From 9c0399238a0a93defb7123799978bfb33689396b Mon Sep 17 00:00:00 2001 From: ross Date: Sun, 18 Oct 2026 01:56:40 +1100 Subject: [PATCH] research: compare V45 recovery access and consumed directions --- research/v45-recovery-transfer/EXPECTED.json | 24527 ++++++++++++++++ research/v45-recovery-transfer/PROOF.md | 168 + research/v45-recovery-transfer/README.md | 164 + research/v45-recovery-transfer/RESULT.json | 4189 +++ research/v45-recovery-transfer/SOURCES.json | 152 + research/v45-recovery-transfer/TASK.json | 88 + research/v45-recovery-transfer/VALIDATION.md | 51 + research/v45-recovery-transfer/VERIFY.json | 35 + research/v45-recovery-transfer/compare.py | 284 + research/v45-recovery-transfer/cost.py | 268 + research/v45-recovery-transfer/independent.py | 501 + research/v45-recovery-transfer/verify.py | 86 + 12 files changed, 30513 insertions(+) create mode 100644 research/v45-recovery-transfer/EXPECTED.json create mode 100644 research/v45-recovery-transfer/PROOF.md create mode 100644 research/v45-recovery-transfer/README.md create mode 100644 research/v45-recovery-transfer/RESULT.json create mode 100644 research/v45-recovery-transfer/SOURCES.json create mode 100644 research/v45-recovery-transfer/TASK.json create mode 100644 research/v45-recovery-transfer/VALIDATION.md create mode 100644 research/v45-recovery-transfer/VERIFY.json create mode 100644 research/v45-recovery-transfer/compare.py create mode 100644 research/v45-recovery-transfer/cost.py create mode 100644 research/v45-recovery-transfer/independent.py create mode 100644 research/v45-recovery-transfer/verify.py diff --git a/research/v45-recovery-transfer/EXPECTED.json b/research/v45-recovery-transfer/EXPECTED.json new file mode 100644 index 0000000000..e5cd27a691 --- /dev/null +++ b/research/v45-recovery-transfer/EXPECTED.json @@ -0,0 +1,24527 @@ +{ + "V45": [ + 256, + 128, + 64, + 35, + 16, + 11, + 5 + ], + "common_observation_U12": [ + 2, + 61, + 62, + 63, + 70, + 71, + 72, + 94, + 249, + 251, + 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Z[1/2]. For each pinned provider let L be its 520 live non-target +registers. The input cut is immediately after the 84-event prelude. Give every +register in L an independent arbitrary entrance value in a D-module W. The +middle M is the non-target part of A after the prelude, then B with its +chronological formal warps, then restore. Formal warp generators act by +arbitrary invertible D-linear maps on W. Target writes, compensation, inverse +cleanup and native/physical realization are separate obligations. + +H consists of live helpers with index at least 224, excluding restored +`helper_final` coordinates, `start_extra` coordinates and initial-correction +sources. Its size changes with the construction. In particular P = +{249,251,265,267} is eligible before the PR2942 extraction and protected afterward. +A zero entrance frame does not mean a zero entrance value. + +Fix V45 = span_F2(256,128,64,35,16,11,5), and the twelve-register allowance +U = {2,61,62,63,70,71,72,94,249,251,265,267}. Define R(V45) by replaying every +literal frame incident and selecting all live non-target registers with terminal +frame contained in V45. Protected/restored rows remain in R. This is not the +historical solver-lowered support search: U is an explicit algebraic observation +allowance, and its physical availability must be established separately. + +As in the pinned source, separate target-add records use the inherited center-cut +convention. The frame replay checks the recorded center frames and the literal +A/B/restore scalar incidents and warp resets. It does not reconstruct additional +native moves for those separate target records. + +## What the exact comparison establishes + +Both providers give the same dimensions and supports below. The checker uses +all coefficients of each observed free-operator row, rather than specializing +warps to commuting or identity maps. + +| Construction | Size of H | Literal R(V45) | Scalar left/right/pairing dimensions on U | +|---|---:|---|---| +| PR2894 | 226 | empty | 4 / 4 / 4 | +| PR2917 | 216 | empty | 4 / 4 / 4 | +| PR2942 | 212 | empty | 0 / 0 / 0 | +| PR2979 stage 1 | 212 | U | 0 / 0 / 0 | +| PR2979 final | 207 | U minus {61,63} | 0 / 0 / 0 | + +The complete rows M[U,:] are equal between PR2894 and PR2917 (98 nonzero +coefficients), and equal between PR2942, stage 1 and final (42 coefficients). +The four-dimensional old pairing has determinant -128. Eight selected nuisance +columns B0 have an eight-row minor of determinant -2, and the twelve-column +completion [Y,B0] has determinant 256. All are dyadic units. Thus +PR2917 did not create these four directions on U: they were already available +algebraically in PR2894. Neither old shipped circuit makes U available at V45. +The paid frame and boundary changes are essential to the implemented recovery. + +On every later word, M[U,H] is identically zero. This is stronger than a rank-zero +pairing. Moreover the U nuisance rows admit a purely scalar square minor on +protected columns with determinant 2, a unit of D. The final ten-row literal +support has a protected scalar unit minor with determinant 1. If P is returned +to the eligible set solely as a diagnostic, the left/right/pairing dimensions +are again 4 / 4 / 4. The four rows indexed by P are their restored identity rows. +This does not authorize treating those protected helpers as fresh resources. + +## The old quotient over every dyadic module + +The receipt records four covectors Alpha, four eligible quantities U0=Alpha M, +four eligible columns V, and Y=M V, with Alpha B0=0. Set K=Alpha Y. Both +K and C=[Y,B0] are invertible over D by their unit determinants. Every readout +has unique coordinates Y a+B0 b, and Alpha reads K a. Consequently +ker Alpha=im B0 on W^12 for every D-module W. Since all nuisance columns lie +in ker Alpha and B0 consists of nuisance columns, im B=im B0. + +Two eligible states h,h' can yield a common U readout after choosing independent +nuisance values exactly when U0(h-h')=0. Every exactly recoverable function of h +therefore factors through the four displayed quantities U0 h. Conversely they +are read directly by Alpha. This proves the quotient description over D-modules, +not only a dimension statement over Q. For nonlinear H-only recoding S, replace +U0 h by U0 S(h); no four-scalar information-capacity bound follows for unrestricted +nonlinear encodings. The later zero-block obstruction below remains unchanged. + +## No fresh nonlinear recovery on the later words + +Write the entrance tuple as (h,z), with h on H and z on L minus H. For every +later word the complete U observation is + + y = M[U,H] h + M[U,L minus H] z = B z. + +Fix z and vary h arbitrarily. The observation remains identical. Any function +of h exactly determined by this observation for every independent entrance tuple +must therefore be constant. This argument also permits an arbitrary H-only +entrance recoding S(h), because the coefficient of S(h) is still zero. No +statistical distribution or information-theoretic entropy assumption is needed. +Ancillas may be fixed or jointly independent of the entrance tuple; data-bearing +side observations are outside the contract. The unit minors independently +certify nuisance saturation but are not needed for the stronger zero-block step. + +The conclusion holds for every D-module and every allowed representation of the +formal warps, since zero formal coefficients specialize to zero operators. It +does not require freeness of the specialized native operators. + +A finite appended computation inherits this conclusion if every data and control +dependency is explicit, frame inclusions are monotone, its output identities and +frames are fixed, and it uses no new warp resets or additional source, target or +earlier-snapshot reads. Every initial register in the causal cone of an output +at V45 must have terminal frame contained in V45. Therefore that output depends +only on R(V45), a subset of U, and independent ancillas. Arbitrary nonlinear +local gates and additional intermediate buffers cannot supply missing h +information. Pooling incomparable endpoints or changing the middle is not covered. + +## Paired rank is a separate condition + +For a fixed observation set, define the scalar left space by alpha M supported +on H, and the scalar right space by M v supported on that set with v supported +on H. Pair them using alpha M v. The reported dimensions are exact rational +formal-space dimensions with explicit witnesses, not a universal native-cost +claim. A zero pairing alone would not establish the nonlinear result above: +for M(h,z)=(h,h+z), observing the first coordinate recovers h, although +M^{-1} e_1=(1,-1) is not supported on H. Here the complete zero eligible block, +not the absence of a normalized pair by itself, establishes the obstruction. + +## Complete-cost decision + +The four directions and their V45 endpoint saving already occur in PR2979. +They cannot be counted again. The published frozen-owner audit PR3014 also +shows that the local V45 saving can lose after idle capacity is charged; that +existing result is credited, not presented as a new calculation here. + +The accompanying exact cost certificate derives a marginal screen in PR2979's +fixed bin-capacity relaxation. At its rational complex parameter b0, use +H_r(b0)=r(73/r)^b0. One freed width unit raises the optimal fractional idle bill +per call by + + D(b0) = (H_48(b0) - H_3(b0) - 5 H_5(b0))/20. + +The checker solves the retained basis with exact rationals, verifies nonnegative +changed counts, and checks every feasible pattern against the dual with rigorous +rational tariff intervals. Thus it proves the marginal at b0 for the specified +single-helper