From b3f5aabddbae2d65f80bb8356e6993e0a65cd245 Mon Sep 17 00:00:00 2001 From: Jonathan Capalbo Date: Wed, 28 Oct 2026 00:34:09 -0400 Subject: [PATCH] Certify scoped P104 fixed-word negative searches --- .../CARRIER-PROOF.md | 174 + .../ENDPOINT-PROOF.md | 141 + .../EXPECTED.json | 55977 ++++++++++++++++ .../NOTICE.md | 27 + .../README.md | 102 + .../SOURCES.json | 24 + .../TASK.json | 123 + .../VALIDATION.json | 26 + .../VENDOR.json | 24 + .../VERIFY.json | 42 + .../carrier.py | 538 + .../endpoints.py | 281 + .../package_controls.py | 68 + .../private_queries.py | 75 + .../review_controls.py | 238 + .../vendor/pr6045/inputs/shapesplit.py | 176 + .../vendor/pr6045/leakfix.py | 377 + .../verify.py | 103 + 18 files changed, 58516 insertions(+) create mode 100644 research/p104-fixed-word-negative-screens/CARRIER-PROOF.md create mode 100644 research/p104-fixed-word-negative-screens/ENDPOINT-PROOF.md create mode 100644 research/p104-fixed-word-negative-screens/EXPECTED.json create mode 100644 research/p104-fixed-word-negative-screens/NOTICE.md create mode 100644 research/p104-fixed-word-negative-screens/README.md create mode 100644 research/p104-fixed-word-negative-screens/SOURCES.json create mode 100644 research/p104-fixed-word-negative-screens/TASK.json create mode 100644 research/p104-fixed-word-negative-screens/VALIDATION.json create mode 100644 research/p104-fixed-word-negative-screens/VENDOR.json create mode 100644 research/p104-fixed-word-negative-screens/VERIFY.json create mode 100644 research/p104-fixed-word-negative-screens/carrier.py create mode 100644 research/p104-fixed-word-negative-screens/endpoints.py create mode 100644 research/p104-fixed-word-negative-screens/package_controls.py create mode 100644 research/p104-fixed-word-negative-screens/private_queries.py create mode 100644 research/p104-fixed-word-negative-screens/review_controls.py create mode 100644 research/p104-fixed-word-negative-screens/vendor/pr6045/inputs/shapesplit.py create mode 100644 research/p104-fixed-word-negative-screens/vendor/pr6045/leakfix.py create mode 100644 research/p104-fixed-word-negative-screens/verify.py diff --git a/research/p104-fixed-word-negative-screens/CARRIER-PROOF.md b/research/p104-fixed-word-negative-screens/CARRIER-PROOF.md new file mode 100644 index 0000000000..addefb3327 --- /dev/null +++ b/research/p104-fixed-word-negative-screens/CARRIER-PROOF.md @@ -0,0 +1,174 @@ +# Fixed-word sequential combination-carrier exclusion + +This note concerns the 4,033 **leaking unit-injection classes** returned by the +pinned PR6045/PR6040 census on the selected PR6030 word. It does not concern every +helper split, every injection, or every correction mechanism. + +The result is a scoped negative: none of these classes admits a repair by the +sequential zero-original-value, chart-local corrections defined below, with the +original events, paid MOVEs and owned lifetimes fixed. No improved paid profile +or new κ is claimed. + +## Sources and contribution + +The package source manifest authenticates the PR6030 word and the unmodified +vendored files. The word originates from DreamingOfClouds's PR6030, head +`772dd10a5859a1d15f4851feb371519789213ad8`, as retained in main +`721c03822c421b7f7fcbb2598993b947c4d88419`. Its compressed SHA256 is +`7834725d9e34ee846a9ccc615221ea81e0201613938afa185d2eda0c9a6c232f`. + +Josie Elliston's [PR6045](https://github.com/CrocSwap/integer-mult-bounds/pull/6045), +head `23abc00773a72d8e2b4e733b46c453b0f71f6368`, supplies the leak census, suffix +columns, and exact pure-subspace interface. Its inherited census is Nick +Petalas's PR6040 extension of Matarener's PR5994 and flyingviper's PR5718 split +shape. Their notices remain in the vendored source. PR6045 identified combination +carriers as an open direction after its individual-carrier screen. + +The additions here are a small-kernel global prefilter, a full first-combination +chart screen, and a dynamic affine closure for the two survivors. The latter +includes combinations enabled by earlier corrections; it does not freeze the +available carriers to those of the uncorrected trajectory. The new code and +proof were prepared with substantial OpenAI Codex assistance under Apache-2.0. + +## Model + +Let `R_t` map the original 770 public inputs to all live register values after +event `t` of the original word. An owned register is a temporary zero-initialized +row; CLEAR removes its row. At a selected cut `i`, replace pivot register `p` by +a new independent scalar input `z`. Put `ell(x) = (R_i x)_p`. The modified state +can be written + +`R_t x + beta_t (z - ell(x))`, + +with `beta_i = e_p`. The original events propagate `beta` linearly. Let `V` be +the pivot group's final chart and `O` the public output roles whose final chart +is not `V`. The leaking classes have nonzero uncorrected `beta_final` on `O`. +A successful independent-target repair needs both + +`beta_final|_O = 0` and `beta_final != 0`. + +We allow an inserted rank-one correction + +`beta -> beta + q e_r (c^T beta)` + +at any original event seam, where `q` is rational, `c^T R_t = 0`, the support of +`c` lies entirely in one current chart, and receiver `r` is already in that +chart. The correction's combined source has zero value in the **original** word +and equals `(c^T beta)(z - ell(x))` in the modified word. It preserves the +reference matrix `R_t` under the substitution `z = ell(x)`. + +This is an optimistic model. A linear combination is allowed as a single +operation; every same-chart receiver is allowed, including self/noninvertible +updates; coefficients need not be dyadic; and existing owned COPY/CLEAR events +may overwrite or erase the modified signal, even when that would violate a +modified word's zero/erasure obligation. These permissions enlarge reachability. +No construction, +native lifting, or extra paid operation is inferred from a relaxed possibility. + +## Baseline kernel and its premises + +Write `D_t = {c : c^T R_t = 0}`. The original public-input rank stays 770: +ADD and nonzero SCALE are invertible row operations; INIT adds a zero row; +COPY into a zero destination is equivalent to ADD on `R_t`; and a CLEAR removes +a row dependent on the remaining rows. Consequently the kernel dimension is the +number of live owned registers, at most 13 for this word. + +`carrier.py` explicitly transports a complete basis of `D_t`. An ADD +`row_r += a row_s` changes each kernel covector by +`c_s -= a c_r`; SCALE divides `c_r` by its nonzero coefficient; INIT adds `e_r`. +Before CLEAR it selects a kernel vector with nonzero `r` coefficient, eliminates +that coordinate from the other vectors, and drops that vector. This proves that +the removed row is dependent and that the transported basis remains complete. +MOVE changes chart membership but not the scalar rows or kernel. + +The first pass independently replays every original row. It validates owned +lifetimes, every COPY destination's zero row, every operation's actual common +chart, nonzero SCALE, all MOVE endpoints and nesting, and final chart boundaries. +At every INIT/CLEAR and every globally surviving cut, it explicitly checks +kernel independence and `D_t R_t = 0`; the CLEAR dependency is checked before +removal as well. All checks raise exceptions and remain active under `python -O`. + +## First two exclusions + +**Global condition.** If every vector in `D_i` has zero `p` coordinate, then +`e_p` belongs to the column space of `R_i`. Thus `R_i x_0 = e_p` for some fixed +original-input vector `x_0`. Under the uncorrected suffix, `beta_t = R_t x_0`. +Every zero-original-value combination satisfies `c^T beta_t = 0`. No first +nontrivial allowed correction can occur, so a sequence of such corrections +cannot start. This excludes 4,009 classes and leaves 24. + +**First chart-local condition.** For each of the 24 survivors, transport the +uncorrected signal through every later seam. At each seam compute the exact +intersection of `D_t` with each chart's coordinate subspace. If every resulting +covector annihilates `beta_t`, no first allowed correction exists. Testing a +basis is sufficient by linearity. This excludes another 22 classes. + +The two surviving classes have pivot 572 and cuts after events 13637 and 13639. +Their first chart-local relation is `e_778 - e_572` at chart 595. This relation +alone does not prove that a useful repair exists. + +## Dynamic affine enclosure + +For each remaining cut, maintain an affine enclosure `b_t + W_t` of all signals +reachable by any finite correction sequence before that seam. Initially +`b_i = e_p` and `W_i = {0}`. + +For every chart-kernel basis covector `c`, test its pairing with `b_t` and every +basis direction of `W_t`. If any pairing is nonzero, add all receiver directions +`e_r` at that chart to `W_t`. Repeat until no direction is added. A chart needs +activation only once per seam because all its receivers have then been added. +The loop terminates in finite dimension. The implementation explicitly checks +the resulting saturation property. + +To prove soundness, suppose the enclosure contains every reachable signal before +one inserted correction. If `c` annihilates the enclosure, that correction acts +trivially. Otherwise the saturated direction space contains its receiver `e_r`, +so `beta + q e_r(c^T beta)` remains in `b_t + W_t`. Every allowed correction is +therefore covered, including ones made possible by preceding corrections. A +fixed-word linear event transports the enclosure to another affine enclosure. +Induction over all seams proves the necessary reachability claim. There is no +claim that every enclosed point is reachable by a legal finite program. + +At each of the two cuts, the first closure adds the six receiver directions +`127, 572, 581, 582, 731, 778` at chart 595. No later saturation adds a direction. +After the suffix, the correction space has dimension 5 and its projection onto +`O` also has rank 5. The affine offset belongs to that correction space. Hence + +`(b_final + W_final) intersect {beta : beta|_O = 0} = {0}`. + +Both classes fail the necessary nonzero independent-target condition. Combined +with the preceding two exclusions, this closes all 4,033 leaking classes in +the stated model. The census also contains 390 single-leak classes; all of them +are removed by the global condition. + +## Terminal certificate and controls + +The final rational basis is included in the semantic output. A separate dense +suffix implementation checks the original pivot column. A five-by-five minor +on protected roles `116, 120, 127, 134, 176` has nonzero determinant, evaluated +by the independent Leibniz formula. Solving that minor expresses the affine +offset in the final basis, and the expression is