diff --git a/research/native-suffix-errors/.gitattributes b/research/native-suffix-errors/.gitattributes new file mode 100644 index 0000000000..fa1385d99a --- /dev/null +++ b/research/native-suffix-errors/.gitattributes @@ -0,0 +1 @@ +* -text diff --git a/research/native-suffix-errors/ATTRIBUTION.md b/research/native-suffix-errors/ATTRIBUTION.md new file mode 100644 index 0000000000..36511845cd --- /dev/null +++ b/research/native-suffix-errors/ATTRIBUTION.md @@ -0,0 +1,13 @@ +# Attribution and overlap + +Immediate predecessor [#4505](https://github.com/CrocSwap/integer-mult-bounds/pull/4505), Dugongue, head b03db272bd6428e3d00953333d4c5f03d974f731, supplies the complete native splice, guarded source/window mapping and its explicit suffix-sensitivity handoff. native_source.py and PATCHES.json are retained from that exact head; their notices remain. [#4502](https://github.com/CrocSwap/integer-mult-bounds/pull/4502), head 10b01f96f3b99afe587124425627d67cbdb0da4b, supplies borrowed adapters and 666 local allowance. [#4499](https://github.com/CrocSwap/integer-mult-bounds/pull/4499), head fd18b37415986d818f643d74a69a2148374bead4, supplies exact gauges; #4494 supplies rank compilation/source selectors, and #4489 the owned rank-one sum. This package adds suffix responses, explicit weighted defect certificates, independent forward-injection tests and a sufficient feedback corollary. It does not claim another scalar saving or new κ. + +Reverse-mode linear sensitivity, impulse-response expansion, triangle bounds and feedback absorption are classical. The new source-bound application and quantitative ledgers are the contribution, not priority for these methods. The native/compiler and retained interpreter lineage belongs to zxv and earlier contributors. Retain Jacob Alan Sussman's mixed-target recursion (#4268), Cinna Davis's dirty-helper/padding/query/retiming work (#4088/#4416/#4440/#4441/#4447/#4470), Dugongue's earlier terminal-width-five infrastructure (#3945), Jeremy Kothe's native lineage (#1758), and all notices in the pinned sources and contributor map. New files are Apache-2.0, prepared with substantial OpenAI assistance. + +MathProof source precedents: Computability/IntegerKappaBorrowFeedback20261014.lean proves absorb_feedback and relative_error_of_feedback from explicit defect hypotheses, separating envelope evidence from numerical closure. Abstraction/VPVNPFixedGateVisiblePricing20260826.lean provides the inherited linear_response_top_sum finite-sum precedent. These are source-only discovery references; no new Lean imports, kernel checks, full-DAG scan or competing catalog is claimed. The canonical DAG remains unchanged. + +Current main guidance, priority revision 7 and the #4505 handoff were checked. The open-PR title/body snapshot covered 357 entries at 2026-10-22T02:45:40Z. Relevant neighboring precision work includes #3181 (QQ16 interior range, adjoint ledger and dyadic-grid exactness), #4501 (cross-cell rounding/inverse bounds) and #371 (Gaussian enclosure final-grid rounding). They concern different concrete words or rounding interfaces; no full diff audit or absence-of-overlap claim is made. Native suffix/error work may exist outside searched titles/bodies. Discussion retrieval was rate-limited; visible handoff browsing and local note coverage were incomplete (4 notes, 5,729 unsearched HEAD paths). + +The model assumes explicit logical post-event defect budgets and isometric free warp representations. It does not certify their physical norm conversion, annotation errors or the full rounded recursion. Local row bounds sometimes increase even though the worst scalar-noise bound is unchanged; that limitation is retained in RESULT.json and README.md. No measured runtime gain, independent human review, formalization or selected-frontier change is claimed. + +Submission checkpoint: canonical main advanced during final refresh to f9f85c1e4fa1e955ff39f10fca447e3e2a4e4adc, archiving the preceding contributions. The branch was rebased onto that exact commit. Current AGENTS.md, autoresearch.md, CONTRIBUTING.md and priorities were reread; guidance, selected record and the four frozen input files are unchanged. SOURCES.json retains the original frozen input/provenance base 2a13eb1827784206202db90e5dc8327cf8a250db; those hashes are checked on the new branch. 