 'verifier_sha256': sha256(Path(__file__).read_bytes()).hexdigest(), + 'scope': 'Conditional charged transformation and finite compiler rank. Native all-column, physical, analytic, precision, storage, fixed-tape and recovery premises remain inherited. No new kappa, selected frontier or practical word.'}) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--out', type=Path) + args = parser.parse_args() + result = verify() + if args.out: + need(not args.out.exists(), 'new output path required') + args.out.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + need(json.loads((HERE/'RESULT.json').read_text()) == result, 'changed saved receipt') + print(json.dumps({'status': result['status'], 'tensor_power': result['strictification']['tensor_power'], + 'uniform_rank': result['uniform_rank']['N'], + 'strict_moment_gap': result['strictification']['strict_moment_gap'], + 'kappa': result['kappa']})) + + +if __name__ == '__main__': + main() diff --git a/research/direct-backward-independent-validation/capsule/repository/research/joint-helper-lattice/CONTROLLER.json b/research/direct-backward-independent-validation/capsule/repository/research/joint-helper-lattice/CONTROLLER.json new 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b/research/direct-backward-independent-validation/capsule/repository/research/joint-helper-lattice/NATIVE.json.gz new file mode 100644 index 0000000000..0910f74138 Binary files /dev/null and b/research/direct-backward-independent-validation/capsule/repository/research/joint-helper-lattice/NATIVE.json.gz differ diff --git a/research/direct-backward-independent-validation/capsule/repository/research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json b/research/direct-backward-independent-validation/capsule/repository/research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json new file mode 100644 index 0000000000..d9a4f84211 --- /dev/null +++ b/research/direct-backward-independent-validation/capsule/repository/research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json @@ -0,0 +1 @@ +{"cover_correction":{"complete_small_cover_checks":[{"n":1,"nonzero_full_kernel_corrections":0,"orthogonal_matrices":1},{"n":2,"nonzero_full_kernel_corrections":0,"orthogonal_matrices":2},{"n":3,"nonzero_full_kernel_corrections":0,"orthogonal_matrices":6},{"n":4,"nonzero_full_kernel_corrections":24,"orthogonal_matrices":48},{"n":5,"nonzero_full_kernel_corrections":600,"orthogonal_matrices":720}],"formula":"delta(g)_i = (weight(row_i(g))-1)/2 mod 2; apply X_delta(g) to EVERY final live stream in cover class g.","mandatory":true,"reason":"P_g C_all P_g^-1 = C_all X_delta(g) exactly. 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b/research/direct-backward-independent-validation/capsule/repository/research/kappa-backward-controller-20261023/README.md new file mode 100644 index 0000000000..c698f5b3e8 --- /dev/null +++ b/research/direct-backward-independent-validation/capsule/repository/research/kappa-backward-controller-20261023/README.md @@ -0,0 +1,276 @@ +# Conditional kappa 0.00302728823 with a direct backward caller + +This construction gives **conditional kappa = 302728823/100000000000 = +0.00302728823**. It improves the selected final +[PR #4610](https://github.com/CrocSwap/integer-mult-bounds/pull/4610) +value 0.0030217758 by 0.00000551243. All 18 full calls use the completed +backward supplier from +[PR #5383](https://github.com/CrocSwap/integer-mult-bounds/pull/5383). +Two explicit caller wrappers replace the two forward calls. The backward +program, its eight relations and its owned storage schedule stay unchanged. + +During this work, the separate +[PR #5392](https://github.com/CrocSwap/integer-mult-bounds/pull/5392) +reached the **same recursive profile** by circuit transposition. This package +uses direct conjugation of the full backward interface. It does not transpose +an instruction, a COPY, a CLEAR or a native phase recipe. Its bound exceeds +that PR's 0.00302725 by **3823/100000000000 = 0.00000003823**. That last increment +comes from a larger compiler threshold, not another paid-profile gain. This +is not a further paid-profile hill-climbing step beyond PR5392. The direct +wrapper is the distinct construction; the same profile gives the same ceiling. + +[CONTROLLER.json](CONTROLLER.json) contains the literal caller. +[RESULT.json](RESULT.json) contains the exact finite evidence and full bill. +[SOURCES.json](SOURCES.json) binds each consumed input. The selected record +and all predecessor packages remain unchanged. + +## Source, scope and coordination + +The branch starts at canonical main +[1ec1119972c9aefe42525172d07b332fcff81cb4](https://github.com/CrocSwap/integer-mult-bounds/commit/1ec1119972c9aefe42525172d07b332fcff81cb4), +priority revision 7. The +[selected admission review](https://github.com/CrocSwap/integer-mult-bounds/blob/1ec1119972c9aefe42525172d07b332fcff81cb4/docs/research/pr-intake-evidence/pr4610/PROOF-REVIEW.md) +records the five inherited framework assumptions. That admission does not +cover this changed caller. + +The local supplier is frozen at PR5383 commit +[4bd6efa51a495a7c7b7754915cf0244e7e60969e](https://github.com/aliromman/integer-mult-bounds/commit/4bd6efa51a495a7c7b7754915cf0244e7e60969e). +Its [native checker](https://github.com/aliromman/integer-mult-bounds/blob/4bd6efa51a495a7c7b7754915cf0244e7e60969e/research/kappa-joint-relations-20261023/native.py) +and [witnesses](https://github.com/aliromman/integer-mult-bounds/blob/4bd6efa51a495a7c7b7754915cf0244e7e60969e/research/kappa-joint-relations-20261023/WITNESS.json) +are copied without changes as runtime dependencies. Their bytes are retained +in this branch's ancestor `9078033224509f184e3da4ccfd9837d1e1ad314e`. +The metadata pins that ancestor and also records the original source pins. +A clean checkout needs no separate pending-PR fetch. + +The verifier reconstructs the complete published local word. Its canonical +JSON payload hash is +`2aee5e997df99726fc763e510d9cb69fbe4f86114dc8d2cd33ad26c6c462a21d`. +All 4,429 frames, 72 native maps, retained paid operators and owned operations +come from that source. Cao Yifan's underlying +[final native word](https://github.com/intqwq/integer-mult-bounds/blob/20bb93cd990d2ff683e4d0fc56b87a42cd5d3296/research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz) +has decompressed SHA256 +`cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd`. +All eleven external runtime inputs occur in the recorded main base. + +The [canonical claim](https://github.com/CrocSwap/integer-mult-bounds/discussions/5125#discussioncomment-19154818) +separates this caller construction from the +[transpose claim](https://github.com/CrocSwap/integer-mult-bounds/discussions/5125#discussioncomment-19154367) +and the active +[backward paid-history search](https://github.com/CrocSwap/integer-mult-bounds/discussions/5125#discussioncomment-19154639). +The full open-PR and Discussion snapshot was refreshed during work. Targeted +Git-object searches covered relevant main README and proof text beyond the +sparse working tree. These checks do not certify novelty over all unpublished +or historical work. This package claims no source relation or transpose result. + +## Direct caller identity + +Use the source's +[normalized interfaces](https://github.com/CrocSwap/integer-mult-bounds/blob/1ec1119972c9aefe42525172d07b332fcff81cb4/research/query-thinned-controllers/PROOF.md). +On each port Q is the central Gaussian and D_s is the commuting stage +multiplier. At stage zero, D_0 is the nine-axis Gaussian times Q^-1. +At later full stages, D_s acts on eight fresh axes. Write + +```math +B_s=D_s\begin{pmatrix}1&-Q\\0&1\end{pmatrix},\qquad +F_s=D_s\begin{pmatrix}1&0\\Q^{-1}&1\end{pmatrix}. +``` + +Define the two monomial matrices + +```math +R=\begin{pmatrix}0&1\\-Q^{-2}&0\end{pmatrix},\qquad +R^{-1}=\begin{pmatrix}0&-Q^2\\1&0\end{pmatrix}. +``` + +Direct multiplication gives **F_s = R B_s R^-1**. In execution order, for +the two fields x and y, use: + +```text +(x,y) <- (-y,x) +x <- Q^2 x +execute the unchanged complete B_s supplier +(x,y) <- (y,-x) +y <- Q^-2 y +``` + +The caller changes only the main fields. Each invocation keeps its own 400 +independent productive helper inputs and the source backward helper boundary +normalizers. Its eight prepared pivots and nine owned center/snapshot fields +return zero. The wrappers do not read those fields. Thus the complete main, +helper and owned interface follows from the complete source interface, not +from a two-by-two identity alone. Helper normalizers are charged in the local +backward route allowance. + +This proof needs no linear instruction transposition theorem. A completed +supplier with the same main map, independent helper contract and owned return +can use the wrapper even when its implementation is hidden behind that contract. + +## Physical wrappers and tensor widths + +For every source port q, + +```math +Q=\frac{1+i}{2}I+\frac{1-i}{2}X_q,\qquad Q^2=Q^{-2}=X_q. +``` + +Here X_q is the native address translation. Its phase is exactly +1. +The verifier checks the Gaussian rational coefficients and every one of the +512 nine-axis input columns on all 112 ports at both changed sites. +It also checks the source phase polynomials, the orthogonal route and its +inverse, the preserved central direction and all four native boundary contacts +at **stage 0 and stage 32**. This gives **896 contacts** and **114,688 literal +central-square columns** in the full 265-axis layout. Stage zero uses its own +boundary formula; it is not inferred from a later-stage check. + +At positive tensor width f, `(Q tensor f)^2 = X_q tensor f`. Every D_s commutes +with Q, so the matrix identity still holds after that substitution. Each scalar +minus sign acts on the whole field and stays outside the tensor product. +A signed swap uses three scalar additions and one scalar sign change. Each +translation uses the explicit address map. Neither wrapper needs a positive +Gaussian job or a new independent source. + +The caller verifier replays every rational Laurent coefficient, with Q and all +33 stage variables formal and with no finite-order relation. It checks both +scalar boundary programs and all 32 main outputs. The physical check then +shows that the four even Q powers are legal translations. The source local +free-word proof applies at every positive tensor width; scalar coefficients +remain outside the operator substitution. + +## Complete bill and conditional bound + +Each of the 18 backward calls has + +```text +paid: {1:2193, 2:412, 3:510, 4:127, 5:40} +helpers: {4:28, 7:7, 8:47, 9:318} +``` + +Relative to PR5383, the two replaced forward calls remove **16 H1 and 16 H8 +paid jobs**, and debit **16 H9 productive targets**. For every `00`. To prove the +sign, add `(1/9)^t>1/9` and `(8/9)^t>8/9`, then multiply by `9^t`. +Relative to final PR4610, the full change is minus 144 jobs at each paid rank +1 and 8, and minus 144 targets at rank 9. Relative to PR5392, this recursive +bill is equal. + +Both the event census and a separate delta from the selected bill give +**64,116 paid calls and 10,784 productive fields**, with rank surplus 752. +All 15 thin queries, 15 whole idle jobs and 3,584 main targets remain included. +No prepared helper or snapshot receives independent target credit. + +The unchanged local scalar allowance is 158,744. The local route allowance is +4,818,000, and their sum is below 10^7. The four added signed swaps and four +translations cost at most `4*112*(26+1000)=459648` in the retained fixed-template +accounting. The translation changes only the nine old address bits; the fixed +1000 allowance exceeds those bit operations. The complete raw nonrecursive +allowance is **181,586,816 < 10^9**. Eight additional snapshot slots relative +to PR4610 suffice. Each full call has seventeen owned fields, including eight +old helper slots. The wrappers need no additional owned field. The completed signed swaps +and translations have norm one. The three-ADD swap can temporarily double +the two-field norm; this is a fixed factor. The precision and tape contracts +must use this full template, including that intermediate factor. + +Two rational interval engines check the moment. Exact bounds enclose its +unique crossing in **(0.00302728824993, 0.00302728824994)**. They prove decrease +on `[0,0.05]` and negativity on `[0.05,1]`. This ceiling applies only to the +stated complete profile. The claimed kappa leaves more than `1.993e-11` +raw headroom. + +The tested saving is 0.00302728824. The paid/target ratio is below +`0.999999999989608136845597542013`, with reserve `1e-12`. Both charged tail +ratios are below 0.97. Power 1024, cutoff 20, floor 21, offset 1/5, complement +factor 63/64 and logarithm power 1000 pass. The complete normalized paid bound +is `1048576000976562501/1048576001073741824 < 1`. + +The compiler uses gap `1/700000000000`, integer `j=55099`, +`H=38569300000000000` and `N=2^38569300000000000`. The exact inequality +`(H+1)^1000 < 2^55099` passes; the preceding grid integer fails. All **54 strict +outer predicates and four functional predicates** pass with ordinary BIT +saving 0.0034. The larger threshold funds the smaller gap to the raw root. +The compiler word is specified by the inherited finite algorithm; it is not +materialized. + +## Reproduce and assess the evidence + +Use CPython 3.12 and the standard library. From the repository root: + +```sh +python3 -B scripts/research_package.py --package research/kappa-backward-controller-20261023 --check-only +python3 -B scripts/research_package.py --package research/kappa-backward-controller-20261023 +python3 -B scripts/check_research_commit.py --package research/kappa-backward-controller-20261023 +``` + +The registered commands run normal and optimized modes. Direct replay also +works in the official Git-free export: + +```sh +python3 -B research/kappa-backward-controller-20261023/verify.py +python3 -O -B research/kappa-backward-controller-20261023/verify.py +``` + +Both must print `PASS_CONDITIONAL_KAPPA_00302728823_ALL_BACKWARD_CONTROLLER`. +Normal verification reads files and compares the regenerated caller and result. +The separate `--write` authoring mode writes only those two package artifacts +after all mathematical gates pass. + +Checks cover the exact source word, all 624 independent persistent and 17 +arbitrary owned entry columns, sixteen unrestricted source identities, both +actual wrapper boundaries, the full Laurent caller, two invoices, two interval +engines, completion, compiler and all outer predicates. Seven inherited native +controls reject relation, ownership, snapshot, frame, rank, COPY and return +errors. Four caller controls reject a missing translation, an unpaid odd Q +power, a wrong local orientation and a missing scalar sign. Seven cost/outer +controls reject false helper credit, two invalid reserves and four invalid +outer parameters. Checks use explicit exceptions and remain active under `-O`. +The registered normal and optimized replays passed on CPython 3.12.13. +The direct author replay also passed on CPython 3.14.7. Metadata and source +pins passed. The publication handoff records the committed-byte and export +checks; hosted CI is separate. + +These are author checks. The source absolute-phase lowering and amplitudes, +ordinary BIT native construction, physical tape execution, numerical precision +execution, analytic decomposition, prime avoidance and exact integer recovery +are inherited and not rerun. No Lean, Docker, proof-kernel acceptance or +independent human approval is claimed. The optional full-history preflight is +not claimed in this shallow checkout. The five framework assumptions remain: +native all-column realization, owned erasure, uniform compiler closure, +precision/tape and analytic recovery. This is a conditional mathematical +construction, not a practical timing result or a selected-frontier update. + +## Credit + +Ali Romman, with substantial OpenAI Codex assistance; Apache-2.0. +PR5383 supplies the eight prepared relations, snapshots, zero rows, backward +word and retained native checker. Its +[proof and notices](https://github.com/aliromman/integer-mult-bounds/blob/4bd6efa51a495a7c7b7754915cf0244e7e60969e/research/kappa-joint-relations-20261023/README.md) +credit the earlier +[PR #5377](https://github.com/CrocSwap/integer-mult-bounds/pull/5377) +construction. No discovery credit for those relations is claimed here. + +Cao Yifan supplies the final PR4610 native word and pricing lineage. +Cinna Davis supplies the +[PR #4470](https://github.com/CrocSwap/integer-mult-bounds/pull/4470) +controller and helper lineage. The retained +[pricing source](https://github.com/CrocSwap/integer-mult-bounds/blob/1ec1119972c9aefe42525172d07b332fcff81cb4/research/kappa-interface-round2-20261022/price_profile.py) +and the linked predecessor proof credit Dugongue's frames, zxv's native, +completion and logarithmic compiler work, Jacob Alan Sussman's mixed-target +recursion, Cinna Davis and ToikY's tensor argument, and earlier contributors. +Chris R's +[PR #5241](https://github.com/CrocSwap/integer-mult-bounds/pull/5241) +supplies the selected source admission; it does not admit this changed caller. +The predecessor notices and copied source bytes remain unchanged. + +Dugongue's +[PR #5387](https://github.com/CrocSwap/integer-mult-bounds/pull/5387) +is related smaller-reserve compiler work. PR5392 is the concurrent transpose +construction with the same paid profile. Neither package is a runtime input. +This package's new work is the direct caller identity, both physical boundary +checks, the emitted caller, its scalar bill and the stated full conditional bound. + +## Open next questions + +An independent reviewer should inspect both physical wrapper sites and the +complete price before admitting this caller. A stronger completed backward +supplier can use the same wrapper after its main, helper and owned interfaces +are checked. [TASK.json](TASK.json) records the first checks and blockers. +This result does not reserve the active paid-history, relation or decoder work. diff --git a/research/direct-backward-independent-validation/capsule/repository/research/kappa-backward-controller-20261023/RESULT.json b/research/direct-backward-independent-validation/capsule/repository/research/kappa-backward-controller-20261023/RESULT.json new file mode 100644 index 0000000000..32b2b214ae --- /dev/null +++ b/research/direct-backward-independent-validation/capsule/repository/research/kappa-backward-controller-20261023/RESULT.json @@ -0,0 +1,6557 @@ +{ + "arithmetic": { + "PR5383_raw_root_upper": "37833434601/12500000000000", + "compiler": { + "H": 38569300000000000, + "N": "2^38569300000000000", + "eta": { + "lower": "0.000000198868190185654395415931", + "upper": "0.000000198868190185654395415932" + }, + "gap": "1/700000000000", + "integer_test_exponent": 55099, + "logarithm_power": 1000, + "theta": "63/64", + "uniform_saving": "2119101767/700000000000", + "word_materialized": false + }, + "fixed_profile_ceiling": { + "decreasing_through": "1/20", + "derivative_upper": { + "lower": "-195429.853549519051730354837623051264", + "upper": "-195429.853549519051730354837623051263" + }, + "remaining_interval_moment_upper": { + "lower": "-6817.813214098317476830090331963946", + "upper": "-6817.813214098317476830090331963945" + } + }, + "full_backward": 18, + "full_forward": 0, + "gain_over_PR4610": "551243/100000000000", + "gain_over_PR5387": "122693/200000000000", + "gain_over_PR5392": "3823/100000000000", + "kappa": "302728823/100000000000", + "kappa_decimal": ".00302728823", + "margin_at_previous_kappa": { + "lower": "1.360313469048365037022624303111", + "upper": "1.360313469048365037022624303112" + }, + "margin_at_previous_root_upper": { + "lower": "1.360296002377893907536683455026", + "upper": "1.360296002377893907536683455027" + }, + "negative_controls": { + "closed_epsilon": [ + 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0000000000..9f4365c012 --- /dev/null +++ b/research/direct-backward-independent-validation/capsule/repository/research/kappa-backward-controller-20261023/TASK.json @@ -0,0 +1,96 @@ +{ + "schema_version": 1, + "task_id": "joint-query-controller", + "priority_revision": 7, + "base_commit": "1ec1119972c9aefe42525172d07b332fcff81cb4", + "original_card": { + "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" + } + ] + }, + "scope_status": "changed", + "actual_scope": "Replace both p16 forward calls by the frozen PR5383 backward supplier with exact signed-swap and central-square wrappers. Verify the complete conditional kappa 0.00302728823.", + "scope_change_reason": "The current selected source and completed PR5383 provide a concrete cheaper backward supplier. The original QQ16 service comparison is not this construction. This work changes the p16 caller and prices every removed helper target. PR5392 reached the same recursive profile by a separate transpose construction during this work.", + "bottleneck_link": "The wrapper carries the cheaper backward paid profile into both forward controller sites. It removes real paid work and recomputes the complete bound. It does not solve the general source-encoding bottleneck.", + "budget_minutes": 180, + "stop_rule": "Release if either actual native boundary fails, a wrapper needs an unpaid positive-rank job, an owned input survives, or the complete moment or compiler test fails. End at one checked package and handoff.", + "outcome": "completed", + "evidence": "CONTROLLER.json, RESULT.json and verify.py. The raw crossing is between 0.00302728824993 and 0.00302728824994. The full bill has 64116 paid calls and 10784 productive fields.", + "author": "Ali Romman", + "ai_assistance": "Substantial OpenAI Codex assistance for derivation, implementation, exact checks, documentation and coordination.", + "open_questions": [ + { + "question": "Does an independent reviewer accept both actual wrapper boundaries and the complete bound?", + "why_it_matters": "Author checks do not establish independent admission of this changed caller.", + "first_step": "Replay the frozen package, inspect F_s = R B_s R^-1 at stages 0 and 32, and check all helper debits and compiler predicates.", + "blocked_by": "Independent review and the five inherited framework assumptions." + }, + { + "question": "Can a stronger completed backward supplier use the same caller wrapper?", + "why_it_matters": "The wrapper preserves the full normalized main interface and can transfer a later paid saving.", + "first_step": "After that supplier is published, check its normalized B interface, independent helper targets and owned return, then replace the exact source pin and reprice the whole controller.", + "blocked_by": "A stronger completed supplier. Active relation and paid-history claims retain their own scope." + } + ] +} diff --git a/research/direct-backward-independent-validation/capsule/repository/research/kappa-backward-controller-20261023/VERIFY.json b/research/direct-backward-independent-validation/capsule/repository/research/kappa-backward-controller-20261023/VERIFY.json new file mode 100644 index 0000000000..f1e1cabfce --- /dev/null +++ b/research/direct-backward-independent-validation/capsule/repository/research/kappa-backward-controller-20261023/VERIFY.json @@ -0,0 +1,40 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/higher-moment-strictification/verify.py", + "research/joint-helper-lattice/CONTROLLER.json", + "research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py", + "research/kappa-rebuild/architecture/mixed_target_probe.py", + "research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz", + 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Cinna Davis supplied +its controller; zxv supplied the retained phase convention. Apache-2.0. +New construction by Ali Romman with substantial OpenAI Codex assistance. +""" +from copy import deepcopy +from fractions import Fraction as Q +from native import ROOT, read, load, need + +def replay(word): + """Check the literal p16 word and both rational boundary programs.""" + need((word['kind'], word['pairs'], word['prefix_pairs'], word['ambient_rank']) == ('complex', 16, 7, 145), 'Source p16/a7 controller') + zero = (0,) * 34 + def plus(dst, src, q): + for k, v in src.items(): + value = dst.get(k, Q(0)) + q * v + if value: dst[k] = value + else: dst.pop(k, None) + def shifted(row, term, sign=1): + return [{tuple(a + b for a, b in zip(k, term)): sign * v for k, v in cell.items()} for cell in row] + for side in ('left', 'right'): + matrix = [[Q(i == j) for j in range(32)] for i in range(32)] + for e in word['boundaries'][side + '_program']: + if e[0] == 'SWAP': matrix[e[1]], matrix[e[2]] = matrix[e[2]], matrix[e[1]] + elif e[0] == 'SCALE': matrix[e[1]] = [Q(e[2]) * x for x in matrix[e[1]]] + else: + need(e[0] == 'ADD', 'Boundary scalar opcode') + matrix[e[1]] = [x + Q(e[3]) * y for x, y in zip(matrix[e[1]], matrix[e[2]])] + need(matrix == [[Q(x) for x in row] for row in word['boundaries'][side]], 'Exact scalar boundary program') + rows = [[{zero: Q(x)} if Q(x) else {} for x in row] for row in word['boundaries']['right']] + for e in word['physical_events']: + if e[0] in ('LOCAL', 'QUERY_SHEAR'): + _, stage, pair, back = e + x, y = 2 * pair, 2 * pair + 1 + if back: x, y = y, x + term = (1 if back else -1,) + (0,) * 33 + for dst, src in zip(rows[y], shifted(rows[x], term)): + plus(dst, src, Q(-1 if back else 1)) + if e[0] == 'LOCAL': + term = (0,) + tuple(int(s == stage) for s in range(33)) + for r in (x, y): rows[r] = shifted(rows[r], term) + elif e[0] == 'Q_POWER': + need(e[2] in (-2, 2), 'Only even central powers are free') + rows[e[1]] = shifted(rows[e[1]], (e[2],) + (0,) * 33) + elif e[0] == 'IDLE': + term = (0,) + tuple(int(s in e[2]) for s in range(33)) + for r in (2 * e[1], 2 * e[1] + 1): rows[r] = shifted(rows[r], term) + elif e[0] == 'ADD': + for dst, src in zip(rows[e[1]], rows[e[2]]): plus(dst, src, Q(e[3])) + else: + need(e[0] in ('SWAP', 'SIGNED_SWAP'), 'Controller physical opcode') + rows[e[1]], rows[e[2]] = rows[e[2]], shifted(rows[e[1]], zero, -1 if e[0] == 'SIGNED_SWAP' else 1) + out = [[{} for _ in range(32)] for _ in range(32)] + for i, row in enumerate(word['boundaries']['left']): + for k, q in enumerate(row): + if Q(q): + for j in range(32): plus(out[i][j], rows[k][j], Q(q)) + expected = [[{tuple(word['diagonal'][i]): Q(1)} if i == j else {} for j in range(32)] for i in range(32)] + need(out == expected, 'All p16 Laurent coefficients, central signs and boundary factors') + return word + + + +def construct(): + source = read(ROOT / 'research/joint-helper-lattice/CONTROLLER.json') + replay(source) + word = deepcopy(source) + events = [] + sites = [] + for index, event in enumerate(source['physical_events']): + if event[0] == 'LOCAL' and not event[3]: + _, stage, pair, _ = event + x, y = 2 * pair, 2 * pair + 1 + sites.append({'source_index': index, 'stage': stage, 'pair': pair}) + events += [['SIGNED_SWAP', y, x], ['Q_POWER', x, 2], + ['LOCAL', stage, pair, True], + ['SIGNED_SWAP', x, y], ['Q_POWER', y, -2]] + else: + events.append(deepcopy(event)) + need(len(sites) == 2, 'Exactly the two forward sites change') + word['physical_events'] = events + word['wrapper_sites'] = sites + # This field described the old local provider. The new full bill is separate. + word.pop('invoice') + replay(word) + return word + + +def physical(word): + n = load('research/pr4359-p7-padding/native_inventory.py', 'backward_wrapper_native_phase') + path = 'research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json' + recipes = read(ROOT / path)['recipes'] + need(len(recipes) == 112, 'All actual central ports') + sites = word['wrapper_sites'] + need([site['stage'] for site in sites] == [0, 32], 'Both actual boundary stages') + dimension = 9 + 8 * 32 + axes = tuple(1 << i for i in range(dimension)) + def completed(stage): + return n.norm((axis, 1) for axis in axes[:9 + 8 * stage]) + checks, records = 0, [] + for site in sites: + stage = site['stage'] + spectator = n.norm((axis, 1) for axis in axes[9:9 + 8 * stage]) + for port, recipe in enumerate(recipes): + q = recipe['q'] + need(0 < q < 512, 'Actual nine-axis central operator') + basis = recipe['idle_children'][0]['orthogonal_axes'][:8] + need(all((b & q).bit_count() % 2 == 0 for b in basis), 'Actual route is perpendicular to Q') + need(all((a & b).bit_count() % 2 == int(i == j) for i, a in enumerate(basis) for j, b in enumerate(basis)), 'Actual eight-vector basis is orthonormal') + swaps = [] if stage == 0 else [b ^ axes[9 + 8 * (stage - 1) + i] for i, b in enumerate(basis)] + route = tuple(e ^ n.act(swaps, sum(((e & v).bit_count() % 2) << i for i, v in enumerate(swaps))) for e in axes) + need(all(n.act(route, route[i]) == axes[i] for i in range(dimension)), 'Involutive actual route') + need(all((a & b).bit_count() % 2 == int(i == j) for i, a in enumerate(route) for j, b in enumerate(route)), 'Orthogonal actual route') + need(n.act(route, q) == q, 'Physical routing preserves the central operator') + raw_x = n.norm([(q, 1)]) if stage == 0 else completed(stage - 1) + raw_y = () if stage == 0 else n.norm(list(raw_x) + [(q, -1)]) + raw = (raw_x, raw_y) + entry = (n.norm(list(spectator) + [(q, -1)]), spectator) + local0 = n.norm(list(spectator) + [(a, -1) for a in axes[:9]]) + local_out = (local0, n.norm(list(local0) + [(q, 1)])) + out = (completed(stage), n.norm(list(completed(stage)) + [(q, -1)])) + contacts = [n.contact(a, b, route, dimension) for a, b in list(zip(raw, entry)) + list(zip(local_out, out))] + delta = n.norm([(a, 1) for a in axes[:9]] + [(q, -1)]) if stage == 0 else n.norm((a, 1) for a in axes[9 + 8 * (stage - 1):9 + 8 * stage]) + for incoming, outgoing in zip(raw, out): + need(n.polynomial(n.norm(list(outgoing) + [(a, -v) for a, v in incoming]), dimension) == n.polynomial(delta, dimension), 'Actual backward diagonal is D_s') + cross = n.norm(list(out[0]) + [(a, -v) for a, v in raw[1]]) + need(n.polynomial(cross, dimension) == n.polynomial(n.norm(list(delta) + [(q, 1)]), dimension), 'Actual backward cross term is D_s Q') + positive = n.polynomial(n.norm([(q, 2)]), dimension) + negative = n.polynomial(n.norm([(q, -2)]), dimension) + need(positive == negative and not any(positive[1]) and all(v in (0, 2) for v in positive[0]), 'Both wrapper powers are the same exact translation') + need(positive != n.polynomial((), dimension), 'The central translation cannot be omitted') + # Q = a I + b X_q. Check its square on each nine-axis column. + a, b = (Q(1, 2), Q(1, 2)), (Q(1, 2), Q(-1, 2)) + def mul(z, w): + return (z[0] * w[0] - z[1] * w[1], z[0] * w[1] + z[1] * w[0]) + def add(z, w): + return (z[0] + w[0], z[1] + w[1]) + zero, one = (Q(0), Q(0)), (Q(1), Q(0)) + square = (add(mul(a, a), mul(b, b)), add(mul(a, b), mul(b, a))) + need(square == (zero, one), 'Absolute phase of the Gaussian square') + for address in range(512): + column = {address: square[0], address ^ q: square[1]} + column = {x: v for x, v in column.items() if v != zero} + need(column == {address ^ q: one}, 'Every literal central-square column') + checks += 1 + records.append({'stage': stage, 'pair': site['pair'], 'port': port, 'q': q, 'contacts': contacts, 'central_translation': q}) + return {'ports': 112, 'stages': [0, 32], 'dimension': dimension, + 'literal_square_columns': checks, 'local_boundary_contacts': 4 * len(records), + 'records': records, 'new_positive_rank_jobs': 0, + 'tensor_lift': 'Factorwise tensor products: (Q tensor f)^2 = (X_q tensor f). Scalar minus signs remain outside the tensor substitution.'} + + +def controls(word): + failures = {} + variants = {} + bad = deepcopy(word) + bad['physical_events'].remove(next(e for e in bad['physical_events'] if e[0] == 'Q_POWER')) + variants['omitted_central_translation'] = bad + bad = deepcopy(word) + e = next(e for e in bad['physical_events'] if e[0] == 'Q_POWER') + e[2] = 1 + variants['unpaid_rank_one_wrapper'] = bad + bad = deepcopy(word) + e = next(e for e in bad['physical_events'] if e[0] == 'LOCAL') + e[3] = False + variants['wrong_primitive_orientation'] = bad + bad = deepcopy(word) + e = next(e for e in bad['physical_events'] if e[0] == 'SIGNED_SWAP') + e[0] = 'SWAP' + variants['missing_wrapper_sign'] = bad + for name, candidate in variants.items(): + try: + replay(candidate) + except ValueError as exc: + failures[name] = str(exc) + else: + raise ValueError('Accepted corrupted controller: ' + name) + return failures diff --git a/research/direct-backward-independent-validation/capsule/repository/research/kappa-backward-controller-20261023/native.py b/research/direct-backward-independent-validation/capsule/repository/research/kappa-backward-controller-20261023/native.py new file mode 100644 index 0000000000..cbff46fe6e --- /dev/null +++ b/research/direct-backward-independent-validation/capsule/repository/research/kappa-backward-controller-20261023/native.py @@ -0,0 +1,344 @@ +"""Eight prepared helpers remove sixteen paid jobs in the PR4610 backward word. + +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +This extends Ali Romman's one-relation PR5377 at c448d13c71908647f968b06cddb795ce7d288139. +The source word is by Cao Yifan. The row convention and scalar allowance +follow the credited native work of Cinna Davis and zxv. +""" +from collections import Counter +from copy import deepcopy +from fractions import Fraction as Q +from hashlib import sha1, sha256 +from pathlib import Path +import gzip +import importlib.util +import json +import sys + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +SOURCE = 'research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz' +PHASE = 'research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz' +PAYLOAD = 'cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd' +WITNESSES = json.loads((HERE / 'WITNESS.json').read_text(encoding='utf-8')) +COUNT = 8 +OLD_PAID = {1: 2201, 2: 412, 3: 510, 4: 127, 5: 40, 8: 8} +NEW_PAID = dict(OLD_PAID) +NEW_PAID[1] -= COUNT +NEW_PAID.pop(8) +OLD_HELPERS = {4: 28, 7: 7, 8: 47, 9: 326} + + +def need(ok, why): + if not ok: + raise ValueError(why) + + +def read(path): + data = path.read_bytes() + return json.loads(gzip.decompress(data) if path.suffix == '.gz' else data) + + +def encode(x): + if isinstance(x, Q): + return str(x) + if isinstance(x, dict): + return {str(k): encode(v) for k, v in x.items()} + if isinstance(x, (list, tuple)): + return [encode(v) for v in x] + return x + + +def load(relative, name): + spec = importlib.util.spec_from_file_location(name, ROOT / relative) + module = importlib.util.module_from_spec(spec) + sys.modules[name] = module + spec.loader.exec_module(module) + return module + + +def authenticate(): + pins = read(HERE / 'SOURCES.json') + for row in pins['files']: + if row['usage'] != 'input': + continue + p = ROOT + for part in Path(row['path']).parts: + p /= part + need(not p.is_symlink(), 'No source aliases') + raw = p.read_bytes() + need(sha256(raw).hexdigest() == row['sha256'], 'Changed source: ' + row['path']) + need(sha1(b'blob ' + str(len(raw)).encode() + b'\0' + raw).hexdigest() == row['git_blob'], 'Source Git blob') + need(sha256(gzip.decompress((ROOT / SOURCE).read_bytes())).hexdigest() == PAYLOAD, 'Exact source payload') + return pins + + +def span(basis): + out = {0} + for vector in basis: + need(isinstance(vector, int) and 0 <= vector < 512, 'Binary frame coordinate') + out |= {v ^ vector for v in tuple(out)} + need(len(out) == 2 ** len(basis), 'Independent frame basis') + return out + + +def add(dst, src, q): + for k, v in tuple(src.items()): + value = dst.get(k, Q(0)) + q * v + if value: + dst[k] = value + else: + dst.pop(k, None) + + +def allowance(g): + if g[0] in ('clear', 'copy'): + return 2 + q = Q(*g[3:]) if g[0] == 'add' else Q(*g[2:]) + n, d = abs(q.numerator), q.denominator + need(n > 0 and d & (d - 1) == 0, 'Nonzero dyadic scalar') + if g[0] == 'scale': + need(n & (n - 1) == 0, 'Dyadic unit SCALE') + return 2 * (abs(n.bit_length() - d.bit_length()) + int(q < 0)) + need(g[0] == 'add', 'Known scalar operation') + return 2 * (3 + n.bit_length() - 1 + n.bit_count() + d.bit_length() - 1) + + +def relation_system(): + """Find exact independent pivots and eliminate all other pivot columns.""" + basis = {} + need(len(WITNESSES) == COUNT, 'Eight declared witnesses') + for witness in WITNESSES: + pairs = witness['relation'] + row = {h: Q(q) for h, q in pairs} + need(len(row) == len(pairs) and all(224 <= h < 632 and q for h, q in row.items()), 'Distinct helper coefficients') + for pivot, prior in sorted(basis.items()): + add(row, prior, -row.get(pivot, Q(0))) + need(row, 'Independent helper relations') + pivot = min(row); scale = row[pivot] + row = {h: q / scale for h, q in row.items()} + for prior in basis.values(): + add(prior, row, -prior.get(pivot, Q(0))) + basis[pivot] = row + need(len(basis) == COUNT, 'Eight paid helper outputs removed') + for pivot, row in basis.items(): + need(all(row.get(h, 0) == int(h == pivot) for h in basis), 'Reduced pivot columns') + return dict(sorted(basis.items())) + + +BASIS = relation_system() + + +def construct(source): + c = source['canonical']; old = source['programs']['backward'] + all_helpers = {h for x in WITNESSES for h, _ in x['relation']} + need(all(c['start'][h] == 0 and c['final'][h] == 1 for h in all_helpers), 'Every relation uses cold full-ended helpers') + snapshots, centers, zeros = {}, {}, {} + for slot, x in enumerate(WITNESSES, 1): + frame, role = x['frame'], x['cached_role'] + need(old[x['event']] == ['center', 0, 0, frame, 8], 'Exact source center') + event = old[x['cached_event']] + need(event[0] == 'climb' and event[2] == role and event[4] == frame, 'Exact snapshot source') + need(old[x['zero_event']] == ['climb', 'warp_retimed', x['zero_role'], frame, 1, 1], 'Exact zero source job') + need(x['cached_event'] < x['event'] < x['zero_event'] and Q(x['copy_factor']) == 1, 'Snapshot chronology and COPY coefficient') + snapshots[x['cached_event']] = (slot, x) + centers[x['event']] = (slot, x) + zeros[x['zero_event']] = x + need(len(snapshots) == len(centers) == len(zeros) == COUNT, 'Distinct replacement sites') + word = [] + for pivot, row in BASIS.items(): + word.append(['scalar', ['clear', ['L', pivot]], 0]) + for h, q in sorted(row.items()): + if h != pivot: + word.append(['scalar', ['add', ['L', pivot], ['L', h], -q.numerator, q.denominator], 0]) + for index, event in enumerate(old): + if index in centers: + slot, x = centers[index]; f = x['frame'] + word += [['scalar', ['clear', ['C', 0]], f], + ['scalar', ['copy', ['C', 0], ['C', slot]], f], + ['scalar', ['clear', ['C', slot]], f]] + elif index in zeros: + x = zeros[index] + word.append(['zero_retag', ['L', x['zero_role']], x['frame'], 1]) + else: + word.append(deepcopy(event)) + if index in snapshots: + slot, x = snapshots[index]; f = x['frame'] + word += [['scalar', ['clear', ['C', slot]], f], + ['scalar', ['copy', ['C', slot], ['L', x['cached_role']]], f]] + word += [['scalar', ['clear', ['L', h]], 1] for h in BASIS] + physical = deepcopy(c); physical.pop('local_profile') + return {'schema': 'joint-helper-relations-word/1', 'canonical': physical, + 'relation_basis': encode(BASIS), + 'paid_profiles': {'forward': OLD_PAID, 'backward': NEW_PAID}, + 'owned': {'forward': [['C', 0]], 'backward': [['C', i] for i in range(COUNT + 1)] + [['L', h] for h in BASIS]}, + 'programs': {'forward': deepcopy(source['programs']['forward']), 'backward': word}} + + +def replay(c, program, backward, specialized): + """Run every event on all independent entry columns and exact frames.""" + owned = {('C', 0)} | ({('C', i) for i in range(1, COUNT + 1)} | {('L', h) for h in BASIS} if specialized else set()) + roles = {('L', i) for i in range(632)} | owned + rows = {r: {(r, ()): Q(1)} for r in roles} + frames = {('L', i): f for i, f in enumerate(c['start'])} + frames.update({r: None for r in owned if r[0] == 'C'}) + spaces = [span(b) for b in c['frames']] + paid = Counter() + cost, max_l1, denominator, zero_count = 0, Q(1), 1, 0 + for e in program: + kind, touched = e[0], None + if kind == 'scalar': + g, frame = e[1:] + dst = tuple(g[1]); touched = dst + need(dst in rows and 0 <= frame < len(spaces), 'Declared scalar destination and frame') + cost += allowance(g) + if g[0] == 'clear': + need(dst in owned, 'Only owned fields can be erased') + rows[dst] = {}; frames[dst] = frame + else: + need(frames[dst] == frame, 'Exact scalar destination frame') + if g[0] in ('add', 'copy'): + src = tuple(g[2]) + need(src in rows and frames[src] == frame and dst != src, 'Exact scalar source frame') + if g[0] == 'copy': + need(dst in owned and not rows[dst], 'COPY into cleared owned storage') + rows[dst] = dict(rows[src]) + else: + add(rows[dst], rows[src], Q(g[3], g[4])) + else: + need(g[0] == 'scale', 'Known scalar operation') + rows[dst] = {k: Q(g[2], g[3]) * v for k, v in rows[dst].items()} + elif kind == 'warp': + _, role, op, old, new = e + dst = tuple(role); touched = dst + need(frames[dst] == old and 1 <= abs(op) <= len(c['warps']), 'Exact warp input') + symbol = (1 if op > 0 else -1) * (abs(op) + (10**6 if backward else 0)) + rows[dst] = {(r, w[1:] if w and w[0] == -symbol else (symbol,) + w): q + for (r, w), q in rows[dst].items()} + frames[dst] = new + elif kind in ('climb', 'center'): + if kind == 'climb': + _, _, i, old, new, rank = e + dst = ('L', i) + need(spaces[old] < spaces[new], 'Ascending paid climb') + else: + _, i, old, new, rank = e + dst = ('C', i) + need(spaces[old] < spaces[new] or spaces[new] < spaces[old], 'Nested paid center') + need(frames[dst] == old and rank == abs(len(c['frames'][new]) - len(c['frames'][old])), 'Exact paid rank and frame') + frames[dst] = new; paid[rank] += 1 + elif kind == 'zero_retag': + _, role, old, new = e + dst = tuple(role) + need(specialized and backward and any(dst == ('L', x['zero_role']) and (old, new) == (x['frame'], 1) for x in WITNESSES), 'Declared zero identity') + need(frames[dst] == old and not rows[dst], 'Zero identity requires an identically zero full row') + frames[dst] = new; zero_count += 1 + else: + need(kind in ('phase', 'adapter'), 'Known inert source marker') + if touched is not None: + max_l1 = max(max_l1, sum(map(abs, rows[touched].values()), Q(0))) + denominator = max(denominator, max((q.denominator for q in rows[touched].values()), default=1)) + need([frames['L', i] for i in range(632)] == c['final'], 'Every final native frame') + for i in range(632): + r = ('L', i) + if r in owned: + continue + expected = {(r, ()): Q(1)} + if i < 112 if backward else 112 <= i < 224: + expected[(('L', i + 112 if backward else i - 112), ())] = Q(-1 if backward else 1) + need(rows[r] == expected, 'Every independent main/helper endpoint: ' + str(i)) + need(all(not rows[r] for r in owned), 'Every owned entry column is erased at return') + need(zero_count == COUNT * int(specialized), 'All eight zero identities checked') + helpers = Counter() + for i in range(224, 632): + if ('L', i) in owned: + continue + a, b = c['start'][i], c['final'][i] + need(spaces[a] < spaces[b], 'Strict independent productive helper') + helpers[len(c['frames'][b]) - len(c['frames'][a])] += 1 + return {'paid': dict(sorted(paid.items())), 'helpers': dict(sorted(helpers.items())), + 'independent_persistent_columns': 632 - COUNT if specialized else 632, + 'independent_owned_entry_columns': len(owned), 'owned_outputs_zero': True, + 'real_scalar_allowance': cost, 'max_formal_prefix_l1': str(max_l1), + 'max_denominator': denominator, 'zero_identities': zero_count} + + +def independent_source_identities(source): + """Check unrestricted source identities with the predecessor row engine.""" + v = load('research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py', 'joint_relation_source_rows') + rows = {('L', i): v.identity(('L', i)) for i in range(632)} + rows['C', 0] = v.identity(('C', 0)); saved = {}; checked = [] + for index, e in enumerate(source['programs']['backward']): + if e[0] == 'scalar': + g = e[1]; dst = tuple(g[1]) + if g[0] == 'clear': rows[dst] = {} + elif g[0] == 'copy': rows[dst] = dict(rows[tuple(g[2])]) + elif g[0] == 'scale': rows[dst] = {k: Q(g[2], g[3]) * a for k, a in rows[dst].items()} + else: v.add(rows[dst], rows[tuple(g[2])], Q(g[3], g[4])) + elif e[0] == 'warp': + dst = tuple(e[1]); rows[dst] = v.warp(rows[dst], e[2], True) + for x in WITNESSES: + delta = {(('L', h), ()): Q(q) for h, q in x['relation']} + if index == x['cached_event']: + saved[index] = dict(rows['L', x['cached_role']]) + if index == x['event']: + diff = dict(rows['C', 0]); v.add(diff, saved[x['cached_event']], -Q(x['copy_factor'])) + need(diff == {k: Q(x['difference_factor']) * q for k, q in delta.items()}, 'Independent exact center minus snapshot identity') + checked.append(('center', index)) + if index == x['zero_event']: + need(rows['L', x['zero_role']] == {k: Q(x['zero_factor']) * q for k, q in delta.items()}, 'Independent exact zero-site row identity') + checked.append(('zero', index)) + need(len(checked) == 2 * COUNT, 'Sixteen unrestricted source identities') + need(all(rows['L', i] == v.expected(('L', i), [], True, False) for i in range(632)), 'Independent unrestricted source endpoints') + return {'source_event_indices_are_zero_based': True, 'witnesses': WITNESSES, + 'relation_rank': COUNT, 'owned_pivots': list(BASIS), 'reduced_basis': BASIS, + 'snapshot_terms_before_substitution': {i: len(row) for i, row in saved.items()}, + 'checked': checked} + + +def phase_inheritance(source, candidate): + receipt = read(ROOT / PHASE) + need(receipt['status'] == 'PASS_JOINT_HELPER_MAPS_ALL_ACTUAL_ABSOLUTE_PHASES' and + receipt['actual_word_canonical_sha256'] == PAYLOAD, 'Authenticated source absolute-phase receipt') + physical = deepcopy(source['canonical']); physical.pop('local_profile') + need(candidate['canonical'] == physical, 'Every frame, native map and main adapter unchanged') + for direction, program in candidate['programs'].items(): + old = source['programs'][direction] + for kind in ('warp', 'adapter', 'phase'): + need([e for e in program if e[0] == kind] == [e for e in old if e[0] == kind], 'Exact inherited ' + kind + ' sequence') + old_paid = Counter(tuple(e) for e in old if e[0] in ('climb', 'center')) + new_paid = Counter(tuple(e) for e in program if e[0] in ('climb', 'center')) + expected = Counter() if direction == 'forward' else Counter(tuple(old[i]) for x in WITNESSES for i in (x['event'], x['zero_event'])) + need(old_paid - new_paid == expected and not new_paid - old_paid, 'Only the sixteen proved jobs are removed') + return {'new_gaussian_operators': 0, 'new_native_maps': 0, + 'all_retained_paid_events_and_warps_from_source': True, + 'absolute_phase_receipt_reused': PHASE, + 'source_amplitudes_and_phase_lowering_freshly_replayed': False, + 'new_operations': 'Same-frame COPY, owned CLEAR/ADD, and physical identity on a proved zero row.'