inventory changes; it does not assert that the basis stays optimal +for all parameters. + +For a hypothetical new 9-to-7 helper with local difference E - 2 H_1, the best +fractional local-plus-idle difference is E - 2(H_1-D). This leaves approximately +0.0246870954232 tariff units per call for E. The finite literal comparator has a +small additional fractional slack, explicitly certified in the receipt. This is +a necessary screen within the fixed-capacity model; it does not pay new private +buffers, the actual paired residual T_out T_in^-1, physical access, precision, +stock or a changed compiler interface. Those +must be constructed and charged before any positive supplier claim. + +The bounded comparison finds no unused direction in U on PR2979. It therefore +does not nominate a new extraction to send through owner/native/outer admission. +A cheaper realization of the four existing directions is not excluded. The +observed-row equality does not provide new compensation identities or a strict +paid advantage for moving extraction earlier through other stages. PR2942 +already reports optimization of extraction order within its fixed gate-order, +end-of-restore model; that historical result is not a global optimum for PR2979. + +The stopping decision is specific: adding a decoder or an H-only recoding on +this frozen observation contract cannot produce a fresh V45 helper. Changes to +the middle, cut or accessible coordinates remain possible, but require a new +mathematical and cost argument. No improved kappa or global optimality follows. + +## Evidence boundary + +This is an exact finite comparison plus written proofs for all entrance values +and allowed finite suffixes. Two separately implemented operator propagations +check the observation claims. The cost arithmetic reuses the credited retained +rational interval kernel. No formal proof assistant, independent human review, +new native supplier, complete physical invoice or all-size multiplication theorem +is claimed. diff --git a/research/v45-recovery-transfer/README.md b/research/v45-recovery-transfer/README.md new file mode 100644 index 0000000000..77ec70765b --- /dev/null +++ b/research/v45-recovery-transfer/README.md @@ -0,0 +1,164 @@ +# V45 recovery was already present, and its four directions are already used + +The bounded comparison finds **no new fully costed improvement to PR2979**. +It identifies exactly why the proposed information-recovery route stops: + +* The same four paired directions are already present on twelve named registers + of PR2894 and PR2917. Their complete readout maps are identical. +* Those registers are not available at V45 in either shipped literal frame + schedule. The later paid frame and boundary changes supply access. +* After the four PR2942 extractions, every coefficient from a fresh eligible + input vanishes from that twelve-register readout. PR2979 retains this exact + map. The four observable helper coordinates are already restored/protected. + +Thus the construction did not create four new algebraic information directions. +It made existing ones usable and then consumed their eligibility. Nonlinear +postprocessing or eligible-only entrance recoding cannot expose a fifth fresh +helper through this fixed readout. Cheaper implementations of the existing four, +changed middle circuits and other observation cuts remain open. + +This package adds the exact before/after transfer and its nonlinear consequence, +plus a fixed-target fractional cost screen. It does not repeat the prior pairing +census or claim the existing V45 construction as new. + +## Exact comparison + +For both base and extra providers, let + +```text +V45 = span_F2(256,128,64,35,16,11,5) +U12 = {2,61,62,63,70,71,72,94,249,251,265,267} +P4 = {249,251,265,267} +``` + +H is the actual eligible-input set after the prelude, excluding restored, +nonzero-frame entrance and initial-correction-source coordinates. U12 is a +specified algebraic observation allowance; it is not asserted to be the complete +set accessible under arbitrary frame refits. Literal supports include protected +and restored registers as well as eligible ones. + +| Word | Eligible inputs | Literal V45 readout | Recoverable fresh directions on U12 | +|---|---:|---:|---:| +| PR2894 | 226 | 0 rows | 4 | +| PR2917 | 216 | 0 rows | 4 | +| PR2942 | 212 | 0 rows | 0 | +| PR2979 stage 1 | 212 | all 12 rows | 0 | +| PR2979 final | 207 | 10 rows, omitting 61 and 63 | 0 | + +All 98 scalar coefficients of the old U12 map agree between PR2894 and PR2917. +All 42 coefficients of the later map agree across PR2942, stage 1 and final. +The old four-dimensional pairing has determinant -128; eight nuisance directions +and the four observable directions have a square completion of determinant 256. +These dyadic units give the exact four-quantity observation quotient over every +Z[1/2]-module, as detailed in [PROOF.md](PROOF.md). + +On each later word, the eligible block is exactly zero. The complete U12 nuisance +minor has determinant 2; the final ten-row literal minor has determinant 1. +Reclassifying P4 as eligible solely as a control recovers precisely their four +identity coordinates. It does not make them new resources. + +The nonlinear obstruction also covers finite appended computations at V45 with +fixed output identities and a fixed complete dependency graph, monotone frames, +independent ancillas, and no new warp resets or source/target/earlier-snapshot +reads. It does not cover combining incomparable endpoints. The input cut and +inherited center-cut frame convention are explicit in the proof. + +## Cost and stopping decision + +The existing V45 local saving is already included in PR2979. [PR3014][3014] +previously proved that retaining PR2942's owner assignment makes that local +saving lose after idle children are charged. PR2979 uses a changed allocation; +we do not transfer the frozen-owner negative to it. + +The new cost calculation binds PR2979's actual final inventory, complete profile, +and fixed-bin relaxation. At its rational complex parameter +`b0=0.001729033982646513517717`, write `H_r=r*(73/r)^b0`. An exact basis/dual +calculation over all 2,551 patterns gives the optimal fractional idle charge per +freed helper width: + +```text +D = (H48 - H3 - 5 H5)/20 +``` + +For one hypothetical fresh 9-to-7 extraction with actual local change +`E - 2H1`, the best fractional local-plus-idle difference is +`E - 2(H1-D)`. Only approximately **0.0246870954232** tariff units per call +remain for E. The old literal allocation has an additional fractional slack of +about **0.0000367672400** per call; the receipt gives rigorous rational intervals. +The dual has 12 identically tight patterns and 2,539 strictly positive ones. + +This screen includes the optimal fractional idle adjustment in the stated bin +model. It is not a completed physical invoice: new private buffers, chronological +owners, native access, stock, precision and outer admission must still be paid. +A favorable screen alone cannot certify a new supplier. Existing packing-only +follow-ups already address the old cap gap. + +The comparison yields no unused direction in U12 on PR2979, so no new candidate +reaches the allocation/native/admission stage. We stop this fresh-helper route. +It does not establish global optimality of the existing four-direction circuit. + +## Reproduce and evidence + +Standard library, Python 3.12: + +```sh +python3.12 scripts/research_package.py --package research/v45-recovery-transfer +python3 scripts/check_research_commit.py --package research/v45-recovery-transfer +``` + +[EXPECTED.json](EXPECTED.json) records complete readout coefficients, eligibility, +terminal frames, left/right bases, pairing matrices and dyadic-unit witnesses. +[RESULT.json](RESULT.json) records the independent checker and exact cost screen. +[VALIDATION.md](VALIDATION.md) states executed checks and review boundaries. + +The primary forward engine is the authenticated PR2918 implementation, credited +and reused unchanged. A separately implemented backward-covector/inverse-column +checker imports no predecessor Python and checks every readout coefficient and +basis witness. Both use exact rational arithmetic. The cost basis/dual code is +separate from the predecessor optimizer but uses its authenticated rational +logarithm/exponential enclosure kernel. Neither implementation is a formal-kernel +proof or independent human review. + +## Sources, overlap and credit + +Canonical base: `997e6a9ca7b4f95d50e366f61412fd640d72a88a`, priority revision 6. +Scientific heads: + +| Source | Exact head | +|---|---| +| PR2894, Jeremy Kothe | `18d03c447886895ef9abf888398178e0428533ca` | +| PR2917, Mason Hale | `224bd5e56041c40078ff6b5fa7393733a215de5c` | +| PR2942, Marius-Paul Dumitrean | `a027b0f6fdb0ab2b42ba10fc31b53960166bf2bf` | +| PR2979, Marius-Paul Dumitrean | `be191346391661f4d35fc0d1508d0a6029572576` | +| PR3172, preceding obstruction | `0a632b00ef59a9f43b1f6c7965ff1ca7a3f188f3` | + +The mathematical methods retain Jeremy Diviney's PR2908 paired extraction, +Jeremy Kothe's word/frame/cleanup construction, Mason Hale's extension, +Marius-Paul Dumitrean's coordinated V45 construction and tariff kernel, and +Ross Richardson's PR2918/3172 obstruction. The complete owner/native lineage +retains Yiyang Lu, Tekalign, icekylinx, Dugongue, themilkman216 and the contributors +credited by the frozen packages. Nick Petalas's V45 frame/native/invoice audits +and jwr404's PR3112/3119/3126 audits delimit existing coverage. + +PR2979 already reports rank-four V45 pairing in a solver-lowered search model. +Its exploratory script imports absent local `synth`/`lower` modules; we do not +claim to replay that search. The independent literal-support calculation