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Represent each free warp generator by a linear isometry, and its inverse by its inverse isometry. The retained ideal program is linear: ADD, SCALE, CLEAR and COPY have their stated linear actions; warp changes the named register by its operator; chart transports are represented as logical identity maps with their retained tags. Arbitrary data and owned initial values are allowed. Physical adapter annotations are the exact ideal annotations of this model, not independently rounded arithmetic operations. + +At a supported event e, permit an arbitrary additive defect η_e in that event's target register **after** its ideal action. Supported classes are scalar opcode, warp, and paid rank for climb/center. Defects may depend on the entire previous approximate trajectory; independence or random noise is not assumed. A claimed norm bound on each defect must be in these logical coordinates. No physical implementation contract is supplied by this definition. + +## Theorem 1: exact suffix expansion + +Let L_e be the ideal register map for event e and E_t the insertion into its target t. With the same initial state, the final error is exactly + +Δ = Σ_e (L_N ··· L_(e+1)) E_t η_e. + +Proof. At each event the approximate error satisfies d_e=L_e d_(e−1)+E_t η_e. Substitute repeatedly, starting from d_0=0. The formula is algebraic and remains valid for state-dependent η_e. If initial data also differ by d_0, add the term (L_N ··· L_1)d_0. ∎ + +Write the output-j response of the suffix to an injection in t as a reduced free-word sum Σ_w a_(j,e,w) W_w. Every word W_w is an isometry. Therefore + +‖Δ_j‖ ≤ Σ_e Σ_w |a_(j,e,w)| ‖η_e‖. + +Only adjacent inverse cancellation is used; unrelated warp symbols never commute. + +## Theorem 2: exact reverse recurrence and sufficient class budgets + +Maintain C_t, the column giving all final output responses to an injection at the current register t. Start with C_t equal to its output identity column. Immediately before reversing event e, C_t is its **post-event** injection response. Record its absolute coefficients by final output and event class, then reverse the ideal event: + +- ADD t ← t + q s: C_s ← C_s + q C_t; C_t stays. +- SCALE t ← q t: C_t ← q C_t. +- CLEAR t ← 0: C_t ← 0. +- COPY t ← s, distinct roles: C_s ← C_s + C_t, then C_t ← 0. +- Warp t ← W t: right-compose every term in C_t by W. Free words append on the right and cancel at their last letter. +- Logical chart-only transport leaves these columns unchanged. + +Proof. These are the columns of the suffix matrix multiplied on the right by the event's linear map. In particular warp composition is on the right, whereas forward signal propagation prepends on the left. Reverse induction gives every exact C_t and every recorded coefficient of Theorem 1. ∎ + +For event class c define B_(j,c)=Σ_(e in c) Σ_w |a_(j,e,w)|. If every class-c defect satisfies ‖η_e‖ ≤ d_c, then + +max_j ‖Δ_j‖ ≤ max_j Σ_c B_(j,c) d_c. + +This is a universal sufficient bound for every permitted defect trajectory. It is not a sharpness claim for simultaneous noise in a particular representation. The API requires all class budgets explicitly and rejects negative or omitted values. A class omitted from the physical model is an unclosed implementation obligation, not an implied zero budget. + +The exact reverse endpoint check also shows that the full original and rewritten maps are the expected identity shear with all helpers restored and the owned initial C input erased. Their induced persistent-register maximum norm is at most 2. Thus initial persistent errors of norm at most E₀ contribute at most 2 E₀; initial owned-C differences contribute zero to the ideal endpoint. No additional private input or clean-entry assumption is used. + +## Corollary 3: certified scalar defect tolerances + +In the full source-bound computation, max_j(B_(j,ADD)+B_(j,SCALE)) equals 1,328 forward and 4,879 backward, for both original and rewritten words. Hence, when all other modeled classes are exact and each ADD/SCALE defect is at most δ, the persistent output error is at most 1,328δ or 4,879δ. + +Since 1,328 < 2^11 and 4,879 < 2^13, entire-field absolute logical defect tolerances δ ≤ 2^−(b+11) and δ ≤ 2^−(b+13), respectively, suffice for output error ≤ 2^−b. If initial persistent input error is also ≤ δ, replace the constants by 1,330 and 4,881; the same extra-bit allowances suffice. These are logical defect tolerances, not machine mantissa widths or a claim about dimension-dependent rounding. ∎ + +The row-specific coefficients can increase while the worst coefficient is unchanged. The rewritten ledger has maximal row increases 2 forward and 12 backward. It does not establish coordinatewise domination or unchanged bounds under every unequal defect budget. The explicit weighted evaluator must be used for such budgets. + +## Theorem 4: sufficient feedback