} + + +def controls(c, candidate): + controls = {} + base = candidate['programs']['backward'] + variants = {} + bad = deepcopy(base); bad[1][1][3] *= -1; variants['wrong_relation_sign'] = bad + variants['missing_owned_input_clear'] = deepcopy(base[1:]) + bad = deepcopy(base) + next(e for e in bad if e[0] == 'scalar' and e[1][:2] == ['copy', ['C', 1]])[1][2] = ['L', 63] + variants['wrong_snapshot_source'] = bad + bad = deepcopy(base); next(e for e in bad if e[0] == 'zero_retag')[2] = 0 + variants['wrong_zero_input_frame'] = bad + bad = deepcopy(base); next(e for e in bad if e[0] == 'climb')[5] += 1 + variants['under_or_overstated_paid_rank'] = bad + bad = deepcopy(base) + next(e for e in bad if e[0] == 'scalar' and e[1][:2] == ['copy', ['C', 0]])[2] = 0 + variants['wrong_copy_gauge'] = bad + variants['uncleared_owned_output'] = deepcopy(base[:-1]) + for name, program in variants.items(): + try: + replay(c, program, True, True) + except ValueError as err: + controls[name] = str(err) + else: + raise ValueError('Control accepted: ' + name) + return controls diff --git a/research/direct-backward-independent-validation/capsule/repository/research/kappa-backward-controller-20261023/price.py b/research/direct-backward-independent-validation/capsule/repository/research/kappa-backward-controller-20261023/price.py new file mode 100644 index 0000000000..b68fabab8a --- /dev/null +++ b/research/direct-backward-independent-validation/capsule/repository/research/kappa-backward-controller-20261023/price.py @@ -0,0 +1,157 @@ +"""Complete bill and finite compiler for the all-backward controller. + +The interval and compiler proof follows Cao Yifan's PR4610 pricing, Cinna +Davis's PR4470 controller, zxv's completion and logarithmic majorant, and +Jacob Alan Sussman's mixed-target recursion. Apache-2.0. +Ali Romman, with substantial OpenAI Codex assistance. +""" +from collections import Counter +from fractions import Fraction as Q +from native import ROOT, read, load, need, encode, OLD_HELPERS, COUNT + +KAPPA = Q('.00302728823') +TESTED = Q('.00302728824') +PREVIOUS = Q('.0030217758') +OLD_ROOT_UPPER = Q('.00302177587078') + + +def assemble(native, word): + T, P = Counter(), Counter() + directions = Counter() + thin = 0 + for e in word['physical_events']: + if e[0] == 'LOCAL': + need(e[3] is True, 'Every full primitive uses the backward source') + directions['backward'] += 1 + T.update(native['backward']['helpers']) + P.update(native['backward']['paid']) + elif e[0] == 'QUERY_SHEAR': + thin += 1 + P[1] += 112 + elif e[0] == 'IDLE': + P[8 * len(e[2])] += 224 + for term in word['diagonal']: + need(term[0] in (-1, 1) and all(x in (0, 1) for x in term[1:]), 'Whole main target') + T[1 + 8 * sum(term[1:])] += 112 + need(directions == {'backward': 18} and thin == 15, 'Complete actual call inventory') + old = read(ROOT / 'research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json') + check_T = Counter({int(r): n for r, n in old['targets'].items()}) + check_P = Counter({int(r): n for r, n in old['paid'].items()}) + check_T[9] -= 18 * COUNT + check_P[1] -= 18 * COUNT + check_P[8] -= 18 * COUNT + need(T == check_T and P == check_P, 'Independent full invoice from the selected source') + need(sum(T.values()) == 10784 and sum(P.values()) == 64116, 'Complete field and call counts') + need(sum(r * n for r, n in T.items()) - sum(r * n for r, n in P.items()) == 752, 'Complete rank surplus') + return T, P + + +def run(native, word): + T, P = assemble(native, word) + prior = read(ROOT / 'research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json') + need(Q(prior['kappa']) == PREVIOUS and Q(prior['raw_root_interval'][1]) == OLD_ROOT_UPPER, 'Pinned prior conditional bound and raw crossing') + prior_T = Counter({int(r): n for r, n in prior['targets'].items()}) + prior_P = Counter({int(r): n for r, n in prior['paid'].items()}) + prior_T[9] -= 18 * COUNT; prior_P[1] -= 18 * COUNT; prior_P[8] -= 18 * COUNT + need(T == prior_T and P == prior_P, 'Complete delta from the final PR4610 bill') + E = load('research/higher-moment-strictification/verify.py', 'owned_relation_intervals') + other = load('research/kappa-rebuild/architecture/mixed_target_probe.py', 'owned_relation_second_intervals') + def margin(c): + t, p = E.moment(T, 1 - c), E.moment(P, 1 - c) + return t[0] - p[1], t[1] - p[0] + need(margin(Q('.00302667476808'))[0] > 0, 'Changed invoice beats the PR5383 fixed-profile ceiling') + need(margin(OLD_ROOT_UPPER)[0] > 0, 'Changed invoice beats the prior raw root upper endpoint') + lo, hi, grid = 0, 10**12, 10**14 + while hi - lo > 1: + mid = (lo + hi) // 2 + if margin(Q(mid, grid))[0] > 0: lo = mid + else: hi = mid + root_low, root_high = Q(lo, grid), Q(hi, grid) + need(margin(root_low)[0] > 0 and margin(root_high)[1] < 0, 'Strict rational root enclosure') + need(PREVIOUS < KAPPA < TESTED < root_low, 'New bound and explicit compiler headroom') + # The complete signed profile decreases on [0, .05], and stays negative + # on [.05, 1]. This proves a fixed-profile ceiling, not a circuit ceiling. + signed = {r: T[r] - P[r] for r in T.keys() | P.keys()} + derivative, upper = None, None + for i in range(16): + l, r = Q(i, 320), Q(i + 1, 320); low = Q(0) + for rank, n in signed.items(): + term = E.mul(E.power(rank, 1 - r if n > 0 else 1 - l), E.log_bounds(rank)) + low += n * term[0 if n > 0 else 1] + derivative = low if derivative is None else min(derivative, low) + for i in range(128): + l, r = Q(1, 20) + Q(19 * i, 2560), Q(1, 20) + Q(19 * (i + 1), 2560) + value = sum(n * E.power(rank, 1 - l if n > 0 else 1 - r)[1 if n > 0 else 0] for rank, n in signed.items()) + upper = value if upper is None else max(upper, value) + need(derivative > 0 and upper < 0, 'Fixed-profile ceiling on all 0 < kappa < 1') + t, u, v, c, b = 1 - TESTED, Q(1, 5), 1024, 20, 21 + target, paid = E.moment(T, t), E.moment(P, t) + tl, th = other.moment(T, TESTED); pl, ph = other.moment(P, TESTED) + need(tl > ph and max(tl, target[0]) <= min(th, target[1]) and max(pl, paid[0]) <= min(ph, paid[1]), 'Two exact interval engines agree') + alpha = E.divide(paid, target) + gamma = E.divide(E.moment(P, t + u), E.mul(E.power(c, u), target)) + delta = E.divide((Q(sum(T.values()) * b),) * 2, E.mul(E.power(c, TESTED), target)) + reserve = Q(1, 10**12); g = d = Q(97, 100) + need(alpha[1] < 1 - reserve and gamma[1] < g and delta[1] < d, 'Original and completion tails charged') + need(g**128 < Q(1, 16) and d**128 < Q(1, 16), 'Two strict tail decay blocks') + normalized = 1 / (1 + v * reserve) + Q(4, 2**32) + need(normalized < 1 and c**64 < b**63, 'Paid completion, splitting and rounding') + theta, power = Q(63, 64), 1000 + eta = E.scale(E.power(145, -v * TESTED), t) + need(2 * (20**v)**64 <= (145**v)**63 and eta[0] > theta**power, 'Shifted exits and complement capacity') + need(E.power(145, v * TESTED)[1] < 2**power, 'Compiler initial range') + gap = (TESTED - KAPPA) / 7; need(gap.numerator == 1, 'Finite integer grid') + step = gap.denominator + def wins(j): return (step * j + 1)**power < 2**j + left, right = 1, 2 + while not wins(right): left, right = right, 2 * right + while right - left > 1: + mid = (left + right) // 2 + if wins(mid): right = mid + else: left = mid + height = step * right + need(height > 8 * v and wins(right) and not wins(right - 1), 'Finite uniform-rank threshold') + local_scalar = native['backward']['real_scalar_allowance'] + # Charge both routes for each of eight snapshots and eight owned helpers. + # The eight owned helpers use existing physical slots. + routes = (sum(native['backward']['paid'].values()) + 2 * 408 + 688 + 4 * COUNT) * 1000 + need(local_scalar + routes < 10**7, 'All new preparation, COPY, CLEAR and fixed routes fit') + scalar_upper = 18 * 10**7 + 15 * 1792 + 32 * 112 * (len(word['physical_events']) + sum(len(word['boundaries'][k + '_program']) for k in ('left', 'right'))) + wrapper_allowance = 4 * 112 * (26 + 1000) + scalar_upper += wrapper_allowance + need(scalar_upper < 10**9, 'Complete raw nonrecursive bound with every wrapper') + bit = read(ROOT / 'research/query-thinned-controllers/RESULT.json')['ordinary_BIT'] + atom = Q(bit['atom']); ordinary = (1 - atom) * Q(bit['after_cover']) + atom * Q('.0000384599'); admitted = Q(bit['admitted']) + need(atom == Q('.004') and atom > ordinary > admitted > TESTED and atom < 1 - ordinary, 'Retained stronger BIT admission and stock') + L = load('research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py', 'owned_relation_outer') + params = {'kappa': KAPPA, 'tested_saving': TESTED, 'complex_uniform_saving': KAPPA + 6 * gap, + 'b': KAPPA + 5 * gap, 'a': KAPPA + 4 * gap, 'q': KAPPA + 3 * gap, 'bit_saving': admitted, + 'epsilon': 1 - gap, 'beta': 1 - 3 * gap, 'r0': gap / 10, 'stop': gap, 'layout': gap, 'd': gap} + outer = L.ledger(params); outer['functional_checks']['actual_new_BIT_stock_sublinear'] = params['beta'] * (1 - atom) + need(len(outer['strict_checks']) == 54 and len(outer['functional_checks']) == 4, 'Complete outer predicate inventory') + need(all(x > 0 for key in ('strict_checks', 'functional_checks') for x in outer[key].values()), 'Every outer inequality is strict') + controls = {} + need(alpha[0] > 1 - Q(1, 10**9), 'The former reserve fails at the new tested saving') + need(1 / (1 + v * Q(1, 10**13)) + Q(4, 2**32) > 1, 'A smaller reserve fails the fixed rounding charge') + controls['former_reserve'] = 'Rejected at the new tested saving' + controls['insufficient_rounding_reserve'] = 'Rejected by the complete normalized paid bound' + for name, patch in [('old_BIT', {'bit_saving': Q('.0027')}), ('closed_uniform', {'complex_uniform_saving': params['b']}), ('unfunded_endpoint', {'kappa': TESTED}), ('closed_epsilon', {'epsilon': Q(1)})]: + bad = L.ledger(dict(params, **patch)); failed = [k for k, x in bad['strict_checks'].items() if x <= 0] + need(failed, 'Reject outer patch ' + name); controls[name] = failed + bad_native = {d: dict(x) for d, x in native.items()} + bad_native['backward']['helpers'] = OLD_HELPERS + try: assemble(bad_native, word) + except ValueError: controls['unearned_helper_credit'] = 'Rejected by the independent complete census' + else: raise ValueError('Unowned helper credit was accepted') + return encode({'kappa': KAPPA, 'kappa_decimal': '.00302728823', 'gain_over_PR4610': KAPPA - PREVIOUS, + 'gain_over_PR5387': KAPPA - Q('.003026674765'), 'gain_over_PR5392': KAPPA - Q('.00302725'), 'PR5383_raw_root_upper': Q('.00302667476808'), + 'raw_root_interval': [root_low, root_high], 'raw_headroom': [root_low - KAPPA, root_high - KAPPA], + 'margin_at_previous_kappa': E.display(margin(PREVIOUS)), + 'margin_at_previous_root_upper': E.display(margin(OLD_ROOT_UPPER)), + 'fixed_profile_ceiling': {'decreasing_through': Q(1, 20), 'derivative_upper': E.display((-derivative,) * 2), 'remaining_interval_moment_upper': E.display((upper,) * 2)}, + 'targets': T, 'paid': P, 'productive_fields': sum(T.values()), 'paid_calls': sum(P.values()), 'rank_mass_surplus': 752, + 'full_backward': 18, 'full_forward': 0, 'query_shears': 15, + 'strictification': {'tested': TESTED, 'power': v, 'cutoff': c, 'floor': b, 'tail_offset': u, 'reserve': reserve, 'alpha': E.display(alpha), 'gamma': E.display(gamma), 'delta': E.display(delta), 'normalized_paid_upper': normalized}, + 'compiler': {'theta': theta, 'logarithm_power': power, 'eta': E.display(eta), 'gap': gap, 'uniform_saving': params['complex_uniform_saving'], 'H': height, 'N': '2^' + str(height), 'integer_test_exponent': right, 'word_materialized': False}, + 'nonrecursive': {'local_scalar': local_scalar, 'local_routes': routes, 'raw_scalar_upper': scalar_upper, 'raw_budget': 10**9, 'additional_private_slots': COUNT, 'owned_slots_backward': 2 * COUNT + 1, 'wrapper_allowance': wrapper_allowance}, + 'ordinary_BIT': bit, 'outer': outer, 'negative_controls': controls}) diff --git a/research/direct-backward-independent-validation/capsule/repository/research/kappa-backward-controller-20261023/verify.py b/research/direct-backward-independent-validation/capsule/repository/research/kappa-backward-controller-20261023/verify.py new file mode 100644 index 0000000000..55b904336e --- /dev/null +++ b/research/direct-backward-independent-validation/capsule/repository/research/kappa-backward-controller-20261023/verify.py @@ -0,0 +1,69 @@ +#!/usr/bin/env python3 +"""Verify the all-backward controller and complete conditional kappa. + +Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. +The retained local checker and witnesses are from PR5383. Read README.md. +""" +import argparse +import json +import sys +from hashlib import sha256 +sys.dont_write_bytecode = True +import native as N +import controller as C +import price + +PREDECESSOR_PAYLOAD = '2aee5e997df99726fc763e510d9cb69fbe4f86114dc8d2cd33ad26c6c462a21d' +NATIVE_HASH = '3c8efab1f830868c054d33391ee2f8bc74f9bae9c134edf5b455790eb674c1c4' +WITNESS_HASH = '24599011da06325e1012619b2b84a4dd3aceb90ab42d3caaf6414879e7d16591' + + +def run(): + for name, digest in [('native.py', NATIVE_HASH), ('WITNESS.json', WITNESS_HASH)]: + N.need(sha256((N.HERE / name).read_bytes()).hexdigest() == digest, 'Unchanged published predecessor: ' + name) + N.authenticate() + source = N.read(N.ROOT / N.SOURCE) + local = N.construct(source) + raw = (json.dumps(local, sort_keys=True, separators=(',', ':')) + '\n').encode() + N.need(sha256(raw).hexdigest() == PREDECESSOR_PAYLOAD, 'Exact published PR5383 local word') + c = local['canonical'] + before, after = {}, {} + for direction in ('forward', 'backward'): + back = direction == 'backward' + before[direction] = N.replay(c, source['programs'][direction], back, False) + N.need(before[direction]['paid'] == N.OLD_PAID and before[direction]['helpers'] == N.OLD_HELPERS, 'Selected source calibration') + after['backward'] = N.replay(c, local['programs']['backward'], True, True) + N.need(after['backward']['paid'] == N.NEW_PAID, 'Exact retained backward paid profile') + native_controls = N.controls(c, local) + identities = N.independent_source_identities(source) + phase = N.phase_inheritance(source, local) + word = C.construct() + physical = C.physical(word) + controls = C.controls(word) + arithmetic = price.run(after, word) + result = N.encode({'status': 'PASS_CONDITIONAL_KAPPA_00302728823_ALL_BACKWARD_CONTROLLER', + 'source_native': before, 'backward_native': after['backward'], + 'local_word_sha256': PREDECESSOR_PAYLOAD, + 'unrestricted_source_identities': identities, + 'source_phase_inheritance': phase, + 'physical_wrapper': physical, 'native_controls': native_controls, + 'controller_controls': controls, 'arithmetic': arithmetic}) + return word, result + + +def main(): + ap = argparse.ArgumentParser(description=__doc__) + ap.add_argument('--write', action='store_true') + args = ap.parse_args() + word, result = run() + for name, value in [('CONTROLLER.json', word), ('RESULT.json', result)]: + path = N.HERE / name + if args.write: + path.write_text(json.dumps(value, indent=2, sort_keys=True) + '\n', encoding='utf-8') + else: + N.need(json.loads(path.read_text()) == value, 'Exact published ' + name) + print(json.dumps({'status': result['status'], **{k: result['arithmetic'][k] for k in ('kappa', 'gain_over_PR5392', 'raw_root_interval', 'paid_calls', 'productive_fields')}}, sort_keys=True)) + + +if __name__ == '__main__': + main() diff --git a/research/direct-backward-independent-validation/capsule/repository/research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py b/research/direct-backward-independent-validation/capsule/repository/research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py new file mode 100644 index 0000000000..5a55034ec9 --- /dev/null +++ b/research/direct-backward-independent-validation/capsule/repository/research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py @@ -0,0 +1,351 @@ +#!/usr/bin/env python3 +"""Independent literal native replay with arbitrary dirty cleanup buffers. + +The retained emitter supplies words; this module imports no retained evaluator. +Free warp symbols distinguish primal and inverse-transpose operators. Physical +phase receipts are authenticated inherited evidence, not regenerated here. +Apache-2.0. Substantial OpenAI assistance. +""" +from collections import Counter, defaultdict +from fractions import Fraction +from hashlib import sha256 +from pathlib import Path +import argparse +import ast +import gzip +import json + + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[2] +CORE = ROOT / "research/kappa-native-resume/native-source/rebased-core" +PACKET = ROOT / "research/kappa-native-resume/causal-controller/sources/research/joint-query/certificate.json.gz" +TAGS = ("THREE-base", "THREE-extra", "FOUR-base", "FOUR-extra") +Q = Fraction + + +def need(condition, message): + if not condition: + raise ValueError(message) + + +def read(path): + raw = path.read_bytes() + return json.loads(gzip.decompress(raw) if path.suffix == ".gz" else raw) + + +def digest(path): + return sha256(path.read_bytes()).hexdigest() + + +def authenticate(): + pins = read(HERE / "SOURCES.json") + for relative, expected in pins.items(): + need(digest(ROOT / relative) == expected, "Changed retained source: " + relative) + return pins + + +def emit_original(canonical): + """Reuse only the pinned source's pure writer; no source verifier executes.""" + source = CORE / "sources/bw_emit.py" + names = {"basis", "reg", "dual", "scalar", "lregs", "expand", "emit", "primitive_bound"} + tree = ast.parse(source.read_text()) + functions = [n for n in tree.body if isinstance(n, ast.FunctionDef) and n.name in names] + need({n.name for n in functions} == names, "Exact writer function inventory") + context = dict(c=canonical, frames=canonical["frames"], v=112, R=408, h=9, n=632, Q=Q) + exec(compile(ast.Module(body=functions, type_ignores=[]), str(source), "exec"), context) + return {"forward": context["emit"](False), "backward": context["emit"](True)} + + +def span(basis): + points = {0} + for vector in basis: + need(isinstance(vector, int) and 0 <= vector < 512, "Nine-dimensional frame") + points |= {v ^ vector for v in tuple(points)} + return frozenset(points) + + +def identity(role): + return {(role, ()): Q(1)} + + +def add(destination, source, coefficient): + for key, value in tuple(source.items()): + value = destination.get(key, Q(0)) + coefficient * value + if value: + destination[key] = value + else: + destination.pop(key, None) + + +def warp(row, operator, backward): + symbol = (1 if operator > 0 else -1) * (abs(operator) + (10**6 if backward else 0)) + out = {} + for (variable, word), coefficient in row.items(): + moved = word[1:] if word and word[0] == -symbol else (symbol,) + word + key = variable, moved + out[key] = out.get(key, Q(0)) + coefficient + return {k: v for k, v in out.items() if v} + + +def expected(role, R, backward, clean): + out = identity(role) + name, i = role + if name != "L": + return out + target = i < 112 if backward else 112 <= i < 224 + if not target: + return out + port = i if backward else i - 112 + source_offset = 112 if backward else 0 + sign = -1 if backward else 1 + add(out, identity(("L", source_offset + port)), Q(sign)) + if clean: + for query in R: + if port in query: + for j, value in query.items(): + add(out, identity(("L", source_offset + j)), -sign * query[port] * value / 4) + return out + + +def replay(program, canonical, R, backward, clean, omit_cleanup_last=False): + """All L inputs and all Z inputs are independent, including dirty outputs.""" + n = 2 * canonical["v"] + canonical["R"] + need(n == 632, "Retained compact width") + rows = {("L", i): identity(("L", i)) for i in range(n)} + current = {("L", i): frame for i, frame in enumerate(canonical["start"])} + center_indices = set() + for event in program: + if event[0] == "scalar": + op = event[1] + for register in op[1:3] if op[0] in ("add", "copy") else op[1:2]: + if register[0] == "C": + center_indices.add(register[1]) + elif event[0] == "center": + center_indices.add(event[1]) + need(center_indices <= set(range(8)), "Known center workspace indices") + for i in center_indices: + rows["C", i] = identity(("C", i)) + current["C", i] = None + spaces = [span(vectors) for vectors in canonical["frames"]] + dimensions = [len(s).bit_length() - 1 for s in spaces] + need(dimensions[1] == 9, "Cleanup uses the full native frame") + live = set() + profile = Counter() + counts = Counter() + scalar_primitives = 0 + cleanup_start = next(i for i, event in enumerate(program) if event == ["phase", "full_frame_cleanup"]) + last_scalar = max(i for i, event in enumerate(program) if event[0] == "scalar" and i > cleanup_start) + for position, event in enumerate(program): + kind = event[0] + counts[kind] += 1 + if kind in ("climb", "center"): + if kind == "climb": + _, part, index, old, new, rank = event + role = "L", index + need(spaces[old] < spaces[new], "Non-nested or empty paid climb") + else: + _, index, old, new, rank = event + role = "C", index + need(spaces[old] < spaces[new] or spaces[new] < spaces[old], "Center residual is not nested") + need(current[role] == old and rank == abs(dimensions[new] - dimensions[old]), "Paid edge source/rank") + current[role] = new + profile[rank] += 1 + elif kind == "zero_buffer": + _, action, index = event + role = "Z", index + if action == "alloc": + need(role not in rows and role not in live, "Cleanup buffer duplicate") + rows[role] = identity(role) + current[role] = 1 + live.add(role) + else: + need(action == "free" and role in live and current[role] == 1, "Cleanup buffer retirement") + live.remove(role) + elif kind == "warp": + _, role, operator, old, new = event + role = tuple(role) + need(current[role] == old, "Warp entrance frame") + rows[role] = warp(rows[role], operator, backward) + current[role] = new + elif kind == "scalar": + op, frame = event[1:] + target = tuple(op[1]) + if op[0] == "clear": + need(target[0] == "C", "A borrowed input was cleared") + rows[target] = {} + current[target] = frame + scalar_primitives += 1 + continue + need(current[target] == frame, "Scalar target frame") + if op[0] in ("add", "copy"): + source = tuple(op[2]) + need(current[source] == frame, "Scalar source frame") + if op[0] == "copy": + need(target[0] == "C", "Copy overwrites borrowed state") + rows[target] = dict(rows[source]) + scalar_primitives += 1 + continue + coefficient = Q(op[3], op[4]) + need(target != source, "Self-ADD is not a reversible shear") + numerator, denominator = abs(coefficient.numerator), coefficient.denominator + need(numerator and denominator & (denominator - 1) == 0, "Non-dyadic ADD") + scalar_primitives += 3 + numerator.bit_length() - 1 + numerator.bit_count() + denominator.bit_length() - 1 + if not (omit_cleanup_last and position == last_scalar): + add(rows[target], rows[source], coefficient) + else: + need(op[0] == "scale", "Unknown scalar event") + coefficient = Q(op[2], op[3]) + numerator, denominator = abs(coefficient.numerator), coefficient.denominator + need(numerator and numerator & (numerator - 1) == 0 and denominator & (denominator - 1) == 0, + "Nonunit dyadic SCALE") + scalar_primitives += abs(numerator.bit_length() - denominator.bit_length()) + int(coefficient < 0) + if not (omit_cleanup_last and position == last_scalar): + rows[target] = {k: coefficient * v for k, v in rows[target].items()} + else: + need(kind in ("phase", "adapter", "residual_adapter"), "Unknown native event") + need(not live and [current["L", i] for i in range(n)] == canonical["final"], "Retired fields/final frames") + need(dict(profile) == {int(k): v for k, v in canonical["local_profile"].items()}, "Complete paid profile") + mismatches = [] + for role, actual in rows.items(): + wanted = {} if role[0] == "C" else expected(role, R, backward, clean) + if actual != wanted: + mismatches.append({"role": list(role), "unequal_coefficients": sum(actual.get(k, 0) != wanted.get(k, 0) for k in set(actual) | set(wanted))}) + if not omit_cleanup_last: + need(not mismatches, "Native dirty-buffer operator mismatch: " + repr(mismatches[:3])) + else: + need(mismatches, "Missing-cleanup negative control unexpectedly accepted") + buffer_count = sum(role[0] == "Z" for role in rows) + return dict(direction="backward" if backward else "forward", clean_J=clean, + independent_borrowed_input_fields=632+buffer_count, original_data_fields=224, + expected_restored_helpers=408, expected_restored_arbitrary_cleanup_buffers=buffer_count, + explicitly_owned_C_fields_cleared=len(center_indices), event_counts=dict(counts), + paid_profile=dict(sorted(profile.items())), paid_rank_mass=sum(k*v for k,v in profile.items()), + conservative_real_scalar_primitive_allowance=2*scalar_primitives, + all_scalar_frames_checked=True, dyadic_coefficients_and_unit_scales_checked=True, + free_warp_operator_endpoint_matches=not mismatches, + negative_control_omitted_last_cleanup_scalar=omit_cleanup_last, + mismatch_examples=mismatches[:3]) + + +def liveness(canonical): + times = defaultdict(list) + for i, event in enumerate(canonical["cleanup"]): + for role in event[1:3] if event[0] == "add" else event[1:2]: + role = tuple(role) if isinstance(role, list) else ("L", role) + times[role].append(i) + full = [i for i, f in enumerate(canonical["final"]) if f == 1] + candidates = [] + for z in canonical["zero_buffers"]: + begin, end = min(times["Z", z]), max(times["Z", z]) + possible = [i for i in range(112) if all(t < begin or t > end for t in times["L", i])] + candidates.append(dict(buffer=z, first_use=begin, last_use=end, + noninterfering_same_call_X_candidates=possible, + noninterfering_full_frame_L_candidates=[i for i in full if all(t < begin or t > end for t in times["L", i])])) + return dict(full_frame_live_roles=len(full), full_frame_roles_unused_in_cleanup=[i for i in full if not times["L", i]], + same_call_X_outputs_touched=sum(bool(times["L", i]) for i in range(112)), + buffers_with_no_noninterfering_same_call_X=sum(not row["noninterfering_same_call_X_candidates"] for row in candidates), + buffers_with_no_noninterfering_full_frame_L=sum(not row["noninterfering_full_frame_L_candidates"] for row in candidates), + intervals=candidates, + conclusion="Arbitrary-buffer restoration does not establish a legal same-call completed-output alias.", + external_same_frame_bank_requirement=91, + external_bank_hosting_constructed=False) + + +def find_aliases(canonical): + """Injective lifetime-safe matching; no native L access during its Z span.""" + options = {row["buffer"]: row["noninterfering_full_frame_L_candidates"] + for row in liveness(canonical)["intervals"]} + owner = {} + + def augment(z, seen): + for role in options[z]: + if role in seen: + continue + seen.add(role) + if role not in owner or augment(owner[role], seen): + owner[role] = z + return True + return False + + for z in sorted(options, key=lambda z: (len(options[z]), z)): + augment(z, set()) + bindings = {z: role for role, z in owner.items()} + need(len(set(bindings.values())) == len(bindings), "Alias must be injective") + need(all(role in options[z] for z, role in bindings.items()), "Interfering alias") + return bindings + + +def alias_program(program, bindings): + """Replace only Z register operands, retaining every native/scalar event.""" + out = [] + + def mapped(role): + return ["L", bindings[role[1]]] if role[0] == "Z" and role[1] in bindings else list(role) + + for event in program: + if event[0] == "zero_buffer" and event[2] in bindings: + continue + if event[0] == "scalar": + op = event[1].copy() + op[1] = mapped(op[1]) + if op[0] in ("add", "copy"): + op[2] = mapped(op[2]) + out.append(["scalar", op, event[2]]) + elif event[0] == "warp": + out.append([event[0], mapped(event[1]), *event[2:]]) + else: + out.append(event) + return out + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--output", type=Path, default=HERE / "RESULT.json") + args = parser.parse_args() + pins = authenticate() + R = [{int(k): Q(v) for k, v in row.items()} for row in read(PACKET)["R_rows"]] + providers = {} + for tag in TAGS: + providers[tag] = {} + for clean in (False, True): + folder = "converted" if clean else "sources" + canonical = read(CORE / folder / (tag + "-CANONICAL.json.gz")) + programs = read(CORE / folder / (tag + "-NATIVE-WORD.json.gz")) if clean else emit_original(canonical) + checks = [replay(programs[direction], canonical, R, direction == "backward", clean) + for direction in ("forward", "backward")] + bindings = find_aliases(canonical) + aliases = {direction: alias_program(program, bindings) for direction, program in programs.items()} + aliased_checks = [replay(aliases[direction], canonical, R, direction == "backward", clean) + for direction in ("forward", "backward")] + need(len(bindings) == 53, "Expected source-bound 53-field lifetime match") + for original, aliased in zip(checks, aliased_checks): + need(original["paid_profile"] == aliased["paid_profile"] and + original["conservative_real_scalar_primitive_allowance"] == aliased["conservative_real_scalar_primitive_allowance"], + "Aliasing changes the charged operation list") + providers[tag]["clean_J" if clean else "ordinary"] = dict(checks=checks, liveness=liveness(canonical), + lifetime_alias_bindings={str(z): role for z, role in sorted(bindings.items())}, + aliased_checks=aliased_checks, + eliminated_cleanup_fields=len(bindings), remaining_cleanup_fields=91-len(bindings), + aliased_word_sha256={direction: sha256(json.dumps(program, sort_keys=True, separators=(",", ":")).encode()).hexdigest() + for direction, program in aliases.items()}) + print("PASS all arbitrary cleanup inputs", tag, flush=True) + canonical = read(CORE / "converted/THREE-base-CANONICAL.json.gz") + programs = read(CORE / "converted/THREE-base-NATIVE-WORD.json.gz") + controls = [replay(programs[direction], canonical, R, direction == "backward", True, True) + for direction in ("forward", "backward")] + result = dict(schema="literal-native-dirty-buffers/1", status="PASS_NATIVE_ARBITRARY_DIRTY_BUFFER_REPLAY", + new_multiplication_kappa=False, physical_phase_generation_rerun=False, + phase_evidence="Pinned inherited exact native phase receipts; unchanged native edges.", + source_hashes=pins, verifier_sha256=digest(Path(__file__)), providers=providers, + negative_controls=controls, + lifetime_safe_local_full_frame_aliases_per_word=53, + remaining_external_bank_fields_per_word=38, + all_91_local_output_alias_claim=False, external_bank_placement_and_cost_closed=False) + args.output.parent.mkdir(parents=True, exist_ok=True) + args.output.write_text(json.dumps(result, indent=2) + "\n") + print(result["status"], flush=True) + + +if __name__ == "__main__": + main() diff --git a/research/direct-backward-independent-validation/capsule/repository/research/kappa-rebuild/architecture/mixed_target_probe.py b/research/direct-backward-independent-validation/capsule/repository/research/kappa-rebuild/architecture/mixed_target_probe.py new file mode 100644 index 0000000000..4fc05ab081 --- /dev/null +++ b/research/direct-backward-independent-validation/capsule/repository/research/kappa-rebuild/architecture/mixed_target_probe.py @@ -0,0 +1,291 @@ +#!/usr/bin/env python3 +"""Exact tariffs for productive helpers with heterogeneous target sizes. + +This is a conditional recursion-contract probe, not a new kappa claim. The +native helper adapters, main controller closure, scalar/precision charges, +and the mixed-target outer theorem remain separate obligations. + +Apache-2.0. Substantial OpenAI assistance. The original pruned native profile +and helper inventory come from the preserved kappa-function-composition work. +Mixed-target balance follows Jacob Alan Sussman's PR4268 proposal; this file +does not reprove or admit its all-size or integer-multiplication transfer. +The rational elementary-function enclosure follows the independently retained +productive_helper_forest.py recovery certificate, with fresh source identity. +""" +from collections import Counter +from fractions import Fraction as Q +from functools import lru_cache +from hashlib import sha256 +from pathlib import Path +import argparse +import json +import math +import sys + +sys.dont_write_bytecode = True +HERE = Path(__file__).resolve().parent +NATIVE = Counter({1:2453, 2:716, 3:224, 4:74, 5:48}) +HELPERS = Counter({5:28, 6:18, 7:56, 8:93, 9:213}) +OLD_PAIRS = [(56,9,7),(56,7,9),(18,9,6),(18,6,9), + (16,9,5),(16,5,9),(44,8,8)] +OLD_MIDDLE = [(93,8),(56,7),(18,6),(28,5),(29,0)] + +def need(ok, message): + if not ok: + raise AssertionError(message) + +@lru_cache(None) +def log_interval(r): + def odd_series(x): + z = (x-1)/(x+1) + n = 80 + low = 2*sum((z**(2*j+1)/(2*j+1) for j in range(n)), Q(0)) + high = low+2*z**(2*n+1)/((2*n+1)*(1-z*z)) + return low, high + exponent = r.bit_length()-1 + a,b = odd_series(Q(2)) + c,d = odd_series(Q(r,2**exponent)) + return exponent*a+c, exponent*b+d + +def exp_interval(x): + need(0 <= x < 1, 'Enclosure range') + term = total = Q(1) + n = 48 + for j in range(1,n+1): + term *= x/j + total += term + following = term*x/(n+1) + return total, total+following/(1-x/(n+2)) + +@lru_cache(None) +def h_interval(r,c): + if r in (0,1): + return Q(r),Q(r) + a,b = log_interval(r) + low,_ = exp_interval(c*a) + _,high = exp_interval(c*b) + return Q(r)/high,Q(r)/low + +def moment(profile,c): + low=high=Q(0) + for r,n in profile.items(): + a,b=h_interval(r,c) + low += n*(a if n >= 0 else b) + high += n*(b if n >= 0 else a) + return low,high + +def show(bounds): + scale=10**35 + low,high=bounds + a=low.numerator*scale//low.denominator + b=-((-high.numerator*scale)//high.denominator) + def fixed(n): + sign='-' if n<0 else '' + s=str(abs(n)).rjust(36,'0') + return sign+s[:-35]+'.'+s[-35:] + return {'lower':fixed(a),'upper':fixed(b)} + +def split_rank(r,maximum): + """Least concave tariff partition with positive integers <= maximum.""" + need(maximum>=1 and r>=0, 'Legal split') + q,remainder=divmod(r,maximum) + result=Counter() + if q: + result[maximum]+=q + if remainder: + result[remainder]+=1 + return result + +def split_profile(profile,maximum): + result=Counter() + for r,n in profile.items(): + for child,count in split_rank(r,maximum).items(): + result[child]+=n*count + return result + +def add_scaled(target,source,multiple=1): + for key,value in source.items(): + target[key]+=multiple*value + +def base_case(p,minimum,pairs=None,middle=None): + """Expand all role inventories; one fresh global field per unhosted role.""" + need(p in (1,2), 'Only reconstructed p1 and p2 schedules are in scope') + need(2<=minimum<=41, 'Finite minimum-target menu') + calls=2*p+1 + main_fields=224*p + main_rank=16*p+9 + inventories=[Counter(HELPERS) for _ in range(calls)] + paid=split_profile(NATIVE,minimum-1) + paid=Counter({r:calls*n for r,n in paid.items()}) + paid[1]+=8*calls # same-width H completion, never waived + targets=Counter({main_rank:main_fields}) + if p==1: + need(pairs is None and middle is None, 'p1 has no original idle bins') + else: + pairs=pairs if pairs is not None else [(224,0,0)] + middle=middle if middle is not None else [(224,0)] + need(sum(n for n,a,b in pairs)==224, 'Each pair window has 224 bins') + need(sum(n for n,a in middle)==224, 'Middle window has 224 bins') + for stages in [(0,1),(3,4)]: + for n,a,b in pairs: + need(a+b<=16 and a in (0,5,6,7,8,9) and b in (0,5,6,7,8,9), 'Pair capacities') + for stage,r in zip(stages,(a,b)): + if r: + inventories[stage][r]-=n + add_scaled(paid,split_rank(16-a-b,minimum-1),n) + for n,r in middle: + need(r in (0,5,6,7,8), 'Middle capacity') + if r: + inventories[2][r]-=n + add_scaled(paid,split_rank(8-r,minimum-1),n) + global_roles=Counter() + for inventory in inventories: + need(all(n>=0 for n in inventory.values()), 'No helper role used twice') + global_roles.update(inventory) + for r,n in global_roles.items(): + if not n: + continue + target=max(r,minimum) + targets[target]+=n + add_scaled(paid,split_rank(target-r,minimum-1),n) + paid=+paid + targets=+targets + need(max(paid)0] + # Middle bins are independent single slots; choose positive-gain roles first. + candidates=sorted(((sp(8)-sp(8-r)-value(r),r) for r in (5,6,7,8)),reverse=True) + middle=[] + left=224 + for gain,r in candidates: + if gain>1e-12: + n=min(HELPERS[r],left) + if n: + middle.append((n,r)) + left-=n + if left: + middle.append((left,0)) + return pairs,middle,{'status':int(out.status),'message':out.message,'not_an_exact_optimality_claim':True} + +def run(discover=False): + candidates=[] + for p in (1,2): + for minimum in range(2,26): + candidates.append(base_case(p,minimum)) + candidates.append(base_case(2,9,OLD_PAIRS,OLD_MIDDLE)) + discovery=[] + if discover: + for c in (.001745,.004): + for minimum in range(5,18): + pairs,middle,meta=discover_pair_patterns(minimum,c) + case=base_case(2,minimum,pairs,middle) + case['discovery_target']=str(c) + case['solver']=meta + discovery.append(case) + candidates.extend(discovery) + best={} + for p in (1,2): + for text in ('0.001745','0.004'): + c=Q(text) + rows=[case for case in candidates if case['p']==p] + ranked=sorted(rows,key=lambda case:-numerical_value(case['signed'],float(c))) + winner=ranked[0] + # Certify that this displayed winner beats all numerically distinct + # profiles in the finite scanned menu, not all possible schedules. + win=moment(winner['signed'],c) + for case in ranked[1:]: + if dict(case['signed'])!