and +fixed U12 map comparison here avoid that dependency. No frozen source is edited +or re-vendored. PR3133/3148 and the separate active whole-word investigation are +outside this bounded comparison. + +New work by Ross Richardson with substantial OpenAI Codex assistance, including +separately assigned mathematical, source, cost and verifier reviewers. Apache-2.0. +The underlying quotient and linear-programming principles are standard. + +## Open next questions + +A useful positive continuation must name a changed middle, observation cut or +implementation of the four already-used directions. Its first step is an exact +before/after program and full local histogram that passes the applicable cost +screen while preserving compensation and restoration. The current zero block +will not price or validate that changed program. Repeating nonlinear decoding +on unchanged U12, or recounting the four existing helpers, cannot reopen this +route. See [TASK.json](TASK.json) for the bounded handoff and blockers. + +[3014]: https://github.com/CrocSwap/integer-mult-bounds/pull/3014 diff --git a/research/v45-recovery-transfer/RESULT.json b/research/v45-recovery-transfer/RESULT.json new file mode 100644 index 0000000000..066e12d007 --- /dev/null +++ b/research/v45-recovery-transfer/RESULT.json @@ -0,0 +1,4189 @@ +{ + "additional_controls": [ + "changed_frame_edit_preimage", + "source_hash_before_import" + ], + "cost": { + "dual_census": { + "minimum_reduced_cost_lower": 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"research/rank7-joint-endframes/data/WORD-extra.json.gz", + "byte_equal": true + } + ] +} diff --git a/research/v45-recovery-transfer/TASK.json b/research/v45-recovery-transfer/TASK.json new file mode 100644 index 0000000000..9fe0cc6aaa --- /dev/null +++ b/research/v45-recovery-transfer/TASK.json @@ -0,0 +1,88 @@ +{ + "schema_version": 1, + "task_id": "complex-new-helper-inventory", + "priority_revision": 6, + "base_commit": "997e6a9ca7b4f95d50e366f61412fd640d72a88a", + "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": "changed", + "actual_scope": "User-assigned bounded V45 comparison: exact old/new observation quotients and eligibility, nonlinear no-fresh-recovery certificate, and necessary fractional cost screen against PR2979.", + "scope_change_reason": "The assigned comparison stopped at a decisive zero eligible block on the final word. This is a reusable scoped obstruction and transfer clarification, not the card's new physically realized interface or a new kappa.", + "bottleneck_link": "Distinguish information already consumed by existing extraction from unused helper opportunities, and charge optimal fractional idle changes before pursuing a candidate.", + "budget_minutes": 235, + "stop_rule": "Compare only U12 and literal V45 supports of both providers across five pinned stages. Expand only if a distinct legal candidate has a favorable complete optimistic bill; otherwise preserve the exact decision and stop without broad search.", + "outcome": "completed", + "evidence": "EXPECTED.json, RESULT.json, PROOF.md and VALIDATION.md; exact forward/reverse checks and fixed-target fractional dual census. No positive supplier or new kappa.", + "author": "Ross Richardson", + "ai_assistance": "Substantial OpenAI Codex assistance; separately assigned source, observation, cost, independent-verifier and mathematical review agents. No independent human or formal-kernel proof.", + "open_questions": [ + { + "question": "Can a changed middle or a cheaper realization of the existing four directions beat the pinned full cost?", + "why_it_matters": "The frozen U12 has no fresh eligible information; the obstruction does not establish optimality of the existing implementation.", + "first_step": "Specify one exact changed program, access cut and paired residual, prove target compensation/restoration, then screen its complete local histogram and inventory against the applicable fractional dual before constructing owners.", + "blocked_by": "No concrete cheaper realization was identified. A changed private-buffer or physical interface requires explicit additional costs; passing the fractional screen is not admission." + } + ], + "scope_key": "v45-old-new-observation-eligibility-transfer-and-paid-screen", + "coordination": { + "canonical": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2612#discussioncomment-18970763", + "entry_checked_utc": "2026-10-17T14:38:21.652719Z", + "open_prs": 294, + "discussion_records": 1951, + "complete_pagination": true, + "limitations": "All open PR bodies and discussion records, local package notes and ledger. Not every diff or external literature. Other active PR3133/3148/531 construction scope excluded.", + "presubmit_coverage": { + "open_prs": { + "fetched_at": "2026-10-17T14:52:20.569906+00:00", + "complete_pagination": true, + "records": 295 + }, + "discussions": { + "fetched_at": "2026-10-17T14:53:06.978832+00:00", + "complete_pagination": true, + "records": 1956 + } + }, + "presubmit_warnings": [] + } +} diff --git a/research/v45-recovery-transfer/VALIDATION.md b/research/v45-recovery-transfer/VALIDATION.md new file mode 100644 index 0000000000..059cb1f7e4 --- /dev/null +++ b/research/v45-recovery-transfer/VALIDATION.md @@ -0,0 +1,51 @@ +# Validation and review + +Scientific base: `997e6a9ca7b4f95d50e366f61412fd640d72a88a`; canonical guidance +refreshed unchanged at 2026-10-17 14:52 UTC. Exact scientific-head checks bind all +eight provider copies to PR2894/2917/2942/2979. SOURCES.json contains those +byte-equality correspondences and SHA256/Git-blob pins for all fourteen live +inputs. Historical selected record and catalogue are provenance only. + +## Executed local coverage + +* CPython 3.12, isolated optimized primary replay: all 520 forward rows are + reconstructed for each of five stages and both providers. The bounded claims + concern all coefficients in the named U12 readouts and complete scalar + extraction-space constraints; this is not another all-endpoint census. +* A separately written reverse-covector/inverse-column implementation executes + no predecessor Python. It checks every U12 coefficient, all primary left/right + basis witnesses and their completeness, pairing entries, nuisance minors, + and the paired/nuisance completion. Independent finite F2 span propagation + checks literal terminal supports and the inherited center-cut convention. +* Fixed-target cost check: independent exact basis inversion, nonnegative + inventory perturbations, all 2,551 dual patterns and signed rational interval + charges. The authenticated predecessor log/exp enclosure kernel is reused. +* Eleven named rejection controls: five independent observation/minor controls, + four cost/source controls, and two frame-preimage/source-binding controls. + Four exact noncommuting/free-reduction fixtures also pass. +* Six development sensitivity mutations were detected: five check deletions and + wrong noncommuting multiplication order. These are separate sensitivity tests, + not six additional mathematical identities. +* Registered replay: + `python3.12 scripts/research_package.py --package research/v45-recovery-transfer` + passes with `PASS_V45_RECOVERY_TRANSFER` and + `PASS_REGISTERED_RESEARCH_PACKAGE ... outcome=completed`. + +* A source-identical Git-free export of the package and all fourteen live inputs + passes isolated optimized CPython 3.14 with the same stored result. + +## Review and limitations + +Separately assigned source, cost, verifier and mathematical reviews led to the +explicit literal-versus-refitted observation distinction, zero-block proof, +changed eligibility accounting, and fixed-target fractional-cost limitations. +The independent checker uses its own normalized pairing basis (determinant 1/2) +and also checks the primary basis determinant -128; determinants depend on the +basis, while nondegeneracy and the recovered directions agree. + +Review found no unresolved mathematical defect within the declared contract. +This does not certify optimality of the existing four-direction implementation. +No full native chain, chronological owner construction, physical invoice, +selected cold replay, formal-kernel proof, independent human review or new +outer kappa was performed or claimed. Hosted CI is separate from these local +checks; no manual rerun or no-op retrigger was requested. diff --git a/research/v45-recovery-transfer/VERIFY.json b/research/v45-recovery-transfer/VERIFY.json new file mode 100644 index 0000000000..6b80fbcf1c --- /dev/null +++ b/research/v45-recovery-transfer/VERIFY.json @@ -0,0 +1,35 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/helper408-rank7-pairing/sources/data/PARENT-base.json.gz", + "research/helper408-rank7-pairing/sources/data/PARENT-extra.json.gz", + "research/helper408-rank7-pairing/verify_boundary.py", + "research/paired-helper-extension/data/WORD-base.json.gz", + "research/paired-helper-extension/data/WORD-extra.json.gz", + "research/rank7-joint-endframes/CLAIM.json", + "research/rank7-joint-endframes/allocation/PROFILE.json", + "research/rank7-joint-endframes/certificates/RELAX-CAP.json", + "research/rank7-joint-endframes/data/PARENT-base.json.gz", + "research/rank7-joint-endframes/data/PARENT-extra.json.gz", + "research/rank7-joint-endframes/data/STAGE1-FRAME-EDITS.json", + "research/rank7-joint-endframes/data/WORD-base.json.gz", + "research/rank7-joint-endframes/data/WORD-extra.json.gz", + "research/rank7-joint-endframes/tools/root.py" + ], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-O", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 120, + "checks": "Exact five-stage V45 readouts, independent reverse/covector certificates, dyadic quotient identities, fixed-target full fractional cost screen and semantic rejection controls." + } + ] +} diff --git a/research/v45-recovery-transfer/compare.py b/research/v45-recovery-transfer/compare.py new file mode 100644 index 0000000000..6cd1961dea --- /dev/null +++ b/research/v45-recovery-transfer/compare.py @@ -0,0 +1,284 @@ +#!