closure from supplied recursive contracts + +Suppose the actual implementation supplies, for every supported class c, a post-event defect bound + +‖η_e‖ ≤ u (α_c B + β_c E), + +where u, α_c, β_c, B are nonnegative and E is the maximum final persistent error. Start from exact persistent inputs. Set A=max_j Σ_c B_(j,c) α_c and D=max_j Σ_c B_(j,c) β_c. If uD < 1, then + +E ≤ u A B / (1 − uD). + +In particular uD ≤ 1/2 implies E ≤ 2uAB. + +Proof. Theorem 2 gives E ≤ uAB+uDE. Rearrange (1−uD)E ≤ uAB and divide by the positive denominator. Under uD ≤ 1/2, its inverse is at most 2. This matches the feedback-absorption pattern of MathProof's IntegerKappaBorrowFeedback20261014.lean, without asserting that a new physical implementation satisfies its premises. ∎ + +This is a sufficient assembly theorem, not a list of necessary conditions. The remaining work is to prove the concrete physical/recursive defect contracts in the chosen norm and discharge any missing annotation errors. No bound on u, α or β for the actual all-size recursion is invented here, and no new κ is derived. + +## Finite certificate and controls + +Every source byte is pinned; the rewritten word is regenerated from the exact #4505 patch rules, whose local maps and field inventory are checked. Complete reverse endpoints cover all 633 independent variables. Eight whole-word suffix impulses and 720 all-event impulses on small noncommuting programs agree with an independent forward oracle using the retained source helper functions. Whole-word class ledgers and maxima are computed in exact rational arithmetic and committed for replay. The finite computations specialize the universal algebra above; they are not Lean kernel certificates or an independent human review. diff --git a/research/native-suffix-errors/README.md b/research/native-suffix-errors/README.md new file mode 100644 index 0000000000..accede173c --- /dev/null +++ b/research/native-suffix-errors/README.md @@ -0,0 +1,36 @@ +# Suffix-weighted logical error certificates for the complete native word + +This continues [#4505](https://github.com/CrocSwap/integer-mult-bounds/pull/4505)'s explicit missing suffix-sensitivity task. It computes exact free-word responses to an additive logical defect after **every scalar, warp, climb and center event** in both complete original and rewritten THREE-base native words. The output is a proved sufficient perturbation bound with explicit per-output/per-event-class coefficients. It is **not a new κ or the full rounded recursive induction**. + +## Concrete sufficient guarantee + +Assume each entire-field ADD and SCALE introduces an additive defect of norm at most δ in the retained logical chart model; other event classes are exact, initial data are exact, and free warp operators act isometrically in the chosen norm. Then every one of the 632 persistent output errors has norm at most: + +| Word | Original | #4505 rewrite | Extra logical defect bits sufficient for target 2^−b | +|---|---:|---:|---:| +| Forward | 1,328 δ | 1,328 δ | 11: δ ≤ 2^−(b+11) | +| Backward | 4,879 δ | 4,879 δ | 13: δ ≤ 2^−(b+13) | + +Thus the 100-unit scalar saving of #4505 preserves these worst-output error coefficients. The bit statement concerns the absolute defect of an **entire logical field**, not a floating-point mantissa or a per-coordinate rounding quantum. Actual physical/recursive implementations must supply those contracts separately. + +The certificate supports unequal defects: each output has a rational weighted sum over ADD, SCALE, CLEAR, COPY (where present), warp and each paid rank class. The API requires an explicit nonnegative budget for **every** present class; a missing unknown is rejected instead of treated as zero. Initial persistent input error at most E₀ adds at most 2 E₀. PROOF.md also supplies a quantitative feedback-absorption corollary for caller-provided recursive defect contracts. + +Worst-case equality does not mean coordinatewise nonregression. The rewrite changes 33 forward and 90 backward row bounds; individual bounds rise by at most 2 and 12, respectively. The complete rational row ledger is retained. For ADD-only noise with all other classes exact, the backward class maximum changes from 4,308 to 4,300; this does not assume SCALE is exact in a real implementation. + +## Replay + +```sh +python3 -I -O -B research/native-suffix-errors/verify.py +python3 scripts/research_package.py --package research/native-suffix-errors +``` + +The verifier authenticates main inputs, regenerates #4505's guarded rewrite, checks the complete reverse-response endpoint on all 633 initial variables, and checks sampled