checked in all 770 output +coordinates. The wrapper compares deterministic semantic outputs; runtime and +environment metadata are separate. + +Controls include a snapshot creating a kernel relation, an independent pivot +with no such relation, inverse transport through ADD/SCALE, rejection of COPY +over a nonzero row, rejection of zero SCALE, a stale MOVE and duplicate CLEAR, +and a singular terminal minor. The dynamic positive control has original rows +`x=y` and `u=v`: writing the first carrier `y-x` into `u` enables a later carrier +`v-u`, which then reaches a previously unavailable receiver. A concrete two-step +sequence is checked. The static test misses that opportunity, and the dynamic +closure includes it. An affine-offset negative control prevents replacing the +affine terminal question by an unconstrained homogeneous span question. + +## Open next questions and boundaries + +The result does **not** exclude programs whose combined corrections temporarily +change the original scalar map and restore it later. In particular, it is not +a theorem about arbitrary multi-time noncarrier operations. It also excludes +from its claim changed unit injections, changed original events, new or moved +paid transitions, changed owned lifetimes, new storage, and different words. +Those changes require separate source, delivery, restoration and complete +paid/target accounting. No further search along those directions is claimed +here. A useful reopening condition is a concrete changed premise with a fully +priced repair; repeating this exact fixed-word carrier search is unnecessary. diff --git a/research/p104-fixed-word-negative-screens/ENDPOINT-PROOF.md b/research/p104-fixed-word-negative-screens/ENDPOINT-PROOF.md new file mode 100644 index 0000000000..a8cfbdeed0 --- /dev/null +++ b/research/p104-fixed-word-negative-screens/ENDPOINT-PROOF.md @@ -0,0 +1,141 @@ +# Two finite scalar exclusions on the selected PR6030 word + +This proof concerns only the authenticated PR6030 scalar word. It supplies +necessary-condition failures for two specified rewrite classes. It supplies no +new kappa, complete supplier, global P104 optimum, or universal impossibility. +Every source productive endpoint and the source word remain unchanged. + +Prepared by Jonathan Capalbo (jon314159), with OpenAI Codex assistance. +Apache-2.0. Credit PR5827 and Ali Romman for the earlier endpoint-resynthesis +mechanism, PR6030 and DreamingOfClouds for the selected word, and all retained +P104/native/ownership/compiler authors. Rational elimination and linear-span +invariance are standard facts, not new general theorems. + +## Exact source semantics + +Use one independent rational coordinate for every arbitrary public input. The +770 public rows start as distinct coordinate vectors. An owned role enters at +INIT with zero scalar row under the source's retained owned contract. ADD, +SCALE and COPY act literally on these rows. MOVE changes the canonical chart +but leaves the decoded scalar row unchanged. CLEAR ends the owned lifetime. + +Both modules replay all 22,803 events and verify every final row and chart: +the prescribed 104 source-to-target additions, restoration of all other public +rows, and cleared owned roles. Thus 770 arbitrary public columns and all 799 +final roles are checked. This scalar check does not re-prove the source native +frame construction or discharge its framework assumptions. + +All operations use exact rational arithmetic. No modular rank failure, +floating-point tolerance, sampled input or heuristic span decision is used. + +## Endpoint-combination screen + +For each role, consider consecutive MOVE events + +`A -> B` and `B -> C`. + +There are 2,664 such pairs in the complete word. Exclude a pair if its receiver +is read, scaled, copied, initialized or cleared strictly between the MOVEs. +Exactly 1,900 pairs are excluded. Each of the remaining 764 has only incoming +ADDs there; none has an empty interior contact list. + +Let r be the receiver. Its first legal endpoint window runs from the slot just +after its last preceding contact to the slot just before the first MOVE. Its +second window runs from just after the second MOVE to just before its next +contact. A slot is the state before an event. The receiver has no contact in +the interior of either window, and is respectively at charts A and C. Windows +at the ends of the word use the initial or final slot. + +At each original interior ADD, capture the donor's row at that exact version, +and multiply it by the original coefficient. Their sum is Delta, the net +incoming functional. Using the sum, instead of testing each donor separately, +permits cancellation and splitting a replacement between both endpoints. + +For a window at chart F, form S_F from: + +1. every other live role's row at F at the beginning of the window; and +2. every other role's row when a MOVE arrives at F during the window. + +Retain departed or cleared values optimistically. Exclude r throughout. Each +source value has a label containing endpoint side, slot and role, so two +versions of one role cannot overwrite one another. + +**Accumulated-span lemma.** Every actual unchanged donor row available at F +anywhere in the window lies in the rational span of S_F. + +Proof: proceed through the original events. Same-chart ADD and SCALE remain +in the existing span. COPY into a zero owned role does too; INIT adds zero. +CLEAR and departure cannot enlarge the accumulated span. Every MOVE arrival +is explicitly included. No read of r occurs inside the window, so hypothetical +receiver ADDs there cannot alter the other original donor values. This proves +the inclusion by induction. + +A replacement that changes only the receiver's incoming endpoint ADDs and +replaces the two MOVEs by a direct transition must therefore satisfy + +`Delta in span_Q(S_A union S_C)`. + +This grants rational coefficients, free retention and the complete union of +the two banks. It is at least as permissive as the specified dyadic endpoint +ADD rewrite. The condition fails for all 764 pairs. In 693 cases, some original +input coordinate in Delta is absent from every generator. In the remaining +71, exact echelon elimination leaves a nonzero residue outside the row span. + +The elimination checker independently reconstructs Delta as its recorded +linear combination plus residue. The residue has zero coefficients at every +echelon pivot. A nonzero row-span vector must have a nonzero pivot coordinate, +so a nonzero such residue proves nonmembership. Complete interval records and +hashes of the exact target and generator rows are in the deterministic receipt. + +The conclusion excludes precisely these 764 endpoint-ADD rewrites of the +fixed word. It does not cover receiver scaling/recoding, modified other-role +programs, intermediate receiver reads, new owned lifetimes, changed endpoints, +new targets or cross-invocation reuse. It does not say that every positive +scalar identity would have a valid native implementation. + +PR5827 already supplies one earlier constructive example of endpoint +resynthesis, and that construction is inherited by PR6030. This new finite +screen checks the broader linear-combination condition on the remaining +eligible intervals of the current word. It does not invalidate that earlier +construction or prove its mechanism exhausted on other words. + +## Five private-query output seams + +The nominated zero-based MOVE events and roles are: + +| Event | Role | Source chart | Destination chart | +| ---: | ---: | ---: | ---: | +| 12805 | 798 | 267 | 1091 | +| 13495 | 773 | 1031 | 597 | +| 13510 | 781 | 518 | 240 | +| 13563 | 782 | 517 | 243 | +| 13592 | 779 | 477 | 1090 | + +Each is an owned nested rank-four transport. Immediately after the MOVE, test +its nonzero decoded output row against every other live role at the same chart. +Exclude the queried role itself. A second, more favorable test additionally +grants free identification of chart presentations whose binary spans agree. + +All five values fail both exact rational row-span tests. The receipt includes +the target rows, donor rows, charts, reductions and nonzero residues. This +excludes only immediate output reconstruction from those banks. It does not +exclude a changed continuation, earlier observations, a different native +monomial, new storage, or another query/target contract. No private query is +removed and no hypothetical deletion is priced. + +## Controls and reproducibility + +The endpoint controls include a two-source positive, missing-coordinate and +correlated-span negatives, a cross-bank cancellation that fails in either bank +alone, the same role at distinct endpoint versions, rejection of duplicate +version labels, and a trace whose correct net contribution depends on donor +versions and original ADD coefficients. Private-query controls include a +dyadic positive, an independent-column negative, explicit nondyadic-witness +labeling, receiver exclusion, and equal versus unequal binary-subspace +presentations. + +All checks use explicit exceptions and remain active under Python `-O`. +`endpoints.run(word)` and `private_queries.run(word)` return deterministic +JSON-ready dictionaries without file writes, local paths, runtime measurements +or environment fields. Authentication, source binding and expected-receipt +comparison are performed by the package wrapper. diff --git a/research/p104-fixed-word-negative-screens/EXPECTED.json b/research/p104-fixed-word-negative-screens/EXPECTED.json new file mode 100644 index 0000000000..c1587e8be0 --- /dev/null +++ b/research/p104-fixed-word-negative-screens/EXPECTED.json @@ -0,0 +1,55977 @@ +{ + "carrier": { + "all_tested_leak_classes_excluded": true, + "census": { + "evaluations": 8734, + "kind_leak": 4033, + "kind_pairing": 4, + "no_helper_prefix": 6275, + "pivots": 516, + "witnesses": 0 + }, + "controls": { + "affine_offset_negative": true, + "concrete_sequential_witness": true, + "determinant_positive": true, + "duplicate_clear_rejected": true, + "independent_pivot_negative": true, + "inverse_add_scale": true, + "nonzero_copy_rejected": true, + "sequential_new_carrier_positive": true, + "singular_minor_rejected": true, + "snapshot_positive": true, + "stale_move_rejected": true, + "static_screen_misses_later_carrier": true, + "zero_scale_rejected": true + }, + "dynamic_screen": { + "results": [ + { + "activations": [ + { + "added_directions": 6, + "after_event": 13637, + "charts": [ + 595 + ], + "rank_after": 6, + "rank_before": 0, + "receivers": [ + 127, + 572, + 581, + 582, + 731, + 778 + ] + } + ], + "affine_remainder": {}, + "case": { + "cut_after": 13637, + "frame": 595, + "group": [ + 3, + 127 + ], + "leak": 7, + "pivot": 572, + "ranks": [ + 1, + 8 + ] + }, + "final_basis": [ + { + "126": "1", + "127": "1", + "164": "1", + "165": "1" + }, + { + "120": "1", + "126": "1", + "138": "1", + "178": "1", + "179": "-1", + "192": "-1", + "200": "-1", + "205": "1", + "207": "1", + "242": "-1", + "243": "1", + "247": "1", + "249": "-1", + "252": "1", + "306": "2", + "311": "2", + "456": "-2", + "457": "2", + "498": "-2", + "499": "-2", + "502": "2", + "572": "-2", + "709": "-1/2" + }, + { + "116": "1", + "117": "1", + "208": "-1", + "209": "-1", + "310": "-1", + 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The coefficient-weighted original net contribution fails the rational sum of both full endpoint-window accumulated spans, with the receiver excluded. No receiver scaling, changed other-role program, new lifetime, target change or global optimum is claimed.", + "status": "PASS_ENDPOINT_COMBINATION_SCREEN" + }, + "independent_review": { + "endpoint_boundary_controls": { + "accumulated_distinct_versions_positive": true, + "intermediate_receiver_read_excluded": true, + "net_cancellation_positive_despite_unavailable_summands": true, + "receiver_scaling_excluded": true, + "word_boundary_slots_included": true + }, + "private_dual_certificates": { + "checks": [ + { + "after_event_zero_based": 12805, + "role": 798, + "same_span_bank": { + "donors_annihilated": 11, + "functional": { + "2": "1" + }, + "target_pairing": "1" + } + }, + { + "after_event_zero_based": 13495, + "role": 773, + "same_span_bank": { + "donors_annihilated": 2, + "functional": { + "2": "1" + }, + "target_pairing": "1/4" + } + }, + { + "after_event_zero_based": 13510, + "role": 781, + "same_span_bank": { + "donors_annihilated": 4, + "functional": { + "2": "1" + }, + "target_pairing": "-1" + } + }, + { + "after_event_zero_based": 13563, + "role": 782, + "same_span_bank": { + "donors_annihilated": 4, + "functional": { + "2": "1" + }, + "target_pairing": "1" + } + }, + { + "after_event_zero_based": 13592, + "role": 779, + "same_span_bank": { + "donors_annihilated": 3, + "functional": { + "4": "1" + }, + "target_pairing": "-1" + } + } + ], + "correlated_span_dual_positive": true, + "scope": "Each displayed rational functional annihilates every reported same-span donor and pairs nontrivially with the target. Source replay and exhaustive bank enumeration remain the private-query module responsibility.", + "self_as_donor_mutation_rejected": true, + "status": "PASS_FIVE_EXPLICIT_DUAL_CERTIFICATES" + }, + "review_type": "Independent AI-assisted code and mathematical-scope review; not human or formal verification.", + "status": "PASS_INDEPENDENT_CERTIFICATES_AND_BOUNDARY_CONTROLS", + "terminal": { + "checks": [ + { + "baseline_coefficients": [ + "0", + "-1", + "0", + "0", + "0" + ], + "baseline_in_span": true, + "checked_public_coordinates": 770, + "conclusion": "The only protected-zero point of this reported affine set is zero.", + "cut_after": 13637, + "determinant": "1", + "pivot": 572, + "projection_injective": true, + "protected_rows": [ + 116, + 120, + 127, + 134, + 176 + ] + }, + { + "baseline_coefficients": [ + "0", + "-1", + "0", + "0", + "0" + ], + "baseline_in_span": true, + "checked_public_coordinates": 770, + "conclusion": "The only protected-zero point of this reported affine set is zero.", + "cut_after": 13639, + "determinant": "1", + "pivot": 572, + "projection_injective": true, + "protected_rows": [ + 116, + 120, + 127, + 134, + 176 + ] + } + ], + "scope": "Rechecks the reported terminal bases, protected projection and independently propagated suffix offsets. Carrier census, kernel completeness and dynamic enclosure induction require the separate source replay and mathematical proof.", + "status": "PASS_INDEPENDENT_TERMINAL_MINOR" + }, + "terminal_controls": { + "affine_offset_omission_rejected": true, + "dependent_basis_rejected": true, + "protected_kernel_rejected": true, + "terminal_positive": true + } + }, + "private_queries": { + "cases": [ + { + "after_event_zero_based": 12805, + "destination_frame": 1091, + "donor_frames": { + "224": 1091, + "225": 1091, + "227": 1091, + "229": 1091, + "234": 1091, + "742": 1091, + "753": 1091, + "754": 1091, + "755": 1091, + "761": 1091, + "92": 1091 + }, + "donor_rows": { + "224": { + "0": "1", + "226": "-1", + "229": "1", + "230": "-1", + "233": "1", + "234": "1", + "235": "-2", + "237": "1", + "238": "1", + "239": "-2", + "27": "-1", + "57": "-1", + "7": "1", + "81": "-1", + "87": "1", + "92": "1" + }, + "225": { + "225": "1" + }, + "227": { + "0": "-1/2", + "224": "-1/2", + "230": "1/2", + 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+ "288": "1", + "29": "-1", + "292": "-1", + "296": "-1", + "30": "1", + "302": "-1", + "303": "-2", + "320": "1", + "324": "-1", + "33": "-1", + "334": "-1", + "335": "-1", + "34": "1", + "352": "1", + "356": "-1", + "36": "1", + "366": "-1", + "367": "-1", + "37": "-1", + "384": "1", + "388": "-1", + "39": "-1", + "398": "-1", + "399": "-1", + "4": "-1", + "40": "1", + "400": "1", + "401": "1", + "402": "-1", + "406": "-1", + "409": "1", + "41": "1", + "410": "1", + "411": "-2", + "413": "1", + "414": "1", + "415": "-2", + "42": "-1", + "433": "-1", + "434": "1", + "437": "1", + "438": "1", + "441": "-1", + "442": "-1", + "445": "-1", + "446": "1", + "447": "-2", + "46": "-1", + "47": "1", + "49": "1", + "5": "1", + "50": "-1", + "52": "1", + "53": "-1", + "54": "1", + "55": "-1", + "59": "1", + "60": "-1", + "62": "-1", + "63": "1", + "64": "1", + "65": "-1", + "68": "1", + "69": "-1", + "70": "1", + "71": "-1", + "73": "1", + "74": "-1", + "83": "1", + "84": "-1", + "90": "1", + "91": "-1", + "96": "1", + "97": "-1" + } + } + ], + "controls": { + "different_frame_spans_distinguished": true, + "duplicate_frame_presentations_recognized": true, + "dyadic_two_donor_positive": true, + "independent_column_negative": true, + "nondyadic_witness_labeled": true, + "receiver_excluded": true + }, + "exact_frame_candidates": 0, + "peak_live_owned": 13, + "replay": { + "arbitrary_public_columns": 770, + "final_frames_checked": true, + "final_roles_checked": 799, + "final_scalar_rows_sha256": "54bf744c6f7969b773477ae7b51d40b77dcdd9a17754db4fb814209222181a97" + }, + "same_span_relaxed_candidates": 0, + "scope": "Only the five nominated immediate output seams. All other live same-chart rows are available, with the receiver excluded. A further relaxation identifies duplicate binary-subspace presentations for free. No changed continuation, new lifetime, different native monomial, query deletion, paid improvement or global optimum is claimed.", + "status": "PASS_FIVE_PRIVATE_QUERY_OUTPUT_RECONSTRUCTION_SCREEN" + }, + "schema_version": 1, + "sources": { + "decoded_sha256": "bdb99bde29de80e90bacbfb516bd37f636b36b52d870794851d07a3ecf639c01", + "vendor_sha256": { + "vendor/pr6045/inputs/shapesplit.py": "11e8ef691b28fb4f401a8c2e97b6d462e7a004f0e215a28579d6a654b4ca3304", + "vendor/pr6045/leakfix.py": "dbbdc9ff9ebb55f1b9e832dcbe1aa5e407e7932a8d958a006bdaca6055e7f4ee" + }, + "word_path": "research/p104-helper470-twin-rung-removal/WORD.json.gz", + "word_sha256": "7834725d9e34ee846a9ccc615221ea81e0201613938afa185d2eda0c9a6c232f" + } +} diff --git a/research/p104-fixed-word-negative-screens/NOTICE.md b/research/p104-fixed-word-negative-screens/NOTICE.md new file mode 100644 index 0000000000..16c26ac367 --- /dev/null +++ b/research/p104-fixed-word-negative-screens/NOTICE.md @@ -0,0 +1,27 @@ +# Sources and credit + +This package was prepared for Jonathan Capalbo (`jon314159`) with substantial +OpenAI Codex assistance, including separate AI implementation and review agents. +Their checks are not independent human or formal-kernel approval. New code and +notes are provided under the repository's Apache-2.0 license. + +The unmodified sources in `vendor/pr6045/` are retained from Josie Elliston's +[PR6045](https://github.com/CrocSwap/integer-mult-bounds/pull/6045), head +`23abc00773a72d8e2b4e733b46c453b0f71f6368`. Its `leakfix.py` extends Nick +Petalas's [PR6040](https://github.com/CrocSwap/integer-mult-bounds/pull/6040). +The nested `inputs/shapesplit.py` retains Nick Petalas's original notice and +credits Matarener's PR5994 and flyingviper's PR5718. All source notices remain +in their original files. Exact source paths, blob identities and SHA-256 pins +are in `VENDOR.json`; no pending commit must be fetched to run this package. + +The unchanged PR6030 word is DreamingOfClouds's P104 helper-470 construction, +on the accumulated work identified by the selected source's own notices. +It remains a declared repository input rather than a duplicate archive. +The endpoint experiment follows the unread-path construction in PR5827. +PR6019 provides related abstract chronological repair theory; the present +proof is a source-specific affine enclosure and does not import a new native +repair construction from that theory. + +The repository package scaffold and replay tooling are Douglas Colkitt's work +with the attribution retained in their original files. No predecessor package, +selected record, shared replay tool or historical certificate is modified. diff --git a/research/p104-fixed-word-negative-screens/README.md b/research/p104-fixed-word-negative-screens/README.md new file mode 100644 index 0000000000..51774daa4a --- /dev/null +++ b/research/p104-fixed-word-negative-screens/README.md @@ -0,0 +1,102 @@ +# Fixed-word negative screens on PR6030 + +**Three scoped negative results; no new kappa.