=dict(winner['signed']): + need(win[0]>moment(case['signed'],c)[1], 'Exact finite-menu ordering') + best[f'p{p}_{text}']=serialize_case(winner) + controls={} + wrong=base_case(1,6) + wrong['targets'][6]+=1 + controls['unearned_output_credit_rejected']=(sum(r*n for r,n in wrong['targets'].items())-wrong['rank_bill']!=wrong['rank_margin']) + controls['rank5_child_with_job5_rejected']=not(5<5) + need(all(controls.values()), 'Corruption controls') + return {'schema':'productive-helper-mixed-target-tariff/1', + 'status':'PASS_CONDITIONAL_EXACT_ACCOUNTING', + 'source_sha256':sha256(Path(__file__).read_bytes()).hexdigest(), + 'native_profile':dict(NATIVE),'helper_inventory':dict(HELPERS), + 'assumed_recursive_rule':'sum_paid n_r r^(1-C) < sum_targets W_k k^(1-C); max_paid_rank < min_target_rank', + 'best_in_finite_menu':best, + 'fixed_p2_minimum9':serialize_case(base_case(2,9,OLD_PAIRS,OLD_MIDDLE)), + 'discovery_candidates':[serialize_case(c) for c in discovery], + 'controls':controls, + 'not_proved':['native whole-helper adapters and arbitrary-input block diagonal contract', + 'correct main controller and all its heads/caches/cleanup', + 'literal eligibility of any displayed head-cut grant', + 'mixed-target all-size recursion in this native model', + 'finite-precision integer-multiplication transfer and scalar/stock costs'], + 'new_kappa':False} + +def main(): + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('--discover',action='store_true') + parser.add_argument('--output',type=Path,default=HERE/'MIXED-TARGET-PROBE.json') + args=parser.parse_args() + result=run(args.discover) + args.output.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + print(json.dumps({'status':result['status'],'best':{k:v['targets_at_C'][k.split('_',1)[1]]['after_native_completion_before_main_closure'] for k,v in result['best_in_finite_menu'].items()}},sort_keys=True)) + +if __name__=='__main__': + main() diff --git a/research/direct-backward-independent-validation/capsule/repository/research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz b/research/direct-backward-independent-validation/capsule/repository/research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz new file mode 100644 index 0000000000..46d929df83 Binary files /dev/null and b/research/direct-backward-independent-validation/capsule/repository/research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz differ diff --git a/research/direct-backward-independent-validation/capsule/repository/research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz b/research/direct-backward-independent-validation/capsule/repository/research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz new file mode 100644 index 0000000000..ac77b78547 Binary files /dev/null and b/research/direct-backward-independent-validation/capsule/repository/research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz differ diff --git a/research/direct-backward-independent-validation/capsule/repository/research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json b/research/direct-backward-independent-validation/capsule/repository/research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json new file mode 100644 index 0000000000..0fdb65f946 --- /dev/null +++ b/research/direct-backward-independent-validation/capsule/repository/research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json @@ -0,0 +1,241 @@ +{ + "compiler": { + "H": 38569300000000000, + "N": "2^38569300000000000", + "eta": { + "lower": "0.000000204535199106284215364833", + "upper": "0.000000204535199106284215364834" + }, + "gap": "1/700000000000", + "integer_test_exponent": 55099, + "logarithm_power": 1000, + "theta": "63/64", + "uniform_saving": "1057621533/350000000000", + "word_materialized": false + }, + "gain_over_PR4535": "4027/2500000000", + "kappa": "15108879/5000000000", + "local_helpers": { + "4": 28, + "7": 7, + "8": 47, + "9": 326 + }, + "local_paid": { + "1": 2201, + "2": 412, + "3": 510, + "4": 127, + "5": 40, + "8": 8 + }, + "margin_at_old_root_upper": [ + "78072058023577019965454984044224523228758899702419408235/196159429230833773869868419475239575503198607639501078528", + "1249152928377232319447279744707592371660142395238823308861/3138550867693340381917894711603833208051177722232017256448" + ], + "native_receipt_sha256": "eec3b14241430b6c9f5de3cbf0e3d45a172d8071d2dccd2b59d56a1fbac3d428", + "negative_controls": { + "closed_epsilon": [ + "epsilon_below_one", + "global_gamma_power_slack", + "actual_logarithmic_gamma_guard", + "source_axis_superpolynomial", + "gaussian_above_main", + "new_semantic_guard_with_C1_one" + ], + "closed_uniform": [ + "new_complex_uniform_saving_above_b" + ], + "old_BIT": [ + "actual_bit_above_effective" + ], + "unfunded_endpoint": [ + "main_transform_above_kappa", + "global_coordinate_router_above_kappa", + "fused_gaussian_above_kappa", + "group_bit_router_above_kappa", + "boundary_algebraic_matrix_above_kappa" + ] + }, + "nonrecursive": { + "local_routes": 4802000, + "local_scalar": 158168, + "raw_scalar_upper": 181098496 + }, + "ordinary_BIT": { + "admitted": "17/5000", + "after_cover": "69/20000", + "atom": "1/250", + "before_cover": "3459/1000000", + "ordinary_saving": "8590884599/2500000000000", + "prime_rule": "odd q > 2^26*N^5 avoiding all fixed denominators and rank witnesses" + }, + "outer": { + "functional_checks": { + "actual_new_BIT_stock_sublinear": "174299999999253/175000000000000", + "fixed_halo_explicit_metadata_branch": "13475000000001/175000000000", + "new_BIT_row_stock_sublinear_in_active_group": "697899999997009/700000000000000", + "new_semantic_group_guard": "3/700000000000" + }, + "margins": { + "boundary_algebraic_matrix": "1480670144797884756937/490000000000000000000000", + "fused_gaussian": "1480670144793654270811/490000000000000000000000", + "global_coordinate_router": "264405383/87500000000", + "group_bit_router": "185083768186706783851/61250000000000000000000", + "group_scans": "349999999999/350000000000", + "main_transform": "1480670144097884756937/490000000000000000000000", + "microbox_face_corrections": "13475000000001/175000000000", + "polynomial_products": "699999999999/700000000000", + "sparse_union_movement": "200543170144797884756937/490000000000000000000000" + }, + "parameters": { + "a": "264405383/87500000000", + "b": "423048613/140000000000", + "beta": "699999999997/700000000000", + "bit_saving": "17/5000", + "cap_xi": "445543170144097884756937/490000000000000000000000", + "complex_uniform_saving": "1057621533/350000000000", + "d": "1/700000000000", + "epsilon": "699999999999/700000000000", + "kappa": "15108879/5000000000", + "lambda_": "199395644839/200000000000", + "lambda_prime": "697884756937/700000000000", + "layout": "1/700000000000", + "q": "2115243063/700000000000", + "r0": "1/7000000000000", + "stop": "1/700000000000", + "tested_saving": "302177581/100000000000" + }, + "strict_checks": { + "actual_bit_above_effective": "33094617/87500000000", + "actual_logarithmic_gamma_guard": "1/700000000000", + "actual_logarithmic_group_guard": "44456829856952115243063/245000000000000000000000", + "alpha_logarithm_absorption": "1/7000000000000", + "boundary_algebraic_matrix_above_kappa": "2797884756937/490000000000000000000000", + "cap_above_band": "200543170144097884756937/490000000000000000000000", + "cap_below_cell": "44456829855202115243063/490000000000000000000000", + "cap_below_phase_cell_power": "534456829855902115243063/490000000000000000000000", + "complex_above_effective": "1/700000000000", + "complex_below_one_over_32": "3951951387/140000000000", + "complex_endpoint": "1/350000000000", + "epsilon_below_one": "1/700000000000", + "epsilon_positive": "699999999999/700000000000", + "fine_prime_halo_umbrella": "7/2", + "fused_gaussian_above_kappa": "2793654270811/490000000000000000000000", + "gaussian_above_main": "347884756937/245000000000000000000000", + "global_coordinate_router_above_kappa": "1/175000000000", + "global_gamma_power_slack": "9/7000000000000", + "group_below_dimension": "1/350000000000", + "group_bit_router_above_kappa": "436706783851/61250000000000000000000", + "group_gauge_power_slack": "44456829856917115243063/245000000000000000000000", + "group_key_fits_record": "1/350000000000", + "group_positive": "699999999997/700000000000", + "group_scans_above_kappa": "348942378469/350000000000", + "halo_covers_generic_inverse_radius": "5", + "improvement_over_user_baseline": "645402690400418148631/500000000000000000000000", + "lambda_above_internal": "1/1400000000000", + "lambda_above_sigma": "3/1400000000000", + "lambda_above_tau": "1/1400000000000", + "lambda_prime_above_lambda": "1/1400000000000", + "lambda_prime_above_leaf": "279576951387/98000000000000000000000", + "leaf_saving_above_effective": "139576951387/98000000000000000000000", + "main_transform_above_kappa": "2097884756937/490000000000000000000000", + "membership_arithmetic_fits_record": "1/700000000000", + "microbox_face_corrections_above_kappa": "3368617797309/43750000000", + "microbox_halo_volume": "55300000000003/700000000000", + "new_complex_uniform_saving_above_b": "1/700000000000", + "new_semantic_guard_with_C1_one": "1/700000000000", + "polynomial_products_above_kappa": "697884756939/700000000000", + "positive_layout_slack": "1/700000000000", + "q_below_effective": "1/700000000000", + "q_below_internal": "1/700000000000", + "q_below_leaf": "279576951387/98000000000000000000000", + "q_positive": "2115243063/700000000000", + "short_record_fallback": "139576951387/140000000000", + "source_axis_superpolynomial": "1/700000000000", + "sparse_union_movement_above_kappa": "199062500002797884756937/490000000000000000000000", + "stop_below_one": "699999999999/700000000000", + "stop_positive": "1/700000000000", + "strassen_integer_power_gap": "1951441519231", + "support_router_span": "3/700000000000", + "theta_positive_polynomial_power": "2", + "union_header_fits_record": "3/700000000000", + "union_tag_work_per_visit_fits_record": "3/700000000000" + } + }, + "paid": { + "1": 41298, + "16": 448, + "2": 7416, + "24": 448, + "3": 9180, + "32": 448, + "4": 2286, + "40": 448, + "48": 448, + "5": 720, + "56": 448, + "64": 448, + "72": 224, + "8": 144 + }, + "paid_calls": 64404, + "productive_fields": 10928, + "rank_mass_surplus": 752, + "raw_root_interval": [ + "302177587077/100000000000000", + "151088793539/50000000000000" + ], + "scope": "Exact changed-profile arithmetic only. Requires separately admitted changed native programs, paid transports and absolute phases. Retained compiler/native/precision/tape/analytic/recovery assumptions.", + "source_sha256": { + "research/fresh-helper-boundary/native.py": "9b55a2d3c3972148fae9d112e745d9244968166bd89bd900c938f429fc76ab29", + "research/higher-moment-strictification/verify.py": "0ce7e7137422d5ffeda22085c81fa88471bbe963100fdad62e659f1e3bf89326", + "research/joint-helper-lattice/CONTROLLER.json": "1f5d6aa267e4e66048818714b5d3b5eae17a58abe91d15deeaa34574f7391a5f", + "research/joint-helper-lattice/native_joint.py": "50869b1bcad7493e6b4cb2a4cd5d2fd9a193a5921100483fa2c3f2c999ddfd46", + "research/joint-helper-lattice/verify.py": "8eb13f77a94315f811612cb557a17edeecb6b9d9a75dfa238b112dd6520c336f", + "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/bit-compression/carrier-reuse/reference/joint_pair_dag.py": "8a0de761642d21919e969475c3f13e5d01a4bae7343c1e1f37c586d94b676a85", + "research/kappa-rebuild/architecture/mixed_target_probe.py": "011c3c9d0cf81103dc84d709a0e36793eb7c5ae3f23c85eac27650ef13afa04a", + "research/kappa-rebuild/bit/complex_controller_factor.py": "1de9aaf918e6a4f2f5448754c1f3c3da3b85e6257849ebd097af09859c4e5497", + "research/kappa-rebuild/bit/mixed_productive_bit.py": "b32291b0db7fc0d332ec444c70746ab0fb03351d2e50546f8bcb64060e3ff95e", + "research/kappa-round6-compiler-tightening-20261022/arithmetic.py": "960864e5427a1ca2c319a7b2dee292b6fe50bd5964830031e611591af10dac38", + "research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py": "d097e55f06c3f244f2074ffd7c1a0a5f3c4b4b6a6accf9619d1dde5c0ae85e15", + "research/query-thinned-controllers/RESULT.json": "6ebfc8c0f09166f4834e9d7427410cb31aefff2cd4d4ce588c8e52c9c70e9a0f", + "research/query-thinned-controllers/controller.py": "8b462d660487b1be4940357c4c7522967b1bfaede3c02b1c66109b85acae0fd2" + }, + "status": "PASS_CHANGED_PROFILE_ARITHMETIC_NATIVE_ADMISSION_SEPARATE", + "strictification": { + "alpha": { + "lower": "0.999999999936687383304469699479", + "upper": "0.999999999936687383304469699480" + }, + "cutoff": 20, + "delta": { + "lower": "0.958285308639504859158849914083", + "upper": "0.958285308639504859158849914084" + }, + "floor": 21, + "gamma": { + "lower": "0.956217509753795293454516855483", + "upper": "0.956217509753795293454516855484" + }, + "normalized_paid_upper": "104857600097656251/104857601073741824", + "power": 1024, + "tail_offset": "1/5", + "tested": "302177581/100000000000" + }, + "targets": { + "145": 224, + "17": 448, + "25": 448, + "33": 448, + "4": 504, + "41": 448, + "49": 448, + "57": 448, + "65": 448, + "7": 126, + "73": 224, + "8": 846, + "9": 5868 + } +} diff --git a/research/direct-backward-independent-validation/capsule/repository/research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py b/research/direct-backward-independent-validation/capsule/repository/research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py new file mode 100644 index 0000000000..340e1f0ffb --- /dev/null +++ b/research/direct-backward-independent-validation/capsule/repository/research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py @@ -0,0 +1,240 @@ +#!/usr/bin/env python3 +"""Exact endpoint refill conditional on the source PR4359 construction. + +Apache-2.0. Substantial OpenAI assistance. The mixed inventory and elementary +function enclosure are zxv's PR4359; mixed-target flow is Jacob Alan Sussman's +Theorem 1G. Outer formulas retain the attribution in PR4359 outer_parameters.py. +This file checks arithmetic, not the native or all-size proof hypotheses. +""" +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from pathlib import Path +import argparse +import gzip +import importlib.util +import json +import sys + +sys.dont_write_bytecode = True +HERE = Path(__file__).resolve().parent +PREFIX = Path('research/kappa-rebuild') +OLD_BASELINE = Q('0.001730970419199163702738') +KAPPA = Q('0.00230509') +TESTED = Q('0.00230509019') +ROOT_UPPER = Q('0.002306') + + +def need(value, message): + if not value: + raise AssertionError(message) + + +def read(path): + raw = path.read_bytes() + return json.loads(gzip.decompress(raw) if path.suffix == '.gz' else raw) + + +def ceil(value): + value = Q(value) + return -((-value.numerator) // value.denominator) + + +def encode(value): + if isinstance(value, Q): + return str(value) + if isinstance(value, dict): + return {str(k): encode(v) for k, v in value.items()} + if isinstance(value, (tuple, list)): + return [encode(v) for v in value] + return value + + +def family(kappa, tested): + """One explicit slack family approaching the same source mixed root.""" + need(Q(0) < kappa < tested < ROOT_UPPER, 'Positive strictly ordered savings') + d = (tested-kappa)/7 + return {'kappa': kappa, 'tested_saving': tested, + 'complex_uniform_saving': kappa+6*d, + 'b': kappa+5*d, 'a': kappa+4*d, 'q': kappa+3*d, + 'bit_saving': Q('0.0027'), 'epsilon': 1-d, 'beta': 1-3*d, + 'r0': d/10, 'stop': d, 'layout': d, 'd': d} + + +def ledger(p): + """Recompute all 54 named PR4359 checks with freely supplied parameters.""" + kappa, b, a, q = (p[key] for key in ('kappa', 'b', 'a', 'q')) + epsilon, beta, r0, stop, layout = (p[key] for key in + ('epsilon', 'beta', 'r0', 'stop', 'layout')) + sigma, tau = 1-b, 1-a + internal = tau+(1-stop)*max(sigma-tau, Q(0)) + leaf = sigma+stop*(1-sigma) + lam, c = 1-(q+a)/2, Q(3, 32) + xi, key = epsilon*(1+q)-c+layout, beta+1-epsilon + margins = { + 'main_transform': epsilon*q, + 'global_coordinate_router': a, + 'fused_gaussian': 1-epsilon+q*beta, + 'group_bit_router': 1-epsilon+a*beta, + 'group_scans': 1-epsilon+beta, + 'boundary_algebraic_matrix': c+xi-epsilon, + 'sparse_union_movement': xi+Q(1, 2)-epsilon, + 'polynomial_products': epsilon, + 'microbox_face_corrections': 1-(epsilon+beta+48-128+2), + } + checks = { + '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': stop, 'stop_below_one': 1-stop, + 'leaf_saving_above_effective': (1-stop)*b-a, + 'q_below_internal': 1-internal-q, 'q_below_leaf': 1-leaf-q, + 'lambda_above_tau': lam-tau, 'lambda_above_sigma': lam-sigma, + 'lambda_above_internal': lam-internal, + 'lambda_prime_above_lambda': 1-q-lam, + 'lambda_prime_above_leaf': 1-q-leaf, + 'epsilon_positive': epsilon, 'epsilon_below_one': 1-epsilon, + 'cap_above_band': xi-Q(1, 2), 'cap_below_cell': epsilon-xi, + 'group_positive': beta, 'group_below_dimension': epsilon-beta, + 'support_router_span': 1-beta, + 'group_gauge_power_slack': 1-(2*xi-2)-r0-beta, + 'actual_logarithmic_group_guard': 1-(2*xi-2)-beta, + 'global_gamma_power_slack': 1-epsilon-r0, + 'actual_logarithmic_gamma_guard': 1-epsilon, + 'alpha_logarithm_absorption': r0, + 'group_key_fits_record': 1-key, + 'membership_arithmetic_fits_record': 1-beta-2*(1-epsilon), + 'microbox_halo_volume': 128-48-beta, + 'positive_layout_slack': layout, + 'short_record_fallback': epsilon-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(48-43), + 'union_tag_work_per_visit_fits_record': 1-beta, + 'union_header_fits_record': 1-beta, + 'source_axis_superpolynomial': 1-epsilon, + 'gaussian_above_main': margins['fused_gaussian']-margins['main_transform'], + 'new_complex_uniform_saving_above_b': p['complex_uniform_saving']-b, + 'improvement_over_user_baseline': kappa-OLD_BASELINE, + 'new_semantic_guard_with_C1_one': 1-epsilon, + 'fine_prime_halo_umbrella': 10-(2*2+2+Q(1, 2)), + } + checks.update({name+'_above_kappa': value-kappa for name, value in margins.items()}) + # These are the additional functional conditions in the independent + # PR4359 outer_transfer_audit.py, beyond the 54-row parameter ledger. + functional = { + 'new_semantic_group_guard': 1-beta, + 'new_BIT_row_stock_sublinear_in_active_group': beta*(1-Q(3, 1000)), + 'fixed_halo_explicit_metadata_branch': 128-48-epsilon-beta-1, + } + return {'parameters': dict(p, cap_xi=xi, lambda_=lam, lambda_prime=1-q), + 'margins': margins, 'strict_checks': checks, 'functional_checks': functional} + + +def compiler_rank(E, targets, paid, tested, uniform): + """The original sufficient bound, re-instantiated for the new exponent.""" + m, kmin, rmax = max(targets), min(targets), max(paid) + need((m, kmin, rmax) == (57, 6, 5), 'Pinned complex separation') + t, z = 1-tested, 1-uniform + z0, h = (t+z)/2, Q(1, 10) + delta = z0-t + need(0 < t < z0 < z < 1, 'Compiler exponent order') + need(5**10 < 6**9 and 57 < 2**10, 'Exact source rank bounds') + need(z0 > Q(1, 2) and (1-z0)*E.log_interval(m)[1] < E.log_interval(2)[0], + 'Original eta strictly exceeds 1/4') + H0 = ceil((3+4*delta)/(h*delta)) + ratio = H0*(1-z0)/(z-z0) + H1 = ratio.numerator//ratio.denominator+1 + need(H0 >= m.bit_length() and H0*h*delta >= 3+4*delta, 'Induction starts') + need(H1*(z-z0) > H0*(1-z0), 'Strict winning uniform rank') + need((H0-1)*h*delta < 3+4*delta, 'Reject one lower threshold exponent') + need((H1-1)*(z-z0) <= H0*(1-z0), 'Reject one lower final exponent') + return {'t': t, 'z0': z0, 'z': z, 'theta_upper': Q(9, 10), + 'H0': H0, 'H1': H1, 'N_encoding': '2^H1', + 'strict_final_gap': H1*(z-z0)-H0*(1-z0), + 'winning_word_materialized': False, + 'bound': 'Original sufficient inequality; a sharper bound is separate.'} + + +def run(source_root): + base = source_root/PREFIX + interval_path = base/'architecture/mixed_target_probe.py' + spec = importlib.util.spec_from_file_location('pr4359_moment', interval_path) + E = importlib.util.module_from_spec(spec) + spec.loader.exec_module(E) + cover = read(base/'controller/P3-NATIVE-COVER.json.gz')['cover'] + targets = {int(k): int(v) for k, v in cover['targets'].items()} + paid = {int(k): int(v) for k, v in cover['paid'].items()} + need(targets == {6: 192, 7: 56, 8: 93, 9: 1229, 25: 448, 57: 224}, + 'Exact source productive inventory') + need(paid == {1: 17623, 2: 5065, 3: 1738, 4: 714, 5: 254}, + 'Exact source paid inventory') + signed = Counter(targets) + signed.subtract(paid) + need(sum(k*v for k, v in signed.items()) == 224, 'Rank-one surplus') + bracket = {'lower': E.moment(signed, TESTED), 'upper': E.moment(signed, ROOT_UPPER)} + need(bracket['lower'][0] > 0 and bracket['upper'][1] < 0, + 'Strict mixed test and upper root bound') + + original = read(base/'controller/OUTER-PARAMETERS.json')['outer'] + old = ledger({'kappa': Q('0.0023'), 'complex_uniform_saving': Q('0.002304'), + 'b': Q('0.002303'), 'a': Q('0.0023025'), 'q': Q('0.002302'), + 'bit_saving': Q('0.0027'), 'epsilon': Q('0.99999'), + 'beta': Q('0.99997'), 'r0': Q(1, 10**6), + 'stop': Q(1, 10**8), 'layout': Q(1, 10**6)}) + for group in ('margins', 'strict_checks'): + frozen = {key: Q(value['rational']) for key, value in original[group].items()} + need(old[group] == frozen, 'Exact reproduction of every old '+group) + p = family(KAPPA, TESTED) + result = ledger(p) + need(all(v > 0 for v in result['strict_checks'].values()), 'All 54 new outer predicates') + need(all(v > 0 for v in result['functional_checks'].values()), 'Additional functional predicates') + need(min(result['margins'].values()) == result['margins']['main_transform'], + 'Main transform remains limiting') + need(result['parameters']['cap_xi'] == Q(29, 32)+(1-p['d'])*p['q'], + 'Cofinal cap simplification') + controls = {} + for label, updates in [('closed_epsilon_gap', {'epsilon': Q(1)}), + ('missing_layout', {'layout': Q(0)}), + ('unfunded_kappa', {'kappa': Q('0.002306')}), + ('BIT_below_effective', {'bit_saving': OLD_BASELINE}), + ('no_complex_slack', {'complex_uniform_saving': p['b']})]: + tested = ledger(dict(p, **updates)) + failures = {k: v for k, v in tested['strict_checks'].items() if v <= 0} + need(failures, 'Mutation rejected: '+label) + controls[label] = failures + need(E.moment(signed, Q('0.004'))[1] < 0, 'Unsupported mixed target is rejected') + inputs = [interval_path, base/'controller/P3-NATIVE-COVER.json.gz', + base/'controller/OUTER-PARAMETERS.json'] + return encode({'schema': 'pr4359-cofinal-outer-refill/1', + 'status': 'PASS_EXACT_CONDITIONAL_ENDPOINT_REFILL', + 'kappa': KAPPA, 'gain_over_PR4359': KAPPA-Q('0.0023'), + 'unchanged_paid': paid, 'unchanged_targets': targets, + 'mixed_test_saving': TESTED, 'mixed_test_margin': E.show(bracket['lower']), + 'root_upper_test': ROOT_UPPER, 'root_upper_margin': E.show(bracket['upper']), + 'old_ledger_crosscheck': {'matched_savings': len(old['margins']), + 'matched_checks': len(old['strict_checks'])}, + 'outer': result, 'limiting_margin': min(result['margins'].values())-KAPPA, + 'compiler': compiler_rank(E, targets, paid, TESTED, p['complex_uniform_saving']), + 'negative_controls': controls, + 'source_sha256': {str(p.relative_to(source_root)): sha256(p.read_bytes()).hexdigest() + for p in inputs}, + 'scope': 'Conditional arithmetic and specified finite rank. The PR4359 native, compiler, cover, precision, fixed-tape and outer hypotheses remain premises; no full theorem or practical word is certified.'}) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--source-root', type=Path, default=HERE/'source') + parser.add_argument('--out', type=Path) + args = parser.parse_args() + result = run(args.source_root) + if args.out: + args.out.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + print(json.dumps({key: result[key] for key in + ('status', 'kappa', 'gain_over_PR4359', 'limiting_margin', 'compiler')}, sort_keys=True)) + + +if __name__ == '__main__': + main() diff --git a/research/direct-backward-independent-validation/capsule/repository/research/pr4359-p7-padding/native_inventory.py b/research/direct-backward-independent-validation/capsule/repository/research/pr4359-p7-padding/native_inventory.py new file mode 100644 index 0000000000..8d2d96e399 --- /dev/null +++ b/research/direct-backward-independent-validation/capsule/repository/research/pr4359-p7-padding/native_inventory.py @@ -0,0 +1,270 @@ +#!/usr/bin/env python3 +"""Dimension-independent exact native phase audit for an all-fresh controller. + +Uses the original nine-axis native supplier, with fresh eight-axis blocks. +No helper is hosted in a main idle field. Source all-column semantics remain +a written premise; this checks each finite raw contact and endpoint phase. +""" +from collections import Counter +from fractions import Fraction as Q +from functools import lru_cache +from hashlib import sha256 +from pathlib import Path +import gzip +import importlib.util +import json +import sys + +sys.dont_write_bytecode = True +HERE = Path(__file__).resolve().parent +NATIVE = HERE/'dependencies/tensor-strictification/native_inventory.py' + + +def need(test, why): + if not test: + raise AssertionError(why) + + +def load(path, name): + spec = importlib.util.spec_from_file_location(name, path) + module = importlib.util.module_from_spec(spec) + sys.modules[name] = module + spec.loader.exec_module(module) + return module + + +def read(path): + data = path.read_bytes() + return json.loads(gzip.decompress(data) if path.suffix == '.gz' else data) + + +def norm(terms): + out = Counter() + for axis, value in terms: + out[axis] += value + return tuple(sorted((axis, value % 4) for axis, value in out.items() if axis and value % 4)) + + +def act(columns, value): + result = 0 + while value: + low = value & -value + result ^= columns[low.bit_length()-1] + value ^= low + return result + + +@lru_cache(None) +def polynomial(terms, dimension): + linear = [0]*dimension + quadratic = [0]*dimension + for axis, value in terms: + support = [i for i in range(dimension) if axis >> i & 1] + for i in support: + linear[i] = (linear[i]+value) % 4 + if value % 2: + for j in support: + if i < j: + quadratic[i] ^= 1 << j + return tuple(linear), tuple(quadratic) + + +def contact(old, new, route, dimension): + moved = norm((act(route, axis), value) for axis, value in old) + left, right = polynomial(moved, dimension), polynomial(new, dimension) + need(left[1] == right[1], 'Actual native contact has identical quadratic part') + delta = tuple((a-b) % 4 for a, b in zip(right[0], left[0])) + need(all(value in (0, 2) for value in delta), 'Even linear phase is a physical translation') + shift = sum((value//2) << i for i, value in enumerate(delta)) + need(polynomial(norm(list(moved)+[(shift, 2)]), dimension) == right, 'Full native forward phase') + inverse_shift = act(route, shift) + inverse = norm([(act(route, axis), value) for axis, value in new]+[(inverse_shift, 2)]) + need(polynomial(inverse, dimension) == polynomial(old, dimension), 'Full inverse contact phase') + return {'translation': shift, 'inverse_translation': inverse_shift} + + +def scalar_invoice(case, native_scalar): + word = case['right_program']+case['left_program'] + counts = Counter(row[0] for row in word) + need(all(Q(row[-1]) in (1, -1) for row in word if row[0] in ('ADD', 'SCALE')), + 'Literal boundary word has only unit coefficients') + adds = counts['ADD']+3*counts['SWAP'] + negs = counts['SCALE']+counts['SWAP'] + bridges = sum(row[0] == 'ADD' for row in case['physical_events']) + swaps = sum(row[0] == 'SIGNED_SWAP' for row in case['physical_events']) + return native_scalar+112*(8*(adds+bridges+3*swaps)+2*negs) + + +def run(source_root, p=7, keep=232127, output_dir=None): + root = Path(source_root).resolve() + base = root/'research/kappa-rebuild' + need((p, keep) == (7, 232127), 'This source-bound native admission is p7 keep232127') + inventory = load(NATIVE, 'checked_native_inventory') + native_gate = inventory.run(root) + factor = load(HERE/'factor_receipt.py', 'fixed_p7_factor') + case, factor_pins = factor.run(root) + replay_path = base/'transfer-audit/p3_native_audit.py' + need(sha256(replay_path.read_bytes()).hexdigest() == '5504a55a50546418d10c522984438cdeedb44993f7c1dab7bd4aa1ae0515d902', + 'Exact independent Laurent replay source') + audit = load(replay_path, 'independent_laurent_replay') + audit.replay(case) + corrupted = json.loads(json.dumps(case)) + next(row for row in corrupted['physical_events'] if row[0] == 'LOCAL' and row[3])[3] = False + wrong_orientation_rejected = False + try: + audit.replay(corrupted) + except AssertionError: + wrong_orientation_rejected = True + need(wrong_orientation_rejected, 'A wrong native reverse orientation fails the exact whole Laurent word') + phase_path = root/'research/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json' + if not phase_path.exists(): + phase_path = root/'research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json' + need(sha256(phase_path.read_bytes()).hexdigest() == 'c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa', + 'Exact original native port phase source') + phases = read(phase_path) + dimension = 9+16*p + axes = tuple(1 << i for i in range(dimension)) + def completed(stage): + return norm((axis, 1) for axis in axes[:9+8*stage]) + def stage_frame(stage, q): + return norm([(axis, 1) for axis in axes[:9]]+[(q, -1)] if stage == 0 + else [(axis, 1) for axis in axes[9+8*(stage-1):9+8*stage]]) + contacts = [] + stages = [row for row in case['physical_events'] if row[0] == 'LOCAL'] + need([row[1] for row in stages] == list(range(2*p+1)), 'Exact chronological stage sequence') + for _, stage, pair, backward in stages: + sign = -1 if backward else 1 + spectator = norm((axis, 1) for axis in axes[9:9+8*stage]) + for port, recipe in enumerate(phases['recipes']): + q = recipe['q'] + basis = recipe['idle_children'][0]['orthogonal_axes'][:8] + need(all((b & q).bit_count() % 2 == 0 for b in basis), 'Actual owner basis is orthogonal to q') + need(all((a & b).bit_count() % 2 == int(i == j) for i, a in enumerate(basis) + for j, b in enumerate(basis)), 'Actual eight-vector basis is orthonormal') + swaps = [] if stage == 0 else [b ^ axes[9+8*(stage-1)+i] for i, b in enumerate(basis)] + route = tuple(e ^ act(swaps, sum(((e & v).bit_count() % 2) << i for i, v in enumerate(swaps))) + for e in axes) + need(all(act(route, route[i]) == axes[i] for i in range(dimension)), 'Full dimension route is an involution') + need(all((a & b).bit_count() % 2 == int(i == j) for i, a in enumerate(route) + for j, b in enumerate(route)), 'Full dimension route is orthogonal') + need(act(route, q) == q, 'Actual q is fixed') + raw_x = norm([(q, 1)]) if stage == 0 else completed(stage-1) + raw_y = () if stage == 0 else norm(list(raw_x)+[(q, -1)]) + local_x0 = norm(list(spectator)+[(q, sign)]) + local_y0 = spectator + local_x1 = norm(list(spectator)+[(axis, sign) for axis in axes[:9]]) + local_y1 = norm(list(local_x1)+[(q, -sign)]) + out_x = completed(stage) + out_y = norm(list(out_x)+[(q, -1)]) + maps = {name: contact(old, new, route, dimension) for name, old, new in ( + ('entry_X', raw_x, local_x0), ('entry_Y', raw_y, local_y0), + ('exit_X', local_x1, out_x), ('exit_Y', local_y1, out_y))} + delta = stage_frame(stage, q) + for incoming, outgoing in ((raw_x, out_x), (raw_y, out_y)): + need(polynomial(norm(list(outgoing)+[(a, -c) for a, c in incoming]), dimension) + == polynomial(delta, dimension), 'Raw diagonal operator is exactly D_s') + cross = norm(list(out_y if sign == 1 else out_x)+ + [(a, -c) for a, c in (raw_x if sign == 1 else raw_y)]) + need(polynomial(cross, dimension) == polynomial(norm(list(delta)+[(q, -sign)]), dimension), + 'Raw cross operator is exactly D_s Q^(-sign)') + contacts.append({'stage': stage, 'pair': pair, 'port': port, 'backward': backward, + 'route': route, 'maps': maps}) + endpoints = [] + target_main = Counter() + omitted_endpoint_phase_rejected = 0 + for role, term in enumerate(case['exact_diagonal_monomials']): + qp, selected = term[0], term[1:] + need(qp in (-1, 1) and set(selected) <= {0, 1}, 'Actual endpoint exponent alphabet') + for port, recipe in enumerate(phases['recipes']): + q = recipe['q'] + physical = norm([(q, qp)]+[entry for stage, yes in enumerate(selected) if yes for entry in stage_frame(stage, q)]) + positive = list(axes[:9]) if selected[0] else [q] + positive += [axis for stage in range(1, len(selected)) if selected[stage] + for axis in axes[9+8*(stage-1):9+8*stage]] + shift = q if qp == -1 else 0 + need(inventory.independent_axes(positive), 'Actual endpoint target axes independent') + need(len(positive) == 1+8*sum(selected), 'Exact productive endpoint rank') + need(polynomial(norm(list(physical)+[(shift, 2)]), dimension) + == polynomial(norm((axis, 1) for axis in positive), dimension), 'Complete endpoint phase normalization') + if shift: + need(polynomial(physical, dimension) != polynomial(norm((axis, 1) for axis in positive), dimension), + 'Omitting the endpoint translation fails') + omitted_endpoint_phase_rejected += 1 + endpoints.append({'role': role, 'port': port, 'rank': len(positive), 'axes': positive, 'translation': shift}) + target_main[len(positive)] += 1 + recorded = Counter((row['pair'], tuple(row['stages'])) for row in case['retained_idle_windows']) + literal = Counter((row[1], tuple(row[2])) for row in case['physical_events'] if row[0] == 'IDLE') + need(recorded == literal, 'Bijection of every paid whole idle and every literal controller IDLE') + need(all(row['rank'] == 8*len(row['stages']) for row in case['retained_idle_windows']), + 'Every paid window rank matches the literal stage count') + idle = Counter() + idle_records = [] + for window in case['retained_idle_windows']: + selected = window['stages'] + need(case['physical_events'].count(['IDLE', window['pair'], selected]) == 1, + 'Each full idle is attached to its original literal pair and event') + for port, recipe in enumerate(phases['recipes']): + q = recipe['q'] + if 0 in selected: + need(selected == list(range(len(selected))) and len(selected) >= 2, 'Initial window contiguous from stage0') + positive = recipe['idle_children'][0]['orthogonal_axes'][:] + positive += [axis for stage in selected[2:] for axis in axes[9+8*(stage-1):9+8*stage]] + shift = recipe['idle_children'][0]['translation_after'] + else: + positive = [axis for stage in selected for axis in axes[9+8*(stage-1):9+8*stage]] + shift = 0 + desired = norm(entry for stage in selected for entry in stage_frame(stage, q)) + actual = norm([(axis, 1) for axis in positive]+[(shift, 2)]) + need(inventory.independent_axes(positive) and len(positive) == window['rank'], 'Exact whole idle rank') + need(polynomial(actual, dimension) == polynomial(desired, dimension), 'Exact complete whole idle phase') + idle[len(positive)] += 2 + idle_records.append({'window': window['index'], 'pair': window['pair'], 'stages': selected, + 'port': port, 'owners': [f'X{window["pair"]}:{port}', f'Y{window["pair"]}:{port}'], + 'axes': positive, 'translation': shift}) + receipt = read(base/'complex/full-identity-certificates/RESULT.json')['providers']['THREE-base'] + target_helpers = Counter({int(k): v*(2*p+1) for k, v in receipt['helper_boundary']['widths'].items()}) + targets = target_main+target_helpers + paid = Counter({int(k): v*(2*p+1) for k, v in receipt['unsplit_replays']['forward']['paid_profile'].items()}) + paid.update(idle) + scalar = scalar_invoice(case, sum(receipt['split_replays']['backward' if row[3] else 'forward'] + ['independent_native_replay']['conservative_real_scalar_primitive_allowance'] for row in stages)) + artifact = {'contacts': contacts, 'endpoints': endpoints, 'whole_idles': idle_records, 'formal': case} + artifact_json = json.dumps(artifact, sort_keys=True, separators=(',', ':')).encode() + artifact_bytes = gzip.compress(artifact_json, compresslevel=9, mtime=0) + if output_dir is not None: + output = Path(output_dir) + output.mkdir(parents=True, exist_ok=True) + (output/'NATIVE-GEOMETRY.json.gz').write_bytes(artifact_bytes) + result = {'status': 'PASS_EXACT_LAURENT_ALL_MAIN_CONTACTS_ENDPOINTS_AND_FULL_IDLE_PHASES', + 'p': p, 'keep': keep, 'dimension': dimension, 'contacts': 4*len(contacts), + 'main_fields': 224*p, 'fresh_helper_fields': 408*(2*p+1), + 'targets': dict(sorted(targets.items())), 'paid': dict(sorted(paid.items())), + 'native_scalar_allowance': scalar, 'scalar_allowance': scalar, + 'productive_fields': sum(targets.values()), 'paid_calls': sum(paid.values()), 'whole_idle_profile': dict(sorted(idle.items())), + 'rank_margin': sum(k*v for k, v in targets.items())-sum(k*v for k, v in paid.items()), + 'artifact_sha256': sha256(artifact_json).hexdigest(), + 'artifact_hash_encoding': 'Uncompressed UTF-8 JSON, sort_keys=True, separators=(comma,colon)', + 'native_source_gate': native_gate['status'], + 'negative_controls': {'wrong_native_orientation_rejected': wrong_orientation_rejected, + 'omitted_endpoint_translation_rejected': omitted_endpoint_phase_rejected}, + 'source_sha256': {str(path.relative_to(root)): sha256(path.read_bytes()).hexdigest() + for path in (phase_path, base/'transfer-audit/p3_native_audit.py', + base/'complex/full-identity-certificates/RESULT.json')}, + 'limits': 'Finite exact physical controller admission; inherited all-column local word, tensor strictification, new full-word precision/stock and outer transfer remain written proof obligations.'