complete suffixes against independent forward error injection. It also checks 720 all-event impulse responses from 30 small programs in both orientations, including noncommuting warp words, clear, copy, negative scalars and cancellation. Exact class budgets and malformed-budget controls are included. + +`RESULT.json.results.rewritten.forward` and `.backward` each contain the per-output rows. `suffix.py.bound_from_rows(receipt, defects)` returns their exact worst weighted bound. Use a verified/recomputed receipt; the function is an evaluator, not an authenticator of arbitrary caller-supplied certificates. + +Standard-library Python; Windows tested. No Linux execution was available. The shared canonical DAG and selected frontier remain unchanged. + +## Open next questions + +1. Bind physical rounding and recursive-callee defects to the precise post-event logical norm used here, including dimensions, normalization and conversion errors. Supply explicit budgets for all classes; this package does not declare unknown implementation errors zero. +2. Use the row ledger with actual rank-dependent recursive error contracts and the feedback theorem in PROOF.md to close the rounded induction. 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"scale": "1", + "warp": "0" + } + }, + { + "role": [ + "L", + 631 + ], + "weights": { + "add": "31/2", + "clear": "0", + "rank-1": "9", + "rank-2": "7/2", + "rank-3": "3/2", + "rank-4": "0", + "rank-5": "1", + "scale": "1", + "warp": "0" + } + } + ], + "class_maxima": { + "add": "4300", + "clear": "16", + "rank-1": "1463/2", + "rank-2": "110", + "rank-3": "135/2", + "rank-4": "32", + "rank-5": "29", + "scale": "579", + "warp": "14" + }, + "uniform_add_scale_bound": "4879", + "sufficient_extra_logical_defect_bits": 13, + "max_single_injection_total_output_l1": "457", + "semantic_word_sha256": "45e470e2d8014c24c61216f685e132873cab0948ec48d21728b5811e0f855dd4" + } + } + }, + "per_output_changes": { + "forward": { + "changed_output_bounds": 33, + "max_increase": "2", + "max_decrease": "109/4" + }, + "backward": { + "changed_output_bounds": 90, + "max_increase": "12", + "max_decrease": "4" + } + }, + "complete_suffix_oracle_checks": 8, + "tiny_programs": 30, + "tiny_all_event_oracle_checks": 720, + "uniform_forward_add_scale_bound": "1328", + "uniform_backward_add_scale_bound": "4879", + "extra_logical_defect_bits_both_directions": 13, + "physical_defect_contracts_verified": false, + "rounded_recursive_induction_verified": false, + "new_kappa": false +} diff --git a/research/native-suffix-errors/SOURCES.json b/research/native-suffix-errors/SOURCES.json new file mode 100644 index 0000000000..6c50435d10 --- /dev/null +++ b/research/native-suffix-errors/SOURCES.json @@ -0,0 +1,42 @@ +{ + "schema_version": 1, + "base_commit": "2a13eb1827784206202db90e5dc8327cf8a250db", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "ed33caef5c5827693e9572d252a66f99cbb73d40", + "sha256": "5732707cc1e460b090b53f2463162749ad860de878a18f7408938671d295a9d9" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "64bfc5af6709ed9811171e0a2108f05e1219cb65", + "sha256": "352a6184713b8843d96fd2c2071eb7aeaa655906b7c51d45ad444912666c8a96" + }, + { + "path": "research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py", + "usage": "input", + "git_blob": "5a55034ec9e6185d981e16c28e1e2e455069e2cb", + "sha256": "106b4d5e052427230df452f0c901d5390a0583782960b80a8af94d9a984022c7" + }, + { + "path": "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-CANONICAL.json.gz", + "usage": "input", + "git_blob": "4a8c4ed26e53a72362d571c972e65aff546be784", + "sha256": "6418ec3da24d548a57f5c3fe5b9062c26c9478e638504a61c387f5cfb5f4ed61" + }, + { + "path": "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-NATIVE.json.gz", + "usage": "input", + "git_blob": "b46d44c6ee624968dd57be928b0c15d9d45f3b2c", + "sha256": "c54b0a3e129d28e6dbf74fa731fc3bb70fe3c6705f07256750fbecddcc842d39" + }, + { + "path": "research/kappa-rebuild/complex/rebuild_native.py", + "usage": "input", + "git_blob": "78a7b1b0e6e43a1347fb361f45c6e0eaff8dd27b", + "sha256": "f94c527cc02215de49350d477618188c4c0da48bc8fb05b4e37b24c482cad7d5" + } + ] +} diff --git a/research/native-suffix-errors/TASK.json b/research/native-suffix-errors/TASK.json new file mode 100644 index 0000000000..ed854371b2 --- /dev/null +++ b/research/native-suffix-errors/TASK.json @@ -0,0 +1,66 @@ +{ + "schema_version": 1, + "task_id": "complex-new-helper-inventory", + "priority_revision": 7, + "base_commit": "2a13eb1827784206202db90e5dc8327cf8a250db", + "original_card": { + "id": "complex-new-helper-inventory", + "question": "Can