** The unchanged input is the +PR6030 word selected at main `721c03822c421b7f7fcbb2598993b947c4d88419`, where +conditional kappa is `0.003125804`. This package does not change that selection. + +## Scope and evidence + +| Tested domain | Exact result | +| --- | --- | +| 4,033 leaking PR5718-shape unit-injection classes on PR6030 | 4,009 fail the global dependency condition; 22 of the remaining 24 have no first same-chart combination carrier; the final two fail dynamic closure. | +| Sequential corrections in those two surviving cases | Earlier corrections may enable later carriers. Even this enlarged rational affine enclosure can clear protected outputs only by erasing the entire new-helper signal. | +| All 764 adjacent MOVE intervals with only incoming ADDs | No coefficient-weighted net contribution belongs to the sum of both complete legal endpoint-window spans: 693 missing-coordinate exclusions and 71 exact elimination exclusions. | +| Five nominated private rank-four query outputs | No reconstruction from other live destination-chart rows at the immediate output seam, even allowing equivalent binary-frame presentations for free. | + +[PR6045](https://github.com/CrocSwap/integer-mult-bounds/pull/6045) excludes +single-field carriers but leaves combination carriers open. Our low-dimensional +kernel filter and dynamic affine enclosure address a specified extension of +that question. This includes opportunities enabled by earlier corrections, +which a screen of the uncorrected trajectory alone would miss. The final +protected projection has rank five and an independently checked minor of +determinant `1` for both cuts. See [CARRIER-PROOF.md](CARRIER-PROOF.md). + +The endpoint test extends the mechanism of +[PR5827](https://github.com/CrocSwap/integer-mult-bounds/pull/5827). It allows +arbitrary rational combinations across both endpoint windows, different donor +versions, and cancellations among the original incoming ADDs. It optimistically +retains departed donor values. The five private-output tests are a separate, +narrow necessary condition. See [ENDPOINT-PROOF.md](ENDPOINT-PROOF.md). + +These statements hold only for their fixed-word models. They do not exclude +programs that temporarily change the original scalar map, changed unit +injections, other-role continuations, receiver scaling in the endpoint model, +new paid MOVEs or owned lifetimes, changed cut eligibility, or new architectures. +No native implementation, improved invoice, full caller, compiler, precision or +outer-transfer claim follows. The five inherited framework assumptions remain. + +The deterministic full receipts are in `EXPECTED.json`; replay reconstructs +them and fails on any difference. Source and catalogue provenance are in +[SOURCES.json](SOURCES.json). The selected record is historical provenance, so +a later selected result does not silently retarget these tests. The only +external live input is the unchanged PR6030 `WORD.json.gz`. Pending predecessor +code is retained byte-for-byte inside this package and authenticated through +[VENDOR.json](VENDOR.json); no unmerged Git commit or network request is needed +for a mathematical replay. + +## Reproduce + +From the repository root, with Python 3.12 and its standard library: + +```sh +python3.12 -B scripts/research_package.py --package research/p104-fixed-word-negative-screens --check-only +python3.12 -B scripts/research_package.py --package research/p104-fixed-word-negative-screens +``` + +The registered replay runs both normal and optimized isolated interpreters, +with a 300-second limit per command. All new guards use explicit exceptions. +It checks the complete arbitrary-input scalar boundary, actual frames and +owned lifetimes, baseline kernel premises, scientific positive/negative controls, +and an independently computed terminal certificate. No full historical +supplier/native replay is required or claimed for these necessary exclusions. + +For a source export containing this package and its declared word input: + +```sh +python3.12 -I -B research/p104-fixed-word-negative-screens/verify.py +python3.12 -I -O -B research/p104-fixed-word-negative-screens/verify.py +``` + +Direct runs also isolate bytecode caches before loading research dependencies. +`--output NEW_FILE.json` optionally writes the checked semantic receipt. Neither +command overwrites scientific inputs or silently regenerates `EXPECTED.json`. +The optional full-Git-history publication audit is separate from the source +export replay; it cannot be claimed from a shallow checkout. + +The registered checks passed on CPython 3.12.3 under Linux, including normal +and optimized replay, 27 module controls, independently implemented terminal +and dual certificates, a clean exported-package replay, and rejection of +altered word/vendor bytes and a forged receipt. Both ordinary replays produced +the same semantic SHA-256. Exact coverage and unrun obligations are recorded +in [VALIDATION.json](VALIDATION.json). + +## Open next questions + +The structured questions and blockers are in [TASK.json](TASK.json). A useful +successor must supply a concrete changed premise: for example, a correction +that temporarily changes the original scalar map and restores it, or an altered +receiver/query continuation outside these windows. Start with one explicit +source-bound chronological word and arbitrary-input/frame/restoration checks, +then charge its complete paid and productive invoice. No such candidate is +provided here, and no further exploratory search is warranted by these results +alone. The assigned scope was refined from the revision-8 `p104-side-correction` +card to the newer selected PR6030 word; that change is recorded in TASK.json. + +## Credit + +Prepared for Jonathan Capalbo (`jon314159`) with substantial OpenAI Codex +assistance, including separate implementation and review agents. These are +AI-assisted checks, not independent human approval or formal verification. +See [NOTICE.md](NOTICE.md) for Josie Elliston, Nick Petalas, Matarener, +flyingviper, DreamingOfClouds and inherited source attribution. New work is +Apache-2.0; frozen predecessors and the selected construction are unchanged. diff --git a/research/p104-fixed-word-negative-screens/SOURCES.json b/research/p104-fixed-word-negative-screens/SOURCES.json new file mode 100644 index 0000000000..c46dd7611f --- /dev/null +++ b/research/p104-fixed-word-negative-screens/SOURCES.json @@ -0,0 +1,24 @@ +{ + "schema_version": 1, + "base_commit": "721c03822c421b7f7fcbb2598993b947c4d88419", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "d59b5035e7b4cbaa9d688a1d32dd0d6eb79c466a", + "sha256": "9b8d0eea95b3bf0dfcb7938a732a6439b87a2685dec2a5ab9e525b3b34debbfa" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "3404fbdd5e7529a0674eef26114b5071e4586cec", + "sha256": "ead6cdc9d0af6d58e8a49744d8ec8c7c15e13d2ba93c276c434bcf9b51b93a81" + }, + { + "path": "research/p104-helper470-twin-rung-removal/WORD.json.gz", + "usage": "input", + "git_blob": "22f9ab02d1b73ea0aa4b07ce445a14cc2602c760", + "sha256": "7834725d9e34ee846a9ccc615221ea81e0201613938afa185d2eda0c9a6c232f" + } + ] +} diff --git a/research/p104-fixed-word-negative-screens/TASK.json b/research/p104-fixed-word-negative-screens/TASK.json new file mode 100644 index 0000000000..7389f77584 --- /dev/null +++ b/research/p104-fixed-word-negative-screens/TASK.json @@ -0,0 +1,123 @@ +{ + "schema_version": 1, + "task_id": "p104-side-correction", + "priority_revision": 8, + "base_commit": "721c03822c421b7f7fcbb2598993b947c4d88419", + "original_card": { + "id": "p104-side-correction", + "question": "Can joint helper bases and a legal causal split improve the complete P104 productive/paid invoice?", + "starting_points": [ + "docs/research/current-priorities.md", + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "docs/research/pr-intake-evidence/pr5599-completion/PROOF-REVIEW.md", + "research/p104-helper-subspace-splits/README.md", + "research/dyadic-helper-channel-capacity/README.md" + ], + "methods": [ + "Construct and independently check one source-bound instance of the stated first experiment.", + "Seek an exact counterexample or target-specific complete-budget obstruction to that same proposed change." + ], + "acceptance_gate": "An exact arbitrary-input identity, source/target frame availability and restoration at the chosen cut, plus the complete channel+correction+idle/hosting bill or an explicit favorable bound. The native channel alone is not a supplier. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_selected_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read revision 8, the selected review and live exact-source handoffs. Then follow this card's bounded first_experiment.", + "scope": "Source-bound orientation only, not a supplier replay or theorem proof." + }, + "first_experiment": "Start with the selected #5599 emitted word and review pending #5718 distinct input/output bases plus #5717/#5719 coverage before claiming work. Pick one uncovered source word, helper group and cut region. Prove the arbitrary-input relation and legal entry/exit corrections, then compare full target and paid profiles. Reject if completion, owned lifetimes or consumer costs repay the gain. A static pairing rank alone is not a physical split.", + "bottleneck_link": "Judge the actual current supplier contract and complete signed target/paid bill; frozen-profile ceilings require an applicability proof.", + "allowed_variations": [ + "One exact source head, helper/cut region or quantified proposition and changed hypothesis; check live handoffs first. Different seeds are not different scopes." + ], + "scope_change_triggers": [ + "Changing source head, helper/cut domain, operation alphabet or caller boundary without recording the new scope.", + "Treating an archived proposal or local numerical pass as complete supplier admission." + ], + "overlap_terms": [ + "P104", + "helper basis", + "helper split", + "5718", + "dyadic capacity" + ], + "existing_checks": [ + { + "scope": "PR #4133: literal-slot defect", + "evidence": "research/p104-literal-slot-defect/README.md", + "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.", + "status": "author-checked", + "source_commit": "88666f1dee93fbd85b31fd5d6f91a219e111b5f4", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4136: uniform commutation gap", + "evidence": "research/p104-uniform-commutation-gap/README.md", + "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.", + "status": "author-checked", + "source_commit": "281ce601a8be9db470de630759179c23e1dfaa88", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4140: uniform encoding gap", + "evidence": "research/p104-uniform-encoding-gap/README.md", + "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.", + "status": "author-checked", + "source_commit": "de25c6525aa866962309df5d107b32d55e6e5628", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4153: source-chart shortcut exhausts its optimistic allowance", + "evidence": "research/p104-source-chart-shortcut/README.md", + "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.", + "status": "author-checked", + "source_commit": "9123241fea53df77e51ffe30d9aca1625d4bf3a8", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4154: fiber-tag seam mismatch", + "evidence": "research/p104-fiber-tag-seam/README.md", + "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.", + "status": "author-checked", + "source_commit": "4ffcdaee5d6255a9cea1fe53a5424435068089d0", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "Selected PR5599: complete helper-subspace construction and independent caller replay; five framework assumptions remain.", + "evidence": "docs/research/pr-intake-evidence/pr5599-completion/PROOF-REVIEW.md", + "remaining": "The next experiment must identify uncovered source-specific work. Successor archive intake does not transfer this admission.", + "status": "reviewed", + "source_commit": "09dd0965711ca7eeb169057a420abab1c9052137", + "selected_record_sha256": "2a0220e866417774606e0f991e41b9c1d26b1f43b97857238cf478dbc7d330b5" + } + ] + }, + "scope_status": "changed", + "actual_scope": "Publish