/usr/bin/env python3 +# SPDX-License-Identifier: Apache-2.0 +"""Exact bounded V45 information comparison on five authenticated provider stages. + +The complete forward free-group replay and rational kernel implementation are +reused, with attribution, from research/helper408-rank7-pairing/verify_boundary.py. +This file supplies the changed five-stage observation contract, full readout +comparisons, known-helper separation and exact scalar nuisance certificates. +""" +import argparse +import copy +from fractions import Fraction as Q +import gzip +import hashlib +import importlib.util +import json +from pathlib import Path + +PACKAGE = Path(__file__).resolve().parent +ROOT = PACKAGE.parent.parent +ENGINE = 'research/helper408-rank7-pairing/verify_boundary.py' +FRAME_EDITS = 'research/rank7-joint-endframes/data/STAGE1-FRAME-EDITS.json' +V45 = (256, 128, 64, 35, 16, 11, 5) +U12 = (2, 61, 62, 63, 70, 71, 72, 94, 249, 251, 265, 267) +P4 = (249, 251, 265, 267) +STAGES = ('PR2894', 'PR2917', 'PR2942', 'PR2979_stage1', 'PR2979_final') +EXPECTED_H = (226, 216, 212, 212, 207) + + +def need(condition, message): + if not condition: + raise ValueError(message) + + +def read(path): + raw = path.read_bytes() + return json.loads(gzip.decompress(raw) if raw[:2] == b'\x1f\x8b' else raw) + + +def authenticated_sources(): + manifest = read(PACKAGE / 'SOURCES.json') + pins = {} + for row in manifest['files']: + if row['usage'] != 'input': + continue + rel = row['path'] + need(rel not in pins, 'duplicate input pin: ' + rel) + path = (ROOT / rel).resolve() + need(path.is_relative_to(ROOT.resolve()), 'input outside repository') + need(hashlib.sha256(path.read_bytes()).hexdigest() == row['sha256'], 'input hash mismatch: ' + rel) + pins[rel] = row['sha256'] + return pins + + +def source_paths(variant): + return { + 'PR2894': f'research/helper408-rank7-pairing/sources/data/PARENT-{variant}.json.gz', + 'PR2917': f'research/paired-helper-extension/data/WORD-{variant}.json.gz', + 'PR2942': f'research/rank7-joint-endframes/data/PARENT-{variant}.json.gz', + 'PR2979_final': f'research/rank7-joint-endframes/data/WORD-{variant}.json.gz', + } + + +def stage1(parent, record): + """Apply exactly the shipped frame-only record, without source synthesis code.""" + child = copy.deepcopy(parent) + for helper, change in record['helper_final_changes'].items(): + need(child['helper_final'][helper] == change['old'], 'stage1 helper preimage') + child['helper_final'][helper] = change['new'] + seen = set() + for edit in record['frame_edits']: + key = edit['section'], edit['index'] + need(key not in seen and key[0] in ('A', 'B', 'restore'), 'stage1 duplicate/unknown frame edit') + seen.add(key) + gate = child[key[0]][key[1]] + need(gate[:-1] == edit['gate'] and gate[-1] == edit['old_frame'], 'stage1 gate preimage') + gate[-1] = edit['new_frame'] + need(all(g[:-1] == h[:-1] for sec in ('A', 'B', 'restore') + for g, h in zip(parent[sec], child[sec])), 'stage1 changed a scalar operator') + return child + + +def matrix_rank(rows, engine): + variables = sorted({k for row in rows for k in row}) + return engine.kernel(rows, variables)[1]['rank'] + + +def determinant(matrix): + a = [[Q(c) for c in row] for row in matrix] + n = len(a) + need(all(len(row) == n for row in a), 'determinant requires square matrix') + result = Q(1) + for k in range(n): + pivot = next((i for i in range(k, n) if a[i][k]), None) + if pivot is None: + return Q(0) + if pivot != k: + a[k], a[pivot] = a[pivot], a[k] + result = -result + value = a[k][k] + result *= value + for i in range(k + 1, n): + ratio = a[i][k] / value + for j in range(k + 1, n): + a[i][j] -= ratio * a[k][j] + return result + + +def dyadic_unit(value): + def power_of_two(n): + return n > 0 and n & (n - 1) == 0 + return power_of_two(abs(value.numerator)) and power_of_two(value.denominator) + + +def encoded_rows(matrix, support): + return [[r, c, list(word), str(value)] for r in sorted(support) + for (c, word), value in sorted(matrix[r].items())] + + +def rows_digest(rows): + return hashlib.sha256(json.dumps(rows, separators=(',', ':')).encode()).hexdigest() + + +def nuisance_certificate(matrix, H, support, engine): + """Greedy independent, exactly scalar forbidden columns, with full entries.""" + selected, columns = [], [] + for c in sorted(set(matrix) - set(H)): + if any(word for r in support for (column, word) in matrix[r] if column == c): + continue + vector = {r: matrix[r][c, ()] for r in support if (c, ()) in matrix[r]} + if vector and matrix_rank(columns + [vector], engine) > len(columns): + selected.append(c) + columns.append(vector) + if len(columns) == len(support): + break + entries = [[str(column.get(r, Q(0))) for column in columns] for r in support] + det = determinant(entries) if len(selected) == len(support) else None + pivot_rows, independent_rows = [], [] + for r, row in zip(support, entries): + sparse = {j: Q(c) for j, c in enumerate(row) if Q(c)} + if matrix_rank(independent_rows + [sparse], engine) > len(independent_rows): + pivot_rows.append(r) + independent_rows.append(sparse) + rank_entries = [[str(row.get(j, Q(0))) for j in range(len(columns))] for row in independent_rows] + rank_det = determinant(rank_entries) + need(len(pivot_rows) == len(columns) and rank_det != 0, 'nuisance rank witness failed') + return {'rank_witness_rows': pivot_rows, 'rank_witness_matrix': rank_entries, + 'rank_witness_determinant': str(rank_det), 'rank_witness_dyadic_unit': dyadic_unit(rank_det), + 'rows': list(support), 'columns': selected, 'matrix': entries, + 'rank': len(columns), 'determinant': str(det) if det is not None else None, + 'dyadic_unit': dyadic_unit(det) if det is not None else False, + 'nonempty_word_coefficients': 0} + + +def analyze_support(matrix, H, support, engine): + result = engine.analyze(matrix, H, support) + answer = {key: [engine.encode_vector(v) for v in result[key]] + for key in ('V', 'Y', 'Alpha', 'U')} + answer.update({'forward': result['forward'], 'inverse': result['inverse'], + 'pairing': [[str(c) for c in row] for row in result['pairing']], + 'pairing_rank': matrix_rank([dict(enumerate(row)) for row in result['pairing']], engine), + 'nuisance_certificate': nuisance_certificate(matrix, H, support, engine)}) + pairing = result['pairing'] + square = bool(pairing) and all(len(row) == len(pairing) for row in pairing) + answer['pairing_determinant'] = str(determinant(pairing)) if square else None + terms = [(r, c, word, value) for r in support for (c, word), value in matrix[r].items() if c in H] + answer['eligible_block_coefficient_count'] = len(terms) + answer['eligible_block_zero'] = not terms + nuisance = answer['nuisance_certificate'] + Y = result['Y'] + if len(Y) + nuisance['rank'] == len(support): + completion = [[str(y.get(r, Q(0))) for y in Y] + nuisance['matrix'][i] + for i, r in enumerate(support)] + completion_det = determinant(completion) + alpha_B = [[sum(alpha.get(r, Q(0)) * Q(nuisance['matrix'][i][j]) + for i, r in enumerate(support)) for j in range(nuisance['rank'])] + for alpha in result['Alpha']] + need(not any(c for row in alpha_B for c in row), 'Alpha times nuisance is nonzero') + answer['paired_nuisance_completion'] = { + 'column_order': 'Y basis, then scalar nuisance columns', 'matrix': completion, + 'determinant': str(completion_det), 'dyadic_unit': dyadic_unit(completion_det), + 'alpha_times_nuisance': [[str(c) for c in row] for row in alpha_B], + } + else: + answer['paired_nuisance_completion'] = None + # For this bounded support every coefficient is scalar. Thus ordinary + # rational rank(B) is the full nuisance rank, not a wordwise surrogate. + need(not any(word for r in support for c, word in matrix[r]), 'nonscalar bounded readout') + scalar_rows = [{c: value for (c, _), value in matrix[r].items()} for r in support] + nuisance_rows = [{c: value for c, value in row.items() if c not in H} for row in scalar_rows] + answer['readout_rank'] = matrix_rank(scalar_rows, engine) + answer['nuisance_rank'] = matrix_rank(nuisance_rows, engine) + answer['recoverable_scalar_dimension'] = answer['readout_rank'] - answer['nuisance_rank'] + need(answer['recoverable_scalar_dimension'] == result['inverse']['dimension'], 'quotient/kernel dimensions disagree') + return answer + + +def compute(): + pins = authenticated_sources() + required = {ENGINE, FRAME_EDITS} | {path for tag in ('base', 'extra') for path in source_paths(tag).values()} + need(required <= set(pins), 'consumed input lacks authentication') + spec = importlib.util.spec_from_file_location('v45_boundary_engine', ROOT / ENGINE) + engine = importlib.util.module_from_spec(spec) + spec.loader.exec_module(engine) + record = read(ROOT / FRAME_EDITS) + output = {'schema_version': 1, 'status': 'PASS_BOUNDED_V45_OBSERVATION_COMPARISON', + 'V45': list(V45), 'common_observation_U12': list(U12), 'known_pivots_P4': list(P4), + 'consumed_input_sha256': {p: pins[p] for p in sorted(required)}, 'variants': {}} + for variant in ('base', 'extra'): + paths = source_paths(variant) + providers = {label: read(ROOT / path) for label, path in paths.items()} + providers['PR2979_stage1'] = stage1(providers['PR2942'], record) + reports, raw_readouts = {}, {} + for index, label in enumerate(STAGES): + word = providers[label] + matrix = engine.replay(word) + frames, frame_counts = engine.terminal_frames(word) + protected = (set(map(int, word['helper_final'])) | set(map(int, word['start_extra'])) + | {c['source'] for c in word['initial_corrections']}) + H = sorted(r for r in matrix if r >= 224 