a new local cost interface change the deficit-to-recursive-cost ratio beyond current packing?", + "starting_points": [ + "docs/research/research-family-status.md", + "research/complex-local-word-ceiling/README.md", + "research/heterogeneous-owner-assembly/README.md", + "certificates/selected-result.json", + "research/selected-k8-unrestricted-ends/README.md" + ], + "methods": [ + "Propose a changed helper inventory and derive an optimistic exact moment.", + "Design a small completed instance and independently verify its endpoint and rank bill." + ], + "acceptance_gate": "A new physically realizable contract outside the frozen catalogue whose per-call profile, screened with ceiling.ceiling(), beats the selected word's packing ceiling; a lower cap does not establish identical circuitry or order attainable optima, and is insufficient to pass the stronger-budget target under this model. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "research/complex-local-word-ceiling/verify.py" + ], + "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING", + "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.", + "scope": "Positive control and planning budget only; this is not a new construction or full cold replay." + }, + "first_experiment": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin.", + "bottleneck_link": "Packing of the selected word is capped at +0.87% (ceiling model); only a lower local excess spend or a changed coverage law raises the cap.", + "allowed_variations": [ + "Narrow to one changed boundary or helper type with explicit counts.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "scope_change_triggers": [ + "Mixing only providers already inside the pinned catalogue.", + "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.", + "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts." + ], + "overlap_terms": [ + "helper inventory", + "heterogeneous-owner", + "mutable leaver" + ] + }, + "scope_status": "refined", + "actual_scope": "Exact suffix-weighted post-event logical perturbation certificates for the complete original and #4505 rewritten native word, with a sufficient feedback theorem.", + "scope_change_reason": "Take the explicit suffix-sensitivity obligation left by #4505 rather than expand another scalar search. Actual physical defect/rounded recursion contracts remain separate.", + "bottleneck_link": "Provides the missing finite suffix weights needed to combine concrete per-class logical errors; unchanged ideal prefix bounds alone do not supply them.", + "budget_minutes": 20, + "stop_rule": "Finish within 20 minutes after exact certificates, independent injection checks and release preflight; do not invent physical budgets or infer kappa.", + "outcome": "partial", + "evidence": "RESULT.json: worst uniform ADD/SCALE defect factors 1328 and 4879, unchanged after the splice; eight complete-suffix and 720 small all-event oracle checks; PROOF.md universal sufficient budget/feedback theorems.", + "author": "Dugongue", + "ai_assistance": "Substantial OpenAI assistance in mathematics, code and exact verification; no Lean or external solver.", + "open_questions": [ + { + "question": "What physical and recursive contracts bound every post-event defect in the logical isometric norm?", + "why_it_matters": "Needed before using the certificate to close the rounded induction.", + "first_step": "Translate actual recursive and coordinate-rounding bounds into explicit nonnegative budgets for every present class, and account for physical annotation errors.", + "blocked_by": "Not proved by this finite suffix analysis." + } + ] +} diff --git a/research/native-suffix-errors/VALIDATION.md b/research/native-suffix-errors/VALIDATION.md new file mode 100644 index 0000000000..b99c6b1abf --- /dev/null +++ b/research/native-suffix-errors/VALIDATION.md @@ -0,0 +1,9 @@ +# Validation + +CPython 3.12 on Windows; standard-library exact Fraction arithmetic. The verifier runs with -I -O -B and explicit exceptions. Four retained main input hashes are checked before extracting the exact interpreter helpers. The #4505 guarded installer regenerates the rewritten word and verifies its local all-column maps. + +Both full original and rewritten words in both orientations are processed by the new reverse suffix evaluator. The resulting initial columns are checked against the exact complete identity-shear endpoint, helper restoration and erasure of the arbitrary original owned-C input. This checks all 633 initial variables. Every event's post-event response contributes to its class ledger, with exact free-word cancellation and no commutation assumptions. + +Eight