exact finite exclusions for zero-original-value sequential combination corrections, both-window additive endpoint relocation, and five immediate private-query reconstruction seams on the pinned PR6030 word.", + "scope_change_reason": "The user assigned a source-specific follow-up to PR6030 and PR6045; the revision8 card still names PR5599. No random task was drawn. The results preserve the fixed word and provide negative scalar necessary conditions, not a new supplier.", + "bottleneck_link": "Zero-paid changes would improve the selected complex bill; these screens close explicitly bounded ways of attempting them. No paid or target invoice is changed.", + "budget_minutes": 60, + "stop_rule": "All nominated tests are negative; publish their exact scope and reproducible checks without extending the search.", + "outcome": "negative-result", + "evidence": "EXPECTED.json, CARRIER-PROOF.md, ENDPOINT-PROOF.md and registered normal/optimized replay.", + "author": "Jonathan Capalbo (jon314159), with OpenAI Codex assistance", + "ai_assistance": "Substantial OpenAI Codex assistance, including separate implementation and review agents; not independent human or formal verification.", + "open_questions": [ + { + "question": "Can a correction sequence that temporarily changes the original scalar map give a legal improved construction?", + "why_it_matters": "Such programs are outside the fixed-original-map carrier exclusion.", + "first_step": "Supply one concrete source-bound cut and complete chronological correction word; verify arbitrary inputs, all frames and restoration before pricing.", + "blocked_by": "No concrete candidate is supplied; new paid operations, storage and target changes need a complete invoice." + }, + { + "question": "Can changing receiver contacts or query continuation yield a paid improvement outside the fixed endpoint windows?", + "why_it_matters": "Endpoint and immediate-output exclusions do not cover altered continuations.", + "first_step": "Provide one explicit changed continuation with legal contacts and unchanged or fully charged targets.", + "blocked_by": "No such continuation was found; these results justify no further search without a new witness." + } + ] +} diff --git a/research/p104-fixed-word-negative-screens/VALIDATION.json b/research/p104-fixed-word-negative-screens/VALIDATION.json new file mode 100644 index 0000000000..25c65ca9f0 --- /dev/null +++ b/research/p104-fixed-word-negative-screens/VALIDATION.json @@ -0,0 +1,26 @@ +{ + "status": "PASS_REGISTERED_RESEARCH_PACKAGE", + "date_local": "2026-10-28", + "environment": "CPython3.12.3 on Ubuntu via WSL; standard library only", + "command": ["python3", "-B", "scripts/research_package.py", "--package", "research/p104-fixed-word-negative-screens"], + "metadata_and_provenance_pins": "PASS", + "normal_isolated_replay": "PASS", + "optimized_isolated_replay": "PASS", + "semantic_receipt_sha256": "e9de43aef960895096b75c5e057ee0119276cdbdbbbc81fe698be60dae61f683", + "scientific_module_controls": 27, + "independent_checks": [ + "Dense suffix replay and exact protected minor/affine certificate for both surviving cuts", + "Affine-offset, protected-kernel and dependent-basis rejection controls", + "Endpoint receiver-contact, net-cancellation, time-specific value and boundary controls", + "Explicit dual separating functionals for all five private-query output banks" + ], + "cold_export": "PASS: only this package and the declared WORD input, without Git objects or scratch dependencies", + "package_rejection_controls": { + "changed_word_bytes": "PASS_REJECTED", + "changed_frozen_vendor_bytes": "PASS_REJECTED", + "forged_semantic_receipt": "PASS_REJECTED" + }, + "full_source_history_audit": "Not run: shallow checkout. The base commit is available locally; pending predecessor code is included byte-for-byte and cold-export replay passed.", + "scope": "Exact scalar necessary-condition exclusions and package integrity only. No native/compiler/caller/outer replay, new kappa, maintainer admission, independent human approval or formal-kernel verification is claimed.", + "assistance": "OpenAI Codex implementation and separate AI-assisted code/mathematical-scope review. Final GitHub review is anchored to the submitted commit." +} diff --git a/research/p104-fixed-word-negative-screens/VENDOR.json b/research/p104-fixed-word-negative-screens/VENDOR.json new file mode 100644 index 0000000000..6cb3711dc8 --- /dev/null +++ b/research/p104-fixed-word-negative-screens/VENDOR.json @@ -0,0 +1,24 @@ +{ + "schema_version": 1, + "scope": "Byte-exact committed exports of pending predecessor inputs; no external Git ancestry required for replay.", + "files": [ + { + "path": "vendor/pr6045/leakfix.py", + "source_path": "research/p104-pr5718-leak-correction/leakfix.py", + "source_head": "23abc00773a72d8e2b4e733b46c453b0f71f6368", + "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/23abc00773a72d8e2b4e733b46c453b0f71f6368/research/p104-pr5718-leak-correction/leakfix.py", + "sha256": "dbbdc9ff9ebb55f1b9e832dcbe1aa5e407e7932a8d958a006bdaca6055e7f4ee", + "git_blob": "c54c16899a22f83b9b982159ee941c3eb9e18bdc", + "bytes": 17726 + }, + { + "path": "vendor/pr6045/inputs/shapesplit.py", + "source_path": "research/p104-pr5718-leak-correction/inputs/shapesplit.py", + "source_head": "23abc00773a72d8e2b4e733b46c453b0f71f6368", + "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/23abc00773a72d8e2b4e733b46c453b0f71f6368/research/p104-pr5718-leak-correction/inputs/shapesplit.py", + "sha256": "11e8ef691b28fb4f401a8c2e97b6d462e7a004f0e215a28579d6a654b4ca3304", + "git_blob": "6eedc849e7b9503d2b88aea4fc6497004adcb45e", + "bytes": 7779 + } + ] +} diff --git a/research/p104-fixed-word-negative-screens/VERIFY.json b/research/p104-fixed-word-negative-screens/VERIFY.json new file mode 100644 index 0000000000..2ffd964fdd --- /dev/null +++ b/research/p104-fixed-word-negative-screens/VERIFY.json @@ -0,0 +1,42 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/p104-helper470-twin-rung-removal/WORD.json.gz" + ], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 300, + "checks": "All4033 leaking unit-injection classes,764 joint endpoint intervals,five output seams,baseline premises,positive/negative controls and independent terminal certificate." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 300, + "checks": "Same exact semantic receipt with optimization; explicit checks remain active." + }, + { + "argv": [ + "{python}", + "-I", + "-B", + "{package}/package_controls.py" + ], + "timeout_seconds": 600, + "checks": "Cold self-contained exported-package replay plus rejection of changed word, changed frozen vendor and forged semantic receipt, all child runs under optimization." + } + ] +} diff --git a/research/p104-fixed-word-negative-screens/carrier.py b/research/p104-fixed-word-negative-screens/carrier.py new file mode 100644 index 0000000000..7c41ed900e --- /dev/null +++ b/research/p104-fixed-word-negative-screens/carrier.py @@ -0,0 +1,538 @@ +"""Exact fixed-word combination-carrier screens. Apache-2.0. + +API: run(word, vendor_path) -> deterministic JSON-compatible dictionary. +vendor_path contains the pinned PR6045 leakfix.py and inputs/shapesplit.py. +The caller authenticates source bytes before calling this module. No files are +written, and no scratch-tree imports, optional packages, or subprocesses are used. +See CARRIER-PROOF.md for the mathematical scope and predecessor attribution. +""" + +from collections import defaultdict +from fractions import Fraction as Q +from itertools import permutations +from pathlib import Path +import importlib.util +import sys + + +def need(condition, message): + if not condition: + raise ValueError(message) + + +def add(destination, source, coefficient): + for role, value in source.items(): + new = destination.get(role, Q(0)) + coefficient * value + if new: + destination[role] = new + else: + destination.pop(role, None) + + +def dot(left, right): + return sum(value * right.get(role, Q(0)) for role, value in left.items()) + + +def serial(vector): + return {str(role): str(value) for role, value in sorted(vector.items())} + + +class Span: + """Sparse rational echelon basis, with an optional coordinate ordering.""" + + def __init__(self, vectors=(), order=None): + self.pivots = {} + self.order = order + for vector in vectors: + self.insert(vector) + + def reduce(self, vector): + vector = dict(vector) + while vector: + pivot = min(vector) if self.order is None else min(vector, key=self.order.__getitem__) + if pivot not in self.pivots: + return vector, pivot + add(vector, self.pivots[pivot], -vector[pivot]) + return vector, None + + def insert(self, vector): + vector, pivot = self.reduce(vector) + if pivot is None: + return False + divisor = vector[pivot] + self.pivots[pivot] = {role: value / divisor for role, value in vector.items()} + return True + + +def load_vendor(directory): + """Load exactly this vendor directory, without trusting a prior module cache.""" + directory = Path(directory) + shapes_path = directory / "inputs" / "shapesplit.py" + leak_path = directory / "leakfix.py" + need(shapes_path.is_file() and leak_path.is_file(), "missing carrier vendor sources") + shapes_spec = importlib.util.spec_from_file_location("_carrier_shapesplit", shapes_path) + need(shapes_spec is not None and shapes_spec.loader is not None, "cannot load shapesplit") + shapes = importlib.util.module_from_spec(shapes_spec) + shapes_spec.loader.exec_module(shapes) + # PR6045 looks up this historical name. Scope that cache entry to this load. + cache_key = "pr6040_shapesplit" + previous = sys.modules.get(cache_key) + sys.modules[cache_key] = shapes + try: + leak_spec = importlib.util.spec_from_file_location("_carrier_leakfix", leak_path) + need(leak_spec is not None and leak_spec.loader is not None, "cannot load leakfix") + leak = importlib.util.module_from_spec(leak_spec) + leak_spec.loader.exec_module(leak) + need(leak.SS is shapes, "vendor module binding mismatch") + finally: + if previous is None: + sys.modules.pop(cache_key, None) + else: + sys.modules[cache_key] = previous + return leak + + +def transport(vector, event): + """Primal transport, including optimistic deletion at existing owned CLEARs.""" + operation, role = event[:2] + if operation in ("INIT", "CLEAR"): + vector.pop(role, None) + elif operation == "COPY": + value = Q(event[-2]) * vector.get(event[2], Q(0)) + vector.pop(role, None) + if value: + vector[role] = value + elif operation == "ADD": + add(vector, {role: Q(1)}, Q(event[-2]) * vector.get(event[2], Q(0))) + elif operation == "SCALE": + if role in vector: + vector[role] *= Q(event[-2]) + else: + need(operation == "MOVE", "unknown primal operation") + + +class Baseline: + """Original rows, their complete left kernel, and actual chart membership. + + The first pass tracks rows and explicitly validates baseline premises. + Later passes reuse the same authenticated word and transport its kernel. + """ + + def __init__(self, word, frame_spans, track_rows=False): + self.n = word["public"] + self.total = self.n + word["owned_fields"] + need(len(word["initial"]) == self.n == len(word["final"]), "boundary length mismatch") + self.frames = frame_spans + self.current = list(word["initial"]) + [None] * (self.total - self.n) + self.at = defaultdict(set) + for role, chart in enumerate(self.current): + if chart is not None: + need(0 <= chart < len(self.frames), "invalid initial chart") + self.at[chart].add(role) + self.rows = [{role: Q(1)} if role < self.n else {} for role in range(self.total)] if track_rows else None + self.kernel = [] + self.owned = set() + self.peak = 0 + self.checks = 0 + self.copies_checked = 0 + self.lifetimes = 0 + self.nonzero_clears = 0 + self.dirty = True + self.pure_cache = [] + + def check_kernel(self): + need(len(Span(self.kernel).pivots) == len(self.kernel), "dependent kernel basis") + if self.rows is not None: + for covector in self.kernel: + image = {} + for role, coefficient in covector.items(): + need(self.current[role] is not None, "kernel uses dead register") + add(image, self.rows[role], coefficient) + need(not image, "kernel does not annihilate original rows") + self.checks += 1 + + def step(self, event): + operation, role = event[:2] + need(type(role) is int and 0 <= role < self.total, "invalid role") + if operation == "INIT": + need(len(event) == 3 and role >= self.n and self.current[role] is None, "invalid INIT") + chart = event[2] + need(type(chart) is int and 0 <= chart < len(self.frames), "invalid INIT chart") + self.owned.add(role) + self.current[role] = chart + self.at[chart].add(role) + self.kernel.append({role: Q(1)}) + if self.rows is not None: + self.rows[role] = {} + self.lifetimes += 1 + self.dirty = True + elif operation == "CLEAR": + need(len(event) == 3 and role in self.owned and self.current[role] == event[2], "invalid CLEAR") + if self.rows is not None: + self.check_kernel() + self.nonzero_clears += bool(self.rows[role]) + choices = [j for j, vector in enumerate(self.kernel) if vector.get(role)] + need(bool(choices), "CLEAR removes an independent original row") + vector = self.kernel.pop(choices[0]) + divisor = vector[role] + vector = {key: value / divisor for key, value in vector.items()} + for other in self.kernel: + if other.get(role): + add(other, vector, -other[role]) + self.at[self.current[role]].remove(role) + self.current[role] = None + self.owned.remove(role) + if self.rows is not None: + self.rows[role] = {} + self.dirty = True + elif operation in ("ADD", "COPY"): + need(len(event) == 5, "invalid binary operation") + source = event[2] + need(type(source) is int and 0 <= source < self.total and source != role, "invalid source") + need(self.current[role] is not None and self.current[role] == self.current[source] == event[-1], "binary operation lacks common chart") + coefficient = Q(event[-2]) + if operation == "COPY": + need(role in self.owned, "COPY destination is not owned") + if self.rows is not None: + need(not self.rows[role], "COPY overwrites a nonzero original row") + self.copies_checked += 1 + if self.rows is not None: + add(self.rows[role], self.rows[source], coefficient) + for covector in self.kernel: + if covector.get(role): + add(covector, {source: Q(1)}, -coefficient * covector[role]) + self.dirty = True + elif operation == "SCALE": + need(len(event) == 4 and self.current[role] is not None and self.current[role] == event[-1], "invalid SCALE") + coefficient = Q(event[-2]) + need(bool(coefficient), "zero SCALE") + if self.rows is not None: + self.rows[role] = {key: coefficient * value for key, value in self.rows[role].items()} + for covector in self.kernel: + if role in covector: + covector[role] /= coefficient + self.dirty = True + else: + need(operation == "MOVE" and len(event) == 5, "unknown operation") + old, new = event[2:4] + need(self.current[role] is not None and self.current[role] == old, "stale MOVE source") + need(type(new) is int and 0 <= new < len(self.frames), "invalid MOVE destination") + need(self.frames[old] <= self.frames[new] or self.frames[new] <= self.frames[old], "nonnested MOVE") + self.at[old].remove(role) + self.at[new].add(role) + self.current[role] = new + if any(role in covector for covector in self.kernel): + self.dirty = True + need(len(self.kernel) == len(self.owned), "kernel dimension differs from live owned count") + self.peak = max(self.peak, len(self.kernel)) + if operation in ("INIT", "CLEAR"): + self.check_kernel() + + def finish(self, word): + need(not self.owned and not self.kernel, "unfinished owned lifetimes") + need(self.current[:self.n] == word["final"], "final chart mismatch") + + def chart_kernel(self, shapes): + if self.dirty: + by_chart = defaultdict(set) + for role in {role for vector in self.kernel for role in vector}: + need(self.current[role] is not None, "dead role in kernel support") + by_chart[self.current[role]].add(role) + self.pure_cache = [] + for chart in sorted(by_chart): + support = by_chart[chart] + for _, image in shapes.pure_subspace(self.kernel, range(len(self.kernel)), support): + need(bool(image) and set(image) <= support, "invalid chart-kernel intersection") + self.pure_cache.append((chart, image)) + self.dirty = False + return self.pure_cache + + +def case_id(case): + return [case["cut_after"], case["frame"], case["pivot"]] + + +def brief(case): + result = {key: case[key] for key in ("cut_after", "frame", "pivot", "group", "ranks", "leak")} + result["group"] = list(case["group"]) + return result + + +def global_screen(word, cases, shapes): + state = Baseline(word, shapes.spans(word), track_rows=True) + at_cut = defaultdict(list) + for case in cases: + at_cut[case["cut_after"]].append(case) + excluded, survived, witnesses = [], [], [] + for index, event in enumerate(word["program"]): + state.step(event) + check_cut = False + for case in at_cut.get(index, ()): + witness = next((v for v in state.kernel if v.get(case["pivot"])), None) + if witness is None: + excluded.append(case_id(case)) + else: + survived.append(case) + witnesses.append(dict(brief(case), dependency=serial(witness))) + check_cut = True + if check_cut: + state.check_kernel() + state.finish(word) + need(len(excluded) + len(survived) == len(cases), "unvisited global-screen cut") + return survived, dict( + excluded_count=len(excluded), excluded_ids=excluded, + surviving_count=len(survived), survivors=witnesses, + peak_kernel_dimension=state.peak, kernel_snapshots_checked=state.checks, + copy_zero_checks=state.copies_checked, owned_lifetimes=state.lifetimes, + nonzero_owned_clears=state.nonzero_clears, + ) + + +def first_carrier_screen(word, cases, shapes): + state = Baseline(word, shapes.spans(word)) + starts = defaultdict(list) + for key, case in enumerate(cases): + starts[case["cut_after"]].append(key) + signals, found = {}, {} + for index, event in enumerate(word["program"]): + for signal in signals.values(): + transport(signal, event) + state.step(event) + for key in starts.get(index, ()): + signals[key] = {cases[key]["pivot"]: Q(1)} + if not signals: + continue + pure = state.chart_kernel(shapes) + for key, signal in signals.items(): + if key in found: + continue + for chart, covector in pure: + pairing = dot(covector, signal) + if pairing: + found[key] = dict(case=brief(cases[key]), after_event=index, chart=chart, + beta_pairing=str(pairing), combination=serial(covector)) + break + state.finish(word) + need(len(signals) == len(cases), "unvisited first-carrier cut") + return [cases[key] for key in sorted(found)], dict( + tested=len(cases), excluded_count=len(cases)-len(found), + excluded_ids=[case_id(case) for key, case in enumerate(cases) if key not in found], + surviving_count=len(found), survivors=[found[key] for key in sorted(found)], + ) + + +def saturate(offset, directions, pure, membership): + """Smallest affine enclosure invariant under relaxed current-chart controls.""" + span = Span(directions) + activated, receivers = set(), set() + changed, added = True, 0 + while changed: + changed = False + for chart, covector in pure: + if chart in activated: + continue + if dot(covector, offset) or any(dot(covector, vector) for vector in span.pivots.values()): + activated.add(chart) + for role in sorted(membership[chart]): + receivers.add(role) + if span.insert({role: Q(1)}): + added += 1 + changed = True + for chart, covector in pure: + if dot(covector, offset) or any(dot(covector, vector) for vector in span.pivots.values()): + need(all(not span.reduce({role: Q(1)})[0] for role in membership[chart]), "unsaturated affine enclosure") + return list(span.pivots.values()), activated, receivers, added + + +def determinant(matrix): + """Independent Leibniz formula; used only for small terminal certificates.""" + size = len(matrix) + need(size <= 8 and all(len(row) == size for row in matrix), "terminal minor is not small and square") + result = Q(0) + for permutation in permutations(range(size)): + term = Q((-1) ** sum(permutation[i] > permutation[j] for i in range(size) for j in range(i+1, size))) + for row, column in enumerate(permutation): + term *= matrix[row][column] + result += term + return result + + +def dense_suffix(word, cut, pivot): + """Separate dense primal implementation for the final-column certificate.""" + signal = [Q(0)] * (word["public"] + word["owned_fields"]) + signal[pivot] = Q(1) + for event in word["program"][cut+1:]: + operation, role = event[:2] + if operation in ("INIT", "CLEAR"): + signal[role] = Q(0) + elif operation == "COPY": + signal[role] = Q(event[-2]) * signal[event[2]] + elif operation == "ADD": + signal[role] += Q(event[-2]) * signal[event[2]] + elif operation == "SCALE": + signal[role] *= Q(event[-2]) + else: + need(operation == "MOVE", "unknown dense suffix operation") + need(not any(signal[word["public"]:]), "nonzero terminal owned signal") + return signal[:word["public"]] + + +def solve_square(matrix, rhs): + rows = [list(row)+[value] for row, value in zip(matrix, rhs)] + for column in range(len(matrix)): + candidates = [i for i in range(column, len(matrix)) if rows[i][column]] + need(bool(candidates), "singular terminal minor") + pivot = candidates[0] + rows[column], rows[pivot] = rows[pivot], rows[column] + divisor = rows[column][column] + rows[column] = [value/divisor for value in rows[column]] + for i in range(len(matrix)): + if i != column: + coefficient = rows[i][column] + rows[i] = [x-coefficient*y for x, y in