} + result['source_sha256'].update(native_gate['source_sha256']) + result['source_sha256'].update(factor_pins) + result['factor_receipt_sha256'] = factor.RECEIPT_SHA256 + result['schema'] = 'source-bound-p7-all-fresh-complete-native-controller/1' + return result + + +if __name__ == '__main__': + import argparse + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--source-root', type=Path, default=HERE/'source') + parser.add_argument('--output-dir', type=Path) + args = parser.parse_args() + result = run(args.source_root, output_dir=args.output_dir) + if args.output_dir: + (args.output_dir/'NATIVE.json').write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + print(json.dumps({k:result[k] for k in ('status','contacts','dimension','productive_fields','paid_calls','targets','paid','native_scalar_allowance')}, sort_keys=True)) diff --git a/research/direct-backward-independent-validation/capsule/repository/research/query-thinned-controllers/RESULT.json b/research/direct-backward-independent-validation/capsule/repository/research/query-thinned-controllers/RESULT.json new file mode 100644 index 0000000000..e0695152c9 --- /dev/null +++ b/research/direct-backward-independent-validation/capsule/repository/research/query-thinned-controllers/RESULT.json @@ -0,0 +1,356 @@ +{ + "bit_invoice": { + "main": { + "127": 222, + "15": 444, + "22": 444, + "29": 444, + "36": 444, + "43": 444, + "50": 444, + "57": 444, + "64": 222 + }, + "owned_streams_reused_sequentially": 1, + "paid": { + "1": 25479, + "14": 444, + "2": 24156, + "21": 444, + "28": 444, + "3": 1422, + "35": 444, + "4": 792, + "42": 444, + "49": 444, + "5": 1836, + "56": 444, + "6": 198, + "63": 222, + "7": 342 + }, + "paid_calls": 57555, + "productive_fields": 11454, + "rank_surplus": 753, + "raw_scalar_record_bound": 1000000000, + "targets": { + "127": 222, + "15": 444, + "22": 444, + "29": 444, + "36": 444, + "43": 444, + "50": 444, + "57": 444, + "64": 222, + "8": 7902 + }, + "thick_calls": 18, + "thick_stages": [ + 0, + 1, + 3, + 5, + 7, + 9, + 11, + 13, + 15, + 17, + 19, + 21, + 23, + 25, + 27, + 29, + 31, + 32 + ], + "thin_queries": 1665, + "whole_idle": { + "14": 444, + "21": 444, + "28": 444, + "35": 444, + "42": 444, + "49": 444, + "56": 444, + "63": 222 + } + }, + "bit_strictification": { + "alpha": { + "lower": "0.999995735238059506641600561767", + "upper": "0.999995735238059506641600561768" + }, + "compiler_H0": 3755884544, + "cutoff_base": 17, + "delta": { + "lower": "0.949707924144871179442776557218", + "upper": "0.949707924144871179442776557219" + }, + "gamma": { + "lower": "0.957429821066420278606254392110", + "upper": "0.957429821066420278606254392111" + }, + "normalized_surplus_lower": "68719461047/16845935476736", + "tail_exponent": "1/5", + "target_floor_base": 18, + "tensor_power": 1024, + "tested_saving": "173/50000", + "uniform_H1": 25986965159937, + "uniform_N": "2^25986965159937", + "uniform_saving": "3459/1000000", + "winning_word_materialized": false + }, + "complex_invoice": { + "main": { + "153": 224, + "17": 448, + "25": 448, + "33": 448, + "41": 448, + "49": 448, + "57": 448, + "65": 448, + "73": 448 + }, + "owned_streams_reused_sequentially": 1, + "paid": { + "1": 49045, + "16": 448, + "2": 13547, + "24": 448, + "3": 4256, + "32": 448, + "4": 1938, + "40": 448, + "48": 448, + "5": 380, + "56": 448, + "64": 448, + "72": 448, + "8": 152 + }, + "paid_calls": 72902, + "productive_fields": 11560, + "rank_surplus": 800, + "raw_scalar_record_bound": 1000000000, + "targets": { + "153": 224, + "17": 448, + "25": 448, + "33": 448, + "41": 448, + "49": 448, + "5": 532, + "57": 448, + "6": 342, + "65": 448, + "7": 1064, + "73": 448, + "8": 1767, + "9": 4047 + }, + "thick_calls": 19, + "thick_stages": [ + 0, + 1, + 3, + 5, + 7, + 9, + 11, + 13, + 15, + 17, + 19, + 21, + 23, + 25, + 27, + 29, + 31, + 33, + 34 + ], + "thin_queries": 1792, + "whole_idle": { + "16": 448, + "24": 448, + "32": 448, + "40": 448, + "48": 448, + "56": 448, + "64": 448, + "72": 448 + } + }, + "complex_strictification": { + "alpha": { + "lower": "0.999999952117240859760145478345", + "upper": "0.999999952117240859760145478346" + }, + "compiler_H0": 75415467350, + "cutoff_base": 20, + "delta": { + "lower": "0.941649713484853845388929204840", + "upper": "0.941649713484853845388929204841" + }, + "gamma": { + "lower": "0.967466409565147920980822933859", + "upper": "0.967466409565147920980822933860" + }, + "normalized_surplus_lower": "8589700209/251666829934592", + "tail_exponent": "1/5", + "target_floor_base": 21, + "tensor_power": 1024, + "tested_saving": "29603/10000000", + "uniform_H1": 10418370291022217, + "uniform_N": "2^10418370291022217", + "uniform_saving": "103609/35000000", + "winning_word_materialized": false + }, + "kappa": "37/12500", + "minimum_outer_margin_minus_kappa": "629378373/4900000000000000", + "native": { + "binary_charts": 111, + "complex_contacts_and_inverses": 896, + "owned_stream_restored_zero": true, + "thin_paid_rank_per_port": 1, + "thin_productive_credit": 0 + }, + "negative_controls": { + "closed_epsilon": [ + "epsilon_below_one", + "global_gamma_power_slack", + "actual_logarithmic_gamma_guard", + "source_axis_superpolynomial", + "gaussian_above_main", + "new_semantic_guard_with_C1_one" + ], + "closed_uniform_gap": [ + "new_complex_uniform_saving_above_b" + ], + "missing_layout": [ + "positive_layout_slack" + ], + "old_BIT_cap": [ + "actual_bit_above_effective" + ], + "unfunded_kappa": [ + "main_transform_above_kappa", + "global_coordinate_router_above_kappa", + "fused_gaussian_above_kappa", + "group_bit_router_above_kappa", + "boundary_algebraic_matrix_above_kappa" + ] + }, + "old_atom_rejected": true, + "ordinary_BIT": { + "admitted": "17/5000", + "after_cover": "69/20000", + "atom": "1/250", + "before_cover": "3459/1000000", + "ordinary_saving": "8590884599/2500000000000", + "prime_rule": "odd q > 2^26*N^5 avoiding all fixed denominators and rank witnesses" + }, + "outer": { + "functional_checks": { + "actual_new_BIT_stock_sublinear": "17429997759/17500000000", + "fixed_halo_explicit_metadata_branch": "1347500003/17500000", + "new_BIT_row_stock_sublinear_in_active_group": "69789991027/70000000000", + "new_semantic_group_guard": "9/70000000" + }, + "margins": { + "boundary_algebraic_matrix": "14504839378373/4900000000000000", + "fused_gaussian": "14504838135119/4900000000000000", + "global_coordinate_router": "51803/17500000", + "group_bit_router": "3626262033773/1225000000000000", + "group_scans": "34999997/35000000", + "main_transform": "14504629378373/4900000000000000", + "microbox_face_corrections": "1347500003/17500000", + "polynomial_products": "69999997/70000000", + "sparse_union_movement": "2005129839378373/4900000000000000" + }, + "parameters": { + "a": "51803/17500000", + "b": "41443/14000000", + "beta": "69999991/70000000", + "bit_saving": "17/5000", + "cap_xi": "4455129629378373/4900000000000000", + "complex_uniform_saving": "103609/35000000", + "d": "3/70000000", + "epsilon": "69999997/70000000", + "kappa": "37/12500", + "lambda_": "19940797/20000000", + "lambda_prime": "69792791/70000000", + "layout": "3/70000000", + "q": "207209/70000000", + "r0": "3/700000000", + "stop": "3/70000000", + "tested_saving": "29603/10000000" + }, + "strict_checks": { + "actual_bit_above_effective": "7697/17500000", + "actual_logarithmic_gamma_guard": "3/70000000", + "actual_logarithmic_group_guard": "444870685621627/2450000000000000", + "alpha_logarithm_absorption": "3/700000000", + "boundary_algebraic_matrix_above_kappa": "839378373/4900000000000000", + "cap_above_band": "2005129629378373/4900000000000000", + "cap_below_cell": "444870160621627/4900000000000000", + "cap_below_phase_cell_power": "5344870370621627/4900000000000000", + "complex_above_effective": "3/70000000", + "complex_below_one_over_32": "396057/14000000", + "complex_endpoint": "3/35000000", + "epsilon_below_one": "3/70000000", + "epsilon_positive": "69999997/70000000", + "fine_prime_halo_umbrella": "7/2", + "fused_gaussian_above_kappa": "838135119/4900000000000000", + "gaussian_above_main": "104378373/2450000000000000", + "global_coordinate_router_above_kappa": "3/17500000", + "global_gamma_power_slack": "27/700000000", + "group_below_dimension": "3/35000000", + "group_bit_router_above_kappa": "262033773/1225000000000000", + "group_gauge_power_slack": "444870675121627/2450000000000000", + "group_key_fits_record": "3/35000000", + "group_positive": "69999991/70000000", + "group_scans_above_kappa": "34896397/35000000", + "halo_covers_generic_inverse_radius": "5", + "improvement_over_user_baseline": "614514790400418148631/500000000000000000000000", + "lambda_above_internal": "3/140000000", + "lambda_above_sigma": "9/140000000", + "lambda_above_tau": "3/140000000", + "lambda_prime_above_lambda": "3/140000000", + "lambda_prime_above_leaf": "83875671/980000000000000", + "leaf_saving_above_effective": "41875671/980000000000000", + "main_transform_above_kappa": "629378373/4900000000000000", + "membership_arithmetic_fits_record": "3/70000000", + "microbox_face_corrections_above_kappa": "1347448203/17500000", + "microbox_halo_volume": "5530000009/70000000", + "new_complex_uniform_saving_above_b": "3/70000000", + "new_semantic_guard_with_C1_one": "3/70000000", + "polynomial_products_above_kappa": "69792797/70000000", + "positive_layout_slack": "3/70000000", + "q_below_effective": "3/70000000", + "q_below_internal": "3/70000000", + "q_below_leaf": "83875671/980000000000000", + "q_positive": "207209/70000000", + "short_record_fallback": "13958557/14000000", + "source_axis_superpolynomial": "3/70000000", + "sparse_union_movement_above_kappa": "1990625839378373/4900000000000000", + "stop_below_one": "69999997/70000000", + "stop_positive": "3/70000000", + "strassen_integer_power_gap": "1951441519231", + "support_router_span": "9/70000000", + "theta_positive_polynomial_power": "2", + "union_header_fits_record": "9/70000000", + "union_tag_work_per_visit_fits_record": "9/70000000" + } + }, + "relative_gain_over_p7": "27353/268647", + "schema": "query-thinned-productive-controllers/1", + "scope": "Conditional native construction; all-column, erasure, whole-job matching, fixed-tape, precision, analytic, prime and exact-recovery premises retained. 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Apache-2.0. +This extends Ali Romman's one-relation PR5377 at c448d13c71908647f968b06cddb795ce7d288139. +The source word is by Cao Yifan. The row convention and scalar allowance +follow the credited native work of Cinna Davis and zxv. +""" +from collections import Counter +from copy import deepcopy +from fractions import Fraction as Q +from hashlib import sha1, sha256 +from pathlib import Path +import gzip +import importlib.util +import json +import sys + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +SOURCE = 'research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz' +PHASE = 'research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz' +PAYLOAD = 'cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd' +WITNESSES = json.loads((HERE / 'WITNESS.json').read_text(encoding='utf-8')) +COUNT = 8 +OLD_PAID = {1: 2201, 2: 412, 3: 510, 4: 127, 5: 40, 8: 8} +NEW_PAID = dict(OLD_PAID) +NEW_PAID[1] -= COUNT +NEW_PAID.pop(8) +OLD_HELPERS = {4: 28, 7: 7, 8: 47, 9: 326} + + +def need(ok, why): + if not ok: + raise ValueError(why) + + +def read(path): + data = path.read_bytes() + return json.loads(gzip.decompress(data) if path.suffix == '.gz' else data) + + +def encode(x): + if isinstance(x, Q): + return str(x) + if isinstance(x, dict): + return {str(k): encode(v) for k, v in x.items()} + if isinstance(x, (list, tuple)): + return [encode(v) for v in x] + return x + + +def load(relative, name): + spec = importlib.util.spec_from_file_location(name, ROOT / relative) + module = importlib.util.module_from_spec(spec) + sys.modules[name] = module + spec.loader.exec_module(module) + return module + + +def authenticate(): + pins = read(HERE / 'SOURCES.json') + for row in pins['files']: + if row['usage'] != 'input': + continue + p = ROOT + for part in Path(row['path']).parts: + p /= part + need(not p.is_symlink(), 'No source aliases') + raw = p.read_bytes() + need(sha256(raw).hexdigest() == row['sha256'], 'Changed source: ' + row['path']) + need(sha1(b'blob ' + str(len(raw)).encode() + b'\0' + raw).hexdigest() == row['git_blob'], 'Source Git blob') + need(sha256(gzip.decompress((ROOT / SOURCE).read_bytes())).hexdigest() == PAYLOAD, 'Exact source payload') + return pins + + +def span(basis): + out = {0} + for vector in basis: + need(isinstance(vector, int) and 0 <= vector < 512, 'Binary frame coordinate') + out |= {v ^ vector for v in tuple(out)} + need(len(out) == 2 ** len(basis), 'Independent frame basis') + return out + + +def add(dst, src, q): + for k, v in tuple(src.items()): + value = dst.get(k, Q(0)) + q * v + if value: + dst[k] = value + else: + dst.pop(k, None) + + +def allowance(g): + if g[0] in ('clear', 'copy'): + return 2 + q = Q(*g[3:]) if g[0] == 'add' else Q(*g[2:]) + n, d = abs(q.numerator), q.denominator + need(n > 0 and d & (d - 1) == 0, 'Nonzero dyadic scalar') + if g[0] == 'scale': + need(n & (n - 1) == 0, 'Dyadic unit SCALE') + return 2 * (abs(n.bit_length() - d.bit_length()) + int(q < 0)) + need(g[0] == 'add', 'Known scalar operation') + return 2 * (3 + n.bit_length() - 1 + n.bit_count() + d.bit_length() - 1) + + +def relation_system(): + """Find exact independent pivots and eliminate all other pivot columns.""" + basis = {} + need(len(WITNESSES) == COUNT, 'Eight declared witnesses') + for witness in WITNESSES: + pairs = witness['relation'] + row = {h: Q(q) for h, q in pairs} + need(len(row) == len(pairs) and all(224 <= h < 632 and q for h, q in row.items()), 'Distinct helper coefficients') + for pivot, prior in sorted(basis.items()): + add(row, prior, -row.get(pivot, Q(0))) + need(row, 'Independent helper relations') + pivot = min(row); scale = row[pivot] + row = {h: q / scale for h, q in row.items()} + for prior in basis.values(): + add(prior, row, -prior.get(pivot, Q(0))) + basis[pivot] = row + need(len(basis) == COUNT, 'Eight paid helper outputs removed') + for pivot, row in basis.items(): + need(all(row.get(h, 0) == int(h == pivot) for h in basis), 'Reduced pivot columns') + return dict(sorted(basis.items())) + + +BASIS = relation_system() + + +def construct(source): + c = source['canonical']; old = source['programs']['backward'] + all_helpers = {h for x in WITNESSES for h, _ in x['relation']} + need(all(c['start'][h] == 0 and c['final'][h] == 1 for h in all_helpers), 'Every relation uses cold full-ended helpers') + snapshots, centers, zeros = {}, {}, {} + for slot, x in enumerate(WITNESSES, 1): + frame, role = x['frame'], x['cached_role'] + need(old[x['event']] == ['center', 0, 0, frame, 8], 'Exact source center') + event = old[x['cached_event']] + need(event[0] == 'climb' and event[2] == role and event[4] == frame, 'Exact snapshot source') + need(old[x['zero_event']] == ['climb', 'warp_retimed', x['zero_role'], frame, 1, 1], 'Exact zero source job') + need(x['cached_event'] < x['event'] < x['zero_event'] and Q(x['copy_factor']) == 1, 'Snapshot chronology and COPY coefficient') + snapshots[x['cached_event']] = (slot, x) + centers[x['event']] = (slot, x) + zeros[x['zero_event']] = x + need(len(snapshots) == len(centers) == len(zeros) == COUNT, 'Distinct replacement sites') + word = [] + for pivot, row in BASIS.items(): + word.append(['scalar', ['clear', ['L', pivot]], 0]) + for h, q in sorted(row.items()): + if h != pivot: + word.append(['scalar', ['add', ['L', pivot], ['L', h], -q.numerator, q.denominator], 0]) + for index, event in enumerate(old): + if index in centers: + slot, x = centers[index]; f = x['frame'] + word += [['scalar', ['clear', ['C', 0]], f], + ['scalar', ['copy', ['C', 0], ['C', slot]], f], + ['scalar', ['clear', ['C', slot]], f]] + elif index in zeros: + x = zeros[index] + word.append(['zero_retag', ['L', x['zero_role']], x['frame'], 1]) + else: + word.append(deepcopy(event)) + if index in snapshots: + slot, x = snapshots[index]; f = x['frame'] + word += [['scalar', ['clear', ['C', slot]], f], + ['scalar', ['copy', ['C', slot], ['L', x['cached_role']]], f]] + word += [['scalar', ['clear', ['L', h]], 1] for h in BASIS] + physical = deepcopy(c); physical.pop('local_profile') + return {'schema': 'joint-helper-relations-word/1', 'canonical': physical, + 'relation_basis': encode(BASIS), + 'paid_profiles': {'forward': OLD_PAID, 'backward': NEW_PAID}, + 'owned': {'forward': [['C', 0]], 'backward': [['C', i] for i in range(COUNT + 1)] + [['L', h] for h in BASIS]}, + 'programs': {'forward': deepcopy(source['programs']['forward']), 'backward': word}} + + +def replay(c, program, backward, specialized): + """Run every event on all independent entry columns and exact frames.""" + owned = {('C', 0)} | ({('C', i) for i in range(1, COUNT + 1)} | {('L', h) for h in BASIS} if specialized else set()) + roles = {('L', i) for i in range(632)} | owned + rows = {r: {(r, ()): Q(1)} for r in roles} + frames = {('L', i): f for i, f in enumerate(c['start'])} + frames.update({r: None for r in owned if r[0] == 'C'}) + spaces = [span(b) for b in c['frames']] + paid = Counter() + cost, max_l1, denominator, zero_count = 0, Q(1), 1, 0 + for e in program: + kind, touched = e[0], None + if kind == 'scalar': + g, frame = e[1:] + dst = tuple(g[1]); touched = dst + need(dst in rows and 0 <= frame < len(spaces), 'Declared scalar destination and frame') + cost += allowance(g) + if g[0] == 'clear': + need(dst in owned, 'Only owned fields can be erased') + rows[dst] = {}; frames[dst] = frame + else: + need(frames[dst] == frame, 'Exact scalar destination frame') + if g[0] in ('add', 'copy'): + src = tuple(g[2]) + need(src in rows and frames[src] == frame and dst != src, 'Exact scalar source frame') + if g[0] == 'copy': + need(dst in owned and not rows[dst], 'COPY into cleared owned storage') + rows[dst] = dict(rows[src]) + else: + add(rows[dst], rows[src], Q(g[3], g[4])) + else: + need(g[0] == 'scale', 'Known scalar operation') + rows[dst] = {k: Q(g[2], g[3]) * v for k, v in rows[dst].items()} + elif kind == 'warp': + _, role, op, old, new = e + dst = tuple(role); touched = dst + need(frames[dst] == old and 1 <= abs(op) <= len(c['warps']), 'Exact warp input') + symbol = (1 if op > 0 else -1) * (abs(op) + (10**6 if backward else 0)) + rows[dst] = {(r, w[1:] if w and w[0] == -symbol else (symbol,) + w): q + for (r, w), q in rows[dst].items()} + frames[dst] = new + elif kind in ('climb', 'center'): + if kind == 'climb': + _, _, i, old, new, rank = e + dst = ('L', i) + need(spaces[old] < spaces[new], 'Ascending paid climb') + else: + _, i, old, new, rank = e + dst = ('C', i) + need(spaces[old] < spaces[new] or spaces[new] < spaces[old], 'Nested paid center') + need(frames[dst] == old and rank == abs(len(c['frames'][new]) - len(c['frames'][old])), 'Exact paid rank and frame') + frames[dst] = new; paid[rank] += 1 + elif kind == 'zero_retag': + _, role, old, new = e + dst = tuple(role) + need(specialized and backward and any(dst == ('L', x['zero_role']) and (old, new) == (x['frame'], 1) for x in WITNESSES), 'Declared zero identity') + need(frames[dst] == old and not rows[dst], 'Zero identity requires an identically zero full row') + frames[dst] = new; zero_count += 1 + else: + need(kind in ('phase', 'adapter'), 'Known inert source marker') + if touched is not None: + max_l1 = max(max_l1, sum(map(abs, rows[touched].values()), Q(0))) + denominator = max(denominator, max((q.denominator for q in rows[touched].values()), default=1)) + need([frames['L', i] for i in range(632)] == c['final'], 'Every final native frame') + for i in range(632): + r = ('L', i) + if r in owned: + continue + expected = {(r, ()): Q(1)} + if i < 112 if backward else 112 <= i < 224: + expected[(('L', i + 112 if backward else i - 112), ())] = Q(-1 if backward else 1) + need(rows[r] == expected, 'Every independent main/helper endpoint: ' + str(i)) + need(all(not rows[r] for r in owned), 'Every owned entry column is erased at return') + need(zero_count == COUNT * int(specialized), 'All eight zero identities checked') + helpers = Counter() + for i in range(224, 632): + if ('L', i) in owned: + continue + a, b = c['start'][i], c['final'][i] + need(spaces[a] < spaces[b], 'Strict independent productive helper') + helpers[len(c['frames'][b]) - len(c['frames'][a])] += 1 + return {'paid': dict(sorted(paid.items())), 'helpers': dict(sorted(helpers.items())), + 'independent_persistent_columns': 632 - COUNT if specialized else 632, + 'independent_owned_entry_columns': len(owned), 'owned_outputs_zero': True, + 'real_scalar_allowance': cost, 'max_formal_prefix_l1': str(max_l1), + 'max_denominator': denominator, 'zero_identities': zero_count} + + +def independent_source_identities(source): + """Check unrestricted source identities with the predecessor row engine.""" + v = load('research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py', 'joint_relation_source_rows') + rows = {('L', i): v.identity(('L', i)) for i in range(632)} + rows['C', 0] = v.identity(('C', 0)); saved = {}; checked = [] + for index, e in enumerate(source['programs']['backward']): + if e[0] == 'scalar': + g = e[1]; dst = tuple(g[1]) + if g[0] == 'clear': rows[dst] = {} + elif g[0] == 'copy': rows[dst] = dict(rows[tuple(g[2])]) + elif g[0] == 'scale': rows[dst] = {k: Q(g[2], g[3]) * a for k, a in rows[dst].items()} + else: v.add(rows[dst], rows[tuple(g[2])], Q(g[3], g[4])) + elif e[0] == 'warp': + dst = tuple(e[1]); rows[dst] = v.warp(rows[dst], e[2], True) + for x in WITNESSES: + delta = {(('L', h), ()): Q(q) for h, q in x['relation']} + if index == x['cached_event']: + saved[index] = dict(rows['L', x['cached_role']]) + if index == x['event']: + diff = dict(rows['C', 0]); v.add(diff, saved[x['cached_event']], -Q(x['copy_factor'])) + need(diff == {k: Q(x['difference_factor']) * q for k, q in delta.items()}, 'Independent exact center minus snapshot identity') + checked.append(('center', index)) + if index == x['zero_event']: + need(rows['L', x['zero_role']] == {k: Q(x['zero_factor']) * q for k, q in delta.items()}, 'Independent exact zero-site row identity') + checked.append(('zero', index)) + need(len(checked) == 2 * COUNT, 'Sixteen unrestricted source identities') + need(all(rows['L', i] == v.expected(('L', i), [], True, False) for i in range(632)), 'Independent unrestricted source endpoints') + return {'source_event_indices_are_zero_based': True, 'witnesses': WITNESSES, + 'relation_rank': COUNT, 'owned_pivots': list(BASIS), 'reduced_basis': BASIS, + 'snapshot_terms_before_substitution': {i: len(row) for i, row in saved.items()}, + 'checked': checked} + + +def phase_inheritance(source, candidate): + receipt = read(ROOT / PHASE) + need(receipt['status'] == 'PASS_JOINT_HELPER_MAPS_ALL_ACTUAL_ABSOLUTE_PHASES' and + receipt['actual_word_canonical_sha256'] == PAYLOAD, 'Authenticated source absolute-phase receipt') + physical = deepcopy(source['canonical']); physical.pop('local_profile') + need(candidate['canonical'] == physical, 'Every frame, native map and main adapter unchanged') + for direction, program in candidate['programs'].items(): + old = source['programs'][direction] + for kind in ('warp', 'adapter', 'phase'): + need([e for e in program if e[0] == kind] == [e for e in old if e[0] == kind], 'Exact inherited ' + kind + ' sequence') + old_paid = Counter(tuple(e) for e in old if e[0] in ('climb', 'center')) + new_paid = Counter(tuple(e) for e in program if e[0] in ('climb', 'center')) + expected = Counter() if direction == 'forward' else Counter(tuple(old[i]) for x in WITNESSES for i in (x['event'], x['zero_event'])) + need(old_paid - new_paid == expected and not new_paid - old_paid, 'Only the sixteen proved jobs are removed') + return {'new_gaussian_operators': 0, 'new_native_maps': 0, + 'all_retained_paid_events_and_warps_from_source': True, + 'absolute_phase_receipt_reused': PHASE, + 'source_amplitudes_and_phase_lowering_freshly_replayed': False, + 'new_operations': 'Same-frame COPY, owned CLEAR/ADD, and physical identity on a proved zero row.'} + + +def controls(c, candidate): + controls = {} + base = candidate['programs']['backward'] + variants = {} + bad = deepcopy(base); bad[1][1][3] *= -1; variants['wrong_relation_sign'] = bad + variants['missing_owned_input_clear'] = deepcopy(base[1:]) + bad = deepcopy(base) + next(e for e in bad if e[0] == 'scalar' and e[1][:2] == ['copy', ['C', 1]])[1][2] = ['L', 63] + variants['wrong_snapshot_source'] = bad + bad = deepcopy(base); next(e for e in bad if e[0] == 'zero_retag')[2] = 0 + variants['wrong_zero_input_frame'] = bad + bad = deepcopy(base); next(e for e in bad if e[0] == 'climb')[5] += 1 + variants['under_or_overstated_paid_rank'] = bad + bad = deepcopy(base) + next(e for e in bad if e[0] == 'scalar' and e[1][:2] == ['copy', ['C', 0]])[2] = 0 + variants['wrong_copy_gauge'] = bad + variants['uncleared_owned_output'] = deepcopy(base[:-1]) + for name, program in variants.items(): + try: + replay(c, program, True, True) + except ValueError as err: + controls[name] = str(err) + else: + raise ValueError('Control accepted: ' + name) + return controls diff --git 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b/research/direct-backward-independent-validation/capsule/reuse/5396/CLAIMS.json new file mode 100644 index 0000000000..daa01b7985 --- /dev/null +++ b/research/direct-backward-independent-validation/capsule/reuse/5396/CLAIMS.json @@ -0,0 +1,58 @@ +{ + "schema_version": 1, + "review_status": "READY_FOR_COLD_REPLAY", + "canonical_main": "1ec1119972c9aefe42525172d07b332fcff81cb4", + "selected_baseline": ".0030217758", + "selected_metadata_role": "Frozen historical provenance; future selected-result updates do not invalidate this review.", + "candidates": [ + { + "pr": 5383, + "head": "4bd6efa51a495a7c7b7754915cf0244e7e60969e", + "author": "Ali Romman", + "kappa": "151333/50000000", + "decimal": ".00302666", + "package": "research/kappa-joint-relations-20261023", + "word_payload_sha256": "2aee5e997df99726fc763e510d9cb69fbe4f86114dc8d2cd33ad26c6c462a21d", + "last_pivot": 288 + }, + { + "pr": 5387, + "head": "b1ab650d36f59e5be682a813145b7c67e219e341", + "author": "Dugongue", + "kappa": "605334953/200000000000", + "decimal": ".003026674765", + "package": "research/eight-owned-relations", + "word_payload_sha256": "9aa0d7112b4e13f1aa13a93dab0af6f4435ffe99b842aad841685becdafee492", + "last_pivot": 261 + } + ], + "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." + } + ], + "selection_authorized": false, + "construction_claim": "No new native construction is claimed by this independent review.", + "selected_kappa": "15108879/5000000000", + "same_selected_assumptions_required": true, + "new_unconditional_or_Lean_theorem": false, + "uniform_word_materialized": false, + "selected_record_changed": false +} diff --git a/research/direct-backward-independent-validation/capsule/reuse/5396/PROOF.md b/research/direct-backward-independent-validation/capsule/reuse/5396/PROOF.md new file mode 100644 index 0000000000..96c22c58d4 --- /dev/null +++ b/research/direct-backward-independent-validation/capsule/reuse/5396/PROOF.md @@ -0,0 +1,217 @@ +# Joint validation and exact dependency argument + +## Claim and five retained premises + +For each of the two exact literal words in CLAIMS.json, the new independent +engines establish the algebra, ownership, complete invoice and numerical +compiler/outer specialization described below. The implication remains +conditional on the **same five literal premises** in CLAIMS.json, which the +source guard compares with the authenticated selected PR5241 claim: + +1. Native operators, phase conventions, spectators and whole-job adapters work + at every positive column multiplicity. +2. Owned streams and suspended centers obey the retained allocation, erasure + and ownership contracts. +3. The finite mixed-target compiler and chronological product, completion and + splitting satisfy the retained uniform closure contract. +4. The retained fixed-tape movement and precision/storage prescriptions apply + to the new fixed finite template. +5. Analytic decomposition, fine-prime avoidance and exact integer recovery + follow the retained upstream/outer framework. + +The frozen selected record is 15108879/5000000000 = .0030217758 at canonical main +1ec1119972c9aefe42525172d07b332fcff81cb4. It is historical provenance, with an exact +vendored copy; no future live selected-file equality is a premise. No source +object is fetched or substituted for missing working input during replay. + +## Distinct literal words and algebraic domains + +| Item | Ali Romman PR5383 | Dugongue PR5387 | +| --- | --- | --- | +| Source head | 4bd6efa51a495a7c7b7754915cf0244e7e60969e | b1ab650d36f59e5be682a813145b7c67e219e341 | +| Conditional κ | 151333/50000000 = .00302666 | 605334953/200000000000 = .003026674765 | +| Last pivot | L288 | L261 | +| Eighth snapshot source event/role | 11306 / L288 | 11296 / L256 | +| Eighth zero source event/role | 17580 / L288 | 17233 / L256 | +| Backward scalar allowance | 158744 | 158776 | + +Both eighth substitutions use frame 281, but the unrestricted source relation +and the retained arbitrary input domain differ. Equal invoices cannot establish +their semantic equivalence. Each algebra invocation independently replays all +21,449 original backward events, derives eight source-center-minus-snapshot rows +and their eight matching later zero rows, reduces the simultaneous rank-eight +system, and checks the actual preparation. It then replays the entire respective +candidate on 624 independent retained inputs plus 17 arbitrary owned entry +inputs. The pivots are 225,227,229,230,241,245,257 and the candidate-specific last +pivot above. No relation basis, WITNESS, author evaluator or PASS receipt is the +source of those identities. See reports/algebra/REPORT.md. + +The independent dyadic row engine keeps integer numerators and a common power +of two denominator. Terms are independent inputs acted on by reduced free words. +Only adjacent generator/inverse pairs cancel; different generators do not +commute. For every positive width f, substitute the inherited actual f-column +operator for each generator and its inverse for the inverse symbol. Evaluation +is an algebra homomorphism, so the unrestricted formal identities hold on all +payload vectors, including nonseparable inputs. Rational coefficients stay +outside evaluation. No tensor power is distributed over a sum. + +All new preparation coefficients use the checked same-frame ADD/CLEAR grammar. +The emitted preparation equals the independent joint RREF assignments and has +no pivot on any pivot right-hand side. All eight snapshots coexist before the +first center substitution, each in a distinct cleared owned bank. Same-frame +COPY substitutes the exact source output with its physical gauge; identity at +a proved complete zero vector removes the later job. Identity does not transport +an arbitrary nonzero value between frames or erase approximate error. + +## Chronology, physical factors and owners + +The independent owner parser separately checks both whole backward words and +both unchanged forward words, all frame transitions, exact retained endpoints, +zero retags and owned returns. Each backward has 17 distinct complete owners +(eight pivots and C0..C8); each forward has one C0 owner. Arbitrary dirt is cleared +only in owned fields. Every removed pivot loses its productive target. No +snapshot, suspended center, query scratch or parked bank receives productive +credit. The raw p16 controller needs at least 16*17+2=274 separately tagged LOCAL +banks before its other controller/compiler storage. + +Every retained warp, phase marker and adapter has exact original chronology; +canonical operators and frames are unchanged. Source signed native and paid +phase facts are **authenticated historical reuse** from the selected PR5241 +foundation, whose full 31-file proof/checker/receipt closure is retained under +capsule/agents/sources/pr5241. The receipt binds the original source payload +cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd, +180 native classes, all 408 helpers in both orientations, and 5710 oriented paid +classes/6596 paid event instances. The historical first-cold wrapper differs +from canonical verify.py; its mathematical phase/native/helper checkers and +regeneration code retain the recorded hashes. No new phase lowering is claimed. +The canonical maintainer PROOF-REVIEW authorizes this unchanged foundation reuse. +New scalar chronology, joint identities and owner domains are checked afresh. +PR5384's single-relation review supplies generic COPY/zero/all-f interpretation, +not the simultaneous joint proof or new inventory. + +## Whole-controller invoice, directed prices and outer point + +The event census computes paid ranks from actual endpoint frame dimensions, +checks physical scalar tariffs and reads the literal p16 controller. It obtains +64,148 paid jobs and 10,800 productive fields for each word. Relative to the +source controller it removes 128 H1 and 128 H8 paid calls and surrenders all +128 H9 productive targets; the rank surplus remains 752. This is a complete +controller invoice, not eight added local savings. It includes main, idle, +query and completion terms. See reports/prices/REPORT.md. + +A fresh independent fixed-point rational interval engine uses directed rounding +at 10^-65, an atanh logarithm series and exponential Taylor remainder. It checks +the actual signed moments, unique fixed-profile crossing, both completion tails, +strict alpha reserve, eta/complement capacity and splitting. It independently +recomputes both candidate parameter choices; source-identical profile reuse is +justified by the separate literal event censuses. The raw crossing is strictly +between .00302667476807 and .00302667476808. This is a ceiling for this exact +invoice, not an optimum over native constructions or relation systems. + +| Quantity | PR5383 | PR5387 | +| --- | --- | --- | +| Tested complex saving | .00302667 | .003026674766 | +| Reserved alpha slack | 1e-9 | 1e-12 | +| Tensor exponent / cutoff / floor | 1024 / 20 / 21 | 1024 / 20 / 21 | +| Outer gap | 1/700000000 | 1/7000000000000 | +| Least winning j on stated sufficient grid | 44836 | 58507 | +| Compiler H, N=2^H | 31385200000000 | 409549000000000000 | + +The new rational outer engine derives all 54 strict and four functional rows +from its own exact parameter family, checks all positive, and independently +finds the winning compiler integer and failure at the preceding sufficient-grid +index. It compares author parameter records only after fresh computation. +Ordinary BIT is source-bound to 17/5000=.0034 with the exact unchanged ABI; +its native/interface admission is retained, not replayed. The compiler threshold +is an algorithmic finite specification. The enormous expanded word is not +materialized. See reports/outer/REPORT.md and reports/applicability/REPORT.md. + +The author engines' separate normal/optimized cold replay evidence is an +external execution gate. This review's own replay independently recomputes the +invoice, directed moments and outer predicates; it does not promote author +RESULT status labels into a premise. + +## Effective expanded bounds and exact physical domain + +The detailed construction and strong-induction proof are retained in +reports/applicability/REPORT.md, with exact canonical FINITE-PRECOMPILATION and +FINITE-TEMPLATE-CLOSURE notes under capsule/repository. For the explicitly chosen +integer batch clearing, sequential base kernels, full routes and separately +tagged owned banks, define + +``` +D = 2^262144 +F(0) = D +X_n = (n+1)*(D+1)*(F(n-1)+1) (n>=1) +F(n) = X_n^(16*(n+1)^2) (n>=1) +N = 2^H, M = F(N) +Wbar = Pbar = Obar = Rbar = Gbar = M +Zbar = 2*M +Ebar = 64*(Zbar+N+Pbar+Gbar+1)^3 +Bbar = Pbar+Ebar +C0bar = 32*N*Bbar^2 +``` + +These are terminating integer recursions and fixed finite constants, with +candidate-specific H. D pays the squared complete role inventory and rank-router +factors of the strictified 1024-fold unit. For top rank n, there are at most +(D+1)^(2n+2) mixed-unit instances; product clearing over distinct smaller widths +is at most F(n-1)^(n-1). Expanded incidence fits X_n^(3n+5); routing and coefficient +height fit X_n^(9n+20). For every n>=1, +16(n+1)^2-(9n+20)=16n^2+23n-4>=35, proving the strong induction. The finite probe +of this inequality corroborates the algebraic proof; it does not replace it. +The raw 181098496 bound is never reused as the expanded cap. + +The actual W/P still determines efficiency; enlarged envelopes create no +productive outputs. The fresh semantic recurrence is +A(e)<=A(floor(e/N))+Pbar*floor(e/N)+Ebar, with elementary leaves <=8e. +It gives A(e)<=2*Bbar*e and complete-layer height below C0bar*d. The actual +identity at zero retags propagates residual error through this changed program; +there is no artificial numerical reset at a symbolic zero. + +For d<=c*p^(a/b), choose +Lprec=bit_length(4*C0bar*ceil(c)), +tprec=max(4,ceil(b*Lprec/(b-a))) and p_prec=2^tprec. +For p>=p_prec the retained fine-grid prescription uses at most 2p bits per signed +component. Fixed-tape class restrictions remain f<=p, A=O(p), +K/log(p)->infinity, complete compact/control fields, restored dirty temporaries +and the source superpolynomial record fiber. Their asymptotic domain-entry +threshold remains the retained premise where no numerical growth rate is given. + +With Dord(e)=0 below N and 1+Dord(floor(e/N)) otherwise, reserve complex stock +[Wbar*(Obar+1)]^Dord(d), **multiply** it by simultaneous BIT stock, and pad once +to the full product. For retained BIT coefficient L_BIT, define +Lstock=ceil(log2 Wbar)+ceil(log2(Obar+1))+L_BIT+2. +Above d>=2^(2*(Lstock+2)), the combined reserve uses fewer than d/4 complete +chunks; padding costs a factor below 2. Include stopping, precision, movement +and descriptor cutoffs in the final maximum. This pays all suspended banks and +preserves the retained movement exponent and spectator restoration. + +## Independence, controls and invalidation + +No new engine imports an author native, price, interval or endpoint evaluator. +The only cross-engine import is the independent algebra implementation used by +the actual-word semantic falsifier. The wrapper runs both exact words separately, +then checks fresh coverage fields and source/K/payload identities. Fresh result +files do not enter the frozen input inventory and cannot form a hash cycle. +The normal/-O schedule is identical, with explicit optimization propagated to +every scientific subprocess and fresh bytecode caches before scientific imports. + +Independent controls cover preparation sign/coefficient/pivot, wrong saved row, +wrong COPY gauge, omitted relation, arbitrary owned dirt, missing owner returns, +source chronology, borrowed erasure, storage alias, productive credit, extra H1, +reserve, compiler grid and outer boundary failures. Six actual-word mutants +recompute their payload digests and reach the mathematical parser directly; +rejection is not an old-digest comparison. Source and headline mutation controls +separately exercise the working-input guard and offline Git membership binding. + +An early algebra parser rejected legal signed-denominator SCALE [2,-1]; sign +normalization corrected that checker defect before the frozen successful runs. +Early applicability/falsifier resource failures and the wrong-marker parser +attempt remain reported as implementation failures, never candidate evidence. +Source phase, ordinary BIT native construction, physical precision/tape execution, +analytic decomposition, prime avoidance and integer recovery are reused in +explicit quantified domains. This is not an unconditional theorem, Lean/kernel +verification, independent human acceptance, selected promotion or practical +speedup. 