complete-word suffix injections are checked by independent forward propagation. Thirty deterministic 12-event programs in both orientations yield 720 all-event oracle checks, exercising ADD, SCALE, CLEAR, COPY, distinct noncommuting warps, signs and cancellation. Complete explicit defect budgets reproduce the uniform scalar bound; missing and negative class budgets are rejected. Global maxima and the actual per-output increases are recorded separately. + +Registered replay, committed-byte transport, isolated optimized Git-free export and publisher preflight are performed. Linux execution is unavailable and not claimed. Mathematical sufficiency is conditional on the stated logical norm/defect contracts; the actual physical contracts, all annotation errors and recursive precision induction remain unverified. This is not a new κ certificate. diff --git a/research/native-suffix-errors/VERIFY.json b/research/native-suffix-errors/VERIFY.json new file mode 100644 index 0000000000..0590f16b84 --- /dev/null +++ b/research/native-suffix-errors/VERIFY.json @@ -0,0 +1,23 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/kappa-causal-continuation/buffer-borrowing/verify_buffers.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/rebuild_native.py" + ], + "commands": [ + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 120, + "checks": "Source-authenticated full reverse-response endpoints, exact per-output/class suffix weights, eight complete suffix oracle checks, 720 tiny all-event checks, complete defect budgets and malformed controls." + } + ] +} diff --git a/research/native-suffix-errors/native_source.py b/research/native-suffix-errors/native_source.py new file mode 100644 index 0000000000..aa2653154a --- /dev/null +++ b/research/native-suffix-errors/native_source.py @@ -0,0 +1,135 @@ +"""Guarded native scalar splice and whole-word replay. Apache-2.0. +Dugongue with substantial OpenAI assistance. No new kappa claim. +""" +from pathlib import Path +from fractions import Fraction as Q +from collections import Counter +import ast,gzip,hashlib,json,types +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] + +def need(ok,why): + if not ok:raise ValueError(why) + +def canonical(value):return json.dumps(value,sort_keys=True,separators=(',',':')).encode() +def digest(value):return hashlib.sha256(canonical(value)).hexdigest() +def read(name):return json.loads((HERE/name).read_text(encoding='utf-8')) + +def authenticated(): + inputs={} + for row in read('SOURCES.json')['files']: + if row['usage']=='input': + data=(ROOT/row['path']).read_bytes() + need(hashlib.sha256(data).hexdigest()==row['sha256'],'Changed pinned source: '+row['path']) + inputs[row['path']]=data + return inputs + +def extract(data,names): + tree=ast.parse(data.decode('utf-8'));nodes=[x for x in tree.body if isinstance(x,ast.FunctionDef) and x.name in names] + need({x.name for x in nodes}==set(names),'Exact audited function inventory') + namespace={'Q':Q,'need':need,'Counter':Counter} + exec(compile(ast.Module(body=nodes,type_ignores=[]),'authenticated source functions','exec'),namespace) + return types.SimpleNamespace(**namespace) + +def sources(inputs): + def pick(ending):return next(v for k,v in inputs.items() if k.endswith(ending)) + word=json.loads(gzip.decompress(pick('-NATIVE.json.gz'))) + chart=json.loads(gzip.decompress(pick('-CANONICAL.json.gz'))) + v=extract(pick('/verify_buffers.py'),{'identity','add','warp','span','expected','replay'}) + n=extract(pick('/rebuild_native.py'),{'primitive_allowance','replay_extended'}) + return word,chart,v,n + +def local_check(source,replacement,rule): + xs=rule['source_roles'];ys=rule['target_roles'];frame=rule['frame'];M=[[Q(x) for x in row] for row in rule['matrix']] + need(xs and ys and len(set(xs+ys))==len(xs+ys),'Disjoint injective source roles') + need(all(type(i)==int and 0<=i<632 for i in xs+ys),'Original persistent field ABI') + need(len(M)==len(ys) and all(len(row)==len(xs) for row in M),'Matrix dimensions') + allowed={('L',i) for i in xs+ys};roles=sorted(allowed);size=len(roles) + def replay(program): + rows={role:[Q(i==j) for j in range(size)] for i,role in enumerate(roles)} + for e in program: + need(e[0]=='scalar' and len(e)==3 and e[2]==frame,'Pure common-frame scalar window') + op=e[1];dst=tuple(op[1]);need(dst in rows,'No new field') + if op[0]=='add': + src=tuple(op[2]);q=Q(op[3],op[4]);need(src in rows and src!