and r not in protected) + need(len(H) == EXPECTED_H[index], 'eligible helper cardinality') + prelude = [g for g in word['A'][:word['prelude_events']] if not engine.target(g[1])] + need(all(g[0] == 'warp' and g[1] not in H for g in prelude), 'prelude violates independent eligible cut') + literal = sorted(r for r in matrix if engine.contained(frames[r], V45)) + wanted = () if index < 3 else U12 if index == 3 else tuple(r for r in U12 if r not in (61, 63)) + need(literal == list(wanted), 'literal V45 support differs') + observed = {r: matrix[r] for r in U12} + raw_readouts[label] = observed + coefficients = encoded_rows(matrix, U12) + report = { + 'eligible_H': H, 'known_pivots_in_H': sorted(set(P4) & set(H)), + 'literal_V45_support': literal, + 'U12_terminal_frames': {str(r): list(frames[r]) for r in U12}, + 'middle_gate_count': len(engine.literal_program(word)), + 'middle_operator_sha256': engine.operator_digest(matrix), + 'middle_coefficient_count': sum(map(len, matrix.values())), + 'prelude_events': word['prelude_events'], 'non_target_prelude_warps': len(prelude), + 'frame_replay': frame_counts, + 'U12_coefficients': coefficients, 'U12_coefficient_count': len(coefficients), + 'U12_coefficients_sha256': rows_digest(coefficients), + } + for support_name, support in (('U12', U12), ('literal', literal)): + report[support_name] = analyze_support(matrix, set(H), support, engine) + report[support_name]['with_known_P4'] = analyze_support(matrix, set(H) | set(P4), support, engine) + need(report['U12']['inverse']['dimension'] == (4 if index < 2 else 0), 'fresh left dimension') + need(report['U12']['forward']['dimension'] == (4 if index < 2 else 0), 'fresh right dimension') + need(report['U12']['with_known_P4']['inverse']['dimension'] == 4, 'known-helper left dimension') + if index < 2: + need(report['U12']['pairing_determinant'] == '-128', 'original paired determinant') + need(report['U12']['paired_nuisance_completion']['determinant'] == '256', 'original dyadic completion') + else: + need(report['U12']['eligible_block_zero'], 'fresh input block is not zero') + need(report['U12']['nuisance_certificate']['determinant'] == '2', 'full nuisance determinant') + need(report['U12']['with_known_P4']['U'] == [{str(h): '1'} for h in P4], 'known helper quotient differs') + reports[label] = report + need(raw_readouts['PR2894'] == raw_readouts['PR2917'], 'old-to-2917 complete observation changed') + need(raw_readouts['PR2942'] == raw_readouts['PR2979_stage1'] == raw_readouts['PR2979_final'], + 'post-extraction complete observation changed') + output['variants'][variant] = {'stages': reports, + 'complete_U12_equalities': [['PR2894', 'PR2917'], ['PR2942', 'PR2979_stage1', 'PR2979_final']]} + # Different source placements must produce the same bounded map and spaces. + for label in STAGES: + a, b = [output['variants'][tag]['stages'][label] for tag in ('base', 'extra')] + need(a['U12_coefficients'] == b['U12_coefficients'], 'provider bounded observations differ') + need(a['eligible_H'] == b['eligible_H'] and a['U12'] == b['U12'] and a['literal'] == b['literal'], + 'provider bounded spaces differ') + return output + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--emit', action='store_true', help='emit complete deterministic JSON instead of comparing EXPECTED.json') + args = parser.parse_args() + result = compute() + if args.emit: + print(json.dumps(result, indent=2, sort_keys=True)) + else: + need(result == read(PACKAGE / 'EXPECTED.json'), 'complete bounded comparison differs from EXPECTED.json') + print(json.dumps({'status': result['status'], 'providers': 2, 'stages_per_provider': 5, + 'common_observation_rows': len(U12), 'no_new_kappa': True}, sort_keys=True)) + + +if __name__ == '__main__': + main() diff --git a/research/v45-recovery-transfer/cost.py b/research/v45-recovery-transfer/cost.py new file mode 100644 index 0000000000..02475f0e6c --- /dev/null +++ b/research/v45-recovery-transfer/cost.py @@ -0,0 +1,268 @@ +#!/usr/bin/env python3 +# SPDX-License-Identifier: Apache-2.0 +"""Exact fixed-bin marginal cost screen for the frozen PR2979 inventory. + +The independent basis/dual implementation is new to this package. Rational +logarithm/exponential enclosures are executed from authenticated PR2979 root.py, +credited to Marius-Paul Dumitrean and that package's inherited moment lineage. +This is a finite fractional relaxation at a fixed complex saving parameter; +it supplies neither an extraction nor physical/supplier/outer admission. +""" + +import hashlib +import itertools +import json +import types +from fractions import Fraction as Q +from pathlib import Path + +SOURCE = "research/rank7-joint-endframes/" +PINS = { + "CLAIM.json": "436e0d297cbdf195445d3697d496ac675e95210b79e70ce602a6a6667a4c6ce9", + "certificates/RELAX-CAP.json": ( + "b272680de5842f7fd5f442cd0aeadfd317fe6af266ddee1a1e0738a919ba856e" + ), + "tools/root.py": "55f5aca39b5ee2fe4687ac8863e6c24569010f27a332883c069b8e14b8fe09e3", + "allocation/PROFILE.json": ( + "94a819747f3ced41f1544ada0036c983fc0c92847b9644380f877a06cd7931cf" + ), +} +CAPS = (8, 16, 32, 48) +WIDTHS = (4, 5, 6, 7, 8, 9) +BINS = (672, 448, 448, 448) +CALLS = 9 + + +def need(condition, message): + """Keep every acceptance condition live under optimized Python.""" + if not condition: + raise ValueError(message) + + +def authenticate(raw, expected): + need(len(raw) <= 65536, "cost input exceeds fixed byte cap") + need(hashlib.sha256(raw).hexdigest() == expected, "cost source digest") + + +def unique(pairs): + result = {} + for key, value in pairs: + need(key not in result, "duplicate cost JSON key") + result[key] = value + return result + + +def sources(root): + """Authenticate every input before parsing or executing the retained kernel.""" + raw = {} + for name, digest in PINS.items(): + value = (root / SOURCE / name).read_bytes() + authenticate(value, digest) + raw[name] = value + values = { + name: json.loads(value, object_pairs_hook=unique) + for name, value in raw.items() + if name.endswith(".json") + } + kernel = types.ModuleType("v45_authenticated_tariff") + filename = str(root / SOURCE / "tools/root.py") + exec(compile(raw["tools/root.py"], filename, "exec"), kernel.__dict__) + return values, kernel + + +def pattern(capacity, widths): + need(type(capacity) is int and capacity in CAPS, "cost pattern capacity") + need(len(widths) <= 12, "cost pattern helper count") + need(all(type(w) is int and w in WIDTHS for w in widths), "cost width") + remaining = capacity - sum(widths) + need(remaining >= 0, "cost pattern exceeds capacity") + col = [Q(int(capacity == c)) for c in CAPS] + col += [Q(widths.count(w)) for w in WIDTHS] + return col, remaining + + +def inverse(matrix): + size = len(matrix) + need(size == 10 and all(len(r) == size for r in matrix), "cost basis size") + rows = [r[:] + [Q(int(i == j)) for j in range(size)] for i, r in enumerate(matrix)] + for j in range(size): + choices = [i for i in range(j, size) if rows[i][j]] + need(bool(choices), "singular cost basis") + k = choices[0] + rows[j], rows[k] = rows[k], rows[j] + divisor = rows[j][j] + rows[j] = [v / divisor for v in rows[j]] + for i in range(size): + if i != j: + multiplier = rows[i][j] + rows[i] = [v - multiplier * w for v, w in zip(rows[i], rows[j])] + return [r[size:] for r in rows] + + +def dot(left, right): + need(len(left) == len(right), "cost vector dimensions") + return sum((x * y for x, y in zip(left, right)), Q(0)) + + +def setup(cert): + entries = cert["basis_patterns"] + need(len(entries) == 10, "ten source basis patterns") + columns, idle = zip(*(pattern(e["capacity"], e["widths"]) for e in entries)) + matrix = [[col[i] for col in columns] for i in range(10)] + inv = inverse(matrix) + inventory = {int(k): Q(v) for k, v in cert["inventory_per_call"].items()} + need(set(inventory) == set(WIDTHS), "cost inventory support") + rhs = list(map(Q, BINS)) + [CALLS * inventory[w] for w in WIDTHS] + counts = [dot(row, rhs) for row in inv] + need(all(v >= 0 for v in counts), "primal cost feasibility") + need(counts == [Q(e["count_per_replica"]) for e in entries], "basis count binding") + return matrix, inv, idle, counts + + +def enclosure(coefficients, tariffs): + lower = sum(v * tariffs[r][0 if v > 0 else 1] for r, v in coefficients.items()) + upper = sum(v * tariffs[r][1 if v > 0 else 0] for r, v in coefficients.items()) + need(lower <= upper, "cost interval order") + return lower, upper + + +def serialize_interval(interval): + return {"lower": str(interval[0]), "upper": str(interval[1])} + + +def dual_census(inv, idle, tariffs): + dual = [{} for _ in range(10)] + for j in range(10): + for k, rank in enumerate(idle): + if rank: + dual[j][rank] = dual[j].get(rank, Q(0)) + inv[k][j] + counts = {"patterns": 0, "tight": 0, "strict": 0} + minimum = None + for cap in CAPS: + domains = [range(cap // width + 1) for width in WIDTHS] + for numbers in itertools.product(*domains): + remainder = cap - dot(numbers, WIDTHS) + if remainder < 0: + continue + counts["patterns"] += 1 + col = [Q(int(cap == c)) for c in CAPS] + list(numbers) + coeff = {int(remainder): Q(1)} if remainder else {} + for j, value in enumerate(col): + for rank, multiplier in dual[j].items(): + coeff[rank] = coeff.get(rank, Q(0)) - value * multiplier + coeff = {rank: value for rank, value in coeff.items() if value} + if not coeff: + counts["tight"] += 1 + continue + lower, _ = enclosure(coeff, tariffs) + need(lower > 0, "nonpositive cost reduced-cost lower bound") + minimum = lower if minimum is None else min(minimum, lower) + counts["strict"] += 1 + need(counts == {"patterns": 2551, "tight": 12, "strict": 2539}, "cost census") + counts["minimum_reduced_cost_lower"] = str(minimum) + return counts + + +def check_idle_mass(idle_delta, freed): + need(sum(rank * number