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"unique_union_pairs": 2863 + }, + "specialization": { + "candidate_payload": "cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd", + "controls": [ + "singular affine recipe", + "nonZ4 absolute phase", + "borrowed owner clear", + "unpaid rank change", + "non-dyadic scalar", + "unlifted absolute phase atf2" + ], + "expanded_compiler_counts": "fresh template counts and semantic constants required, not raw1e9 cap", + "families": { + "actual_warp_classes": 180, + "changed_helper_boundaries": 5, + "new_paid_pairs": 105 + }, + "helper_profile": { + "4": 28, + "7": 7, + "8": 47, + "9": 326 + }, + "max_new_elementary_records_per_monomial": 83, + "new_monomials": 800, + "programs": { + "backward": { + "events": { + "adapter": 448, + "center": 8, + "climb": 3290, + "phase": 10, + "scalar": 17453, + "warp": 240 + }, + "profile": { + "1": 2201, + "2": 412, + "3": 510, + "4": 127, + "5": 40, + "8": 8 + }, + "scalar_allowance": 158168 + }, + "forward": { + "events": { + "adapter": 448, 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Executable authenticates actual bytes and finite membership/census/decomposition. No exact recipe phase replay or full physical theorem is claimed by this checker.", + "seconds": 2.0648992329952307, + "selected_monomials_same_schema": 1692, + "source_inputs": 19, + "status": "PASS_EXACT_CATALOGUE_SPECIALIZATION_SCHEMA_AND_RAW_FINITE_TARIFF", + "tape_tariff_unit": "finite retained primitive-record count; not a literal1000-tape-step claim", + "uniform_elementary_bound_one_monomial": 171, + "uniform_elementary_bound_two_adapters": 342 + } + }, + "scope": "Independent source-compatible verification of Cao Yifan PR4610 under exactly selected4470 conditional assumptions. No new construction, unconditional/Lean multiplication theorem, selected-record edit, practical speedup or materialized uniform word.", + "source_manifest_sha256": "25fed1fae88cffefc64cdecf8114718f4f4bcff1ef11e69e7556b8f40110e9a6", + "source_stability": { + "proof_relevant_live_reads": [ + "certificates/frontier4470-source.json", + "certificates/selected-result.json", + "docs/research/pr-intake-evidence/pr4359/PROOF-REVIEW.md", + "docs/research/pr-intake-evidence/pr4416/PROOF-REVIEW.md", + "docs/research/pr-intake-evidence/pr4470/PROOF-REVIEW.md", + "docs/research/pr-intake-evidence/pr4470/REVIEWED-SOURCES.json", + "notes/compact-control-movement.tex", + "notes/general-clifford-frames.tex", + "notes/stopped-product-complex.tex", + "research/fresh-helper-boundary/CHANGES.json", + "research/fresh-helper-boundary/native.py", + "research/higher-moment-strictification/verify.py", + "research/joint-helper-lattice/CONTROLLER.json", + "research/joint-helper-lattice/NATIVE.json.gz", + "research/joint-helper-lattice/PATCH.json", + "research/joint-helper-lattice/PROOF.md", + "research/joint-helper-lattice/RESULT.json", + "research/joint-helper-lattice/native_joint.py", + "research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py", + "research/kappa-function-composition/complex/prune_native.py", + "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-CANONICAL.json.gz", + "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-NATIVE.json.gz", + "research/kappa-rebuild/complex/native_extensions.py", + "research/kappa-rebuild/complex/power_two_balance.py", + "research/kappa-rebuild/complex/rebuild_native.py", + "research/kappa-rebuild/transfer-audit/FINITE-TEMPLATE-CLOSURE.md", + "research/kappa-round3-warp-20261022/ACTUAL-WORD-FREEZE.json", + "research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz", + "research/kappa-round3-warp-20261022/NATIVE-VALIDATION.json", + "research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz", + "research/kappa-round3-warp-20261022/PROOF.md", + "research/kappa-round3-warp-20261022/SOURCES.json", + "research/kappa-round3-warp-lean-20261022/NativeCore.lean", + "research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json", + "research/kappa-round6-compiler-tightening-20261022/arithmetic.py", + "research/missing-join-frame/PATCH.json", + "research/native-warp-extraction-boundary/algebra.py", + "research/native-warp-extraction-boundary/operators.py", + "research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py", + "research/query-thinned-controllers/PROOF.md", + "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py", + "research/transported-warp-frames/PROOF.md", + "research/warp-interface-20261022/ACTUAL-WORD-FREEZE.json", + "research/warp-interface-20261022/ACTUAL-WORD.json.gz", + "research/warp-interface-20261022/PATCH.json", + "research/warp-interface-20261022/PHASE-VALIDATION.json.gz", + "research/warp-interface-20261022/SOURCES.json", + "research/warp-interface-20261022/verify_candidate.py", + "research/warp-interface-20261022/warp_merge.py" + ], + "stable_pre_post_live_inputs": 51 + }, + "status": "PASS_INDEPENDENT_FINAL4610_CONDITIONAL_ADMISSION" +} diff --git a/research/direct-backward-independent-validation/capsule/reuse/5396/capsule/agents/sources/pr5241/research/final4610-independent-admission/SPECIALIZATION.md b/research/direct-backward-independent-validation/capsule/reuse/5396/capsule/agents/sources/pr5241/research/final4610-independent-admission/SPECIALIZATION.md new file mode 100644 index 0000000000..7ee84b3089 --- /dev/null +++ b/research/direct-backward-independent-validation/capsule/reuse/5396/capsule/agents/sources/pr5241/research/final4610-independent-admission/SPECIALIZATION.md @@ -0,0 +1,130 @@ +# P1: specialize the selected physical grammar to final #4610 + +This note proves a conditional **specialization**, not a new physical primitive theorem. Let H_selected denote precisely the native normal-form, compact movement/repair, scalar/owned-storage, completed-call, fixed-tape and outer hypotheses retained by selected #4470 through its reviewed #4359/#4416 lineage. Under H_selected, the actual final #4610 catalogue is an instance of that same physical grammar, with newly counted fixed constants. The proof does not introduce a separate assumption that the new recipes work. + +Candidate #4610 is Cao Yifan/intqwq's existing construction, head `20bb93cd990d2ff683e4d0fc56b87a42cd5d3296`, final local-word payload `cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd`. Pinned canonical source is `ec2780e8aeb1c88acaf5e9e470ef8c68e7fbbb6c`. Selected #4470 remains .00302015; this note does not modify selection or claim construction/gain priority. Exact source bytes, including the following premise texts, are bound in `SOURCES.json`. + +## 1. The selected premise already quantifies over the required class + +The premises used here are the following statements in the selected source closure, with their original physical qualifications retained: + +1. `notes/general-clifford-frames.tex`, “Exact representatives and nested children”: for an arbitrary binary subspace U and deterministic invertible basis extension G, the exact Gaussian-dyadic K_G and its conjugate by F have rank zero and are fixed binary address permutations with unit quadratic phases. For **every** nested U subset V, the exact transition is two rank-zero adapters around a positive coordinate C child. Exact phases and finite movement/scalars are charged. The statement is not restricted to the selected word's list of old frame labels. +2. `notes/compact-control-movement.tex`, “Compact-control selected-bit addition” and “Application to a fixed binary change of basis”: either ordering of two complete slots admits exact selected-bit row addition with restored arbitrary temporary fields; a fixed binary basis change is a fixed number of such additions. The fixed-tape bound is `O(V*((e*log p)^tau+1))`, including repair and descriptor work, under the stated complete-field reservations and record-size hypotheses. Constants and cutoffs are uniform within each fixed parameter family. +3. Selected #4359 `PROOF-REVIEW.md` section2: free-word evaluation allows arbitrary positive column multiplicity by substituting lifted generators, separately tensor-lifting exact paid/helper factorizations. Absolute monomial phase is `a*f+sum q(x_j)`. Helpers are normalized only after their autonomous completed endpoint. Section3 explicitly permits fixed template matrices/matchers to change dimensions/counts/constants while retaining the same movement exponent and tape uniformity. Section4 separately pays address permutations and unit phases and replaces semantic precision constants. +4. Selected #4416 `PROOF-REVIEW.md` section2: exact whole-job normal forms use independent **two-sided** recorded factors. They need not be an inverse pair. Canonicalize the complete job, place its axes by a charged coordinate matcher, execute the child, and restore the prescribed adapters before resuming its parent. Distinct physical owners and separate live centers are preserved. +5. Selected #4470 `PROOF-REVIEW.md` sections1–3 applies these rules to new actual helper normalizers, paid transports, p16/query/idle events and their new finite scalar/route/owner/precision constants. The retained conditions include all-column implementation, whole-job adapters, owned erasure, fixed-tape movement, precision and outer hypotheses. + +Consequently the permitted class is generic fixed finite Gaussian-dyadic monomial/positive-child programs with the stated arbitrary-owner and spectator ABI. It is not the stronger assertion that an arbitrary RAM gather or arbitrary address function is cheap. The reduction below uses only the selected binary row-addition/ordered-movement operations, finite unit phases and the same scalar/child/owned alphabet. + +## 2. A constructive grammar for every actual monomial + +Use the source's exact composition convention. A record m has invertible binary matrix A of size9, affine offset b, constant a modulo4, linear coefficients alpha_i modulo4 and symmetric binary quadratic matrix Q, with `alpha_i mod2=Q_ii`. On a basis address x it acts as + +``` +|x> -> i^(a+q(x)) |A*x xor b>, +q(x) = sum_i alpha_i*x_i + 2*sum_(i A*x_j xor b for every j, +phase = a*f + sum_(j=1..f) q(x_j) (mod4). +``` + +Apply the finite row-addition list to the corresponding pair of complete f-axis slots, and use the pointwise residue above. Each selected slot is a full range; arbitrary intervening, preceding and following spectator fields remain present. The temporary complete compact fields are returned by each addition. Thus the lift is exactly m tensor-powered f, acting as identity on the other address fields. It uses one fixed list of primitive **types/operations**, rather than f separately allocated tapes. Its per-record descriptor arithmetic is polynomial in the same selected address bound, and the number of work tapes stays fixed for the template. + +For a recorded positive-rank recipe, source equality is the ordered product `right.then(C_r).then(left)`. Tensoring this product gives `right_f.then(C_(r*f)).then(left_f)` after the fixed coordinate reordering. This is one ordinary positive rank-r*f child on the actual owner's full stream, with its input and output monomials independently retained. Inverse orientation and Pauli corrections are included by the actual signed recipes. No identity distributes a tensor power over a matrix sum. + +For the scalar word itself, use selected #4359's free-word substitution theorem: replace each warp generator by its f-column lift while leaving ADD/SCALE coefficients and chronology unchanged. This is an algebra homomorphism from the noncommuting free-word algebra; hence the already checked arbitrary-input word identity survives. The scalar program is not itself tensor-powered. Keeping a single constant phase a instead of a*f would violate the lift; a negative control explicitly distinguishes that mutation at f=2. + +The ideal algebraic lift holds for every positive f. Its physical tariff applies only in the selected source domain: f<=p, A=O(p), K/log p tending to infinity, and a superpolynomial record fiber. In the actual layer f<=e<=floor(b_in^epsilon) and p=6*b_in eventually. No tariff is extrapolated to arbitrary independent f,p/geometry. The compact-control parameter hypotheses are unchanged: f slots, complete dirty reservations, `A=O(p)`, record fiber beyond fixed powers, and the same selected movement exponent. The final uniform template may have much larger fixed dimensions and operation counts. That changes constants and thresholds through section6 below, rather than changing these quantifiers or creating a new tape per coordinate. + +## 4. Exhaustive family/owner specialization + +The executable source census is over the actual final payload, not its proposed histogram. It classifies every event in both21449-record orientations, and checks exact scalar coefficients/opcodes/chronology against the selected THREE-base word. Main charts on all224 persistent main owners are exact retained records. Every scalar target/source belongs to the632 declared persistent owners or the one declared owned C0. Clear and overwrite COPY target only C0; ADD arguments are distinct owners; no new borrowed owner, alias or productive C0 is introduced. + +| Actual family | Membership/coverage | Selected physical interpretation | +| --- | --- | --- | +| 180 signed warp classes,240 occurrences | Each actual G is invertible; both signed recipes have rank0;800new monomial records cover this and the changed families below | Fixed affine binary permutation and unit quadratic phase from section2; same all-f native generator | +| 3290 borrowed climbs per orientation | Actual source/target bases strictly nested, correct current owner/frame and rank | The selected arbitrary-U-subset-V factorization: two rank-zero adapters and one positive rank-r*f child | +| Eight center calls per orientation | Actual nested comparable bases, owned C0 only, all eight rank8 jobs billed | Same positive child plus signed adapters; no productive credit, no allocation of a new arbitrary input | +| 408 helper endpoints | Actual strict nested entrance/exit, profile `{4:28,7:7,8:47,9:326}` | Complete two-sided normal form on each distinct arbitrary input field; no internal scalar reframing shortcut | +| 448 main entrance/exit charts | Exact event equality with retained base main charts | Source-identical selected chart/axis interface, with its retained charge | +| 17453 scalar records per orientation | Exact old opcode/coefficient sequence, dyadic grammar and current-frame checks | Retained ADD, dyadic unit SCALE, owned COPY/CLEAR; identical scalar tariff | +| Ten phase labels | Fixed annotations, no new physical instruction | Existing scalar-word scope boundaries; not extra outputs or uncharged operators | + +Exact factorization equality and arbitrary-input endpoints are independently established by the admission dossier's native/phase replays, not by a syntactic schema. This module supplies the missing **physical class implication** for those exact factors. The new phase receipt covers180signedwarp classes,105newpaid pairs and5changedhelper pairs. The382 unchanged helpers are bound to the selected #4470 phase receipt through gain_acceptance's exact ordered-basis/owner lineage;26changed helpers use the new five-pair receipt. The independently replayed all2855paid-pair factorization module supplies the full actual paid-pair coverage. These coverage claims remain separate from this module's fresh class/census checks. + +For owned return, the local word retains one physical C0 and ends its C0 updates with a permitted erase. The existing arbitrary-input native proof establishes completed main/helper endpoints and C0 clearance. During product/compiler substitution, each suspended local occurrence receives its own center bank; all child inputs are distinct actual fields, even when values are correlated or one input is a parent's center. The child finishes and its adapters/role ordering return **before** the parent resumes. The parent clears only its own bank after its last use. Every such bank is excluded from productive W and included in full O. This is exactly the selected compiler ownership rule; no one-bank-per-depth reuse or undeclared initialized input is used. + +## 5. Finite raw tariffs in the selected unit + +The tariff unit here is a retained elementary scalar/movement/phase **record**, each realized with the selected physical primitive's asymptotic bound. It is not one literal tape instruction and does not suppress the f-dependent movement bound. Choose the same common upper unit for the fixed primitive alphabet as in the selected finite-word accounting. Each new two-sided nine-axis recipe has at most342 elementary records, below the retained conservative1000-per-group allowance. Unchanged main charts retain their selected count/unit. The selected primitive implementation constants, record-paid setup, scans and repair remain paid in that common physical unit. Changing the finite catalogue does not require a new asymptotic movement assumption. + +The actual local route groups are + +``` +3298 paid jobs + 2*408 helper wrappers + 240 warps + 448 main charts + = 4802 groups, +4802*1000 = 4,802,000. +``` + +The source scalar allowance formula, reimplemented directly without importing its evaluator, gives158120 forward and158168 backward. Therefore + +``` +158168 + 4802000 = 4960168 < 10^7. +``` + +This is an instantiation of the selected raw-unit bound with a smaller changed paid count, not reuse of an old expanded compiler cap. The controller remains18full calls and15thin queries, with the exact retained physical-event and boundary programs. The complete source raw bound is + +``` +18*10^7 + 15*1792 + + 32*112*(#physical_events + #left_boundary_program + #right_boundary_program) + = 181098496 < 10^9. +``` + +Each thin query's paid rank-one request, owned copy/add/erase and inverse orientation remain in the source invoice. Idle jobs, main normalizations, inherited controller geometry and actual exact phase bills remain charged. No local or controller charge is credited as a new productive output. These numerical bounds concern **raw** supplier records only; they are not the expanded uniform word's operation count, storage or literal physical runtime. + +## 6. Expanded compiler, precision and tape constants + +Apply the selected chronological product, same-owner paid completion, disjoint splitting and integer finite compiler to this now-specialized raw program. The algorithms are finite and only instantiate the same grammar. Their matching uses complete job endpoints and restores adapters, and their owner allocation is the rule just proved applicable. No new movement species occurs when a fixed matcher has a larger fixed rank: binary basis/coordinate permutations have the same finite elimination construction, now with a larger fixed list. + +Let W,P,O be the actual final productive width, paid rank-one count and full owned-bank allocation; let R count the full native/movement/normalizer records, including product, completion, split and compiler routes. Let G be their fresh dyadic coefficient/phase allowance, computed by summing the actual scalar allowances (plus the source's conservative non-scalar charge). These are finite computable integers of the new expanded template. They are fixed before multiplication input size varies. A record-count overestimate and one owned bank per relevant occurrence suffice; no practical materialization or old p3 numerical count is needed. + +Use the **new** values in the selected semantic prescription: + +``` +Z=W+O, +E=64*(Z+N+P+G+1)^3, +B=P+E, +C0=32*N*B^2. +``` + +The selected completed-child argument gives `A(e)<=A(floor(e/N))+P*floor(e/N)+E`, hence `A(e)<=2B*e`. Monomial permutations/unit phases add no coefficient height but do retain their execution/descriptor costs. The new C0 determines a new eventual fine-grid threshold. The compact row reserve, full simultaneous stock products, depth-first parking, fixed tape inventory and polynomial setup degrees also use the new W,P,O,R,N and selected formulas. Fixed enlarged degrees/counts are absorbed by the same retained superpolynomial record fiber and strict outer epsilon<1 after increasing the threshold. In particular, neither raw10^9 nor selected p3/p16 reserve constants stand in for these expanded values. + +Thus P2–P4 can consume a genuine new finite instance of H_selected's grammar and precision/stock/tape prescriptions. This note does not independently prove the historical native movement/repair or outer analytic/recovery stack. Those are exactly the assumptions already retained by selected #4470, with no additional candidate-specific implementation assumption. + +## 7. Conclusion and exact limits + +Given H_selected and the source-bound exact semantic/phase endpoints supplied by the independent native dossier, the final catalogue has permitted explicit all-f realizations, legal actual-owner return, finite raw tariffs and the selected expanded-constant substitution. No extra primitive or changed movement exponent is required. P1 is therefore a **consequence** of H_selected for this instance. It need not be restated as a new hypothesis “the new recipes implement.” + +`checks/specialization.py` runs through the master verifier and its source-authenticated `--repo` working-byte loader; it never substitutes clean Git blobs for dirty inputs. Its new actual catalogue has800monomials with at most83 elementary records each, compared with the uniform171 bound. It also checks1692selected monomial records by the identical schema, exhaustive event/role/rank/scalar census in both orientations, helper geometry, retained main charts, the4802route grouping and raw bounds. Controls reject singular maps, non-Z4 absolute phases, borrowed clear, unpaid rank changes, non-dyadic scalars and an unlifted f=2 global phase. Exact phase/operator equality is intentionally supplied by the separate phase/native verification rather than inferred from membership. + +Credits remain with Cao Yifan/intqwq (#4610), Cinna Davis (#4470/#4416/controller/helper lineage), zxv (#4359/native/compiler/semantic precision), icekylinx and Dugongue (general Clifford/transported frames), Jacob Alan Sussman (mixed integer compiler), and all retained physical/BIT/geometry/analytic contributors. This new specialization/proof/check uses substantial OpenAI assistance. It is a scoped conditional AI verification contribution, not an unconditional multiplication theorem or independent human/kernel acceptance. diff --git a/research/direct-backward-independent-validation/capsule/reuse/5396/capsule/repository/docs/research/pr-intake-evidence/pr4610/PROOF-REVIEW.md b/research/direct-backward-independent-validation/capsule/reuse/5396/capsule/repository/docs/research/pr-intake-evidence/pr4610/PROOF-REVIEW.md new file mode 100644 index 0000000000..bf5ff049da --- /dev/null +++ b/research/direct-backward-independent-validation/capsule/reuse/5396/capsule/repository/docs/research/pr-intake-evidence/pr4610/PROOF-REVIEW.md @@ -0,0 +1,137 @@ +# PR4610: conditional admission through the PR5241 audit + +**Pass under the unchanged five selected framework assumptions:** +κ = 15108879/5000000000 = **0.0030217758**. +This is Cao Yifan / intqwq's construction at +`20bb93cd990d2ff683e4d0fc56b87a42cd5d3296`, independently audited in +Chris R / Clear1nsight's PR5241 at +`13efb5fc5f3b7c14ec2cfa181dd9eb6480972cf2`. +Maintainer review: Douglas Colkitt's OpenAI assistant, with substantial AI +assistance. Apache-2.0. No independent human or end-to-end formal proof is claimed. + +## Changed construction and exact coverage + +The accepted object is the frozen round3 native word and round6 compiler point, +not every exploratory claim or intermediate result in PR4610. Relative to +selected PR4470, 20 native binary maps and 26 helper boundary interfaces change; +all twelve shared prelude maps and the main endpoints remain fixed. The complete +local paid profile becomes `{1:2201, 2:412, 3:510, 4:127, 5:40, 8:8}`. +The productive helper profile remains `{4:28, 7:7, 8:47, 9:326}`. + +The fresh audit passes all eleven required stages. It checks 480 signed warp +events, 180 signed warp classes in both orientations, all 408 helper inputs +through 34 oriented endpoint classes, and all 5,710 oriented paid classes +covering 6,596 local event instances. No earlier receipt's PASS flag substitutes +for phase correctness. The frozen paid catalogue is candidate data; its +compiler is not imported by the acceptance path. + +The reviewer inspected the independent Clifford evaluation and phase test: +equality on the 18 Pauli generators identifies the operator up to a scalar; +equality on an exactly normalized nonzero state fixes that scalar. All factors +are validated monomial/Clifford operations, so this is a complete finite-operator +argument, not a sample of input vectors. Phase-only mutations preserve the +tableau and are nevertheless rejected. Positive recursive ranks are checked +against the actual nested bases, including all eight owned rank-eight calls. + +The chronological symbolic interpreter tracks all 632 independent persistent +inputs, current frames, inverse orientations and the owned C0. It verifies a +free-group identity on arbitrary dirty inputs, with each helper restored and +only the owned stream erased. Left multiplication on reduced free words is +injective; its dictionary update does not silently discard colliding words. +Main chart and scalar opcode/coefficient sequences are compared to retained +source. No arbitrary borrowed input is treated as initialized workspace. + +## Uniform lift and physical specialization + +We reviewed PROOF.md and SPECIALIZATION.md against the pinned PR4359, PR4416 +and PR4470 reviews and the general-frame/compact-movement notes. The retained +contract already permits arbitrary fixed nested binary frames with independent +two-sided monomial adapters. The new recipes lie in that class: invertible +nine-bit affine maps and Z4 quadratic phases. Elimination, translations and +phase operations need at most 171 primitive records per monomial, hence at +most 342 for two adapters, within the retained 1000-record raw allowance. +This counts retained physical primitive records, not constant literal tape +steps at arbitrary column multiplicity. + +Tensor power is applied to products and individual operator factors. The scalar +ADD program instead lifts by evaluation of its proved free-group identity. +Tensor power is never distributed over a sum. Absolute phase is repeated once +per column. Algebraic equality holds at every positive multiplicity; the +physical tariff retains its source hypotheses on complete slots, restored +controls, record fibers and the f,p domain. Spectators and independent ownership +remain explicit. Thus the changed catalogue does not add a candidate-specific +oracle to the old assumptions. + +Expanded template counts, owned banks, routing and coefficient envelopes must +be substituted into the retained precision/stock formulas. The new enormous +compiler does not inherit an old numerical template-size cap. This remains a +conditional application of the selected physical and analytic framework; +finite computations do not independently prove its fixed-tape, precision or +integer-recovery theorems. + +## Invoice, completion and outer transfer + +The unchanged p16/query-thinned controller is source-identical to the selected +review. The audit independently reconstructs its events and boundary programs; +the previously reviewed Laurent endpoint and stage-zero commutation argument +are reused with unchanged main operators. Eighteen full calls, fifteen thin +queries, fifteen idle windows, all main/helper targets and owned centers give +**64,404 paid calls and 10,928 productive fields**. Target and paid rank masses +remain 239,886 and 239,134, giving surplus 752. Compared with PR4470 the whole +paid histogram changes by `{-648 H1, +432 H2, +288 H3, -360 H4, +72 H5}`: +216 fewer calls, without removing rank mass or reusing output credit. + +Two independently implemented directed interval engines check the freshly +derived invoice. The raw crossing is bracketed by +(.00302177587077, .00302177587078). The tested saving .00302177581 exceeds the +claim .0030217758. The old selected invoice fails at the new claim; this is a +changed-construction gain, not decimal refinement of the old crossing. + +At tensor power 1024, cutoff 20, completion floor 21 and tail shift 1/5, +alpha < 1-10^-11 and both charged tail ratios are below 97/100. The complete +bound `1/(1+1024*10^-11)+4/2^32 < 1` is checked exactly. The old 10^-9 reserve +would fail here and is explicitly rejected. The reviewed product/completion +and splitting arguments apply with these new constants and actual profiles. +The compiler's sufficient integer test gives H=38,569,300,000,000,000 and +N=2^H. This is a finite specified construction; no expanded word is materialized. + +The ordinary BIT interface is exactly equal to the selected source and admits +.0034, above the required effective saving. Its already reviewed supplier and +conversion are reused, not established anew by the complex checks. All nine +outer cost rows, 54 strict predicates and four functional predicates pass. +The minimum recorded strict predicate is 1/7,000,000,000,000. Both arithmetic +engines retain the charged targets, owned centers and compiler tails. + +## Execution, provenance and invalidation + +COLD-REPLAY.json and BOUNDED-RUN.json record the complete serial CPython 3.12 +run: 137.25 seconds and 184,928 KiB peak sampled descendant RSS, below the +660-second / 1 GiB guard. All 82 committed-byte bindings, canonical source +ancestry and registered metadata/pins checks passed. No Lean, Docker, hosted +Linux run or historical all-suite replay was performed. + +The current selected metadata is changing, but PR5241 authenticates the exact +old PR4470 record as its baseline. The new reproduction entrypoint therefore +exports that historical record from `certificates/checkpoints/frontier4470.json` +to its original path, explicitly. The research package and scientific source +bytes remain unchanged. Canonical Git objects are used only for ancestry and +stored-blob checks; the mathematical code reads its closed exported input set. +The source manifest also retains the prior reviewed foundation closure. + +Changes to frames, native phases, scalar chronology, helper endpoints, +controller, actual ownership, paid completion, compiler parameters, source +bytes or physical/outer contracts invalidate the affected review. Optional +optimizers, claimed global optima and later scalar-compression variants are +outside this acceptance. The result remains conditional on precisely the five +PR4470 assumption records, copied without weakening or deletion. + +## Credit + +Cao Yifan / intqwq: changed construction and compiler point (PR4610). +Chris R / Clear1nsight: complete independent admission package (PR5241). +Cinna Davis /1337isnot1337: joint-helper, query-thinned controller and preceding +construction chain. zxv: productive-helper native/compiler machinery. +Jacob Alan Sussman: mixed-target recursion. Dugongue: transported frames and +physical interfaces. Mihir Srivastava, Ryanson Jonathan and Mark / Matarener: +retained independent checks and adversarial questions. All BIT, geometry, +Clifford, precision and analytic contributors retain their earlier credit. diff --git a/research/direct-backward-independent-validation/capsule/reuse/5396/capsule/repository/research/kappa-joint-relations-20261023/WORD.json.gz b/research/direct-backward-independent-validation/capsule/reuse/5396/capsule/repository/research/kappa-joint-relations-20261023/WORD.json.gz new file mode 100644 index 0000000000..a4a58afce1 Binary files /dev/null and b/research/direct-backward-independent-validation/capsule/reuse/5396/capsule/repository/research/kappa-joint-relations-20261023/WORD.json.gz differ diff --git a/research/direct-backward-independent-validation/capsule/reuse/5396/capsule/repository/research/pr4359-p7-padding/source/research/kappa-rebuild/architecture/FINITE-PRECOMPILATION.md b/research/direct-backward-independent-validation/capsule/reuse/5396/capsule/repository/research/pr4359-p7-padding/source/research/kappa-rebuild/architecture/FINITE-PRECOMPILATION.md new file mode 100644 index 0000000000..4badb40f09 --- /dev/null +++ b/research/direct-backward-independent-validation/capsule/reuse/5396/capsule/repository/research/pr4359-p7-padding/source/research/kappa-rebuild/architecture/FINITE-PRECOMPILATION.md @@ -0,0 +1,313 @@ +# Finite precompilation of a mixed-target rule + +Status: constructive bridge under the precise native hypotheses below, +independently audited in `../transfer-audit/AUDIT.md`. This is a written +argument, not a formal proof or a completed integer-multiplication admission. +The companion finite scheduler checks actual integer flow and ordering. +The original immediate-normalization BIT interface failed hypothesis 3. +`../bit/DELAYED-COVER-BRIDGE.md` supplies the distinct delayed-cover +implementation, with a finite local-ring check and the native binding in +`../bit/BIT-P3-NATIVE-BINDING.json`. Its fixed rational cover routes are a +costed program schema, not dense coordinate gates in a plain native word. + +Substantial OpenAI assistance. Apache-2.0. The mixed-target asymptotic flow is +Jacob Alan Sussman's Theorem 1G, PR4268, with the detailed proof at commit +`563b4e6e913625637f36ba7869bf5fcd0dd4975a` of +[`wht-power-saving-lean`](https://github.com/jacobalansussman/wht-power-saving-lean). +The source, exact scheduling code and notices are preserved under `sources/`. +The contribution proposed here is clearing the finite flow into a single +uniform native supplier before applying the inherited outer theorem. + +## 1. What needs to be assumed + +Let a job of rank `s` apply a specified tensor operator to `s` selected +coordinate blocks of one array, fixing all other coordinates. A block has +an arbitrary positive tensor multiplicity `f`. A completed rank `s` job +therefore acts on `s*f` axes. All productive inputs are arbitrary. + +Fix one mixed unit with productive targets `W_k` of ranks `k`, a chronological +list of paid child ranks `r_j`, and a finite number of scalar and routing +passes. These assumptions are required, separately from the moment inequality: + +1. **An all-column native word.** At every integer column count `c`, the unit + computes exactly its independent rank `k*c` output jobs. Its paid rounds + are rank `r_j*c` jobs in the stated order. All borrowed data return to the + declared endpoint, and owned storage is explicitly initialized and erased. + Its finite operation count is uniform in `c`. +2. **Disjoint splitting and spectators.** A rank `a+b` job is a rank `a` job + followed by a rank `b` job on disjoint coordinates. The resulting programs + preserve arbitrary complete spectator fields and accept arbitrary data. +3. **Whole-job adapters.** Any job passed between two units has an explicitly + priced, permitted embedding into its destination. For the intended complex + application these are fixed monomial binary address maps and unit quadratic + phases, together with role permutations. The adapters must work at every + tensor multiplicity. Rank equality by itself is insufficient. +4. **Finite-program closure.** A finite composition of these words and + adapters is again a permitted finite supplier. Constantly many owned fields + may be supplied with their full cost and no productive output credit. + The eventual ordinary recursion must have the same arbitrary-input, + restoration, scalar and precision interface as the retained supplier. + +Put `m=max{k:W_k>0}`, `k_min=min{k:W_k>0}`, and +`r_max=max{r_j}`. Require `r_max g*S`, keeps one +external weight throughout the entire finite circuit, and lowers only its +final rank-one leaves. All rational matchers, role routes and their inverses +are fixed before choosing the odd prime and its exclusions. Every route +uses complete equal-multiplicity cover fibers and the retained, costed row +permutation primitive. This gives the same finite DAG argument in the +rational-cover program category. The BIT binding supplies the actual native +projectors; a rank count alone would not provide this implementation. + +## 2. Proposed conclusion + +Suppose the preceding hypotheses hold and the mixed balance has root +`tau` in `(0,1)`: + +``` +sum_j r_j^tau = sum_k W_k k^tau. +``` + +For every `z` with `tau=2`, a fixed number `B_N` of productive arrays, +and only rank-one paid children, whose number `P_N` satisfies + +``` +P_N < B_N * N^z. +``` + +Every productive output is the full rank-`N` job. The construction may have +an enormous finite scalar word, role inventory and owned-storage requirement. +Those quantities affect constants and the eventual input threshold. They are +not omitted and are not credited as extra output jobs. + +If this uniform supplier is admitted under the retained native, precision and +fixed-tape premises, the existing uniform recursion applies directly. A new +dynamic RAM-to-Turing-machine simulation is not being assumed here. + +## 3. The integer lockstep flow at a fixed rank + +This is the part of Theorem 1G used by the compiler. At one fixed top rank +`N`, its units, source jobs and exit jobs have integer multiplicities. +For a multi-index `a` on the target types define + +``` +c(a) = product_k k^(a_k), +u(a) = multinomial(|a|;a) * product_k W_k^(a_k). +``` + +The exact Pascal identity is + +``` +u(b) = sum_{k:b_k>0} W_k*u(b-e_k). +``` + +Let `G` be the largest `|a|` with `m*c(a)<=N`. A class is indexed by a +sequence of paid rounds `s` of length `d<=G`; its dilation is +`rho_s=product r_j`. It contains `u(a)` units at column `rho_s*c(a)` for +each `a` with `|a|=G-d` and `m*rho_s*c(a)<=N`. + +For one parent paid round, the Pascal bijection matches its job copies to +target roles of the child class, at exactly equal integer ranks. Missing +demands are top sources. Separation ensures every parent job is consumed. +The source ranks lie in `(N/m,N]`; only the deepest classes produce exit +jobs, all strictly smaller than `N` once `N` is outside the finite base range. + +Process a class in word order. At round `j`, suspend every unit of that +class, complete the entire child class fed by that round, and only then +advance the parents to round `j+1`. This forbids a unit from requiring both +an earlier and a later round of the same suspended parent. The resulting +dependency graph is finite and acyclic. Its edges carry complete array jobs, +not individual scalar values copied for free. + +These integer quantities exist before normalizing the sources to total +weight one. Let `S_s` be the number of source jobs of rank `s`, let +`S=sum_s S_s`, and let the ordered exit batches be `(e,t)` with `t` jobs +of rank `e` each. This finite integer flow is the compiler input. + +## 4. Clear every batch denominator constructively + +Induct on the integer top rank `N`. For each smaller rank `e` the compiler +has already constructed a uniform program on `B_e` arbitrary arrays, +computing full rank `e` with `P_e` paid rank-one calls. For a sufficiently +small rank use the ordinary sequential program: `B_e=1`, `P_e=e`. + +For the current flow choose an integer `a` divisible by every `B_e` needed +for an exit and every `B_(N-s)` needed for a nonzero source remainder. +The product of those finitely many positive integers is a valid choice; +their least common multiple is a smaller optional choice. Set + +``` +B_N = a*S. +``` + +Assign `a*S_s` of the input arrays to each source rank `s`. On each of those +arrays, first complete its `N-s` complementary coordinates using the +already-compiled smaller uniform program. All such batches are integral +because `a` is divisible by their program widths. This preliminary action +commutes with the intended `s`-coordinate job and fixes its input coordinates. + +Make `a` copies of the integer lockstep flow. Route its source arrays to +their exact input slots using permitted whole-array adapters. At a deepest +exit batch, `a*t` is divisible by `B_e`; replace that batch by copies of +the smaller uniform rank-`e` program. Restore its role ordering and adapters +before resuming the suspended parent class. Execute the finite DAG in the +lockstep order, and finally restore the original source-array ordering. + +Every array has now received its disjoint complementary job and source job, +hence the full rank-`N` transform. No copied scalar input or blank helper is +treated as another independent output. Every original array occurs exactly +once as a source; interior target slots are jobs on those arrays, not new +productive inputs. + +Induction removes all recursive calls: the only remaining paid children +have rank one. Clearing denominators multiplies productive arrays and paid +operations equally, so it preserves the per-array leaf count. In formulas, + +``` +P_N/B_N = (1/S) * [ + sum_s S_s * (P_(N-s)/B_(N-s)) + + sum_(ordered exit batches e,t) t * (P_e/B_e) +]. +``` + +Zero-rank terms vanish. Any plain rank-one exits are the ordinary base +program. Scalar and routing passes have their own analogous nonnegative +count and must be included in the asymptotic cost used to choose `N`. + +This construction uses full integer batches; it does not assume that +fractional pieces of a physical array can be routed at zero cost. Its exact +replication factors can be impractically large, which is acceptable for a +fixed finite supplier existence statement but must be disclosed. + +## 5. Why some fixed N has the required saving + +The independent audit sharpened this step to a direct count of paid leaves. +It does not require a running-time comparison between a RAM flow and native +tapes. Let `L(n)=P_n/B_n`, let `w_s=S_s/S`, and let `x_e` be the exit counts +normalized by the number S of source arrays. The actual integer compiler +satisfies + +``` +L(n) = sum_s w_s L(n-s) + sum_e x_e L(e), +sum_s w_s = 1, +sum_e x_e e^tau = sum_s w_s s^tau. +``` + +The last equality follows by canceling every internal matched job in the +exact tau-potential balance. The source ranks satisfy `n/m0`, concavity gives + +``` +n^z0 - sum_s w_s (n-s)^z0 >= eta * sum_s w_s s^z0. +``` + +Indeed, for `t=s/n` in `[1/m,1]`, +`1-(1-t)^z0 >= z0*t >= eta*t^z0`. For every sufficiently large n the +exit coefficient is less than `eta/2`. Every complement and exit has +smaller rank than n, so strong induction on the exact recurrence proves +`L(n)<=A*n^z0`, with finite A chosen to cover the smaller ranks. Eventually +`L(N)= 2`; +* `W` productive arrays, each receiving the **full** rank-`N` transform; +* `P` rank-one paid children; +* `U` copies of the mixed unit in the completely expanded finite word; +* at most `O=U` owned centers, conservatively one per mixed-unit instance. + +For every rational `z` strictly above the mixed root and below one, the +constructive count argument provides an `N` with `P < W*N^z`. +“Finite” here means fixed before the eventual multiplication input grows. +It can be astronomically large. Neither this note nor the receipts claim +to have materialized the winning near-threshold instance. The later +`../controller/EXPLICIT-TEMPLATE-BOUNDS.md` strengthens the existence +argument to the specified complex rank `N=2^276540184361`, with uniform +saving `0.002304`; no search for a successful rank is left unperformed. +The integer recursion defines its exact finite `W,P,U`, and the constants +below are computable functions of that finite result. + +The fully materialized, depth-zero `N=57` example has `W=2242`, `P=127570`, +and `U=1`. It is a useful independent check that complementary source jobs +are really paid: `57*2242-127570=224`. This small example is not claimed to +attain the limiting mixed exponent. + +## 2. Every column count and every complete spectator field + +The local logical identities were replayed in a free noncommuting operator +word algebra. Apart from rational scalar arithmetic, the checker uses only +composition and cancellation of an operator with its recorded inverse. +For any positive integer `f`, substitute the `f`-column physical operator +for each such generator. This extends to an algebra homomorphism on the +free word algebra and preserves the checked identities. + +This is not the false assertion that tensor power is additive on arbitrary +matrix sums. The role-level scalar word is unchanged. Each physical address +generator is replaced by its column lift, while its formal products and +linear combinations are evaluated on the same independent role arrays. + +A rank-zero native monomial has the form + +``` +|x> -> i^(a+q(x)) |M*x+b>, +``` + +with invertible binary `M` and a permitted quadratic phase `q`. Its column +lift has blockwise address map `M`, translation `b` in every column, and +phase `a*f + sum_j q(x_j)` modulo four. This explicitly retains the absolute +phase. A fixed coordinate matcher in the precompiler becomes the same +fixed permutation of `f`-axis blocks. All untouched axes remain complete +spectator fields. A rank-one leaf becomes the standard rank-`f` child. + +The retained exact Clifford normal form supplies the monomial factors +around each child. The independent p3 audit checks the whole main boundary, +including the output translations required by negative powers of `C_q`. +The fixed THREE/base selection is valid for every column count: THREE/base +and THREE/extra have identical entrance and exit operators; their difference +is an internal frame and its associated warps. No layer-dependent selector +is required for the endpoint contract. + +For any integer input width `e=N*f+r`, first apply the `r=2`, `B=P+E`, and `E>=64`, + +``` +2*B*(N-1) >= P+E, +2*B*f+P*f+E <= 2*B*N*f <= 2*B*e. +``` + +Induction gives `A(e)<=2B e`. Completed disjoint selected-axis pieces have +total width at most `d`. The retained prefix kernels, outer phases and +normalization add at most `18d`, giving + +``` +A_layer <= (2*B+18)*d < C0*d. +``` + +Every calculation remains on one fixed fine grid. A child is never rounded, +compressed, or re-encoded at return. The change is to the proof's bound on a +completed value, not to its stored representation. Other fields remain +parked while the child executes. This is why the linear semantic bound +survives a huge scalar word and why the older pathwise `C1>1` estimate is +unnecessary. + +The stopping rule can be any fixed rational `0=2N`, every internal call has the required positive `f`; +the completed-leaf estimate remains `8e` at the stopping leaves. No old +numerical cutoff is carried over. + +### An effective threshold, including enormous constants + +Suppose `d<=c*p^epsilon`, with fixed `c>=1` and rational +`epsilon=a/b` in `(0,1)`. Let `L` be the binary bit length of +`4*C0*ceil(c)` and choose + +``` +t = max(4, ceil(b*L/(b-a))), p0 = 2^t. +``` + +For all `p>=p0`, `p^(1-epsilon)>4*C0*c`, so the integer guard +`Delta=C0*d` is at most `p/4`. Signed components with `p+Delta` fractional +bits and `Delta+3` magnitude/sign bits have width + +``` +p+2*Delta+3 <= 2p. +``` + +The audit emits `p0` as a compressed power of two. It does not try to +allocate that many bits. This construction proves the eventual `O(p)` word +bound for the new finite template, including the current outer choice +`epsilon=99999/100000`. Huge fixed constants change `p0`, not `C1` or the +power in the final exponent inequalities. + +## 5. Productive stock, owned storage, and native tape closure + +For the ordinary uniform complex word, let + +``` +D(e)=0 if e=W^D(d)` for `K>=1`. Pad complete rows once to the next multiple +of `W^D(d)`. The padding factor is below two. Every descendant then has +exactly `1/W` of its parent's productive volume and enough divisibility for +its remaining depth, with complete active, control and spectator fields. +All-row endpoint correctness restores appended zero rows to zero. + +Owned storage contributes no factor to productive output credit. A safe +choice is one full center field per finite mixed-unit instance, namely +`O=U`. At an ordinary recursion node each such field has the same shape as +one productive role stream, of volume `V/W`. Initialize, retain and clear +it as its actual word prescribes. If simultaneously suspended units keep +live centers, they receive distinct banks. Reusing one bank per recursion +depth would not suffice. Owned-space scans and parking cost fixed multiples +of volume; paid calls on those banks are already in `P`. + +The integer audit checks row divisibility and one-time padding at several +floor-depth boundaries. It also gives an explicit sufficient threshold +for `q00. Physical tariffs retain `f<=p`, address bound `A=O(p)`, `K/log p -> infinity`, complete compact/control fields, restored dirty temporaries, and the source superpolynomial record fiber. At the eventual caller `f<=e<=floor(b_in^epsilon)`, `p=6*b_in`, with fixed epsilon<1. Binary row addition, swap and unit quadratic phase retain descriptor/repair charges. No extra gather, blank productive input, numerical zero predicate, field extension or changed movement exponent is introduced. + +## Exact operation and owner specialization + +The checker independently follows every scalar exact-frame contact and every warp/climb frame update; counts scalar tariffs/paid ranks; checks unchanged forward/canonical records; follows all snapshot lifetimes; and checks cold preparation uses only cleared owned pivots and nonpivot independent sources. It does not independently prove free-word identities: the algebra/ownership reviewers own the 16 unrestricted identities and full return proof. + +Every same-frame COPY targets a distinct cleared owned slot with scalar coefficient 1. At a center replacement its saved row and the old output have the same exact physical frame, so the proved logical equality includes the inherited gauge. At each zero marker the independently proved full row is zero; physical identity preserves zero in the common ambient space. The marker does not implement arbitrary nonzero frame transport. Approximate residuals must be bounded through the actual new circuit, which executes identity there; they cannot be assumed to vanish. The fresh semantic guard below concerns this actual circuit and the retained single fine-grid format. + +| Candidate | Owned L pivots | Backward scalar allowance | Simultaneous snapshots | Backward owners | +|---|---|---:|---:|---:| +| #5383 |225,227,229,230,241,245,257,288|158744|8|17| +| #5387 |225,227,229,230,241,245,257,261|158776|8|17| + +Each forward has one C0 owner and allowance 158120. The 16 backward/2 forward LOCALs conservatively require `16*17+2=274`distinct complete owned banks before query/product/completion/compiler owners. L pivots reuse their physical slots and lose productive credit. Every suspended compiled occurrence gets its own tagged C0..C8 and pivot banks. A child may act on a correlated value on its parent's field, but its own banks are distinct; adapters/order return before its parent resumes. This is the selected arbitrary-input completed-child ABI. Eight live snapshots alone disprove one-bank-per-depth allocation. Borrowed fields cannot be cleared. + +Both backward paid profiles are `{1:2193,2:412,3:510,4:127,5:40}`. The invoice reviewer independently verifies 64148 paid/10800 productive and the joint loss 128 H 9 targets with deletion 128 H 1+128 H 8 paid. This report gives no productive credit to any private pivot, snapshot, query scratch or parked bank. + +## Constructive expanded integer bound, for every top rank + +The copied canonical `FINITE-PRECOMPILATION.md` gives exact integer lockstep flow, product clearing of smaller program widths, complete chronological substitution and one bank per relevant unit instance. The copied `FINITE-TEMPLATE-CLOSURE.md` gives the semantic/stock specialization. We give a conservative computable integer bound for these permitted explicit construction choices; no raw 10^9 cap becomes an expanded cap. + +First bound the strictified mixed unit, after its 1024-fold chronological product, charged completion and disjoint splitting. The raw controller's combined scalar/movement/phase/owner inventory is below 2^40: its charged raw 181098496<2^28, paid/independent arrays<2^17, rank 145<2^8, complete 9 axis recipes 342 records<1000 and 274 LOCALowned banks, with queries and return routes included. This is a record envelope, not a count of literal tape steps. + +For q raw factors, Cartesian role and paid/target label inventories have at most `(2^40)^q`entries. Chronological product substitution charges each copied circuit record and bank by its factor position and paired Cartesian role/paid labels. Thus `q*4^q*(2^40)^(2q)`is a conservative bound before whole-job routes. At q=1024 its ambient rank `m=145^1024<2^8192`. Completing a job uses at most m disjoint unit-axis jobs; splitting gives at most m pieces. Binary coordinate matchers and phases have row-elimination recipes bounded 64(m+1)^3 per whole-field record, and role ordering takes at most the square of the role inventory in swaps. Writing q=1024, the pre-route record logarithm is at most `82*q+10`. Completion and splitting multiply records by at most `m^2`, adding at most `2*8192`. Conservatively square that ENTIRE inventory for routing, and multiply by `64*(m+1)^3`. Its logarithm is at most `2*(82*1024+10+2*8192)+6+3*8193=225309<262144`. This directly pays both the role-square and rank-router factors. Therefore a common envelope for arities, records, coefficient-height charge, productive/paid/owned inventories and routers of this fixed strictified unit is + +`D=2^262144`. + +The coefficient allowance here is an integer SUM of elementary dyadic magnitude/denominator increments and unit-phase allowances, not the bitlength of that sum. Unit phases/permutations have zero height but retain record costs. Preparation coefficients are dyadic; the scalar tariff dominates their logarithmic height increment. Completion/splitting use canonical full jobs and monomial matchers, not new scalar mixing. Thus the same positive record envelope bounds G as a value. + +Define the following integer recursion: + +``` +F(0)=D +X_n=(n+1)*(D+1)*(F(n-1)+1) (n>=1) +F(n)=X_n^(16*(n+1)^2) (n>=1) +``` + +F is monotone and effectively computable by a terminating primitive recursion. We claim F(n) bounds every count W_n/P_n/O_n/R_n/G_n and complete emitted record inventory at top rank n, with concrete choices: use the product of distinct needed smaller widths as denominator clearing factor; sequential rank-one kernels in the finite base range; fresh tagged banks for every relevant instance; row elimination and swaps for complete coordinate/role routes. These choices are explicitly permitted by the source compiler and require no optimization oracle. + +Proof by strong induction. Base programs have one array and n elementary kernels. In a nonbase integer flow, the minimum target rank is at least 2, so depth `G<=log2(n)=1; every smaller expanded program has at most F(n-1)records/banks. Their complete incidence, primitive mixed units, ordinary base kernels and all tagged owner lifetimes therefore fit + +`I_n <= X_n^(3*n+5)`. + +At most the square of the incidence count suffices for role permutations/allocation maps; a cubic overestimate also covers instruction/descriptor passes, forward/inverse adapters and every boundary occurrence. A rank-n coordinate map and phase need at most 64(n+1)^3 elementary records. Thus all counts and emitted records fit + +`64*(n+1)^3*(I_n+1)^3 <= X_n^(9*n+20) <= F(n)`. + +The last inequality holds for EVERY n>=1 because `16*(n+1)^2-(9*n+20)=16*n^2+23*n-4>=35`; preceding inequalities use only the explicit factors of X_n and X_n>128. This proves the all-n induction. The check's finite exponent probes corroborate this algebra and are not its proof. + +For each candidate let `N=2^H`, `M=F(N)`and use the fresh envelopes + +``` +W_actual,P_actual,O_actual,R_actual,G_actual <= M +Wbar=Pbar=Obar=Rbar=Gbar=M +Zbar=Wbar+Obar=2*M +Ebar=64*(Zbar+N+Pbar+Gbar+1)^3 +Bbar=Pbar+Ebar +C0bar=32*N*Bbar^2 +``` + +Actual W/P remain in the efficiency inequality. A larger envelope supplies no productive output and cannot improve P/W. F(N) is an explicit, terminating integer definition, not a practical numeric expansion. It is fixed before multiplication input growth and differs between candidate heights. No expanded word is materialized. + +## Semantic recurrence, error, stock and effective thresholds + +A completed u-axis child adds at most u to denominator excess and magnitude exponent. Unfinished child internals are not parent operands; return is never rounded or re-encoded. Monomial permutations/unit phases add zero coefficient height. Gbar includes the new dyadic preparation and erased-storage passes. The fresh cubic envelope satisfies + +`2*Gbar*Zbar^2+8*Pbar+4*Zbar+4+32*N=1 and N>=2, `2*Bbar*(N-1)>=Pbar+Ebar` proves by induction `A(e)<=2*Bbar*e`. Disjoint completed pieces plus the retained 18*e prefix/normalization allowance then give `A_layer<(2*Bbar+18)*d=1 and rational epsilon=a/b in(0,1), with `d<=c*p^epsilon`, set + +``` +Lprec=bit_length(4*C0bar*ceil(c)) +tprec=max(4,ceil(b*Lprec/(b-a))) +p_prec=2^tprec +``` + +For p>=p_prec, `p^(1-epsilon)>4*C0bar*c`; hence Delta=C0bar*d<=p/4 and the selected signed fine-grid component takes at most 2 p bits. This is a computable threshold expression in the fresh constants, not a new numerical precision model. Conditioning, fine-grid correctness and exact recovery remain the selected conditional prescription. + +For ordinary recursion use `Dord(e)=0`for e=2^(2*(Lstock+2))`, the combined reserve takes at most `Lstock*log2(d)4*Lstock*t` holds at t=2(Lstock+2) and is monotone thereafter. Pad complete rows once to the next multiple of the entire stock product, with factor below 2. Owned volume gains no productive credit. This safe over-reservation includes all simultaneous tagged banks instead of assuming one bank per depth. + +Also require `d^beta>=2*N`above stopping, for example `d>=ceil((2*N)^(1/beta))`. Take the maximum of semantic/stock/stopping cutoffs and the selected movement/descriptor cutoffs for the new fixed Rbar and N. If the retained superpolynomial record-fiber domain is stated only asymptotically, its own domain-entry threshold remains part of that retained hypothesis; no numerical growth rate is invented here. Once inside that domain, the new fixed dimensions, tape inventory and descriptor polynomial degrees fit the same premise. Depth-first execution parks every parent's fields, banks and descriptors while its child runs. There are at most `Pbar^Dord(d)=d^O(1)`ordinary nodes, with a fixed degree. This changes constants and eventual cutoffs, preserving the source movement exponent and spectator restoration. + +## Exact compiler guard and endpoint scope + +| Candidate | Claimed kappa | Tested saving | Reserve | H | j | Outer gap | +|---|---|---|---|---:|---:|---| +| #5383 | .00302666 | .00302667 | 1 e-9 | 31385200000000 | 44836 | 1/700000000 | +| #5387 | .003026674765 | .003026674766 | 1 e-12 | 409549000000000000 | 58507 | 1/7000000000000 | + +The checker directly verifies `(H+1)^1000<2^j`, failure at the preceding sufficient grid, splitting 20^64<21^63, both 97/100 tail-block guards, the product-rank initial size, and `1000*gap>1/(H+1)`. The latter makes the retained logarithmic-majorant ratio decrease beyond its threshold. It directly recomputes + +`normalized=1/(1+1024*reserve)+4/2^32<1`. + +Slacks are `2145530521/2097154147483648`and `97179323/1048576001073741824`respectively. With reserve 1 e-13 the same rounding budget fails. A prior 1 e-9 reserve cannot be applied at the new tested endpoint without a fresh alpha inequality. The independent price reviewer owns that interval premise, gamma/delta paid and target tails, eta/complement capacity, the actual 54 strict+4 functional outer ledger and BIT interface. An author interval receipt is not independently proved by reading it here. + +M=F(2^H) and all stock/precision cutoffs differ between candidates even though the recursive profile is the same. The exact compiler's W/P, rather than the extravagant count majorant, determines efficiency. Majorant inflation changes fixed stock/error constants and eventual thresholds, without creating uncharged child calls. #5387 is a funded reserve refinement of the same paid profile, not a new native saving. + +## Reuse, controls, invalidations and limits + +`check_applicability.py` and final `CHECK.json` are fresh read-only evidence. Mutants reject borrowed erase, missing snapshot owner, altered retained phase/warp itinerary, one-bank storage, stale raw cap and insufficient completion reserve. An initial checker failed on an unhandled inert adapter marker; one deep-copy mutation version exceeded its hard 128 MiB address-space limit. Explicit marker handling and shallow isolated mutations corrected these implementation/resource failures before the final passing run. Neither failure is mathematical evidence against a candidate. + +#5384 can supply the unchanged generic COPY/zero/all-f/selected-grammar lemma and authenticated phase foundation. Its single-relation stock/input inventory, scalar charge, compiler H/reserve and endpoint cannot certify these joint candidates. #5387 additionally changes its pivot choice from L288 to L261, invalidating literal #5383 preparation/owner evidence even though its paid profile matches. Exact joint identities, preparation rank, full owned returns, complete invoice, intervals, BIT/outer predicates, closed source replay and final independent acceptance remain separate coordinator obligations. + +The five retained assumptions remain native_all_columns, owned_erasure, compiler, precision_tape and analytic_recovery in their selected quantified domains. This report provides the candidate-specific finite specialization and fresh computable envelopes. It does not discharge those physical/analytic frameworks, supply independent human or formal-kernel review, publish anything, change selection, or prove an unconditional multiplication theorem. diff --git a/research/direct-backward-independent-validation/capsule/reuse/5396/reports/ownership/REPORT.md b/research/direct-backward-independent-validation/capsule/reuse/5396/reports/ownership/REPORT.md new file mode 100644 index 0000000000..c31fb4b00f --- /dev/null +++ b/research/direct-backward-independent-validation/capsule/reuse/5396/reports/ownership/REPORT.md @@ -0,0 +1,244 @@ +# Independent joint-relation ownership and chronology audit + +Candidate: Ali Romman's #5383, exact head `4bd6efa51a495a7c7b7754915cf0244e7e60969e`. +Canonical base: `1ec1119972c9aefe42525172d07b332fcff81cb4`. +This is the ownership/runtime-contract component of the independent audit. +It neither changes selection nor independently accepts a kappa or full physical theorem. +Forward-transpose extensions are outside this assignment. + +## Evidence and method + +`check.py` imports only Python standard-library modules. It reads literal +source/candidate words and the pinned source phase receipt. It does not import +any candidate Python, call a source row engine, consume WITNESS.json or RESULT.json, +or trust candidate relation_basis, paid_profiles or claimed counts. The author +README/native.py were read to identify the asserted interface; their routines +are not the oracle. `SOURCES.json` binds actual consumed working bytes. + +The source/candidate event zipper proves a stronger chronological fact than +comparing per-kind event multisets: after the explicitly recognized prefix, +snapshot pairs, center triples, zero retags and return clears, every source +event occurs in its original order and with identical bytes. Any missing +retained operation, added borrowed clear or changed phase marker is rejected. +The event/frame pass checks real GF(2) frame inclusion, all scalar current +frames and role distinctions, paid rank differences and every final L frame. +It derives the eight owned pivots and lost rank-nine helper targets from the +actual ownership/preparation/return contract and source endpoints. + +The cheap structural pass plus twelve controls passed under hard 15-second CPU +and wall limits and 128 MiB address-space limit in about 7.1 seconds. See +`STRUCTURE.json`; this receipt explicitly marks exact endpoint replay false. +The root executed the full rational free-word replay through its serial queue. +`RESULT.json` records **PASS_EXACT_RUNTIME_OWNERSHIP** for #5383, with all +641 backward and 633 forward arbitrary entry columns and all twelve controls +checked. No heavy check was launched by this worker. + +## Actual bank and def-use chronology + +Indices below are zero-based. Birth/use/retirement are emitted candidate-word +indices; snapshot production and center are original source indices. A +snapshot is copied immediately after the named source climb has produced the +copied role in precisely the recorded frame. + +| Bank | Source production / role | Frame | Candidate birth | Candidate unique read | Candidate clear | Source center | +|---|---|---:|---:|---:|---:|---:| +| C1 | 11205 / L92 | 254 | 11269 | 11411 | 11412 | 11332 | +| C2 | 11218 / L57 | 274 | 11284 | 11439 | 11440 | 11358 | +| C3 | 11231 / L81 | 619 | 11299 | 11467 | 11468 | 11384 | +| C4 | 11244 / L224 | 279 | 11314 | 11495 | 11496 | 11410 | +| C5 | 11257 / L11 | 621 | 11329 | 11523 | 11524 | 11436 | +| C6 | 11270 / L240 | 280 | 11344 | 11551 | 11552 | 11462 | +| C7 | 11283 / L9 | 624 | 11359 | 11579 | 11580 | 11488 | +| C8 | 11306 / L288 | 281 | 11384 | 11607 | 11608 | 11514 | + +Every birth is preceded immediately by a legal clear of that bank; every read +is followed immediately by its legal clear. At candidate index 11384 all eight +saved values are simultaneously live and none has yet been consumed. Thus a +single sequential scratch bank cannot implement this word. The checker +rejects reusing C1 for the C2 snapshot even if both corresponding clear/COPY +destinations are consistently changed. C0 is a separate owner: its first clear +is 11387 and its final read/clear are 11609/11610. Clearing C0 before each +replacement is legal and does not touch a borrowed helper or a live snapshot. + +The eight pivot lifetimes are also simultaneous with the snapshot lifetimes. +They are existing helper-role slots, while C1..C8 are eight additional slots. +No pivot is used as a preparation source for another pivot. Their inputs are +retained independent cold helpers in frame 0, so there is no dependency cycle +or pivot read before production. + +| Owned helper | First clear | Last read | Final clear | Return frame | +|---|---:|---:|---:|---:| +| L225 | 0 | 21375 | 21543 | 1 | +| L227 | 7 | 21147 | 21544 | 1 | +| L229 | 19 | 21146 | 21545 | 1 | +| L230 | 27 | 15685 | 21546 | 1 | +| L241 | 32 | 21138 | 21547 | 1 | +| L245 | 40 | 21135 | 21548 | 1 | +| L257 | 48 | 21311 | 21549 | 1 | +| L288 | 56 | 21121 | 21550 | 1 | + +The final clears occur strictly after the last reads. These helpers have no +productive output credit: each is an owned temporary and returns zero. In +particular L288 remains an owned pivot even though its intermediate value is +also the source of C8. C8's copy does not transfer ownership of L288 or make +its final helper target available for credit. + +## Arbitrary input and output contract + +Backward entry consists of 224 arbitrary main fields, 400 arbitrary retained +helpers, eight arbitrary owned helper entries, and nine arbitrary owned C +entries. There are 641 independent entry symbols in the direct-sum row model. +Every owner is seeded with its own symbol, just as each borrowed field is. +An owner is cleared before any read; no entry is silently initialized to zero. +After clear/preparation the pivots are prescribed linear combinations of the +400 retained helper inputs, not new borrowed inputs and not productive targets. + +The exact replay initializes a separate basis column for all 641 entries, +tracks rational coefficients and freely reduced native operator words, and +checks the complete endpoint for each retained role. Backward outputs are +`L_i -> L_i-L_(i+112)` for `0<=i<112`; L112..L223 and the 400 retained helpers +are restored in their exact source final frames. All 17 owned outputs are zero. +The unchanged forward word has 632 retained inputs plus arbitrary owned C0, +with the opposite main shear and all retained helper outputs restored. Native +left multiplication is injective on reduced words, so the implementation's +warp dictionary transformation cannot silently overwrite colliding terms. + +Read/write/frame checking alone cannot prove a zero retag's zero value or a +correct snapshot's content. Those are tested by exact mode and proved uniformly +by the independent algebra lane's sixteen unrestricted source identities. +A structure-only PASS must never be promoted to the full algebraic contract. + +## Constructive proof at every positive tensor multiplicity + +Fix an allowed positive multiplicity f and a caller satisfying the selected +native, ownership, compiler and precision/tape hypotheses. Each logical role +is a separate complete slot in its stated actual frame, interpreted in the +source f-fold internal vector space. Preparation uses only rational scalar +ADDs in frame 0 and legal erasures of the eight owned pivot slots. The +independent algebra proof of the joint reduced system therefore sets all +eight relations to zero while leaving the other 624 inputs unrestricted. +This applies to arbitrary correlated vectors as well as independently chosen +ones; the formal columns are a proof device for a universal linear identity. + +Proceed by induction through the source chronology. A retained event is the +identical source event. After a snapshot production, legal clear/COPY stores +that exact vector in a disjoint owner of the same actual frame. All following +source events preserve this bank as a spectator until its unique use. At a +center replacement the source center output minus the saved vector is the +proved relation multiple, hence zero on the prepared domain. The clear/COPY +triple therefore produces exactly the old center output, in the identical +output frame. At a zero replacement the source input vector is exactly zero; +the physical identity leaves it zero and supplies the old job's zero output +in the declared target frame. The source state on every continuing role is +therefore preserved at each replacement. Final retained outputs follow from +the source endpoint, and each owner is legally cleared after its last use. + +For the tensor lift, evaluate each free generator at its exact source +f-fold native operator, including its absolute phase, and each inverse at +that operator's inverse. Evaluation is a rational algebra homomorphism on +finite formal sums of free words. Rational ADD coefficients stay outside +the tensor substitution. The sixteen identities and complete endpoint +identity therefore hold for this f. No tensor power of a scalar sum or +register matrix is taken. Backward inverse-transpose generators are treated +as their own generators and have the same lift argument. + +The zipper preserves every native map, phase marker, adapter and retained +paid event in position relative to all continuing state. Canonical actual +frames/maps are identical. The source absolute-phase receipt is bound to +the exact decompressed word. New operations are same-frame scalar actions on +owned slots and identity on a proved zero vector. Consequently no new native +phase recipe is required. Source phase lowering is reused at these exact pins, +not freshly rerun or inferred from a binary tableau. + +## Recursive suspension and constructive allocation handoff + +At a recursive event, suspend the parent chronological state, including all +live pivot and snapshot slots. Use the retained supplier contract on the +named target field in its actual input frame, with every other parent role +and every external spectator untouched. In particular C1..C8 remain separate +spectators across every intervening child call. A supplier that may overwrite +one of these banks fails this contract even if it later claims a numerically +correct target. + +A constructive address assignment is `(call path, local role)` for each +private slot, with disjoint tagged coordinate ranges for the parent's +persistent fields, its C banks, and every active child. While a child is +active, no other frame at that depth uses its private range. Depth-first +execution returns the child owners as zero before that range can be reused +by a later sibling. The active stack therefore uses a sum of the local +simultaneous bank demands across its ancestor frames. It does not reuse a +live ancestor range, take a maximum in place of that sum, or count eight +snapshots as one slot. This construction is an induction on the finite +recursive execution/compilation tree: distinct path prefixes give disjoint +live private ranges; a completed subtree releases only its own range. +The selected recursive compiler/allocation premise supplies the actual +finite physical hosting and stock bounds for this address construction. + +The changed local caller requires 17 simultaneously owned roles: eight owned +existing helper slots, C0, and eight added C slots. Existing 624 retained roles +remain borrowed and restored. Every child's scratch is additional to these +live parent slots. The physical/precision lane must fund expanded routing, +complete slot sizes, suspended ancestor storage and actual stock/precision +bounds using this template. This report proves the handoff contract and +provides an explicit nonaliasing allocation; it does not substitute the old +numerical template cap or a newly assumed free gather/decoder for that funding. + +## Rejection controls and scope boundary + +Twelve structural mutants reject borrowed erasure, missing initial pivot +clear, duplicate declared ownership, reuse of a live snapshot bank, wrong +snapshot frame or source, missing owned return, removal of a retained output +operation, undeclared storage, changed source phase marker, wrong final owned +frame and wrong center COPY gauge. These tests operate directly on in-memory +candidate event data and run without hash gates, so a freshly recomputed hash +cannot turn a semantic failure into a pass. + +Price, compiler, expanded stock, scientific kappa acceptance and selection are +separate obligations. The event replay gives no credit to the eight owned +helper outputs. No finite replay alone establishes a physical all-size theorem. +The uniform argument above is conditional on the unchanged quantified source +premises and on the independently established joint identities. Ali Romman +retains construction credit; Cao Yifan supplied the source word; Chris R, +Cinna Davis, zxv, ToikY and earlier contributors retain the source/audit credit +recorded in the frozen notices. This audit uses substantial OpenAI Codex assistance. + +## Separate audit of PR5387's actual word + +The execution scope was expanded to Dugongue's #5387, exact head +`b1ab650d36f59e5be682a813145b7c67e219e341`, package `research/eight-owned-relations`. +Its README explicitly credits Ali Romman's public predecessor for the +mechanism and disclaims priority. Its row/price engines are adaptations of +that predecessor, so running those engines would not give independent +ownership evidence. This checker instead processes #5387's own actual word +with `--candidate .../WORD.json.gz --candidate-head ...`. The consumed bytes +are separately pinned in SOURCES.json. #5387 has a different native witness; +an identical recursive invoice does not license reusing #5383's complete +runtime proof. + +Its independently derived pivots are 225, 227, 229, 230, 241, 245, 257, **261**. +The eighth snapshot is **L256**, copied after original source event **11296** +in actual frame 281. It is born at candidate event **11376**, read at **11609**, +and cleared at **11610**; the original center is still source event 11514. +The eighth zero retag is **L256 at original source event 17233**, emitted +candidate event 17329. Thus the #5383 L288/source11306/source17580 identity +is explicitly inapplicable to this eighth replacement. + +The first seven snapshot births/reads/clears are each two candidate events +later than the #5383 table; the source production roles/events and actual +frames for those seven are unchanged. All eight #5387 snapshots are live +by candidate index 11376, preceding the first read at 11413. C0 has first +clear 11389 and final read/clear 11611/11612. Pivot L261 is cleared at 56, +last read at 21316, and finally cleared at 21552 in frame 1. The other seven +pivot first-clear positions are the same as #5383; their last reads and +final clears are two events later. `STRUCTURE-5387.json` records every value. + +The separate #5387 structure/frame pass and all twelve mutation controls +passed under hard 15s/128MiB limits. The root separately executed its independent exact mode through the serial +queue: RESULT-5387.json records **PASS_EXACT_RUNTIME_OWNERSHIP**, all twelve +controls rejected, with 641 backward entry columns and 633 forward entry +columns checked. This is a fresh actual-word proof rather than a proof +transfer from #5383. The uniform direct-sum/tensor argument +and constructive recursive address allocation above apply to this separately +checked chronological contract, conditional on #5387's own unrestricted +identities and the unchanged source framework. Extra prep scalars are +charged by the invoice/physical lanes; no price conclusion follows here. diff --git a/research/direct-backward-independent-validation/capsule/reuse/framework/FINITE-PRECOMPILATION.md b/research/direct-backward-independent-validation/capsule/reuse/framework/FINITE-PRECOMPILATION.md new file mode 100644 index 0000000000..4badb40f09 --- /dev/null +++ b/research/direct-backward-independent-validation/capsule/reuse/framework/FINITE-PRECOMPILATION.md @@ -0,0 +1,313 @@ +# Finite precompilation of a mixed-target rule + +Status: constructive bridge under the precise native hypotheses below, +independently audited in `../transfer-audit/AUDIT.md`. This is a written +argument, not a formal proof or a completed integer-multiplication admission. +The companion finite scheduler checks actual integer flow and ordering. +The original immediate-normalization BIT interface failed hypothesis 3. +`../bit/DELAYED-COVER-BRIDGE.md` supplies the distinct delayed-cover +implementation, with a finite local-ring check and the native binding in +`../bit/BIT-P3-NATIVE-BINDING.json`. Its fixed rational cover routes are a +costed program schema, not dense coordinate gates in a plain native word. + +Substantial OpenAI assistance. Apache-2.0. The mixed-target asymptotic flow is +Jacob Alan Sussman's Theorem 1G, PR4268, with the detailed proof at commit +`563b4e6e913625637f36ba7869bf5fcd0dd4975a` of +[`wht-power-saving-lean`](https://github.com/jacobalansussman/wht-power-saving-lean). +The source, exact scheduling code and notices are preserved under `sources/`. +The contribution proposed here is clearing the finite flow into a single +uniform native supplier before applying the inherited outer theorem. + +## 1. What needs to be assumed + +Let a job of rank `s` apply a specified tensor operator to `s` selected +coordinate blocks of one array, fixing all other coordinates. A block has +an arbitrary positive tensor multiplicity `f`. A completed rank `s` job +therefore acts on `s*f` axes. All productive inputs are arbitrary. + +Fix one mixed unit with productive targets `W_k` of ranks `k`, a chronological +list of paid child ranks `r_j`, and a finite number of scalar and routing +passes. These assumptions are required, separately from the moment inequality: + +1. **An all-column native word.** At every integer column count `c`, the unit + computes exactly its independent rank `k*c` output jobs. Its paid rounds + are rank `r_j*c` jobs in the stated order. All borrowed data return to the + declared endpoint, and owned storage is explicitly initialized and erased. + Its finite operation count is uniform in `c`. +2. **Disjoint splitting and spectators.** A rank `a+b` job is a rank `a` job + followed by a rank `b` job on disjoint coordinates. The resulting programs + preserve arbitrary complete spectator fields and accept arbitrary data. +3. **Whole-job adapters.** Any job passed between two units has an explicitly + priced, permitted embedding into its destination. For the intended complex + application these are fixed monomial binary address maps and unit quadratic + phases, together with role permutations. The adapters must work at every + tensor multiplicity. Rank equality by itself is insufficient. +4. **Finite-program closure.