=dst and q,'Legal ADD roles') + need(q.denominator&(q.denominator-1)==0,'Native dyadic ADD') + rows[dst]=[a+q*b for a,b in zip(rows[dst],rows[src])] + else: + need(op[0]=='scale','No owned clear, copy or query') + q=Q(op[2],op[3]);num,den=abs(q.numerator),q.denominator + need(q and not num&(num-1) and not den&(den-1),'Native unit SCALE') + rows[dst]=[q*a for a in rows[dst]] + return rows + a=replay(source);b=replay(replacement);need(a==b,'Exact local all-column operator') + original={role:[Q(i==j) for j in range(size)] for i,role in enumerate(roles)} + for x in xs:need(a['L',x]==original['L',x],'Source input restored') + for j,y in enumerate(ys): + expected=[original['L',y][k]+sum(M[j][i]*original['L',x][k] for i,x in enumerate(xs)) for k in range(size)] + need(a['L',y]==expected,'Declared shear matrix') + return size + +def install(words,patches,price): + need(set(words)=={'forward','backward'} and len(patches)==8,'Complete two-direction input and eight rules') + out={};receipts=[] + for direction in ('forward','backward'): + rules=sorted([r for r in patches if r['direction']==direction],key=lambda x:x['source_indices']) + need(len(rules)==4,'Four rules per orientation');program=words[direction];cursor=0;new=[] + for rule in rules: + lo,hi=rule['source_indices'];need(type(lo)==int and type(hi)==int and cursor<=lo<=hi0 else -1)*(abs(operator)+(10**6 if backward else 0)) + out={} + for (output,word),q in row.items(): + moved=word[:-1] if word and word[-1]==-symbol else word+(symbol,) + key=(output,moved);out[key]=out.get(key,Q(0))+q + return {k:q for k,q in out.items() if q} +def suffix(program,backward=False,roles=None,samples=()): + roles=roles if roles is not None else [('L',i) for i in range(632)]+[('C',0)] + saved={};columns={r:{(r,()):Q(1)} for r in roles};bounds=defaultdict(lambda:defaultdict(Q));counts=defaultdict(int);max_column=Q(0) + for index in range(len(program)-1,-1,-1): + e=program[index];kind=e[0];target=None;category=None + if kind=='scalar':target=tuple(e[1][1]);category=e[1][0] + elif kind=='warp':target=tuple(e[1]);category='warp' + elif kind=='climb':target=('L',e[2]);category='rank-'+str(e[5]) + elif kind=='center':target=('C',e[1]);category='rank-'+str(e[4]) + if target is not None: + need(target in columns,'Known target role') + if index in samples:saved[index]=dict(columns[target]) + counts[category]+=1 + for (output,word),q in columns[target].items():bounds[category][output]+=abs(q) + max_column=max(max_column,sum(map(abs,columns[target].values()),Q(0))) + if kind=='scalar': + op=e[1] + if op[0]=='add':add(columns[tuple(op[2])],columns[target],Q(op[3],op[4])) + elif op[0]=='scale':columns[target]={key:Q(op[2],op[3])*q for key,q in columns[target].items()} + elif op[0]=='clear':columns[target]={} + elif op[0]=='copy': + need(target!=tuple(op[2]),'Distinct COPY roles');add(columns[tuple(op[2])],columns[target],Q(1));columns[target]={} + else:raise ValueError('Scalar opcode') + elif kind=='warp':columns[target]=warp_right(columns[target],e[2],backward) + else:need(kind in ('phase','adapter','residual_adapter','climb','center'),'Known native event') + return columns,bounds,counts,max_column,saved + +def summarize(program,backward=False): + columns,bounds,counts,mx,samples=suffix(program,backward) + roles=[('L',i) for i in range(632)];categories=sorted(counts) + rows=[{'role':list(r),'weights':{cat:str(bounds[cat][r]) for cat in categories}} for r in roles] + joint=max(sum((bounds[cat][r] for cat in ('add','scale')),Q(0)) for r in roles) + bits=0 + while Q(2)**bits=0 for v in defects.values()),'Nonnegative defects') + return max(sum((Q(row['weights'][cat])*defects[cat] for cat in receipt['categories']),Q(0)) for row in receipt['persistent_output_rows']) diff --git a/research/native-suffix-errors/verify.py b/research/native-suffix-errors/verify.py new file mode 100644 index 0000000000..b8998f3e91 --- /dev/null +++ b/research/native-suffix-errors/verify.py @@ -0,0 +1,83 @@ +"""Exact suffix certificate and forward-injection oracle. Apache-2.0.""" +from pathlib import Path +from fractions import Fraction as Q +import json,types,sys,random +HERE=Path(__file__).resolve().parent + +def load(name,file): + m=types.ModuleType(name);m.__file__=str(HERE/file);sys.modules[name]=m + exec(compile((HERE/file).read_bytes(),m.__file__,'exec'),m.