for rank, number in idle_delta.items()) == CALLS * freed, + "unpaid freed helper width") + + +def marginal(matrix, inv, idle, counts, old, new): + rhs = [Q(0)] * 10 + rhs[4 + WIDTHS.index(old)] = -CALLS + rhs[4 + WIDTHS.index(new)] = CALLS + delta = [dot(row, rhs) for row in inv] + need([dot(row, delta) for row in matrix] == rhs, "inventory perturbation identity") + need(all(x + dx >= 0 for x, dx in zip(counts, delta)), "changed basis feasibility") + idle_delta = {} + for rank, change in zip(idle, delta): + if rank and change: + idle_delta[rank] = idle_delta.get(rank, Q(0)) + change + freed = old - new + expected = {3: -Q(9 * freed, 20), 5: -Q(9 * freed, 4), 48: Q(9 * freed, 20)} + need(idle_delta == expected, "changed optimal idle profile") + check_idle_mass(idle_delta, freed) + return { + "old_width": old, + "new_width": new, + "basis_delta_per_replica": list(map(str, delta)), + "idle_delta_per_replica": {str(r): str(v) for r, v in sorted(idle_delta.items())}, + } + + +def complete_profiles(claim, cert, literal): + need(claim["profile"] == literal, "literal complete profile binding") + need(claim["local_profile"] == cert["local_per_call"], "local profile binding") + need(claim["width_inventory"] == cert["inventory_per_call"], "inventory binding") + replicas = claim["replicas"] + need(type(replicas) is int and replicas == 74, "replica binding") + need(claim["calls"] == CALLS * replicas == 666, "complete local call multiplicity") + paid = {int(r): Q(n) for r, n in literal.items()} + need(sum(r * n for r, n in paid.items()) == 65088 * replicas, "literal rank mass") + fractional = {int(r): CALLS * Q(n) for r, n in cert["local_per_call"].items()} + for rank, number in cert["idle_per_replica"].items(): + fractional[int(rank)] = fractional.get(int(rank), Q(0)) + Q(number) + need(sum(r * n for r, n in fractional.items()) == 65088, "fractional rank mass") + need(all(paid.get(r, 0) >= replicas * n for r, n in + {int(r): CALLS * Q(n) for r, n in cert["local_per_call"].items()}.items()), + "literal profile omits local calls") + return fractional + + +def controls(): + trials = { + "one_of_two_freed_width_units_unpaid": lambda: check_idle_mass( + {3: -Q(9, 20), 5: -Q(9, 4), 48: Q(9, 20)}, 2), + "omitted_rank48_idle_charge": lambda: check_idle_mass( + {3: -Q(9, 10), 5: -Q(9, 2)}, 2), + "overfilled_basis_pattern": lambda: pattern(8, [8, 4]), + "source_corruption_before_execution": lambda: authenticate(b"corrupt", PINS["tools/root.py"]), + } + rejected = [] + for name, action in trials.items(): + try: + action() + except ValueError: + rejected.append(name) + else: + raise ValueError("cost control accepted: " + name) + return rejected + + +def verify_cost(root): + """Return a deterministic receipt; root is the repository/export directory.""" + values, kernel = sources(Path(root)) + claim = values["CLAIM.json"] + cert = values["certificates/RELAX-CAP.json"] + target = Q(claim["complex_lower"]) + need(target == Q("0.001729033982646513517717"), "cost comparator parameter") + matrix, inv, idle, counts = setup(cert) + tariffs = {r: kernel.H(r, target) for r in range(1, 49)} + census = dual_census(inv, idle, tariffs) + changes = [marginal(matrix, inv, idle, counts, old, new) + for old, new in ((8, 7), (9, 8), (9, 7))] + debit = enclosure({48: Q(1, 20), 3: -Q(1, 20), 5: -Q(1, 4)}, tariffs) + budget = enclosure({1: Q(2), 48: -Q(1, 10), 3: Q(1, 10), 5: Q(1, 2)}, tariffs) + fractional = complete_profiles(claim, cert, values["allocation/PROFILE.json"]) + moment = kernel.moment(fractional, target, 896) + slack = (Q(73 * 896, 9) * (1 - moment[1]), Q(73 * 896, 9) * (1 - moment[0])) + need(0 < debit[0] and 0 < budget[0] and 0 < slack[0], "positive cost boundary") + ceiling = (budget[0] + slack[0], budget[1] + slack[1]) + return { + "status": "PASS_FIXED_TARGET_FRACTIONAL_COST_SCREEN", + "parameter": "complex moment b, not a newly released outer kappa", + "target": str(target), + "dual_census": census, + "marginals": changes, + "idle_debit_per_freed_width": serialize_interval(debit), + "two_width_local_overhead_budget": serialize_interval(budget), + "old_literal_fractional_headroom_per_call": serialize_interval(slack), + "two_width_overhead_ceiling_for_old_literal_target": serialize_interval(ceiling), + "rejected_controls": controls(), + "scope": "Fixed bins, one additional inventory change, fractional owners; no extraction or admission.", + } + + +if __name__ == "__main__": + print(json.dumps(verify_cost(Path(__file__).resolve().parents[2]), sort_keys=True)) diff --git a/research/v45-recovery-transfer/independent.py b/research/v45-recovery-transfer/independent.py new file mode 100644 index 0000000000..0b64c3ede5 --- /dev/null +++ b/research/v45-recovery-transfer/independent.py @@ -0,0 +1,501 @@ +#!/usr/bin/env python3 +"""Independent backward verification of the bounded V45 comparison. + +No predecessor Python module or producer/forward replay is imported. Rational +covectors are pulled backward through the literal gates; inverse columns are +obtained by independently reversing the gate operations. Every nonzero free +word coefficient in the twelve requested rows is retained and compared. +""" +# SPDX-License-Identifier: Apache-2.0 +from __future__ import annotations + +import copy +from fractions import Fraction as Q +import gzip +import hashlib +import json +from pathlib import Path +import sys + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parent.parent +U12 = (2, 61, 62, 63, 70, 71, 72, 94, 249, 251, 265, 267) +P4 = (249, 251, 265, 267) +J12 = (2, 9, 10, 11, 70, 71, 72, 79, 249, 251, 265, 267) +V45 = (256, 128, 64, 35, 16, 11, 5) +STEMS = { + '2894': 'research/helper408-rank7-pairing/sources/data/PARENT', + '2917': 'research/paired-helper-extension/data/WORD', + '2942': 'research/rank7-joint-endframes/data/PARENT', + '2979': 'research/rank7-joint-endframes/data/WORD', +} + + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def authenticate(): + """Bind bytes before interpreting data; no imported source or pyc cache.""" + data = {} + sources = json.loads((HERE / 'SOURCES.json').read_bytes()) + for item in sources['files']: + if item['usage'] != 'input': + continue + path = item['path'] + require(path not in data, 'duplicate authenticated input') + resolved = (ROOT / path).resolve() + require(resolved.is_relative_to(ROOT.resolve()), 'input outside repository') + raw = resolved.read_bytes() + require(hashlib.sha256(raw).hexdigest() == item['sha256'], 'source sha256: ' + path) + blob = b'blob ' + str(len(raw)).encode() + b'\0' + raw + require(hashlib.sha1(blob).hexdigest() == item['git_blob'], 'source blob: ' + path) + data[path] = raw + return data + + +def read_data(raw, path): + require(path in raw, 'unauthenticated input: ' + path) + payload = gzip.decompress(raw[path]) if path.endswith('.gz') else raw[path] + return json.loads(payload) + + +def live_registers(provider): + removed = provider['removed'] + require(len(removed) == len(set(removed)), 'duplicate removed register') + require(all(isinstance(r, int) and 0 <= r < 704 for r in removed), 'bad removed register') + return tuple(r for r in range(704) if r not in removed and not 112 <= r < 224) + + +def eligible(provider, live): + protected = set(map(int, provider['helper_final'])) | set(map(int, provider['start_extra'])) + protected.update(x['source'] for x in provider['initial_corrections']) + return frozenset(r for r in live if r >= 224 and r not in protected) + + +def gates(provider): + """Input immediately after prelude; stop after restore, before cleanup.""" + result = list(provider['A'][provider['prelude_events']:]) + resets = {} + for symbol, record in enumerate(provider['warps'], 1): + pos, reg = record[:2] + require(0 <= pos <= len(provider['B']), 'warp position') + resets.setdefault(pos, []).append(['warp', reg, symbol]) + for pos in range(len(provider['B']) + 1): + result.extend(resets.get(pos, ())) + if pos != len(provider['B']): + result.append(provider['B'][pos]) + result.extend(provider['restore']) + kept = [g for g in result if not 112 <= g[1] < 224] + live = set(live_registers(provider)) + for g in kept: + require(g[0] in ('add', 'scale', 'warp'), 'unrecognized gate') + require(g[1] in live, 'gate outside live coordinates') + if g[0] == 'add': + require(g[2] in live and g[1] != g[2], 'illegal add dependency') + if g[0] in ('add', 'scale'): + a, b = g[3:5] if g[0] == 'add' else g[2:4] + require(isinstance(a, int) and isinstance(b, int) and b != 0 and abs(b) & (abs(b) - 1) == 0, 'non-dyadic gate') + if g[0] == 'scale': + require(a != 0 and abs(a) & (abs(a) - 1) == 0, 'non-unit dyadic scale') + return kept + + +def put(vector, key, value): + value += vector.get(key, Q(0)) + if value: + vector[key] = value + else: + vector.pop(key, None) + + +def append_word(word, symbol): + return word[:-1] if word and word[-1] == -symbol else word + (symbol,) + + +def prepend_word(symbol, word): + return word[1:] if word and word[0] == -symbol else (symbol,) + word + + +def backward_row(program, output): + """r <- r G at each reversed gate; warp multiplication is on the right.""" + row = {(output, ()): Q(1)} + for g in reversed(program): + kind, dst = g[:2] + terms = [(w, c) for (r, w), c in row.items() if r == dst] + if not terms: + continue + if kind == 'add': + q = Q(g[3], g[4]) + for word, c in terms: + put(row, (g[2], word), q * c) + elif kind == 'scale': + q = Q(g[2], g[3]) + for word, c in terms: + row[dst, word] = q * c + else: + for word, _ in terms: + del row[dst, word] + for word, c in terms: + put(row, (dst, append_word(word, g[2])), c) + return row + + +def inverse_column(program, output): + """x <- G^-1 x in reverse chronological order; warp acts on the left.""" + state = {output: {(): Q(1)}} + for g in reversed(program): + kind, dst = g[:2] + if