** A finite composition of these words and + adapters is again a permitted finite supplier. Constantly many owned fields + may be supplied with their full cost and no productive output credit. + The eventual ordinary recursion must have the same arbitrary-input, + restoration, scalar and precision interface as the retained supplier. + +Put `m=max{k:W_k>0}`, `k_min=min{k:W_k>0}`, and +`r_max=max{r_j}`. Require `r_max g*S`, keeps one +external weight throughout the entire finite circuit, and lowers only its +final rank-one leaves. All rational matchers, role routes and their inverses +are fixed before choosing the odd prime and its exclusions. Every route +uses complete equal-multiplicity cover fibers and the retained, costed row +permutation primitive. This gives the same finite DAG argument in the +rational-cover program category. The BIT binding supplies the actual native +projectors; a rank count alone would not provide this implementation. + +## 2. Proposed conclusion + +Suppose the preceding hypotheses hold and the mixed balance has root +`tau` in `(0,1)`: + +``` +sum_j r_j^tau = sum_k W_k k^tau. +``` + +For every `z` with `tau=2`, a fixed number `B_N` of productive arrays, +and only rank-one paid children, whose number `P_N` satisfies + +``` +P_N < B_N * N^z. +``` + +Every productive output is the full rank-`N` job. The construction may have +an enormous finite scalar word, role inventory and owned-storage requirement. +Those quantities affect constants and the eventual input threshold. They are +not omitted and are not credited as extra output jobs. + +If this uniform supplier is admitted under the retained native, precision and +fixed-tape premises, the existing uniform recursion applies directly. A new +dynamic RAM-to-Turing-machine simulation is not being assumed here. + +## 3. The integer lockstep flow at a fixed rank + +This is the part of Theorem 1G used by the compiler. At one fixed top rank +`N`, its units, source jobs and exit jobs have integer multiplicities. +For a multi-index `a` on the target types define + +``` +c(a) = product_k k^(a_k), +u(a) = multinomial(|a|;a) * product_k W_k^(a_k). +``` + +The exact Pascal identity is + +``` +u(b) = sum_{k:b_k>0} W_k*u(b-e_k). +``` + +Let `G` be the largest `|a|` with `m*c(a)<=N`. A class is indexed by a +sequence of paid rounds `s` of length `d<=G`; its dilation is +`rho_s=product r_j`. It contains `u(a)` units at column `rho_s*c(a)` for +each `a` with `|a|=G-d` and `m*rho_s*c(a)<=N`. + +For one parent paid round, the Pascal bijection matches its job copies to +target roles of the child class, at exactly equal integer ranks. Missing +demands are top sources. Separation ensures every parent job is consumed. +The source ranks lie in `(N/m,N]`; only the deepest classes produce exit +jobs, all strictly smaller than `N` once `N` is outside the finite base range. + +Process a class in word order. At round `j`, suspend every unit of that +class, complete the entire child class fed by that round, and only then +advance the parents to round `j+1`. This forbids a unit from requiring both +an earlier and a later round of the same suspended parent. The resulting +dependency graph is finite and acyclic. Its edges carry complete array jobs, +not individual scalar values copied for free. + +These integer quantities exist before normalizing the sources to total +weight one. Let `S_s` be the number of source jobs of rank `s`, let +`S=sum_s S_s`, and let the ordered exit batches be `(e,t)` with `t` jobs +of rank `e` each. This finite integer flow is the compiler input. + +## 4. Clear every batch denominator constructively + +Induct on the integer top rank `N`. For each smaller rank `e` the compiler +has already constructed a uniform program on `B_e` arbitrary arrays, +computing full rank `e` with `P_e` paid rank-one calls. For a sufficiently +small rank use the ordinary sequential program: `B_e=1`, `P_e=e`. + +For the current flow choose an integer `a` divisible by every `B_e` needed +for an exit and every `B_(N-s)` needed for a nonzero source remainder. +The product of those finitely many positive integers is a valid choice; +their least common multiple is a smaller optional choice. Set + +``` +B_N = a*S. +``` + +Assign `a*S_s` of the input arrays to each source rank `s`. On each of those +arrays, first complete its `N-s` complementary coordinates using the +already-compiled smaller uniform program. All such batches are integral +because `a` is divisible by their program widths. This preliminary action +commutes with the intended `s`-coordinate job and fixes its input coordinates. + +Make `a` copies of the integer lockstep flow. Route its source arrays to +their exact input slots using permitted whole-array adapters. At a deepest +exit batch, `a*t` is divisible by `B_e`; replace that batch by copies of +the smaller uniform rank-`e` program. Restore its role ordering and adapters +before resuming the suspended parent class. Execute the finite DAG in the +lockstep order, and finally restore the original source-array ordering. + +Every array has now received its disjoint complementary job and source job, +hence the full rank-`N` transform. No copied scalar input or blank helper is +treated as another independent output. Every original array occurs exactly +once as a source; interior target slots are jobs on those arrays, not new +productive inputs. + +Induction removes all recursive calls: the only remaining paid children +have rank one. Clearing denominators multiplies productive arrays and paid +operations equally, so it preserves the per-array leaf count. In formulas, + +``` +P_N/B_N = (1/S) * [ + sum_s S_s * (P_(N-s)/B_(N-s)) + + sum_(ordered exit batches e,t) t * (P_e/B_e) +]. +``` + +Zero-rank terms vanish. Any plain rank-one exits are the ordinary base +program. Scalar and routing passes have their own analogous nonnegative +count and must be included in the asymptotic cost used to choose `N`. + +This construction uses full integer batches; it does not assume that +fractional pieces of a physical array can be routed at zero cost. Its exact +replication factors can be impractically large, which is acceptable for a +fixed finite supplier existence statement but must be disclosed. + +## 5. Why some fixed N has the required saving + +The independent audit sharpened this step to a direct count of paid leaves. +It does not require a running-time comparison between a RAM flow and native +tapes. Let `L(n)=P_n/B_n`, let `w_s=S_s/S`, and let `x_e` be the exit counts +normalized by the number S of source arrays. The actual integer compiler +satisfies + +``` +L(n) = sum_s w_s L(n-s) + sum_e x_e L(e), +sum_s w_s = 1, +sum_e x_e e^tau = sum_s w_s s^tau. +``` + +The last equality follows by canceling every internal matched job in the +exact tau-potential balance. The source ranks satisfy `n/m0`, concavity gives + +``` +n^z0 - sum_s w_s (n-s)^z0 >= eta * sum_s w_s s^z0. +``` + +Indeed, for `t=s/n` in `[1/m,1]`, +`1-(1-t)^z0 >= z0*t >= eta*t^z0`. For every sufficiently large n the +exit coefficient is less than `eta/2`. Every complement and exit has +smaller rank than n, so strong induction on the exact recurrence proves +`L(n)<=A*n^z0`, with finite A chosen to cover the smaller ranks. Eventually +`L(N)= 2`; +* `W` productive arrays, each receiving the **full** rank-`N` transform; +* `P` rank-one paid children; +* `U` copies of the mixed unit in the completely expanded finite word; +* at most `O=U` owned centers, conservatively one per mixed-unit instance. + +For every rational `z` strictly above the mixed root and below one, the +constructive count argument provides an `N` with `P < W*N^z`. +“Finite” here means fixed before the eventual multiplication input grows. +It can be astronomically large. Neither this note nor the receipts claim +to have materialized the winning near-threshold instance. The later +`../controller/EXPLICIT-TEMPLATE-BOUNDS.md` strengthens the existence +argument to the specified complex rank `N=2^276540184361`, with uniform +saving `0.002304`; no search for a successful rank is left unperformed. +The integer recursion defines its exact finite `W,P,U`, and the constants +below are computable functions of that finite result. + +The fully materialized, depth-zero `N=57` example has `W=2242`, `P=127570`, +and `U=1`. It is a useful independent check that complementary source jobs +are really paid: `57*2242-127570=224`. This small example is not claimed to +attain the limiting mixed exponent. + +## 2. Every column count and every complete spectator field + +The local logical identities were replayed in a free noncommuting operator +word algebra. Apart from rational scalar arithmetic, the checker uses only +composition and cancellation of an operator with its recorded inverse. +For any positive integer `f`, substitute the `f`-column physical operator +for each such generator. This extends to an algebra homomorphism on the +free word algebra and preserves the checked identities. + +This is not the false assertion that tensor power is additive on arbitrary +matrix sums. The role-level scalar word is unchanged. Each physical address +generator is replaced by its column lift, while its formal products and +linear combinations are evaluated on the same independent role arrays. + +A rank-zero native monomial has the form + +``` +|x> -> i^(a+q(x)) |M*x+b>, +``` + +with invertible binary `M` and a permitted quadratic phase `q`. Its column +lift has blockwise address map `M`, translation `b` in every column, and +phase `a*f + sum_j q(x_j)` modulo four. This explicitly retains the absolute +phase. A fixed coordinate matcher in the precompiler becomes the same +fixed permutation of `f`-axis blocks. All untouched axes remain complete +spectator fields. A rank-one leaf becomes the standard rank-`f` child. + +The retained exact Clifford normal form supplies the monomial factors +around each child. The independent p3 audit checks the whole main boundary, +including the output translations required by negative powers of `C_q`. +The fixed THREE/base selection is valid for every column count: THREE/base +and THREE/extra have identical entrance and exit operators; their difference +is an internal frame and its associated warps. No layer-dependent selector +is required for the endpoint contract. + +For any integer input width `e=N*f+r`, first apply the `r=2`, `B=P+E`, and `E>=64`, + +``` +2*B*(N-1) >= P+E, +2*B*f+P*f+E <= 2*B*N*f <= 2*B*e. +``` + +Induction gives `A(e)<=2B e`. Completed disjoint selected-axis pieces have +total width at most `d`. The retained prefix kernels, outer phases and +normalization add at most `18d`, giving + +``` +A_layer <= (2*B+18)*d < C0*d. +``` + +Every calculation remains on one fixed fine grid. A child is never rounded, +compressed, or re-encoded at return. The change is to the proof's bound on a +completed value, not to its stored representation. Other fields remain +parked while the child executes. This is why the linear semantic bound +survives a huge scalar word and why the older pathwise `C1>1` estimate is +unnecessary. + +The stopping rule can be any fixed rational `0=2N`, every internal call has the required positive `f`; +the completed-leaf estimate remains `8e` at the stopping leaves. No old +numerical cutoff is carried over. + +### An effective threshold, including enormous constants + +Suppose `d<=c*p^epsilon`, with fixed `c>=1` and rational +`epsilon=a/b` in `(0,1)`. Let `L` be the binary bit length of +`4*C0*ceil(c)` and choose + +``` +t = max(4, ceil(b*L/(b-a))), p0 = 2^t. +``` + +For all `p>=p0`, `p^(1-epsilon)>4*C0*c`, so the integer guard +`Delta=C0*d` is at most `p/4`. Signed components with `p+Delta` fractional +bits and `Delta+3` magnitude/sign bits have width + +``` +p+2*Delta+3 <= 2p. +``` + +The audit emits `p0` as a compressed power of two. It does not try to +allocate that many bits. This construction proves the eventual `O(p)` word +bound for the new finite template, including the current outer choice +`epsilon=99999/100000`. Huge fixed constants change `p0`, not `C1` or the +power in the final exponent inequalities. + +## 5. Productive stock, owned storage, and native tape closure + +For the ordinary uniform complex word, let + +``` +D(e)=0 if e=W^D(d)` for `K>=1`. Pad complete rows once to the next multiple +of `W^D(d)`. The padding factor is below two. Every descendant then has +exactly `1/W` of its parent's productive volume and enough divisibility for +its remaining depth, with complete active, control and spectator fields. +All-row endpoint correctness restores appended zero rows to zero. + +Owned storage contributes no factor to productive output credit. A safe +choice is one full center field per finite mixed-unit instance, namely +`O=U`. At an ordinary recursion node each such field has the same shape as +one productive role stream, of volume `V/W`. Initialize, retain and clear +it as its actual word prescribes. If simultaneously suspended units keep +live centers, they receive distinct banks. Reusing one bank per recursion +depth would not suffice. Owned-space scans and parking cost fixed multiples +of volume; paid calls on those banks are already in `P`. + +The integer audit checks row divisibility and one-time padding at several +floor-depth boundaries. It also gives an explicit sufficient threshold +for `q0 -> i^(a+q(x)) |A*x xor b>, +q(x) = sum_i alpha_i*x_i + 2*sum_(i A*x_j xor b for every j, +phase = a*f + sum_(j=1..f) q(x_j) (mod4). +``` + +Apply the finite row-addition list to the corresponding pair of complete f-axis slots, and use the pointwise residue above. Each selected slot is a full range; arbitrary intervening, preceding and following spectator fields remain present. The temporary complete compact fields are returned by each addition. Thus the lift is exactly m tensor-powered f, acting as identity on the other address fields. It uses one fixed list of primitive **types/operations**, rather than f separately allocated tapes. Its per-record descriptor arithmetic is polynomial in the same selected address bound, and the number of work tapes stays fixed for the template. + +For a recorded positive-rank recipe, source equality is the ordered product `right.then(C_r).then(left)`. Tensoring this product gives `right_f.then(C_(r*f)).then(left_f)` after the fixed coordinate reordering. This is one ordinary positive rank-r*f child on the actual owner's full stream, with its input and output monomials independently retained. Inverse orientation and Pauli corrections are included by the actual signed recipes. No identity distributes a tensor power over a matrix sum. + +For the scalar word itself, use selected #4359's free-word substitution theorem: replace each warp generator by its f-column lift while leaving ADD/SCALE coefficients and chronology unchanged. This is an algebra homomorphism from the noncommuting free-word algebra; hence the already checked arbitrary-input word identity survives. The scalar program is not itself tensor-powered. Keeping a single constant phase a instead of a*f would violate the lift; a negative control explicitly distinguishes that mutation at f=2. + +The ideal algebraic lift holds for every positive f. Its physical tariff applies only in the selected source domain: f<=p, A=O(p), K/log p tending to infinity, and a superpolynomial record fiber. In the actual layer f<=e<=floor(b_in^epsilon) and p=6*b_in eventually. No tariff is extrapolated to arbitrary independent f,p/geometry. The compact-control parameter hypotheses are unchanged: f slots, complete dirty reservations, `A=O(p)`, record fiber beyond fixed powers, and the same selected movement exponent. The final uniform template may have much larger fixed dimensions and operation counts. That changes constants and thresholds through section6 below, rather than changing these quantifiers or creating a new tape per coordinate. + +## 4. Exhaustive family/owner specialization + +The executable source census is over the actual final payload, not its proposed histogram. It classifies every event in both21449-record orientations, and checks exact scalar coefficients/opcodes/chronology against the selected THREE-base word. Main charts on all224 persistent main owners are exact retained records. Every scalar target/source belongs to the632 declared persistent owners or the one declared owned C0. Clear and overwrite COPY target only C0; ADD arguments are distinct owners; no new borrowed owner, alias or productive C0 is introduced. + +| Actual family | Membership/coverage | Selected physical interpretation | +| --- | --- | --- | +| 180 signed warp classes,240 occurrences | Each actual G is invertible; both signed recipes have rank0;800new monomial records cover this and the changed families below | Fixed affine binary permutation and unit quadratic phase from section2; same all-f native generator | +| 3290 borrowed climbs per orientation | Actual source/target bases strictly nested, correct current owner/frame and rank | The selected arbitrary-U-subset-V factorization: two rank-zero adapters and one positive rank-r*f child | +| Eight center calls per orientation | Actual nested comparable bases, owned C0 only, all eight rank8 jobs billed | Same positive child plus signed adapters; no productive credit, no allocation of a new arbitrary input | +| 408 helper endpoints | Actual strict nested entrance/exit, profile `{4:28,7:7,8:47,9:326}` | Complete two-sided normal form on each distinct arbitrary input field; no internal scalar reframing shortcut | +| 448 main entrance/exit charts | Exact event equality with retained base main charts | Source-identical selected chart/axis interface, with its retained charge | +| 17453 scalar records per orientation | Exact old opcode/coefficient sequence, dyadic grammar and current-frame checks | Retained ADD, dyadic unit SCALE, owned COPY/CLEAR; identical scalar tariff | +| Ten phase labels | Fixed annotations, no new physical instruction | Existing scalar-word scope boundaries; not extra outputs or uncharged operators | + +Exact factorization equality and arbitrary-input endpoints are independently established by the admission dossier's native/phase replays, not by a syntactic schema. This module supplies the missing **physical class implication** for those exact factors. The new phase receipt covers180signedwarp classes,105newpaid pairs and5changedhelper pairs. The382 unchanged helpers are bound to the selected #4470 phase receipt through gain_acceptance's exact ordered-basis/owner lineage;26changed helpers use the new five-pair receipt. The independently replayed all2855paid-pair factorization module supplies the full actual paid-pair coverage. These coverage claims remain separate from this module's fresh class/census checks. + +For owned return, the local word retains one physical C0 and ends its C0 updates with a permitted erase. The existing arbitrary-input native proof establishes completed main/helper endpoints and C0 clearance. During product/compiler substitution, each suspended local occurrence receives its own center bank; all child inputs are distinct actual fields, even when values are correlated or one input is a parent's center. The child finishes and its adapters/role ordering return **before** the parent resumes. The parent clears only its own bank after its last use. Every such bank is excluded from productive W and included in full O. This is exactly the selected compiler ownership rule; no one-bank-per-depth reuse or undeclared initialized input is used. + +## 5. Finite raw tariffs in the selected unit + +The tariff unit here is a retained elementary scalar/movement/phase **record**, each realized with the selected physical primitive's asymptotic bound. It is not one literal tape instruction and does not suppress the f-dependent movement bound. Choose the same common upper unit for the fixed primitive alphabet as in the selected finite-word accounting. Each new two-sided nine-axis recipe has at most342 elementary records, below the retained conservative1000-per-group allowance. Unchanged main charts retain their selected count/unit. The selected primitive implementation constants, record-paid setup, scans and repair remain paid in that common physical unit. Changing the finite catalogue does not require a new asymptotic movement assumption. + +The actual local route groups are + +``` +3298 paid jobs + 2*408 helper wrappers + 240 warps + 448 main charts + = 4802 groups, +4802*1000 = 4,802,000. +``` + +The source scalar allowance formula, reimplemented directly without importing its evaluator, gives158120 forward and158168 backward. Therefore + +``` +158168 + 4802000 = 4960168 < 10^7. +``` + +This is an instantiation of the selected raw-unit bound with a smaller changed paid count, not reuse of an old expanded compiler cap. The controller remains18full calls and15thin queries, with the exact retained physical-event and boundary programs. The complete source raw bound is + +``` +18*10^7 + 15*1792 + + 32*112*(#physical_events + #left_boundary_program + #right_boundary_program) + = 181098496 < 10^9. +``` + +Each thin query's paid rank-one request, owned copy/add/erase and inverse orientation remain in the source invoice. Idle jobs, main normalizations, inherited controller geometry and actual exact phase bills remain charged. No local or controller charge is credited as a new productive output. These numerical bounds concern **raw** supplier records only; they are not the expanded uniform word's operation count, storage or literal physical runtime. + +## 6. Expanded compiler, precision and tape constants + +Apply the selected chronological product, same-owner paid completion, disjoint splitting and integer finite compiler to this now-specialized raw program. The algorithms are finite and only instantiate the same grammar. Their matching uses complete job endpoints and restores adapters, and their owner allocation is the rule just proved applicable. No new movement species occurs when a fixed matcher has a larger fixed rank: binary basis/coordinate permutations have the same finite elimination construction, now with a larger fixed list. + +Let W,P,O be the actual final productive width, paid rank-one count and full owned-bank allocation; let R count the full native/movement/normalizer records, including product, completion, split and compiler routes. Let G be their fresh dyadic coefficient/phase allowance, computed by summing the actual scalar allowances (plus the source's conservative non-scalar charge). These are finite computable integers of the new expanded template. They are fixed before multiplication input size varies. A record-count overestimate and one owned bank per relevant occurrence suffice; no practical materialization or old p3 numerical count is needed. + +Use the **new** values in the selected semantic prescription: + +``` +Z=W+O, +E=64*(Z+N+P+G+1)^3, +B=P+E, +C0=32*N*B^2. +``` + +The selected completed-child argument gives `A(e)<=A(floor(e/N))+P*floor(e/N)+E`, hence `A(e)<=2B*e`. Monomial permutations/unit phases add no coefficient height but do retain their execution/descriptor costs. The new C0 determines a new eventual fine-grid threshold. The compact row reserve, full simultaneous stock products, depth-first parking, fixed tape inventory and polynomial setup degrees also use the new W,P,O,R,N and selected formulas. Fixed enlarged degrees/counts are absorbed by the same retained superpolynomial record fiber and strict outer epsilon<1 after increasing the threshold. In particular, neither raw10^9 nor selected p3/p16 reserve constants stand in for these expanded values. + +Thus P2–P4 can consume a genuine new finite instance of H_selected's grammar and precision/stock/tape prescriptions. This note does not independently prove the historical native movement/repair or outer analytic/recovery stack. Those are exactly the assumptions already retained by selected #4470, with no additional candidate-specific implementation assumption. + +## 7. Conclusion and exact limits + +Given H_selected and the source-bound exact semantic/phase endpoints supplied by the independent native dossier, the final catalogue has permitted explicit all-f realizations, legal actual-owner return, finite raw tariffs and the selected expanded-constant substitution. No extra primitive or changed movement exponent is required. P1 is therefore a **consequence** of H_selected for this instance. It need not be restated as a new hypothesis “the new recipes implement.” + +`checks/specialization.py` runs through the master verifier and its source-authenticated `--repo` working-byte loader; it never substitutes clean Git blobs for dirty inputs. Its new actual catalogue has800monomials with at most83 elementary records each, compared with the uniform171 bound. It also checks1692selected monomial records by the identical schema, exhaustive event/role/rank/scalar census in both orientations, helper geometry, retained main charts, the4802route grouping and raw bounds. Controls reject singular maps, non-Z4 absolute phases, borrowed clear, unpaid rank changes, non-dyadic scalars and an unlifted f=2 global phase. Exact phase/operator equality is intentionally supplied by the separate phase/native verification rather than inferred from membership. + +Credits remain with Cao Yifan/intqwq (#4610), Cinna Davis (#4470/#4416/controller/helper lineage), zxv (#4359/native/compiler/semantic precision), icekylinx and Dugongue (general Clifford/transported frames), Jacob Alan Sussman (mixed integer compiler), and all retained physical/BIT/geometry/analytic contributors. This new specialization/proof/check uses substantial OpenAI assistance. 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Colkitt 1792786762 -0400 +committer Douglas R. 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b/research/direct-backward-independent-validation/custody/git-objects/fb7cb53e001cb362075a27c2ade9ab43b9086ea2.tree differ diff --git a/research/direct-backward-independent-validation/receipt_guard.py b/research/direct-backward-independent-validation/receipt_guard.py new file mode 100644 index 0000000000..d81c7e616c --- /dev/null +++ b/research/direct-backward-independent-validation/receipt_guard.py @@ -0,0 +1,77 @@ +"""Validate complete fresh coverage and compare frozen semantic receipts.""" +import copy +import hashlib +import json +from fractions import Fraction as Q + +def require(ok,message): + if not ok:raise ValueError(message) + +def read(root,name):return json.loads((root/name).read_bytes()) +def sha(path):return hashlib.sha256(path.read_bytes()).hexdigest() + +def stable(value): + # These exact fields record execution time/resource samples, never science. + if isinstance(value,dict):return {k:stable(v) for k,v in value.items() if k not in ('seconds','runtime','max_rss_kib')} + if isinstance(value,list):return [stable(v) for v in value] + return value + +def caller_stable(value): + value=copy.deepcopy(value) + # Absolute locations of three already hash-authenticated old receipts move + # to the private scratch tree. Every other field remains compared exactly. + for row in value['supplier_reuse']['receipts'].values(): + row['path']=row['path'].replace('\\','/').split('/')[-1] + return stable(value) + +def validate(root,claims,binding): + c=claims['candidates'][0];head=c['head'];k=Q(c['kappa']) + a=read(root,'agents/caller/RESULT.json') + require(a['status']=='PASS_SOURCE_BOUND_DIRECT_CALLER_WITH_RETAINED_SIGNED_HELPER_NORMALIZERS' and a['head']==head,'Incomplete caller/head') + require(a['checker_sha256']==binding['digests']['capsule/agents/caller/check.py'],'Caller checker binding') + require(a['controller_sha256']==binding['digests']['capsule/repository/research/kappa-backward-controller-20261023/CONTROLLER.json'],'Caller controller binding') + require(a['full_laurent_replay']=={'rows':32,'formal_generators':34,'central_finite_order_used':False,'all_coefficients_exact':True,'signed_swaps_expanded_to_three_ADD':True},'Incomplete literal Laurent endpoint') + require(a['wrapper_sites']==[{'source_index':0,'stage':0,'pair':0},{'source_index':99,'stage':32,'pair':15}],'Wrong physical wrapper sites') + require(a['native']=={'dimension':265,'stages':[0,32],'ports':112,'contacts':896,'columns':114688,'new_positive_jobs':0},'Incomplete physical phase contacts') + require(len(a['controls'])==9 and all(a['controls'].values()),'Missing caller/helper/phase controls') + s=a['supplier_reuse'];require(s['word_payload_sha256']=='2aee5e997df99726fc763e510d9cb69fbe4f86114dc8d2cd33ad26c6c462a21d' and s['supplier_science_rerun'] is False,'Wrong supplier reuse') + require(s['owned_arbitrary_inputs']==17 and s['persistent_independent_inputs']==624 and len(s['helpers'])==400,'Incomplete arbitrary supplier/helper scope') + require(s['helper_profile']=={'9':318,'8':47,'7':7,'4':28},'Wrong positive helper profile') + h=a['helper_normalization'];require(h['adapter_order_preserved'] and h['applied_only_after_autonomous_completed_endpoint'] and h['all_400_raw_helper_maps_unchanged_by_main_wrapper'] and h['no_helper_rank_only_shortcut'] and h['charged_in_invoice_review'],'Unproved helper normalization') + require(h['two_sided_nine_axis_record_bound']==342 and h['retained_per_group_allowance']==1000 and h['existing_helper_route_groups_per_full']==816,'Helper normalizer funding mismatch') + require(a['ownership']['distinct_helper_owners']==7200 and a['ownership']['distinct_owned_bank_positions']==306 and a['ownership']['full_calls']==18,'Incomplete caller ownership') + require(caller_stable(a)==caller_stable(read(root,'expected/caller-RESULT.json')),'Fresh caller semantic output differs from frozen reviewed coverage') + contacts=read(root,'agents/caller/PHYSICAL-CONTACTS.json');require(contacts==read(root,'expected/PHYSICAL-CONTACTS.json'),'Fresh phase contact records differ') + inv=read(root,'agents/numeric/INVOICE-v2.json');f=read(root,'agents/numeric/FUNDING-v1.json') + require(inv==read(root,'expected/INVOICE-v2.json'),'Fresh complete invoice differs from reviewed census') + require(inv['candidate']['head']==head and inv['no_candidate_code_imported'] is True,'Invoice source identity') + require(inv['totals']=={'paid':64116,'productive':10784,'paid_mass':237838,'productive_mass':238590,'rank_surplus':752},'Incomplete complete bill') + require(len(inv['chronology'])==162 and len(inv['helper_normalizers'])==400 and len(inv['controls'])==10,'Incomplete invoice chronology/helpers/controls') + require(inv['controller']['raw_owned']==306 and inv['local']['scalar_units']==158744,'Wrong raw controller/local specialization') + ordinary=inv['ordinary'];require(ordinary['raw_upper']==181586816 and ordinary['raw_upper']0 and Q(f['normalized_paid_upper'])<1 and Q(f['completion_strict_slack'])>0,'Unfunded completion/reserve') + require(Q(f['ratios']['alpha'][1])<1-Q(f['reserve']) and all(Q(f['ratios'][n][1])0 for x in [*outer['strict_checks'].values(),*outer['functional_checks'].values()]),'Incomplete strict/functional outer ledger') + require(set(outer['strict_checks'])==set(f['source_predicates']['strict']) and set(outer['functional_checks'])==set(f['source_predicates']['functional']),'Outer source predicate coverage mismatch') + require(len(f['controls'])==11 and all(f['controls'].values()) and len(f['changed_profile_controls'])==5 and all(f['changed_profile_controls'].values()),'Missing funding controls') + r=f['root'];require(Q(r['strict_signs'][0][0])>0>Q(r['strict_signs'][1][1]) and Q(r['derivative_upper'])<0 and Q(r['remaining_moment_upper'])<0,'Fixed-profile root ceiling incomplete') + require(stable(f)==stable(read(root,'expected/FUNDING-v1.json')),'Fresh funding semantic output differs from reviewed coverage') + p=read(root,'agents/precision/CHECK.json') + require(p['status']=='PASS_SCOPED_DIRECT_CALLER_PRECISION_STOCK_COMPILER' and p['candidate_head']==head,'Incomplete precision/head') + require(p['source_manifest_sha256']==binding['digests']['capsule/agents/precision/SOURCES.json'],'Precision source manifest binding') + require(p['source_bindings']>=30 and p['raw_LOCAL_owned_banks']==306 and p['local_owned_banks']==17 and p['full_backward_calls']==18,'Incomplete fresh bank specialization') + require(p['backward_scalar_allowance']==158744 and p['backward_scalar_height']==29183 and p['signed_swap_three_ADD_prefix_sup_norms']==[2,2,1],'Wrong transient scalar envelope') + require(p['expanded']['unit_log_bound']==225309 and p['expanded']['numerical_majorant_materialized'] is False and p['expanded']['raw_cap_used_as_expanded_stock'] is False,'Wrong expanded all-n bound') + require(p['precision']['C1']==1 and p['precision']['intermediate_swap_factor_paid'] is True and p['stock']['all_suspended_owners_distinct'] is True and p['stock']['owned_productive_credit'] is False,'Incomplete precision/stock applicability') + require(p['compiler']['H']==f['H'] and p['compiler']['j']==f['j'] and Q(p['compiler']['gap'])==Q(f['gap']) and Q(p['compiler']['reserve'])==Q(f['reserve']),'Precision/compiler numerical mismatch') + require(p['controls']['count']==7 and len(p['controls']['rejected'])==7 and len(set(p['controls']['rejected']))==7,'Missing precision controls') + require(p['assumptions']==f['assumptions']==[x['id'] for x in claims['assumptions']],'Changed retained five-premise set') + require(stable(p)==stable(read(root,'expected/precision-CHECK.json')),'Fresh precision semantic output differs from reviewed all-n coverage') + return {'candidate_pr':5398,'candidate_head':head,'kappa':str(k),'paid':64116,'productive':10784,'retained_arbitrary_inputs':624,'local_arbitrary_owned_inputs':17,'raw_owned_bank_positions':306,'productive_helper_owners':7200,'outer_predicates':{'strict':54,'functional':4},'fresh_gates':['literal_caller_and_phase_helper_normalization','complete_invoice_and_exact_funding','fresh_all_n_precision_stock_compiler'],'reused_supplier_review':claims['reused_review'],'assumptions':claims['assumptions']} diff --git a/research/direct-backward-independent-validation/reports/acceptance/REPORT.md b/research/direct-backward-independent-validation/reports/acceptance/REPORT.md new file mode 100644 index 0000000000..5ca3260878 --- /dev/null +++ b/research/direct-backward-independent-validation/reports/acceptance/REPORT.md @@ -0,0 +1,62 @@ +# Independent scientific acceptance: PR5398 direct backward caller + +**Accept the frozen PR5398 instance as a complete same-premise conditional gain**, at exact head `174fb211493b43a42210434083e9702b4fb7a2ce`, kappa `302728823/100000000000 = .00302728823`. Its gain over our previously independently accepted `.003026674765` is `122693/200000000000 = .000000613465`. Canonical baseline remains `1ec1119972c9aefe42525172d07b332fcff81cb4`, selected PR4610/PR5241 `.0030217758`; the gain over that frozen selected point is `.00000551243`. + +This is independent AI scientific review with substantial OpenAI Codex assistance. I reviewed the actual literal source, independent engine code and written proofs, provenance, final output receipts and raw root-run logs. I ran only read-only hash/Git-tree/log readbacks, writing this audit's own new files. I did not execute a scientific engine or import an author evaluator. No independent human or formal-kernel approval is claimed. + +Scientific gates pass for this exact instance. Final review-package committed-byte/export/registered transport and publication remain separate gates. They may not be represented as complete by this scientific verdict. A later change to any scientific engine, input, physical interface or compiler parameter invalidates its affected evidence. + +## Complete direct caller and unchanged supplier + +The new independent caller engine `bef599df7fe431d0e7f9a9cb68376b8390881227107e8ebc225800fffcd824f8` reconstructs both changed sites at source indices0/99, stages0/32, pairs0/15. It checks every physical event and both scalar boundaries. Its exact rational Laurent replay compares all32 final main rows with34 formal generators and uses no Q^4 relation. Signed swaps execute as their actual three ADDs; their intermediate norms are2,2,1. The full caller therefore establishes the complete conjugation identity rather than merely checking an abstract two-by-two matrix. + +The physical gate independently derives the actual265-axis address routes, their inverse, orthogonality and preserved central direction for112 ports at both sites. It checks896 source contacts and114688 literal central-square columns. Exact Gaussian amplitude coefficients establish Q^2=Q^-2=X with absolute phase+1. The exceptional stage-zero raw entries and D_0 formula are checked directly. A phase-only mutation preserves the translation permutation and still rejects; a later-stage formula substituted at stage zero rejects in the contact validator. Whole-field scalar signs remain external to every tensor lift. The positive-width extension evaluates the free algebra at actual f-column factors and does not distribute tensor power over a sum. + +The unchanged5383 supplier is authenticated to previously accepted native.py, WITNESS.json and word payload `2aee5e997df99726fc763e510d9cb69fbe4f86114dc8d2cd33ad26c6c462a21d`. Prior5396 exact head `787efce72a908f92b8a8b4ebb677a6fdb7729e33` supplies the complete624 retained plus17 arbitrary owned input-column proof, sixteen unrestricted identities, simultaneous eight-relation preparation, exact chronological endpoint and all17 owned zero returns. These supplier computations are authenticated reuse, not new replays. My own readback checks all111 runtime files against both their actual current bytes and the published5396 Git tree; all match. Candidate11 package blobs separately match the5398 exact Git tree. The new provenance audit also binds all declared runtime/source aliases and original ancestry. Raw local prior algebra/ownership receipts are explicitly distinguished from the committed5396 proof/report subset; no claim is made that every local execution receipt occurred inside that public tree. + +The caller's main-only wrapper leaves the complete backward helper and owned blocks unchanged. The helper direction is not inferred from rank. All400 actual retained owners match the exact backward signed recipe hashes and frame/rank roles from selected5241's absolute-phase helper proof, including both adapters;17 backward classes are covered out of34 oriented classes. For a source factorization L C_r R, conjugation gives `(conjugate(L) X_all) C_r conjugate(R)`. The Pauli belongs on the indicated side of the left adapter. Selected SPECIALIZATION sections1/3 explicitly permits those independent two-sided monomial factors and autonomous complete endpoint normalization. Section5's342-record pair bound fits the charged1000 group reservation. The full local allowance retains two groups for every original408 helper roles, including the eight now-owned roles, so no helper correction is silently free. Positive canonical phases are validated at all actual ranks4/7/8/9; missing Pauli and wrong direction reject. + +All18 calls receive400 distinct helper inputs and17 private owned positions. The raw full-caller LOCAL allocation is306 before query/product/completion/compiler owners. The wrappers neither read nor erase helpers, pivots or snapshots. The previous274 allocation belongs to a different16-backward/two-forward caller and does not transfer here. + +## Complete invoice and funded endpoint + +I reviewed the final independently derived invoice and arithmetic, excluding the earlier numeric first pass whose reviewer source changed while execution was active. The final reviewer hash is `38a9143de82ec504b8dd8f1050e9e99bdec56e8af1a3b3c881ed0e86360cd837`, exact interval engine `9ef7ee4082631566eb7903c3e21e517ef58039dca2a47104a2279c459589eb47`, and final funding receipt SHA256 `f6b0b1ff2b7ad07022c98b533579bea8fab34b3225e66f4661e7609c355f2fd8`. All match current frozen bytes and the actual final root-run output. + +The independent census parses the actual source backward program/frame deltas and literal controller. It derives64116 paid calls,10784 productive fields, paid rank mass237838, target rank mass238590 and surplus752. All18 LOCALs,15 query shears,15 whole idles,3584 main targets, helper losses and boundaries are included. Relative to5383, two forward replacements remove16 H1 and16 H8 paid calls while debiting16 H9 targets. The exact strict moment improvement is16(1+8^t-9^t)>0 for0=35 closes the induction. These are complete chronological programs with every suspended owner tagged by its full instance path. No DAG aliasing, free gather or one-bank-per-depth allocation is used. + +For this new N, M=F(N) bounds W/P/U/O/R/G and all elementary schemas. Fresh E/B/C0 use those majorants, with C1=1. Completed-child magnitude obeys A(e)<=A(f)+Pbar*f+Ebar. Arbitrary injected errors require the separate contiguous-subinterval bound Jamp(e)<=2Jamp(f)+Pbar*f+Ebar; N>=3 closes its linear induction. The cubic budget includes signed-swap transient factor2, retained residuals at physical identity/zero-retag gates, completed child normalization and all error sites. It does not erase numerical perturbations because an ideal row is zero. + +Stock conservatively reserves[W(O+1)]^Dord, including parked owners, and multiplies this with actual BIT and other simultaneous independent stock. Chunk reservations therefore add. Whole-stock padding occurs once per support-local phase with factor<2. New effective grid, stock, stopping, fixed setup-degree and domain-entry thresholds use this actual finite word. The movement application retains f<=p,A=O(p),K/log p tending to infinity, complete fields and restored dirty controls. Source superpolynomial record fiber absorbs the enlarged fixed polynomial degree only beyond its new cutoff. The proof supplies no practical tape execution claim and does not replace these hypotheses with a new oracle. + +Seven precision tests are accurately labelled algebraic underfunding/grammar sentinels. They are not full-word semantic mutant replays. This distinction is preserved alongside the genuinely executed caller/invoice/arithmetic mutants. + +## Actual execution and decision boundaries + +All four reviewed root-run raw-log SHA256 values match their actual logs. All completed without termination and exit0 under their stated guards: + +| Root run | Seconds | Peak sampled descendant RSS bytes | +| --- | ---: | ---: | +| Unmodified author registered normal/optimized pair |137.751820|166567936| +| Independent caller |16.102025|54734848| +| Final independent funding |22.364703|132218880| +| Final independent precision |.303258|46157824| + +The author cold comparison preserves22 scientific files plus two provenance files exactly. The registered pair's two mathematical PASS results are actual output, not inferred from metadata or hosted CI. The guard samples descendant RSS rather than imposing a cgroup hard limit. Independent evidence hashes and log readbacks are frozen in REVIEW-EVIDENCE-v2.json. + +Exactly five selected assumptions remain: **native_all_columns, owned_erasure, compiler, precision_tape, analytic_recovery**, with their literal statements retained in RESULT.json. This is complete conditional instance admission under those premises. It is not an unconditional integer-multiplication theorem, independent human review, proof-kernel acceptance, global optimum, selected-record promotion or merge. + +The direct caller has the same recursive profile as5392's distinct transpose. Its validity is independently established here without rerunning that other chat's transpose admission or author pair. There is no additional paid-profile gain beyond5392; the advertised.00000003823 difference from5392's endpoint is funded compiler headroom. The independent contribution here is this complete direct-caller admission with fresh full funding and applicability. No construction credit is reassigned. + +Ali Romman retains direct caller and5383/5377 construction credit. Preserve Cao Yifan/intqwq's selected word, Cinna Davis's controller/helper lineage, zxv's native/compiler/precision work, Jacob Alan Sussman's integer recursion, Dugongue's distinct refinement/transport work, Chris R/Clear1nsight's prior independent review, ToikY, and all retained geometry/BIT/phase/analytic contributors and notices. No unresolved scientific blocker remains for this frozen instance; publication transport remains pending at this scientific freeze. diff --git a/research/direct-backward-independent-validation/reports/acceptance/RESULT.json b/research/direct-backward-independent-validation/reports/acceptance/RESULT.json new file mode 100644 index 0000000000..ab822ca97f --- /dev/null +++ b/research/direct-backward-independent-validation/reports/acceptance/RESULT.json @@ -0,0 +1,85 @@ +{ + "schema": "independent-direct-caller-scientific-acceptance/1", + "status": "ACCEPT_COMPLETE_SAME_PREMISE_CONDITIONAL_GAIN", + "candidate": { + "pr": 5398, + "head": "174fb211493b43a42210434083e9702b4fb7a2ce", + "kappa": "302728823/100000000000", + "decimal": ".00302728823", + "author": "Ali Romman" + }, + "canonical_baseline": "1ec1119972c9aefe42525172d07b332fcff81cb4", + "previous_independent_point": ".003026674765", + "gain_over_previous": "122693/200000000000", + "gates": { + "exact_source_custody": "PASS", + "complete_direct_Laurent_caller": "PASS", + "absolute_native_wrapper_phases_and_actual_stage0_32": "PASS", + "unchanged_supplier_641_column_owned_return_reuse": "PASS", + "signed_productive_helper_two_sided_normalizers": "PASS", + "complete_paid_productive_and_ordinary_invoice": "PASS", + "fresh_directed_funding_compiler_outer_BIT": "PASS", + "fresh_expanded_all_n_precision_stock_movement": "PASS", + "completed_root_author_and_independent_runs": "PASS" + }, + "retained_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." + } + ], + "scientific_blockers": [], + "unresolved_gates": [ + { + "id": "publication_transport", + "status": "PENDING_AT_SCIENTIFIC_FREEZE", + "scope": "Final committed/exported registered review package and external publication" + } + ], + "engine_hashes": { + "caller": "bef599df7fe431d0e7f9a9cb68376b8390881227107e8ebc225800fffcd824f8", + "numeric_reviewer": "38a9143de82ec504b8dd8f1050e9e99bdec56e8af1a3b3c881ed0e86360cd837", + "numeric_interval": "9ef7ee4082631566eb7903c3e21e517ef58039dca2a47104a2279c459589eb47", + "precision": "7c3c6b523720841a194b603adeb1f965379a4a4d8a33aaf1c3342adff7ca3789" + }, + "review_evidence_sha256": "3cc925c946d0d21e28be9f1968968a9516eb29652d04821f4ff34ce2c69d839e", + "report_sha256": "4b620a682519723232d93338e904ea22337f951d0f5b4d70205371e40bb2af7e", + "precision_controls": "Seven algebraic/grammar underfunding sentinels, not complete mutated-circuit semantic replays", + "numeric_initial_run": "Historical version-scoped only; final funding run uses frozen38a914 reviewer", + "profile_vs_5392": "Equal recursive profile; distinct direct caller; no further profile gain; endpoint difference is compiler headroom", + "claims": { + "independent_AI_scientific_review": true, + "substantial_OpenAI_Codex_assistance": true, + "independent_human_acceptance": false, + "proof_kernel_acceptance": false, + "unconditional_theorem": false, + "global_optimum": false, + "selected_promotion": false, + "merge_authorized": false, + "science_executed_by_this_chair": false + }, + "conservative_charge_correction": { + "author_local_route_subtotal": 4818000, + "independent_local_route_subtotal": 4828000, + "explicit_phase_groups": 10, + "independent_complete_local_upper": 4986744, + "retained_local_cap": 10000000, + "whole_raw_cap_unchanged": 181586816 + } +} diff --git a/research/direct-backward-independent-validation/reports/acceptance/REVIEW-EVIDENCE-v2.json b/research/direct-backward-independent-validation/reports/acceptance/REVIEW-EVIDENCE-v2.json new file mode 100644 index 0000000000..8785d3596e --- /dev/null +++ b/research/direct-backward-independent-validation/reports/acceptance/REVIEW-EVIDENCE-v2.json @@ -0,0 +1,757 @@ +{ + "schema": "acceptance-readonly-source-log-readback/1", + "candidate_head": "174fb211493b43a42210434083e9702b4fb7a2ce", + "candidate_package_files": [ + { + "path": "research/kappa-backward-controller-20261023/CONTROLLER.json", + "sha256": "60cc512b39cdb9ea2c2ac6c6634c8d3f9627d96ace08ffa659a9d9472444122b", + "git_blob": "01775a36ae1238350bf8cd859b04cb8c4589873b", + "bytes": 57201 + }, + { + "path": "research/kappa-backward-controller-20261023/README.md", + 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+ "scope": "Read-only hashes/Git blobs and root raw-log readback; no scientific execution or verdict. Earlier numeric first pass excluded from final engine binding." +} diff --git a/research/direct-backward-independent-validation/reports/caller/GUARD-RECEIPT.json b/research/direct-backward-independent-validation/reports/caller/GUARD-RECEIPT.json new file mode 100644 index 0000000000..a99e139039 --- /dev/null +++ b/research/direct-backward-independent-validation/reports/caller/GUARD-RECEIPT.json @@ -0,0 +1,21 @@ +{ + "schema": "serial-research-run/v1", + "command": [ + "/usr/bin/python3", + "-B", + "swarm-next-gain-sol-high-20261024/agents/caller/check.py", + "--repository", + "swarm-next-gain-sol-high-20261024/repository" + ], + "cwd": "/home/d3lerium/.codex/.chatgpt-projects/g-p-6ad5817fd84881918865926b6fd51453", + "exit_code": 0, + "termination": null, + "elapsed_seconds": 16.10202534199925, + "sampled_peak_descendant_rss_bytes": 54734848, + "rss_samples": 160, + "memory_limit_mib": 512, + "timeout_seconds": 120.0, + "python": "3.12.3 (main, Aug 31 2026, 10:18:26) [GCC 13.3.0]", + "log_sha256": "2b73169d552c00503fb61cc44957160cba0f6f2cf7d53f3c91c4cf19b50673e7", + "scope": "Fresh command execution only; scientific claim determined by reviewed output." +} diff --git a/research/direct-backward-independent-validation/reports/caller/GUARD-STDOUT.log b/research/direct-backward-independent-validation/reports/caller/GUARD-STDOUT.log new file mode 100644 index 0000000000..6e84a937ea --- /dev/null +++ b/research/direct-backward-independent-validation/reports/caller/GUARD-STDOUT.log @@ -0,0 +1 @@ +{"status": "PASS_SOURCE_BOUND_DIRECT_CALLER_WITH_RETAINED_SIGNED_HELPER_NORMALIZERS", "runtime": {"seconds": 16.017290353775024, "ru_maxrss_bytes": 53858304}, "native": {"dimension": 265, "stages": [0, 32], "ports": 112, "contacts": 896, "columns": 114688, "new_positive_jobs": 0}, "helper_count": 400} diff --git a/research/direct-backward-independent-validation/reports/caller/REPORT.md b/research/direct-backward-independent-validation/reports/caller/REPORT.md new file mode 100644 index 0000000000..d8c422dfd6 --- /dev/null +++ b/research/direct-backward-independent-validation/reports/caller/REPORT.md @@ -0,0 +1,82 @@ +# Independent direct-caller algebra and ownership gate + +Scope: PR5398 exact head `174fb211493b43a42210434083e9702b4fb7a2ce`, Ali Romman's direct backward caller, against the independently admitted PR5383 supplier at `4bd6efa51a495a7c7b7754915cf0244e7e60969e`. This lane does not import or execute candidate Python. It does not rerun the unchanged supplier, and it does not consume PR5392 transpose semantics. Construction and predecessor credit remain with Ali Romman, Cao Yifan, Cinna Davis and the retained source authors. This is independent verification with substantial OpenAI assistance. + +**Execution passed.