__dict__);return m +B=load('suffix_native_source','native_source.py');S=load('suffix_certificate','suffix.py') + +def rejects(action,label): + try:action() + except (ValueError,KeyError,IndexError,StopIteration):return + raise ValueError('Invalid control accepted: '+label) + +def forward_injection(program,event,target,roles,backward,v): + rows={r:{} for r in roles};rows[target]={(('N',0),()):Q(1)} + for e in program[event+1:]: + if e[0]=='scalar': + op=e[1];dst=tuple(op[1]) + if op[0]=='add':v.add(rows[dst],rows[tuple(op[2])],Q(op[3],op[4])) + elif op[0]=='scale':rows[dst]={key:Q(op[2],op[3])*q for key,q in rows[dst].items()} + elif op[0]=='clear':rows[dst]={} + elif op[0]=='copy':rows[dst]=dict(rows[tuple(op[2])]) + else:raise ValueError('Scalar') + elif e[0]=='warp':rows[tuple(e[1])]=v.warp(rows[tuple(e[1])],e[2],backward) + return {(r,word):q for r,row in rows.items() for (noise,word),q in row.items() if q} + +def endpoint(columns,backward): + for r,actual in columns.items(): + wanted={} if r[0]=='C' else {(r,()):Q(1)} + if r[0]=='L': + i=r[1];source=(112<=i<224) if backward else (0<=i<112) + if source: + target=('L',i-112 if backward else i+112);wanted[target,()]=Q(-1 if backward else 1) + B.need(actual==wanted,'Whole reverse-response endpoint including owned dirty input') + +def verify(): + words,chart,v,n=B.sources(B.authenticated());new,local=B.install(words,B.read('PATCHES.json'),n.primitive_allowance) + results={};sample_checks=0;roles=[('L',i) for i in range(632)]+[('C',0)] + for label,ws in [('original',words),('rewritten',new)]: + results[label]={} + for direction in ('forward','backward'): + program=ws[direction];b=direction=='backward' + scalar=[i for i,e in enumerate(program) if e[0]=='scalar'];sample=[scalar[len(scalar)//2],scalar[-3]] + columns,bounds,counts,mx,saved=S.suffix(program,b,samples=sample);endpoint(columns,b) + for index in sample: + target=tuple(program[index][1][1]);B.need(forward_injection(program,index,target,roles,b,v)==saved[index],'Independent complete-suffix impulse response');sample_checks+=1 + result=S.summarize(program,b);B.need(Q(result['uniform_add_scale_bound'])==(4879 if b else 1328),'Exact uniform scalar defect constant') + budget={cat:Q(cat in ('add','scale')) for cat in result['categories']} + B.need(S.bound_from_rows(result,budget)==Q(result['uniform_add_scale_bound']),'Explicit class budget') + result['semantic_word_sha256']=B.digest(program);results[label][direction]=result + rng=random.Random(20261022);tiny_roles=[('L',0),('L',1),('C',0)];tiny_checks=0 + for _ in range(30): + program=[] + for k in range(12): + t=rng.choice(tiny_roles);op=rng.choice(['add','scale','clear','copy','warp']) + if op=='warp':program.append(['warp',list(t),rng.choice([-2,-1,1,2]),0,0]) + elif op=='scale':program.append(['scalar',['scale',list(t),rng.choice([-2,-1,1,2]),2],0]) + elif op=='clear':program.append(['scalar',['clear',list(t)],0]) + elif op=='copy':program.append(['scalar',['copy',list(t),list(rng.choice([r for r in tiny_roles if r!=t]))],0]) + else:program.append(['scalar',['add',list(t),list(rng.choice([r for r in tiny_roles if r!=t])),rng.choice([-3,-1,1,3]),2],0]) + for b in (False,True): + _,_,_,_,saved=S.suffix(program,b,roles=tiny_roles,samples=range(len(program))) + for index,e in enumerate(program): + target=tuple(e[1][1] if e[0]=='scalar' else e[1]);B.need(saved[index]==forward_injection(program,index,target,tiny_roles,b,v),'Tiny all-event forward/backward response');tiny_checks+=1 + changes={} + for d in ('forward','backward'): + a=results['original'][d];b=results['rewritten'][d];delta=[] + for x,y in zip(a['persistent_output_rows'],b['persistent_output_rows']):delta.append(sum(Q(y['weights'][c])-Q(x['weights'][c]) for c in ('add','scale'))) + changes[d]={'changed_output_bounds':sum(q!=0 for q in delta),'max_increase':str(max(delta)),'max_decrease':str(-min(delta))} + B.need(a['uniform_add_scale_bound']==b['uniform_add_scale_bound'],'Unchanged WORST output bound only') + bad={cat:0 for cat in b['categories']};bad.pop('warp');rejects(lambda:S.bound_from_rows(b,bad),'missing explicit class') + bad={cat:0 for cat in b['categories']};bad['warp']=-1;rejects(lambda:S.bound_from_rows(b,bad),'negative defect budget') + return {'status':'PASS_NATIVE_SUFFIX_ERROR_CERTIFICATES','results':results,'per_output_changes':changes,'complete_suffix_oracle_checks':sample_checks,'tiny_programs':30,'tiny_all_event_oracle_checks':tiny_checks,'uniform_forward_add_scale_bound':'1328','uniform_backward_add_scale_bound':'4879','extra_logical_defect_bits_both_directions':13,'physical_defect_contracts_verified':False,'rounded_recursive_induction_verified':False,'new_kappa':False} + +if __name__=='__main__': + import argparse + ap=argparse.ArgumentParser();ap.add_argument('--write',action='store_true');args=ap.parse_args();result=json.loads(json.dumps(verify())) + if args.write:(HERE/'RESULT.json').write_text(json.dumps(result,indent=2)+'\n',encoding='utf-8',newline='\n') + else:B.need(result==B.read('RESULT.json'),'Deterministic exact receipt') + print(json.dumps({k:v for k,v in result.items() if k!='results'},sort_keys=True))