kind == 'add': + src = state.get(g[2], {}) + if src: + dest = state.setdefault(dst, {}) + for word, value in tuple(src.items()): + put(dest, word, -Q(g[3], g[4]) * value) + if not dest: + state.pop(dst) + elif dst in state: + if kind == 'scale': + state[dst] = {w: c * Q(g[3], g[2]) for w, c in state[dst].items()} + else: + moved = {} + for word, value in state[dst].items(): + put(moved, prepend_word(-g[2], word), value) + state[dst] = moved + return {(r, w): c for r, poly in state.items() for w, c in poly.items()} + + +def nullspace(equations, size): + rows = [[Q(v) for v in row] for row in equations if any(row)] + require(all(len(row) == size for row in rows), 'equation width') + pivots = [] + for col in range(size): + selected = next((k for k in range(len(pivots), len(rows)) if rows[k][col]), None) + if selected is None: + continue + k = len(pivots) + rows[k], rows[selected] = rows[selected], rows[k] + q = rows[k][col] + rows[k] = [x / q for x in rows[k]] + for j in range(len(rows)): + if j != k and rows[j][col]: + q = rows[j][col] + rows[j] = [a - q * b for a, b in zip(rows[j], rows[k])] + pivots.append(col) + free = [j for j in range(size) if j not in pivots] + result = [] + for j in free: + v = [Q(0)] * size + v[j] = Q(1) + for k, pivot in enumerate(pivots): + v[pivot] = -rows[k][j] + result.append(v) + return result + + +def allowed_combinations(vectors, H): + keys = sorted({key for vec in vectors for key in vec if key[0] not in H or key[1]}) + equations = [[v.get(key, Q(0)) for v in vectors] for key in keys] + basis = nullspace(equations, len(vectors)) + for b in basis: + image = {} + for c, vector in zip(b, vectors): + for key, value in vector.items(): + put(image, key, c * value) + require(all(r in H and not w for r, w in image), 'kernel image support') + return basis + + +def dyadic_unit(q): + q = Q(q) + a, b = abs(q.numerator), q.denominator + return a != 0 and a & (a - 1) == 0 and b & (b - 1) == 0 + + +def determinant(matrix): + a = [[Q(x) for x in row] for row in matrix] + require(all(len(row) == len(a) for row in a), 'determinant nonsquare') + value = Q(1) + for col in range(len(a)): + p = next((k for k in range(col, len(a)) if a[k][col]), None) + if p is None: + return Q(0) + if p != col: + a[p], a[col] = a[col], a[p] + value = -value + q = a[col][col] + value *= q + for j in range(col + 1, len(a)): + ratio = a[j][col] / q + for k in range(col + 1, len(a)): + a[j][k] -= ratio * a[col][k] + return value + + +def scalar_minor(rows, outputs, columns, H, expected): + require(len(outputs) == len(columns), 'minor dimensions') + require(len(set(columns)) == len(columns) and not set(columns) & H, 'minor protected columns') + require(all(not word for r in outputs for col, word in rows[r] if col in columns), 'minor non-scalar coefficient') + matrix = [[rows[r].get((c, ()), Q(0)) for c in columns] for r in outputs] + require(determinant(matrix) == expected, 'minor determinant') + return matrix + + +def span(values): + """Explicit finite vector subspace, independent of the producer's basis RREF.""" + result = {0} + for v in values: + require(isinstance(v, int) and 0 <= v < 512, 'frame coordinate') + result |= {x ^ v for x in result} + return frozenset(result) + + +def terminals(provider): + live = set(range(704)) - set(provider['removed']) + current = {r: span([provider['ports'][r]]) if r < 112 else frozenset({0}) for r in live} + for r, f in provider['start_extra'].items(): + current[int(r)] = span(f) + + def scalar(g): + f = span(g[-1]) + regs = g[1:3] if g[0] == 'add' else g[1:2] + for r in regs: + require(r in current and current[r] <= f, 'nonmonotone frame incident') + current[r] = f + + for g in provider['A']: + if g[0] == 'warp': + require(current[g[1]] == span(g[3]), 'A warp frame mismatch') + require(provider['warps'][abs(g[2]) - 1][1] == g[1], 'A warp register mismatch') + current[g[1]] = span(g[4]) + else: + scalar(g) + require(all(current[r] == span(f) for r, f in zip(provider['centers'], provider['center_frames'])), 'center frame mismatch') + require(all(g[0] == 'add' and 112 <= g[1] < 224 and g[2] in provider['centers'] for g in provider['cut']), 'center cut convention') + reset = {} + for entry in provider['warps']: + reset.setdefault(entry[0], []).append(entry) + for position in range(len(provider['B']) + 1): + for _, r, _, before, after in reset.get(position, ()): + require(current[r] == span(before), 'B warp frame mismatch') + current[r] = span(after) + if position < len(provider['B']): + scalar(provider['B'][position]) + for g in provider['restore']: + scalar(g) + for r, expected in provider['helper_final'].items(): + require(current[int(r)] == span(expected), 'declared helper final mismatch') + return tuple(r for r in live_registers(provider) if current[r] <= span(V45)) + + +def apply_stage1(provider, edits): + result = copy.deepcopy(provider) + for r, change in edits['helper_final_changes'].items(): + require(result['helper_final'][r] == change['old'], 'stage1 old helper frame') + result['helper_final'][r] = change['new'] + for item in edits['frame_edits']: + g = result[item['section']][item['index']] + require(g[:-1] == item['gate'] and g[-1] == item['old_frame'], 'stage1 old scalar gate') + g[-1] = item['new_frame'] + return result + + +def encode_rows(rows): + return [[r, c, list(w), str(v)] for r in sorted(rows) for (c, w), v in sorted(rows[r].items())] + + +def exact_rows(actual, expected): + require(encode_rows(actual) == encode_rows(expected), 'complete row coefficient mismatch') + + +def rejects(action, label, expected_message): + try: + action() + except ValueError as error: + if str(error) != expected_message: + raise + return label + raise RuntimeError('negative control unexpectedly accepted: ' + label) + + +def fixtures(): + program = [['warp', 0, 1], ['add', 1, 0, 3, 2], ['warp', 1, 2], ['warp', 0, -1]] + expected = {(0, (2, 1)): Q(3, 2), (1, (2,)): Q(1)} + require(backward_row(program, 1) == expected, 'noncommuting right-product order fixture') + require(inverse_column(program, 0) == {(0, ()): Q(1), (1, (1,)): Q(-3, 2)}, 'inverse-column fixture') + require(append_word((1, 2), -2) == (1,), 'free reduction fixture') + require(append_word((1, 2), -1) == (1, 2, -1), 'nonadjacent cancellation fixture') + return ['noncommuting_order', 'inverse_column', 'adjacent_cancellation', 'nonadjacent_no_cancellation'] + + +def decode_scalar(vector, allowed): + require(isinstance(vector, dict), 'malformed scalar vector') + out = {} + for r, coefficient in vector.items(): + r = int(r) + c = Q(coefficient) + require(r in allowed and c != 0, 'scalar vector domain or zero coefficient') + out[r, ()] = c + return out + + +def combine(coefficients, vectors): + out = {} + for (r, word), factor in coefficients.items(): + require(not word and r in vectors, 'combination domain') + for key, value in vectors[r].items(): + put(out, key, factor * value) + return out + + +def check_primary_analysis(analysis, rows, inverse, support, H): + """Verify its full basis witnesses against our independently computed maps.""" + m = len(support) + left = allowed_combinations([rows[r] for r in support], H) + right = allowed_combinations([inverse[r] for r in support], H) + require(analysis['inverse']['dimension'] == len(left), 'primary left dimension') + require(analysis['forward']['dimension'] == len(right), 'primary right dimension') + require(len(analysis['Alpha']) == len(analysis['U']) == len(left), 'primary left basis size') + require(len(analysis['Y']) == len(analysis['V']) == len(right), 'primary right basis size') + alphas = [decode_scalar(a, support) for a in analysis['Alpha']] + ys = [decode_scalar(y, support) for y in analysis['Y']] + us = [decode_scalar(u, H) for u in analysis['U']] + vs = [decode_scalar(v, H) for v in analysis['V']] + for alpha, u in zip(alphas, us): + require(combine(alpha, rows) == u, 'primary complete left witness') + for y, v in zip(ys, vs): + require(combine(y, inverse) == v, 'primary complete right witness') + for basis in (alphas, ys): + columns = [[v.get((r, ()), Q(0)) for v in basis] for r in support] + require(not nullspace(columns, len(basis)), 'primary dependent basis') + pairing = [[sum(a.get((r, ()), Q(0)) * y.get((r, ()), Q(0)) for r in support) for y in ys] for a in alphas] + require([[str(x) for x in row] for row in pairing] == analysis['pairing'], 'primary pairing entries') + expected_det = str(determinant(pairing)) if alphas and len(alphas) == len(ys) else None + require(expected_det == analysis['pairing_determinant'], 'primary basis determinant') + certificate = analysis['nuisance_certificate'] + columns = certificate['columns'] + require(certificate['rows'] == list(support), 'primary nuisance row list') + require(len(set(columns)) == len(columns) and not set(columns) & H, 'primary nuisance column domain') + require(all(not word for r in support for col, word in rows[r] if col in columns), 'primary nuisance scalar restriction') + nuisance = [[rows[r].get((c, ()), Q(0)) for c in columns] for r in support] + require(certificate['matrix'] == [[str(x) for x in row] for row in nuisance], 'primary nuisance entries') + require(certificate['nonempty_word_coefficients'] == 0, 'primary nuisance word count') + rank = len(columns) - len(nullspace(nuisance, len(columns))) + require(certificate['rank'] == rank, 'primary nuisance rank') + witness_rows = certificate['rank_witness_rows'] + require(set(witness_rows) <= set(support) and len(set(witness_rows)) == len(witness_rows), 'primary witness row domain') + witness = [[rows[r].get((c, ()), Q(0)) for c in columns] for r in witness_rows] + require(witness == [[Q(x) for x in row] for row in certificate['rank_witness_matrix']], 'primary witness entries') + require(str(determinant(witness)) == certificate['rank_witness_determinant'], 