** Root ran the frozen checker `bef599df7fe431d0e7f9a9cb68376b8390881227107e8ebc225800fffcd824f8` once under the serial 120-second/512-MiB sampled-RSS guard. It exited zero in 16.102025 seconds with 54,734,848 bytes peak sampled descendant RSS. Its own runtime reports 16.017290 seconds and 53,858,304 bytes `ru_maxrss`. The checker hash remained unchanged after execution. `RESULT.json` records the complete source-bound semantic result and all nine rejecting controls; `PHYSICAL-CONTACTS.json` records every native contact. These measurements are sampled-watchdog/self-report measurements rather than a cgroup hard-memory guarantee. The result is an algebra/physical-class component; the separate numeric, precision, provenance and acceptance lanes decide complete conditional admission. + +## Complete supplier reuse and chronology + +`INPUTS.json` fixes nine current source files and the copied independent evidence. The checker authenticates the target source `native.py` and `WITNESS.json` against the exact previously admitted supplier bytes. It authenticates the original source payload `cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd` and the actual supplier payload `2aee5e997df99726fc763e510d9cb69fbe4f86114dc8d2cd33ad26c6c462a21d`. The unchanged construction consumes the same word and witnesses, so the already proved complete supplier can be reused. The copied independent algebra receipt proves all sixteen unrestricted identities, all 624 retained independent entry columns and seventeen arbitrary owned entry columns. The copied ownership receipt establishes exact zero returns, last writes as clears and complete chronological owned lifetimes. The copied acceptance receipt identifies this exact supplier payload. None of those supplier semantic checks is freshly rerun here. + +The source controller's only two forward LOCAL events are at source indices 0 and 99: stage zero/pair zero and stage 32/pair fifteen. The checker constructs their exact replacements independently and compares every physical event, with all remaining controller fields unchanged except the superseded local invoice. Each replacement is: + +``` +SIGNED_SWAP(y,x) +Q_POWER(x,+2) +LOCAL(stage,pair,backward) +SIGNED_SWAP(x,y) +Q_POWER(y,-2) +``` + +The independent replay stores a row as a rational finite sum indexed by an input owner and 34 arbitrary Laurent exponents. It interprets both literal scalar boundary programs, every controller ADD, LOCAL, QUERY_SHEAR, IDLE, and Q_POWER, and compares all thirty-two final rows to the exact diagonal. It keeps Q formal with no relation Q^4=1; the 33 D variables are separate commuting stage variables. Each signed swap is executed as the actual three ADD operations, not assumed by an opcode table. + +## Local identity and literal swaps + +For commuting D and Q, + +``` +B = [[D,-DQ],[0,D]] +F = [[D,0],[DQ^-1,D]] +R = [[0,1],[-Q^-2,0]] +R^-1 = [[0,-Q^2],[1,0]]. +``` + +Matrix multiplication gives R B R^-1 = F, without using finite order of Q. The emitted chronological prefix gives R^-1 and the suffix gives R. For a signed swap on fields (u,v), the three ADD sequence is + +``` +u += v; v -= u; u += v. +``` + +It maps (u,v) to (v,-u) exactly. Its successive sup-norm operator bounds are 2, 2, 1. Scalar minus signs act once on the whole field. They remain outside any tensor substitution; putting a scalar minus inside an f-fold tensor would incorrectly give +1 when f=2. The retained 26-record signed-swap allowance is conservative: three ADD records already implement the signed exchange, and any additional retained sign allowance is harmless. The four new swaps and four translations are separately counted by the numeric invoice lane. + +## Actual native wrappers at both stages + +The checker reads all 112 actual native port recipes and constructs each exact orthogonal address route in the full 265-axis layout. It checks that each route is involutive and orthogonal and preserves the particular central direction q. It derives the four backward main contacts separately at stage zero and stage 32. In particular, stage zero has raw entries (Q,I) and D_0 equal to the old nine-axis Gaussian times Q^-1. Later-stage raw entries contain the completed preceding frame, and D_s uses the fresh eight axes. The contact proof retains every linear and quadratic Fourier phase modulo four, computes the actual translation correction, and checks its inverse. + +For each port, + +``` +Q = (1+i)/2 I + (1-i)/2 X_q. +``` + +Exact Gaussian rational multiplication gives the square coefficients (0,1), so Q^2=X_q with absolute scalar phase +1. Inverse squaring gives the same translation because X_q^2=I. The checker tests all 512 old-address input columns at each of the two actual sites and all 112 ports: 114,688 columns, alongside 896 complete boundary contacts. Address bits outside those nine bits are spectators; the actual routes are checked in all 265 axes. Each positive column multiplicity f follows by substituting the tensor lifts: (Q tensor f)^2 = X_q tensor f. No tensor power is distributed over a sum. + +## Helpers: exact signed target grammar + +The main-only wrapper leaves all 400 retained helper operators unchanged. In the backward orientation their raw maps are conjugates of the source Gaussian helper maps. Equal rank would not make those maps positive Gaussian targets. An uncorrected conjugate rank-r Gaussian has eigenphase -i at a spectral address of weight one; the positive target has +i. + +The existing exact signed helper normalizers supply the required positive target. If a completed forward helper factorization is L C_r R, then + +``` +conjugate(L C_r R) + = conjugate(L) conjugate(C_r) conjugate(R) + = (conjugate(L) X_all) C_r conjugate(R). +``` + +Here C_r is the product of the r coordinate Gaussian factors, C_r^2=X_all, C_r^4=I, and X_all is the translation flipping all r canonical target coordinates, with phase +1. In execution order the last displayed factorization applies conjugate(R), then the positive C_r, then X_all, then conjugate(L). The position of X_all matters; it need not commute with an arbitrary normalizer. Conjugation and composition preserve the permitted rank-zero binary-affine/unit-quadratic monomial class. At width f, apply the recorded tensor lifts of the complete factors. The scalar circuit is unchanged. + +The checker does more than test that identity in the abstract. It binds every retained actual helper owner and its exact ordered entrance/exit frame pair to the previously proved backward recipe in selected #5241's authenticated `FIRST-COLD-REPLAY.json`. That independent phase proof checked all 34 oriented classes, 17 endpoint pairs and 816 helper-orientation instances through all eighteen Pauli conjugations plus exact nonzero anchor amplitudes. The current recipe's complete JSON hash, including both normalizers, their offsets and absolute phases, must equal the backward class proved there. After excluding exactly the eight admitted owned pivots, all 400 retained actual owners are covered and retain profile {4:28,7:7,8:47,9:318}. Forward recipe hashes cannot substitute for backward hashes. + +The source `SPECIALIZATION.md` sections 1 and 3 licenses these exact independent two-sided adapters around a positive child and explicitly includes inverse orientation/Pauli corrections. It requires helpers to be normalized only after their autonomous completed endpoint. Section 5 bounds a complete two-sided nine-axis recipe by 342 elementary records, below the retained 1000-per-group tariff. The unchanged raw route allowance includes two groups per original helper, `2*408`, per full call. Thus both helper normalizers stay charged even though eight helper slots are owned and receive no productive credit. No missing Pauli translation is silently declared free or absorbed into rank alone. This lane binds and reuses that selected helper phase science; it does not rerun it. + +## Arbitrary owned returns and complete caller ownership + +The complete supplier's map on main fields, helpers and owned entry fields has block form diag(B,H_backward,0). The final zero block is a map from all seventeen arbitrary initial owned values, not an initial-zero assumption. The caller's two boundary maps act as diag(R,I,I) and diag(R^-1,I,I). Their product with the supplier is therefore diag(F,H_backward,0). No wrapper reads a helper, pivot, center or snapshot. Its invertible main transformation preserves arbitrary main inputs; the source contract already admits arbitrary correlated complete payloads by linearity. + +Each of the eighteen complete invocations gets 400 distinct independent helper fields and seventeen distinct full owned bank positions, including the eight existing helper slots surrendered to ownership. This is 7,200 helper owners and 306 owned positions across full calls; thin-query scratch belongs to its separately retained caller contract. The 306 figure does not count or replace that scratch. Suspended calls retain distinct banks and restore their whole-job adapters before the parent resumes. Neither snapshots nor pivots nor any owned return receive productive target credit. + +## Controls and limits + +The independent full Laurent validator processes four altered actual controllers: missing Q translation, odd unpaid Q power, wrong LOCAL orientation and missing signed-swap minus. The native contact validator also processes a wrong actual stage-zero raw-frame convention. The amplitude validator processes a phase-only central-square mutation, preserving the address permutation but reversing its global phase. The canonical positive-target helper validator is run at all actual ranks and then processes dropped-Pauli and wrong-orientation variants. A separate f=2 scalar/tensor sign check tests the placement of the scalar sign. The strategy lane additionally challenges Pauli ordering using noncommuting exact monomial adapters; that is auxiliary evidence, not a substitute for the actual recipe hash bindings. + +The ideal all-f lift uses the selected native realization and physical tariff premises. This lane executes no physical tape, numerical rounding, uniform compiler, moment, outer recovery or Lean proof. Fresh precision/tape/stock constants and the complete charge belong to the separately assigned lanes. Component success must not be reported as unconditional theorem acceptance or a selected-frontier promotion. diff --git a/research/direct-backward-independent-validation/reports/numeric/REPORT.md b/research/direct-backward-independent-validation/reports/numeric/REPORT.md new file mode 100644 index 0000000000..2457b1e5eb --- /dev/null +++ b/research/direct-backward-independent-validation/reports/numeric/REPORT.md @@ -0,0 +1,68 @@ +# Independent #5398 literal invoice and exact funding + +**The independently reconstructed complete invoice and exact arithmetic pass at κ=.00302728823**, tested saving .00302728824 and reserve10^-12, for Ali Romman's exact head174fb211493b43a42210434083e9702b4fb7a2ce. This slice establishes arithmetic and a complete literal ordinary/recursive bill. The direct caller/native and fresh full-template precision gates remain distinct prerequisites to root's conditional endpoint admission. + +The final root-run receipt is `final-run/FUNDING-v1.json`, SHA256`f6b0b1ff2b7ad07022c98b533579bea8fab34b3225e66f4661e7609c355f2fd8`. Its independently regenerated invoice `final-run/INVOICE-v2.json` has SHA256`a53bdbc009830f83b91233cf7cc2c8e9a03d76cff93c73bdd4f52fceb742e73f`, byte-identical to the preflight invoice. The final root guard observed22.364703seconds and132218880sampled descendant bytes; the standalone numerical evaluator recorded19.998606549seconds. Read-only post-run hashes confirm reviewer38a9143de82ec504b8dd8f1050e9e99bdec56e8af1a3b3c881ed0e86360cd837 and engine9ef7ee4082631566eb7903c3e21e517ef58039dca2a47104a2279c459589eb47. Both are frozen. + +An earlier `numeric/FUNDING-v1.json` is retained as a superseded execution: code changed while that process was already running, so its end-of-run source hash cannot authenticate the version actually executed. Only `numeric/final-run/FUNDING-v1.json` is the final numerical evidence. No old receipt was overwritten or silently repaired. + +| Obligation | Independent result | +| --- | --- | +| Complete paid/productive counts |64116/10784 | +| Paid/productive rank masses |237838/238590; surplus752 | +| Actual controller |18backward full calls,15query shears, all whole idles and32main outputs | +| Local paid ranks |H1:2193,H2:412,H3:510,H4:127,H5:40 | +| Productive helper ranks |H4:28,H7:7,H8:47,H9:318;400perfull call | +| Full-call owned positions |306=18×17, plus separate query/completion/split/compiler/internal banks | +| Literal scalar allowance |158744perfull source body | +| Conservative local route units |4828000, including10explicit phase groups | +| Local complete ordinary upper |4986744<10000000 | +| Added wrapper allowance |459648;4signed swaps and4native Q² passes,112ports each | +| Whole raw ordinary upper |181586816<10^9 | +| Strict raw crossing |(.00302728824993,.00302728824994),width10^-14 | +| α upper |approximately0.99999999998960809 | +| Strict reserve slack |9.3918631544024577e-12 | +| γ/δ upper |approximately0.95706296134394919/0.95081884996089538;both<.97 | +| Completion strict slack |97179323/1048576001073741824≈9.2677424335945482e-11 | +| Fixed compiler tuple |1024power,cutoff20,floor21,tail offset1/5,theta63/64,logarithm power1000 | +| Uniform family gap |1/700000000000 | +| Finite compiler |j55099,H38569300000000000,N=2^H; preceding grid fails | +| Outer inventory |54strict+4functional, all source names exactly covered | +| Minimum strict outer slack |1/7000000000000 | +| Gain over independent #5387/.003026674765 |.000000613465 | +| Gain over #5392/.00302725 |.00000003823 | +| Gain over selected #4610/.0030217758 |.00000551243 | + +## Literal derivation and source applicability + +`review5398.py` imports only the standalone independent rational engine and Python's standard library. It authenticates all11candidate package files against exact Git blobs, all11VERIFY runtime inputs against source SHA256/Git blobs, and byte-identical copied `native.py`/`WITNESS.json` against the previously independently reviewed #5383 source. The reused literal WORD is bound by compressed SHA2567883ba0faefc96505bb61ca7312d588fa22dfe2164050c817c1718b8fa28693a and payload2aee5e997df99726fc763e510d9cb69fbe4f86114dc8d2cd33ad26c6c462a21d. Candidate RESULT, evaluator, native, physical or verifier modules are never imported or executed. + +The caller is rebuilt from canonical p16events: replace precisely the old forward LOCALs at stages0and32 by the full signed-swap/Q-power/backward-LOCAL/inverse wrapper sequences. Every other event and every boundary/diagonal/keep-mask field must match literally. Paid rank is the actual frame-dimensional delta of each literal climb/center. Productive helpers come from actual final-minus-start frame dimensions after removing the17owned fields, rather than author helper counters. Every LOCAL/query/idle and every main diagonal target contributes to the full chronological bill. Scalar minus signs remain scalar operations outside tensor powers. + +The source's400backward helpers use retained two-sided positive-child normalizers; they are not credited by silently identifying an unnormalized conjugate Gaussian with a positive Gaussian. The invoice records all400actual role/entry-frame/exit-frame/rank pairs and both normalization sides. Its conservative route cap reserves2×408helper groups perfull source body, including the lost eight helpers. The caller gate independently binds the physical recipes and the selected positive-child grammar. That domain is an external prerequisite; merely naming400helpers in this bill would not prove it. + +The conservative source route bill is3282paid+816helper wrapper+240warp+448adapter+10phase+32owned-lifetime groups, each at the retained1000unit allowance. The full old source scalar body is separately charged. The new signed swap has a threeADD implementation whose maximum intermediate row norm is2;26units conservatively cover it. Both scalar boundary programs are explicitly tariffed, and every changed caller event also remains inside the conservative32units/port envelope. The extra wrapper allowance is retained in addition to that envelope. There are no unknown zero charges and no ordinary counts inserted into recursive rank moments. Larger compiler matchers need their own fresh finite-dimensional recipe fold. + +## Exact profile, compiler and full outer funding + +The standalone rational engine uses outward rounding at10^55, atanh60log bounds, Taylor32exp bounds and dyadic range reduction. All decisions use exact fractions/integers. It proves strict signs on both raw-root endpoints, strict decrease on[0,1/20] with derivative upper about−195429.853549519, and negative moment on[1/20,1] with upper about−6817.813214098. This is a necessary ceiling for this fixed complete profile on00, substitute the source f-column operator for each +free generator and its inverse for each inverse, retaining scalar +coefficients and chronology. This is a free-algebra homomorphism, not a +tensor power of the scalar sum. An actual monomial's phase is +`a*f+sum_j q(x_j) mod4`; all complete spectators remain untouched. +The physical tariff retains the original domain **f<=p, A=O(p), +K/log p -> infinity**, complete compact/control fields, restored arbitrary +dirty temporaries and the superpolynomial record fiber. At the outer layer +`f<=e<=floor(b_in^epsilon)` and `p=6*b_in`, with fixed epsilon<1; thus the +domain holds eventually. Ideal all-f algebra does not extend a physical +tariff to arbitrary unrelated f,p,geometry. There is no unpriced arbitrary +gather, blank productive input, zero predicate or new tape per coordinate. + +## Actual direct wrappers and the new local inventory + +The fresh data-only checker reconstructs the exact physical caller from the +unchanged source controller: each of its two forward sites, at stages0 +and32, becomes a signed swap, even Q power, unchanged backward LOCAL, +signed swap and opposite even Q power. All18 LOCALs are backward, with +15 QUERY_SHEARs,15 complete IDLEs,90 ADDs,20 total signed swaps and4 Q_POWERs. +Four of those20 swaps are new. Complete Laurent/phase/native equality is the +separate caller gate. This syntactic check does not substitute for it. + +The swap `(a,b)->(b,-a)` is executable by + +``` +a += b; b -= a; a += b. +``` + +The exact physical two-register infinity norms after its three ADDs are +`[2,2,1]`; its completed norm is1. Reversed rotation and any separate scalar +sign have the same transient bound2. All scalar signs act once on the +whole field and remain outside tensor substitution. Q^2=Q^-2 is the +phase+1 native translation, proved independently by rational Gaussian +coefficient multiplication. Its all-port/all-column source binding remains +the caller gate. Translating a complete field has zero coefficient-height +increment but its movement/descriptor/restoration bill remains in R/G. + +Fresh literal summation of the unchanged backward scalar data gives +allowance158744 and height29183. Each ADD coefficient a has height bounded +by `ceil(log2(1+abs(a)))+log2(denominator(a))`; SCALE uses max(1,abs(a)). +COPY/CLEAR have zero coefficient height and retain execution charge. +The three-ADD swap contributes three unit-ADD height allowances, so its +factor2 transient is paid. The full new G includes every old/new controller +scalar and every wrapper micro-operation; it never replaces the transient +norm by the completed norm1. The eight pivots, eight snapshots and C0 +remain17 owned banks per LOCAL. No main/helper borrowed field is cleared. + +For each raw caller allocate **18*17=306 complete LOCAL owned banks**, +before query scratch, product/completion/split/compiler owners, parked +parent storage and restored movement auxiliaries. The old274 count belongs +to16 backward+2 source-forward calls and fails for this caller. Each physical +occurrence is independently tagged even when two uses share a syntax node. +Every suspended parent retains all live banks; a child uses distinct private +banks, completes, restores its two-sided adapters/order and returns before +the parent resumes. Productive helpers remain arbitrary independent inputs; +pivots/snapshots/query scratch/parked owners receive zero productive credit. + +The independent invoice lane must establish64116 paid/10784 productive, +paid rank mass237838, productive mass238590, surplus752, all helper direction +adapters, and the raw allowance181586816. The checker binds the published +raw number for consistency only; it does not prove that invoice by reading +RESULT.json. The raw tariff is a finite primitive-schema allowance, not +literal tape steps at arbitrary f,p and **not** an expanded stock cap. + +## Constructive expanded bound at every integer rank + +Here is a deliberately extravagant computable bound for an explicit +permitted implementation of the strictified mixed unit and the integer +compiler. The exact W/P efficiency ratio still belongs to the independent +moment/compiler theorem. Majorant inflation supplies no productive credit. + +Before1024-fold chronological product, raw ranks are at most145, paid/target +label inventories below2^17, the raw scalar/movement inventory is below2^28, +and all306 LOCAL banks and complete route/normalizer/phase records fit a +common **value** bound `A0=2^40`. This also bounds the sum of scalar height +increments plus eight per non-scalar primitive schema, rather than merely +the bitlength of that sum. It includes explicit signed helper normalizers +and dirty-control repair schemas. Any paid global framework constants remain +fixed implementation multipliers under the same source tariff. + +For q chronological factors, Cartesian role/paid/target inventories are +at most A0^q. A conservative bound charging every circuit/bank copy by its +factor position and paired role/paid labels is `q*4^q*A0^(2q)`. At q=1024 +the ambient rank `m=145^1024<2^8192`. Charged full-job completion creates at +most m subjobs and disjoint splitting at most m pieces; this multiplies +the inventory by at most m^2. A fixed rank-m binary coordinate/phase matcher +has at most `64(m+1)^3` elementary schemas, by row elimination, three-XOR +swaps, affine translations and its quadratic unit-phase recipe. Arbitrary +role ordering uses at most the square of the role inventory in swaps. + +Square the **whole** pre-route inventory, then apply the cubic matcher +bound. Its base-two logarithm is at most + +``` +2*(82*1024+10+2*8192)+6+3*8193 = 225309 < 262144. +``` + +Thus `D0=2^262144` bounds every arity, label/record/coefficient-height sum, +paid/productive/owned inventory and router of this new fixed strictified +unit. Completion/splitting use canonical complete jobs and monomial +matchers, not new scalar mixing. Their larger matching recipes retain full +record cost despite having zero coefficient height. + +Define, for **every** nonnegative integer n, + +``` +F(0)=D0, +X_n=(n+1)*(D0+1)*(F(n-1)+1) for n>=1, +F(n)=X_n^(16*(n+1)^2) for n>=1. +``` + +This is a terminating primitive recursion. We prove that F(n) bounds all +actual W_n/P_n/U_n/O_n/R_n/G_n and emitted elementary-schema counts of the +rank-n program obtained by the following explicit choices: sequential rank1 +kernels in the finite base range; product of every **distinct** smaller +needed width for denominator clearance; full chronological substitution; +fresh banks tagged by the entire instance path; row-elimination coordinate +recipes and explicit swaps for role order. These choices are permitted by +the source compiler. No minimization oracle or physical DAG-node alias is +used. + +Use strong induction on n. The sequential base has one productive stream, +n paid kernels and at most a polynomial number of fixed records, below +F(n). In a nonbase flow every target rank is at least2 after strictification, +so the lockstep depth is at most log2 n=1. Each such complete program, including all of its private banks and +restorations, has at most F(n-1) records/banks by induction. Primitive units, +all ordinary base kernels, source/complement/exit incidences and those +smaller complete bodies therefore fit the generous intermediate bound + +``` +I_n <= X_n^(3*n+5). +``` + +This follows directly from the exponents2n+2 for L_n, n-1 for replication, +one for smaller bodies, and spare X_n factors for role/base incidences and +finite sums. W/P/U/O/G obey the same nonnegative copying fold; G is a sum +of elementary allowances, not their maximum or logarithm. + +At most I_n^2 explicit swaps realize a full role/allocation permutation. +A cubic overestimate covers all descriptor/instruction passes, both +directions of every coordinate adapter, each boundary and the source/child +restoration lists. A rank-n binary/phase matcher needs at most64(n+1)^3 +schemas. Consequently every full count fits + +``` +64*(n+1)^3*(I_n+1)^3 <= X_n^(9*n+20) <= F(n). +``` + +The last inequality holds for **all** n>=1 because + +``` +16*(n+1)^2-(9*n+20)=16*n^2+23*n-4 >=35. +``` + +The polynomial is positive and increasing on positive integers. Earlier +constants fit since X_n>128. This completes the strong induction, including +base, denominator clearance, all smaller-rank substitution, matcher growth, +coefficient sums and every suspended bank. Finite exponent probes in the +checker corroborate this proof and are not its logical basis. + +For this actual endpoint set + +``` +N=2^38569300000000000, M=F(N), +W_actual,P_actual,U_actual,O_actual,R_actual,G_actual <= M, +Wbar=Pbar=Ubar=Obar=Rbar=Gbar=M, +Zbar=Wbar+Obar=2M, +Ebar=64*(Zbar+N+Pbar+Gbar+1)^3, +Bbar=Pbar+Ebar, +C0bar=32*N*Bbar^2, C1=1. +``` + +M is a new finite integer defined before multiplication input growth. +The astronomical numerical value and expanded word are not materialized. +Reusing a definition schema is legitimate; the actual5398 F(N), owners, +instruction lists and error/stock thresholds are new objects. Neither +181586816,10^9,oldM,oldC0 nor a printed equalN is substituted for them. + +## Fresh semantic bound and arbitrary injected errors + +The new cubic envelope satisfies + +``` +2*Gbar*Zbar^2+8*Pbar+4*Zbar+4+32*N < Ebar. +``` + +A **completed** u-axis forward or actual inverse Gaussian has denominator +excess at most u and row-sum norm at most2^u. Monomial wrappers preserve +these bounds. Every earlier child has completed before the active child +begins. At most Pbar prior completed calls have total selected width +Pbar*f, where f=floor(e/N). All scalar/owner/remainder passes, including +the signed-swap transient, fit Ebar. No child is rounded, compressed or +re-encoded on return; all stored values retain the one common fine grid. +Thus + +``` +A(e)<=A(f)+Pbar*f+Ebar, A(e)<=8e at elementary leaves. +``` + +Since `2Bbar*(N-1)>=Pbar+Ebar` and f>=1, induction gives +`A(e)<=2Bbar*e`. Disjoint completed pieces total at most d axes; the source +prefix/remainder/outer normalization allowance18d then gives +`A_layer< (2Bbar+18)d < C0bar*d`. Initial values obey the retained normalized +encoded source range. Arbitrary owned entry columns mean arbitrary values +within that fixed encoding format, not constant-cost unbounded encodings. + +For stability one must also control errors inserted at arbitrary physical +instruction boundaries; exact zero identities and final cancellation are +insufficient. Let Jamp(e) bound the logarithmic amplification of **any +contiguous subinterval** of the actual physical program. At a node such an +interval intersects at most two incomplete maximal child bodies: a suffix +of its first and a prefix of its last child. Every child between them is +complete and has the preceding semantic bound. Therefore + +``` +Jamp(e)<=2*Jamp(f)+Pbar*f+Ebar. +``` + +For this N>=3, `4Bbar*f+Pbar*f+Ebar<=5Bbar*f<=2Bbar*N*f` proves +`Jamp(e)<=2Bbar*e` by the same induction; leaves obey8e. This argument +works for arbitrary injected data and never assumes a saved source zero +remains zero after perturbation. At a zero_retag the actual physical gate +is I and carries its residual unchanged. No ghost frame transport or +discarded perturbation is inserted there. + +Ordinary depth `Dord(e)` is0 belowN and +`1+Dord(floor(e/N))` otherwise, hence at most log2e. A conservative number +of vector error sites is + +``` +Jsites(e)<=(Gbar+N+1)*e*(Pbar+1)^(Dord(e)+1), +log2 Jsites(e)<=(Gbar+N+2Pbar+4)*e. +``` + +Combine prefix/suffix amplification and site summation. Their exponent is +below `(4Bbar+36+Gbar+N+2Pbar+4)*d < C0bar*d`. The retained primitive +per-site absolute target `2^(-p-C0bar*d)`, or its relative version after +retaining the prefix magnitude, bounds total output error by2^-p. This is +the fresh application to the actual physical5398 word. The source numerical +implementation/error-allocation theorem itself remains a retained condition. + +For fixed c>=1 and rational epsilon=a/b in(0,1), d<=c*p^epsilon, let + +``` +L=bit_length(4*C0bar*ceil(c)), +t=max(4,ceil(b*L/(b-a))), p_grid=2^t. +``` + +For p>=p_grid, `p^(1-epsilon)>4*C0bar*c`, so +Delta=C0bar*d<=p/4. The signed record width +`p+2Delta+3<=2p` since p>=16. This is an effective symbolic threshold, +not an enormous allocation or a new precision exponent. + +## New stock product, stop rule and fixed tapes + +Actual productive row stock is W^Dord(d), with complete chunk reserve +`ceil(log2W)*Dord(d)`; pads are complete rows. O is private storage with +no productive credit. For an explicit safe over-reservation including all +parked owners, use + +``` +S_complex(d)=[W*(O+1)]^Dord(d). +``` + +It covers both productive divisibility and the sum of full tagged parent +bank allocations through the depth-first recursion. Reserve chunks +`qC=(ceil(log2W)+ceil(log2(O+1)))*Dord(d)+2` suffice for K>=1. If +Lstock is this fixed coefficient plus2, then for +`d>=2^(2*(Lstock+2))`, qC4*Lstock*t at t=2(Lstock+2), and the inequality remains +true for larger t. This threshold uses the fresh W/O, or their majorants. + +Ordinary BIT is source-identical reuse, with actual atom1/250=.004, +after-cover69/20000, ordinary saving8590884599/2500000000000 and admitted +17/5000=.0034. Its native/cover/fallback/final-leaf/prime rules remain +source obligations. Its stock is the actual updated BIT stock; the old +.003 atom is insufficient. Simultaneous reserves multiply: + +``` +S_total >= S_complex*S_BIT*(every additional independent live stock). +``` + +Equivalently their complete chunk reservations add. Taking a maximum loses +simultaneously live row cardinality. The support-local source BIT wrapper +has the retained shape +`C_new*(log2h+h^.004*(log2p)^3+1)` complete chunks. C_new is enlarged for +this actualW/P/O/R/G/N, all signed routes and all parked banks. A threshold +of the form `[1024*C_new*(log2p)^3]^(1/.996)`, enlarged for the logarithmic +term and all base thresholds, retains sublinear reserve. The actual outer +gate must check `beta*(1-.004)>0` together with the other54+4 predicates; +the compiler's complex rank moment alone does not establish this. + +Pad once per actual support-local phase to the next multiple of the +**entire** required stock product, with factor below2. Do not pad once +per recursive depth. Complete endpoints return appended zero rows to zero; +remove them before later support-local phases. Reserved chunks remain +complete, with their selected kernels deferred to the later source phases. + +Use the exact floor recursion for Dord and the selected rational stopping +rule0=2N`; +below stopping use the direct elementary leaf procedure. This guarantees +positive f and the retained strict child ratio where uniform recursion is +invoked. The final threshold is the maximum of the new stop/grid/stock +cutoffs, all new fixed setup-degree thresholds, source movement/compact +control domains, BIT/prime avoidance and analytic/recovery cutoffs. If the +source gives only the asymptotic record-fiber premise, its own domain-entry +threshold remains part of that hypothesis; no invented numerical growth +rate is substituted. + +The fixed5398 F determines a finite number of tape/stream/route types. +Depth-first execution parks parent streams, every live owned bank and their +descriptors while complete children execute, then restores adapters/order. +Levels occupy longer tape regions rather than new tape types. The ordinary +tree has at most `(P+1)^(Dord(d)+1)=d^O(1)` nodes, with a new fixed degree. +Descriptor preparation, bank scans, selected-bit repair, whole-field phases, +parking and return retain their actual tariffs. The source superpolynomial +record fiber absorbs those enlarged fixed costs only after its new cutoff +with epsilon<1. This proves grammar specialization under the same physical +framework; it does not assert practical runtimes or an uncharged RAM simulator. + +## Fresh exact guards, controls and limits + +The new checker independently computes the exact compiler gap +`g=(.00302728824-.00302728823)/7=1/700000000000`, j55099 and the statedH. +It checks `(H+1)^1000<2^55099` and failure at the preceding sufficient +j-grid integer; rank initializationH>8192; the eventual logarithmic derivative +guard1000g>1/(H+1); `20^64<21^63`; both.97 tail-block guards; and shifted-exit +capacity. It freshly computes + +``` +1/(1+1024*10^-12)+4/2^32 + =1048576000976562501/1048576001073741824 <1, +remaining margin=97179323/1048576001073741824. +``` + +The1e-13 reserve fails the same fixed rounding condition. Independent directed +alpha/gamma/delta/eta/initial-range enclosures and all54 strict+4 functional +outer inequalities belong to the numeric lane; reading RESULT.json is only +a consistency comparison after this lane's own exact computations. + +Seven explicit algebraic/grammar rejecting sentinels exercise borrowed erasure, one bank per +depth, old274 banks, completed swap norm substituted for prefix norm, raw10^9 +substituted for expanded stock, insufficient reserve and preceding compiler +grid. These check named hypothetical destinations, allocations, caps and +numeric prescriptions against the proved guards. They do not mutate and +replay the full emitted circuit, and are not new semantic circuit controls +or universal impossibility theorems. The source bytes, input grammar, expanded formula, +fresh semantic constants and source domain must all remain bound. + +The small checker uses only Python standard-library data readers and exact +arithmetic, no candidate Python imports, author evaluator, solver, native +suite, Lean, Docker, cold pair or enormous emitter. Its final run took about +.83seconds with hard15CPU-second/128MiB address-space limits. One earlier +check wrongly expected only the four new signed swaps in a controller +containing sixteen retained swaps; the corrected checker explicitly verifies +twenty total/four new. That implementation error is not mathematical evidence +against the construction. Run from the project root: + +``` +timeout 15s python3 -B swarm-next-gain-sol-high-20261024/agents/precision/check_precision.py +``` + +Portable replay accepts explicit `--root`, `--prior-word`, `--prior-native`, +`--prior-witness`, framework text paths, `--reuse-manifest`, `--sources` and +`--out`. `CHECK.json` records the fresh semantic scope and its unresolved +cross-lane dependencies. Changing5398 source bytes, signed/helper physical +interfaces, invoice, compiler parameters, source domain or closure choices +invalidates the corresponding specialization. + +The same five assumptions remain **native_all_columns, owned_erasure, +compiler, precision_tape, analytic_recovery**. No new candidate-specific +oracle, unconditional multiplication theorem, independent human/kernel +approval, selected-frontier promotion or external publication is claimed. +Open next questions are the caller lane's complete signed helper/main phase +binding; independently funded numeric/outer gate; closed normal/optimized +replay; and final independent acceptance. + +Ali Romman owns the direct caller and5383/5377 relation construction. +Retain Cao Yifan's4610 word/phases, Cinna Davis's controller/helper lineage, +zxv's physical/compiler/precision arguments, Jacob Alan Sussman's integer +recursion, Dugongue's separately scoped transported-frame/refinement work, +Chris R/Clear1nsight's5241/5384/5396 admission, ToikY and all retained BIT, +geometry, analytic contributors and notices. This fresh independent review +is Apache-2.0 with substantial OpenAI Codex assistance. diff --git a/research/direct-backward-independent-validation/source_guard.py b/research/direct-backward-independent-validation/source_guard.py new file mode 100644 index 0000000000..c35298f931 --- /dev/null +++ b/research/direct-backward-independent-validation/source_guard.py @@ -0,0 +1,116 @@ +#!/usr/bin/env python3 +"""Authenticate real package bytes and offline Git membership before any engine runs.""" +import gzip +import hashlib +import json +from fractions import Fraction +from pathlib import Path, PurePosixPath + +MAIN='1ec1119972c9aefe42525172d07b332fcff81cb4' +HEAD='174fb211493b43a42210434083e9702b4fb7a2ce' +REVIEW='787efce72a908f92b8a8b4ebb677a6fdb7729e33' +ASSUMPTIONS=['native_all_columns','owned_erasure','compiler','precision_tape','analytic_recovery'] + +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