'primary witness determinant') + require(dyadic_unit(determinant(witness)) == certificate['rank_witness_dyadic_unit'], 'primary witness unit') + det = determinant(nuisance) if len(nuisance) == len(columns) else None + require((None if det is None else str(det)) == certificate['determinant'], 'primary nuisance determinant') + require((False if det is None else dyadic_unit(det)) == certificate['dyadic_unit'], 'primary nuisance unit') + completion = analysis.get('paired_nuisance_completion') + if completion is not None: + whole = [[y.get((r, ()), Q(0)) for y in ys] + row for r, row in zip(support, nuisance)] + require(whole == [[Q(x) for x in row] for row in completion['matrix']], 'primary nuisance completion entries') + require(str(determinant(whole)) == completion['determinant'], 'primary nuisance completion determinant') + require(dyadic_unit(determinant(whole)) == completion['dyadic_unit'], 'primary nuisance completion unit') + ab = [[sum(alpha.get((r, ()), Q(0)) * rows[r].get((c, ()), Q(0)) for r in support) for c in columns] for alpha in alphas] + require(all(not x for row in ab for x in row), 'primary nuisance kernel inclusion') + require(ab == [[Q(x) for x in row] for row in completion['alpha_times_nuisance']], 'primary nuisance kernel entries') + if analysis.get('with_known_P4') is not None: + check_primary_analysis(analysis['with_known_P4'], rows, inverse, support, H | frozenset(P4)) + + +def check_primary_stage(primary, rows, inverse, support, H): + require(primary['U12_coefficients'] == encode_rows(rows), 'primary complete U12 coefficients') + require(primary['eligible_H'] == sorted(H), 'primary eligibility set') + require(primary['literal_V45_support'] == list(support), 'primary literal support') + check_primary_analysis(primary['U12'], rows, inverse, U12, H) + check_primary_analysis(primary['literal'], rows, inverse, support, H) + + +def run(expected=None): + raw = authenticate() + if expected is None: + expected = json.loads((HERE / 'EXPECTED.json').read_bytes()) + edits = read_data(raw, 'research/rank7-joint-endframes/data/STAGE1-FRAME-EDITS.json') + report = {'method': 'backward_covectors_and_inverse_columns', 'fixtures': fixtures(), 'providers': {}, 'controls': []} + cache = {} + for variant in ('base', 'extra'): + words = {stage: read_data(raw, stem + '-' + variant + '.json.gz') for stage, stem in STEMS.items()} + words['stage1'] = apply_stage1(words['2942'], edits) + for stage in ('2894', '2917', '2942', 'stage1', '2979'): + p = words[stage] + live = live_registers(p) + H = eligible(p, live) + prelude = p['A'][:p['prelude_events']] + require(all(g[0] == 'warp' or 112 <= g[1] < 224 for g in prelude), 'prelude non-target scalar') + require(not H & {g[1] for g in prelude if g[0] == 'warp'}, 'prelude modifies fresh H') + prog = gates(p) + rows = {r: backward_row(prog, r) for r in U12} + inverse = [inverse_column(prog, r) for r in U12] + A = allowed_combinations([rows[r] for r in U12], H) + Y = allowed_combinations(inverse, H) + pairing = [[sum(a * b for a, b in zip(alpha, y)) for y in Y] for alpha in A] + support = terminals(p) + expected_support = U12 if stage == 'stage1' else tuple(r for r in U12 if r not in (61, 63)) if stage == '2979' else () + require(support == expected_support, 'literal terminal support') + old = stage in ('2894', '2917') + require(len(A) == len(Y) == (4 if old else 0), 'fresh pairing spaces dimensions') + if old: + require(determinant(pairing) != 0, 'old pairing degenerate') + else: + require(all(c not in H for row in rows.values() for c, _ in row), 'fresh eligible dependence remains') + scalar_minor(rows, U12, J12, H, Q(2)) + enlarged = H | frozenset(P4) + require(len(allowed_combinations([rows[r] for r in U12], enlarged)) == 4, 'protected pivot left access control') + require(len(allowed_combinations(inverse, enlarged)) == 4, 'protected pivot right access control') + if stage == '2979': + j10 = tuple(c for c in J12 if c not in (9, 11)) + scalar_minor(rows, support, j10, H, Q(1)) + primary_label = {'2894': 'PR2894', '2917': 'PR2917', '2942': 'PR2942', 'stage1': 'PR2979_stage1', '2979': 'PR2979_final'}[stage] + primary = expected['variants'][variant]['stages'][primary_label] + check_primary_stage(primary, rows, dict(zip(U12, inverse)), support, H) + key = variant + ':' + stage + cache[key] = rows + report['providers'][key] = { + 'eligible_count': len(H), 'live_count': len(live), 'middle_gate_count': len(prog), + 'literal_support': list(support), 'row_coefficient_count': sum(map(len, rows.values())), + 'left_dimension': len(A), 'right_dimension': len(Y), + 'independent_basis_pairing_determinant': str(determinant(pairing)), + 'primary_basis_pairing_determinant': primary['U12']['pairing_determinant'], + 'nuisance_determinant': None if old else '2', 'rows': encode_rows(rows), + } + exact_rows(cache[variant + ':2894'], cache[variant + ':2917']) + exact_rows(cache[variant + ':2942'], cache[variant + ':stage1']) + exact_rows(cache[variant + ':2942'], cache[variant + ':2979']) + for stage in ('2894', '2917', '2942', 'stage1', '2979'): + exact_rows(cache['base:' + stage], cache['extra:' + stage]) + oldrows = cache['base:2894'] + corrupt = copy.deepcopy(oldrows) + first = next(iter(corrupt[U12[0]])) + corrupt[U12[0]][first] += 1 + report['controls'].append(rejects(lambda: exact_rows(corrupt, oldrows), 'single_coefficient_corruption', 'complete row coefficient mismatch')) + p = words['2979'] + H = eligible(p, live_registers(p)) + rows = cache['extra:2979'] + report['controls'].append(rejects(lambda: scalar_minor(rows, U12, J12[:-1], H, Q(2)), 'missing_forbidden_column', 'minor dimensions')) + report['controls'].append(rejects(lambda: scalar_minor(rows, U12, J12, H | frozenset(P4), Q(2)), 'protected_pivot_misclassified', 'minor protected columns')) + report['controls'].append(rejects(lambda: require(terminals(p) == U12, 'literal terminal support'), 'wrong_terminal_support', 'literal terminal support')) + non_scalar = copy.deepcopy(rows) + non_scalar[U12[0]][J12[0], (1,)] = Q(1) + report['controls'].append(rejects(lambda: scalar_minor(non_scalar, U12, J12, H, Q(2)), 'non_scalar_minor_coefficient', 'minor non-scalar coefficient')) + return report + + +def main(): + report = run() + if len(sys.argv) == 3 and sys.argv[1] == '--output': + Path(sys.argv[2]).write_text(json.dumps(report, indent=2) + '\n') + else: + require(len(sys.argv) == 1, 'usage: independent.py [--output FILE]') + concise = {key: {k: v for k, v in item.items() if k != 'rows'} for key, item in report['providers'].items()} + print(json.dumps({'independent': 'PASS', 'providers': concise, 'controls': report['controls'], 'fixtures': report['fixtures']}, sort_keys=True)) + + +if __name__ == '__main__': + main() diff --git a/research/v45-recovery-transfer/verify.py b/research/v45-recovery-transfer/verify.py new file mode 100644 index 0000000000..de3fa2a931 --- /dev/null +++ b/research/v45-recovery-transfer/verify.py @@ -0,0 +1,86 @@ +#!/usr/bin/env python3 +# SPDX-License-Identifier: Apache-2.0 +"""Run the bounded exact comparison, separate checker and full fractional screen.""" +import argparse +import copy +import importlib.util +import json +from pathlib import Path +import tempfile + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parent.parent + + +def need(condition, message): + if not condition: + raise ValueError(message) + + +def module(name): + spec = importlib.util.spec_from_file_location('v45_' + name, HERE / (name + '.py')) + value = importlib.util.module_from_spec(spec) + spec.loader.exec_module(value) + return value + + +def controls(primary): + record = primary.read(ROOT / primary.FRAME_EDITS) + parent = primary.read(ROOT / primary.source_paths('base')['PR2942']) + broken = copy.deepcopy(record) + broken['frame_edits'][0]['gate'][1] += 1 + try: + primary.stage1(parent, broken) + except ValueError as error: + need(str(error) == 'stage1 gate preimage', 'frame control wrong rejection') + else: + raise ValueError('changed frame-edit preimage accepted') + original_root, original_package = primary.ROOT, primary.PACKAGE + try: + with tempfile.TemporaryDirectory(prefix='v45-binding-') as temp: + root = Path(temp) + row = {'path': 'source.json', 'usage': 'input', 'sha256': '0' * 64} + (root / 'source.json').write_text('{}\n') + (root / 'SOURCES.json').write_text(json.dumps({'files': [row]})) + primary.ROOT = primary.PACKAGE = root + try: + primary.authenticated_sources() + except ValueError as error: + need(str(error) == 'input hash mismatch: source.json', 'source control wrong rejection') + else: + raise ValueError('changed source bytes accepted') + finally: + primary.ROOT, primary.PACKAGE = original_root, original_package + return ['changed_frame_edit_preimage', 'source_hash_before_import'] + + +def compute(): + primary, independent, cost = [module(name) for name in ('compare', 'independent', 'cost')] + expected = json.loads((HERE / 'EXPECTED.json').read_bytes()) + actual = primary.compute() + need(actual == expected, 'complete primary receipt differs') + return { + 'status': 'PASS_V45_RECOVERY_TRANSFER', + 'no_new_kappa': True, + 'primary': {'providers': 2, 'stages_per_provider': 5, + 'readout_rows': 12, 'fresh_dimensions': [4, 4, 0, 0, 0]}, + 'independent': independent.run(expected), + 'cost': cost.verify_cost(ROOT), + 'additional_controls': controls(primary), + } + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--emit', action='store_true') + args = parser.parse_args() + result = compute() + if args.emit: + print(json.dumps(result, indent=2, sort_keys=True)) + else: + need(result == json.loads((HERE / 'RESULT.json').read_bytes()), 'complete result differs') + print('PASS_V45_RECOVERY_TRANSFER providers=2 stages=5 exact_cost_patterns=2551 no_new_kappa') + + +if __name__ == '__main__': + main()