zip(rows[i], rows[column])] + return [row[-1] for row in rows] + + +def terminal_certificate(word, case, basis, protected_roles, offset): + matrix = [[vector.get(role, Q(0)) for vector in basis] for role in protected_roles] + det = determinant(matrix) + need(bool(det), "terminal protected projection is not injective") + dense = dense_suffix(word, case["cut_after"], case["pivot"]) + need(all(dense[role] == offset.get(role, Q(0)) for role in range(word["public"])), "sparse/dense suffix mismatch") + coefficients = solve_square(matrix, [dense[role] for role in protected_roles]) + need(all(sum(coefficient*vector.get(role, Q(0)) for coefficient, vector in zip(coefficients, basis)) == dense[role] + for role in range(word["public"])), "offset is not in terminal correction span") + return dict(protected_roles=protected_roles, determinant=str(det), + baseline_coefficients=[str(value) for value in coefficients], + checked_output_coordinates=word["public"]) + + +def dynamic_screen(word, cases, shapes): + state = Baseline(word, shapes.spans(word)) + starts = defaultdict(list) + for key, case in enumerate(cases): + starts[case["cut_after"]].append(key) + active = {} + for index, event in enumerate(word["program"]): + for candidate in active.values(): + transport(candidate["offset"], event) + for direction in candidate["directions"]: + transport(direction, event) + state.step(event) + for key in starts.get(index, ()): + active[key] = dict(offset={cases[key]["pivot"]: Q(1)}, directions=[], activations=[], maximum_rank=0) + if not active: + continue + pure = state.chart_kernel(shapes) + for candidate in active.values(): + before = len(candidate["directions"]) + directions, charts, receivers, added = saturate(candidate["offset"], candidate["directions"], pure, state.at) + candidate["directions"] = directions + candidate["maximum_rank"] = max(candidate["maximum_rank"], len(directions)) + if added: + candidate["activations"].append(dict(after_event=index, charts=sorted(charts), receivers=sorted(receivers), + rank_before=before, rank_after=len(directions), added_directions=added)) + state.finish(word) + need(len(active) == len(cases), "unvisited dynamic cut") + results = [] + for key, case in enumerate(cases): + candidate = active[key] + outside = case["outside"] + order = {role: index for index, role in enumerate(sorted(outside)+[r for r in range(word["public"]) if r not in outside])} + need(all(role < word["public"] for vector in [candidate["offset"]]+candidate["directions"] for role in vector), "terminal owned support") + span = Span(candidate["directions"], order) + remainder, pivot = span.reduce(candidate["offset"]) + free = [vector for p, vector in span.pivots.items() if p not in outside] + if pivot in outside: + outcome = "outside_unreachable" + elif not remainder and not free: + outcome = "only_zero_signal" + else: + outcome = "productive_affine_relaxation_survives" + need(candidate["offset"] == case["dall"], "vendor/primal suffix column mismatch") + protected_roles = sorted(p for p in span.pivots if p in outside) + basis = list(span.pivots.values()) + certificate = terminal_certificate(word, case, basis, protected_roles, candidate["offset"]) if outcome == "only_zero_signal" else None + results.append(dict(case=brief(case), outcome=outcome, maximum_correction_rank=candidate["maximum_rank"], + final_correction_rank=len(basis), protected_projection_rank=len(protected_roles), + zero_protected_dimension=len(free), affine_remainder=serial(remainder), + activations=candidate["activations"], final_basis=[serial(v) for v in basis], + independent_terminal=certificate)) + return dict(tested=len(cases), results=results) + + +def expect_rejection(function, message): + try: + function() + except ValueError: + return + raise ValueError(message) + + +def controls(): + """Discriminating algebra and baseline guards, all active under python -O.""" + toy = dict(public=2, owned_fields=1, initial=[0, 0], final=[0, 0]) + frames = [frozenset({0}), frozenset({0, 1})] + state = Baseline(toy, frames, track_rows=True) + state.step(["INIT", 2, 0]) + need(not any(v.get(0) for v in state.kernel), "independent pivot incorrectly dependent") + state.step(["COPY", 2, 0, "1", 0]) + state.check_kernel() + need(any(v.get(0) for v in state.kernel) and not any(v.get(1) for v in state.kernel), "snapshot dependency control failed") + state.step(["ADD", 0, 1, "2", 0]) + state.step(["SCALE", 1, "-2", 0]) + state.check_kernel() + need(any(v.get(1) for v in state.kernel), "inverse kernel transport control failed") + expect_rejection(lambda: state.step(["COPY", 2, 0, "1", 0]), "nonzero COPY accepted") + expect_rejection(lambda: state.step(["SCALE", 1, "0", 0]), "zero SCALE accepted") + expect_rejection(lambda: state.step(["MOVE", 0, 1, 0, False]), "stale MOVE accepted") + state.step(["CLEAR", 2, 0]) + state.finish(toy) + expect_rejection(lambda: state.step(["CLEAR", 2, 0]), "duplicate CLEAR accepted") + + offset = {0: Q(1)} + original_rows = [{0: Q(1)}, {0: Q(1)}, {1: Q(1)}, {1: Q(1)}, {2: Q(1)}] + first = {1: Q(1), 0: Q(-1)} + later = {3: Q(1), 2: Q(-1)} + for covector in (first, later): + image = {} + for role, coefficient in covector.items(): + add(image, original_rows[role], coefficient) + need(not image, "toy carrier has nonzero original value") + directions, _, _, _ = saturate(offset, [], [(0, first)], {0: [0, 1, 2]}) + need(not dot(later, offset) and any(dot(later, vector) for vector in directions), "later carrier was not newly enabled") + dynamic, activated, _, _ = saturate(offset, directions, [(1, later)], {1: [2, 3, 4]}) + need(1 in activated and not Span(dynamic).reduce({4: Q(1)})[0], "sequential carrier positive failed") + static, activated, _, _ = saturate(offset, [], [(1, later)], {1: [2, 3, 4]}) + need(not static and not activated, "static carrier negative failed") + concrete = dict(offset) + add(concrete, {2: Q(1)}, dot(first, concrete)) + add(concrete, {4: Q(1)}, dot(later, concrete)) + need(concrete.get(4) == 1, "concrete sequential witness failed") + remainder, pivot = Span([{1: Q(1)}], {0: 0, 1: 1}).reduce({0: Q(1)}) + need(remainder == {0: Q(1)} and pivot == 0, "affine offset control failed") + need(determinant([[Q(1), Q(2)], [Q(3), Q(4)]]) == -2, "determinant control failed") + expect_rejection(lambda: solve_square([[Q(1), Q(1)], [Q(1), Q(1)]], [Q(1), Q(1)]), "singular certificate accepted") + return dict(snapshot_positive=True, independent_pivot_negative=True, inverse_add_scale=True, + nonzero_copy_rejected=True, zero_scale_rejected=True, stale_move_rejected=True, + duplicate_clear_rejected=True, sequential_new_carrier_positive=True, + static_screen_misses_later_carrier=True, concrete_sequential_witness=True, + affine_offset_negative=True, determinant_positive=True, singular_minor_rejected=True) + + +def run(word, vendor_path): + """Return deterministic exact evidence; source authentication belongs to caller.""" + control_results = controls() + vendor = load_vendor(vendor_path) + classes, census = vendor.leak_classes(word) + leaks = [case for case in classes if case["kind"] == "leak"] + need(len({tuple(case_id(case)) for case in leaks}) == len(leaks), "duplicate leak class identity") + survivors, global_result = global_screen(word, leaks, vendor.SS) + dynamic_cases, first_result = first_carrier_screen(word, survivors, vendor.SS) + dynamic_result = dynamic_screen(word, dynamic_cases, vendor.SS) + all_excluded = all(result["outcome"] in ("outside_unreachable", "only_zero_signal") for result in dynamic_result["results"]) + return dict(schema="p104-fixed-word-carrier-screen/1", controls=control_results, + census=dict(census), leak_classes=len(leaks), single_leak_classes=sum(case["leak"] == 1 for case in leaks), + global_screen=global_result, first_carrier_screen=first_result, dynamic_screen=dynamic_result, + all_tested_leak_classes_excluded=all_excluded, + scope="Unit-injection leak classes of the pinned census; fixed original word, charts and owned lifetimes; arbitrary sequential rational chart-local corrections whose combined source has zero original value. The affine relaxation permits self/noninvertible controls. Nonzero-original correction programs, changed injections/events/MOVEs/storage and different words are excluded from this claim.") diff --git a/research/p104-fixed-word-negative-screens/endpoints.py b/research/p104-fixed-word-negative-screens/endpoints.py new file mode 100644 index 0000000000..fe2684747c --- /dev/null +++ b/research/p104-fixed-word-negative-screens/endpoints.py @@ -0,0 +1,281 @@ +"""Exact, finite endpoint-combination screen on the authenticated PR6030 word. + +Prepared by Jonathan Capalbo (jon314159), with OpenAI Codex assistance. +Apache-2.0. PR5827 supplies the earlier endpoint-resynthesis mechanism; +PR6030 and its retained authors supply the unchanged scalar word. +""" +from bisect import bisect_left, bisect_right +from collections import Counter, defaultdict +from fractions import Fraction as Q +from hashlib import sha256 +import json + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def add(target, source, coefficient): + for key, value in tuple(source.items()): + result = target.get(key, Q(0)) + coefficient * value + if result: + target[key] = result + else: + target.pop(key, None) + + +def encode(row): + return {str(key): str(value) for key, value in sorted(row.items())} + + +def digest(value): + return sha256(json.dumps(value, sort_keys=True, separators=(',', ':')).encode()).hexdigest() + + +def binary_span(basis): + values = {0} + for value in basis: + need(type(value) is int and 0 < value < 512 and value not in values, + 'Independent binary frame basis') + values |= {x ^ value for x in tuple(values)} + return frozenset(values) + + +def initial_state(word): + public = word['public'] + count = public + word['owned_fields'] + return ([{r: Q(1)} if r < public else {} for r in range(count)], + list(word['initial']) + [None] * word['owned_fields']) + + +def advance(rows, levels, event, public): + """Exact scalar semantics; MOVE only changes the current canonical chart.""" + op, r = event[:2] + if op == 'MOVE': + need(levels[r] == event[2] and levels[r] is not None, 'MOVE source chart') + need(event[4] == (r >= public), 'MOVE ownership') + levels[r] = event[3] + elif op == 'INIT': + need(r >= public and levels[r] is None, 'Owned INIT') + rows[r] = {} + levels[r] = event[2] + elif op == 'CLEAR': + need(r >= public and levels[r] == event[2] and levels[r] is not None, 'Owned CLEAR') + rows[r] = {} + levels[r] = None + else: + coefficient, frame = Q(event[-2]), event[-1] + need(coefficient and levels[r] == frame and frame is not None, 'Scalar destination') + if op == 'SCALE': + rows[r] = {key: coefficient * value for key, value in rows[r].items()} + else: + s = event[2] + need(s != r and levels[s] == frame, 'Scalar common chart') + if op == 'COPY': + need(r >= public and not rows[r], 'COPY into owned zero') + else: + need(op == 'ADD', 'Scalar opcode') + add(rows[r], rows[s], coefficient) + + +def finish(word, rows, levels): + public, live = word['public'], set(word['live']) + for r, row in enumerate(rows): + expected = {r: Q(1)} if r < public else {} + if r - 112 in live: + expected[r - 112] = Q(1) + need(row == expected, 'Complete scalar endpoint at role ' + str(r)) + need(levels[:public] == word['final'] and all(x is None for x in levels[public:]), + 'Complete final charts and owned lifetimes') + return {'arbitrary_public_columns': public, 'final_roles_checked': len(rows), + 'final_scalar_rows_sha256': digest([encode(row) for row in rows]), + 'final_frames_checked': True} + + +def span_solve(target, generators, fast=True): + """Rational elimination with unique labels and direct substitution checks. + + A nonzero reduced residue proves nonmembership: it has no coordinate at any + echelon pivot, whereas every nonzero row-span vector has a pivot coordinate. + """ + source = dict(generators) + need(len(source) == len(generators), 'Distinct donor-version labels') + if fast: + support = set().union(*(set(row) for _, row in generators)) if generators else set() + missing = set(target) - support + if missing: + coordinate = min(missing) + return {'in_span': False, 'kind': 'missing_coordinate', + 'coordinate': coordinate, 'target_coefficient': str(target[coordinate]), + 'rank': None, 'witness': None, 'witness_dyadic': None} + pivots = {} + for label, original in generators: + row, combination = dict(original), {label: Q(1)} + while row: + pivot = min(row) + if pivot not in pivots: + scale = row[pivot] + pivots[pivot] = ({key: value / scale for key, value in row.items()}, + {key: value / scale for key, value in combination.items()}) + break + base, coefficients = pivots[pivot] + scale = -row[pivot] + add(row, base, scale) + add(combination, coefficients, scale) + residue, combination = dict(target), {} + for pivot, (base, coefficients) in sorted(pivots.items()): + if pivot in residue: + scale = residue[pivot] + add(residue, base, -scale) + add(combination, coefficients, scale) + reconstructed = {} + for label, coefficient in combination.items(): + add(reconstructed, source[label], coefficient) + add(reconstructed, residue, Q(1)) + need(reconstructed == target, 'Exact elimination substitution') + need(all(pivot not in residue for pivot in pivots), 'Reduced residue avoids every pivot') + return {'in_span': not residue, 'kind': 'in_span' if not residue else 'rational_span_exclusion', + 'rank': len(pivots), 'residue': encode(residue), 'reduction': encode(combination), + 'witness': encode(combination) if not residue else None, + 'witness_dyadic': all(q.denominator & (q.denominator - 1) == 0 + for q in combination.values()) if not residue else None} + + +def controls(): + a, b = {0: Q(1)}, {1: Q(1)} + result = span_solve({0: Q(1), 1: Q(2)}, [('a', a), ('b', b)]) + need(result['in_span'] and result['witness'] == {'a': '1', 'b': '2'}, 'Two-source positive') + need(not span_solve(b, [('a', a)])['in_span'], 'Missing-coordinate negative') + need(not span_solve(a, [('ab', {0: Q(1), 1: Q(1)})])['in_span'], 'Correlated-span negative') + before, after = ('before:start:0:4', {0: Q(1), 1: Q(1)}), ('after:start:9:4', b) + need(not span_solve(a, [before])['in_span'] and not span_solve(a, [after])['in_span'], + 'Each endpoint alone fails the cancellation control') + combined = span_solve(a, [before, after]) + need(combined['in_span'] and combined['witness'] == {before[0]: '1', after[0]: '-1'}, + 'Cross-bank cancellation with the same role in two versions') + try: + span_solve(a, [('role4', before[1]), ('role4', after[1])]) + except ValueError as error: + need(str(error) == 'Distinct donor-version labels', 'Expected duplicate-label failure') + else: + raise ValueError('Duplicate donor-version labels accepted') + # Capture the two actual versions of a donor in a tiny scalar trace. + rows, levels = [dict(a), dict(b), {2: Q(1)}], [0, 0, 0] + original = dict(rows[0]) + net = {} + add(net, rows[0], Q(2)) + advance(rows, levels, ['ADD', 2, 0, '2', 0], 3) + advance(rows, levels, ['ADD', 0, 1, '1', 0], 3) + add(net, rows[0], Q(-1)) + advance(rows, levels, ['ADD', 2, 0, '-1', 0], 3) + need(original == a and net == {0: Q(1), 1: Q(-1)}, 'Original donor versions and ADD coefficients') + need(not span_solve(a, [('latest', rows[0])])['in_span'], 'Stale donor version rejected') + need(span_solve(a, [('captured', original)])['in_span'], 'Captured donor version accepted') + return {'two_source_positive': True, 'missing_coordinate_negative': True, + 'correlated_span_negative': True, 'cross_bank_cancellation_positive': True, + 'same_role_distinct_side_labels': True, 'duplicate_labels_rejected': True, + 'original_donor_versions_and_coefficients': True, 'stale_donor_version_rejected': True} + + +def enumerate_pairs(word): + program = word['program'] + contacts, moves = defaultdict(list), defaultdict(list) + for i, event in enumerate(program): + op, r = event[:2] + contacts[r].append((i, 'move' if op == 'MOVE' else 'incoming' if op == 'ADD' else 'other')) + if op == 'MOVE': + moves[r].append(i) + if op in ('ADD', 'COPY'): + contacts[event[2]].append((i, 'read')) + census = Counter({'adjacent_role_move_pairs': 0, 'excluded_intermediate_contacts': 0, + 'incoming_only_pairs': 0, 'empty_contact_pairs': 0}) + pairs, event_pair, requests = [], {}, defaultdict(list) + for r in sorted(moves): + cc = sorted(contacts[r]) + indices = [i for i, kind in cc] + for first, second in zip(moves[r], moves[r][1:]): + census['adjacent_role_move_pairs'] += 1 + interior = [(i, kind) for i, kind in cc if first < i < second] + if any(kind != 'incoming' for i, kind in interior): + census['excluded_intermediate_contacts'] += 1 + continue + census['incoming_only_pairs' if interior else 'empty_contact_pairs'] += 1 + j = len(pairs) + p, q = bisect_left(indices, first), bisect_right(indices, second) + left = indices[p - 1] + 1 if p else 0 + right = indices[q] if q < len(indices) else len(program) + a, b = program[first][2:4] + b2, c = program[second][2:4] + need(b == b2 and program[first][4] == program[second][4], 'Adjacent MOVE itinerary') + incoming = [i for i, kind in interior] + pairs.append({'pair_index': j, 'role': r, 'move_events': [first, second], + 'frames': [a, b, c], 'private': program[first][4], + 'incoming_events': incoming, + 'windows': {'before': [left, first], 'after': [second + 1, right]}}) + for i in incoming: + need(i not in event_pair, 'Unique receiver interval for each incoming ADD') + event_pair[i] = j + for side, lo, hi, frame in [('before', left, first, a), ('after', second + 1, right, c)]: + need(not any(lo <= i < hi for i in indices), 'Untouched endpoint window') + requests[lo].append((j, side, hi, frame)) + return dict(census), pairs, event_pair, requests + + +def run(word): + """Return deterministic finite-screen evidence; input authentication is external.""" + control_results = controls() + program, public = word['program'], word['public'] + census, pairs, event_pair, requests = enumerate_pairs(word) + need(census == {'adjacent_role_move_pairs': 2664, 'excluded_intermediate_contacts': 1900, + 'incoming_only_pairs': 764, 'empty_contact_pairs': 0}, 'Pinned complete pair census') + desired = [{} for pair in pairs] + arrivals = defaultdict(list) + rows, levels = initial_state(word) + for i, event in enumerate(program): + if i in event_pair: + add(desired[event_pair[i]], rows[event[2]], Q(event[3])) + if event[0] == 'MOVE': + arrivals[event[3]].append((i + 1, event[1], dict(rows[event[1]]))) + advance(rows, levels, event, public) + replay = finish(word, rows, levels) + arrival_times = {frame: [slot for slot, r, row in values] for frame, values in arrivals.items()} + banks, records = defaultdict(dict), [] + counts = Counter({'windows_collected': 0, 'pairs_tested': 0, 'missing_coordinate': 0, + 'rational_span_exclusion': 0, 'candidates': 0}) + rows, levels = initial_state(word) + for slot in range(len(program) + 1): + for j, side, hi, frame in requests.get(slot, []): + receiver = pairs[j]['role'] + need(levels[receiver] == frame, 'Receiver endpoint chart') + generators = [(side + ':start:' + str(slot) + ':' + str(r), dict(rows[r])) + for r, current in enumerate(levels) if current == frame and r != receiver] + times, values = arrival_times.get(frame, []), arrivals.get(frame, []) + for arrival, r, row in values[bisect_right(times, slot):bisect_right(times, hi)]: + if r != receiver: + generators.append((side + ':arrival:' + str(arrival) + ':' + str(r), row)) + banks[j][side] = generators + counts['windows_collected'] += 1 + if len(banks[j]) == 2: + generators = banks[j]['before'] + banks[j]['after'] + result = span_solve(desired[j], generators) + counts['pairs_tested'] += 1 + counts['candidates' if result['in_span'] else result['kind']] += 1 + records.append({'pair': pairs[j], 'generator_count': len(generators), + 'net_contribution_sha256': digest(encode(desired[j])), + 'generators_sha256': digest([[name, encode(row)] for name, row in generators]), + 'result': result}) + del banks[j] + if slot < len(program): + advance(rows, levels, program[slot], public) + need(not banks and len(records) == len(pairs), 'Every endpoint pair tested completely') + need(counts == {'windows_collected': 1528, 'pairs_tested': 764, 'missing_coordinate': 693, + 'rational_span_exclusion': 71, 'candidates': 0}, 'Pinned exact negative endpoint result') + need(finish(word, rows, levels) == replay, 'Both scalar replay passes agree') + return {'status': 'PASS_ENDPOINT_COMBINATION_SCREEN', 'census': census, 'counts': dict(counts), + 'replay': replay, 'controls': control_results, + 'pairs': sorted(records, key=lambda item: item['pair']['pair_index']), + 'scope': 'All 764 incoming-ADD-only adjacent MOVE intervals of the pinned word. ' + 'The coefficient-weighted original net contribution fails the rational sum of both full ' + 'endpoint-window accumulated spans, with the receiver excluded. No receiver scaling, ' + 'changed other-role program, new lifetime, target change or global optimum is claimed.'} diff --git a/research/p104-fixed-word-negative-screens/package_controls.py b/research/p104-fixed-word-negative-screens/package_controls.py new file mode 100644 index 0000000000..bcae60e791 --- /dev/null +++ b/research/p104-fixed-word-negative-screens/package_controls.py @@ -0,0 +1,68 @@ +#!/usr/bin/env python3 +"""Cold export and fail-closed input/certificate controls, standard library. + +Jonathan Capalbo (jon314159), with OpenAI Codex assistance. Apache-2.0. +Only fresh temporary copies are modified; source packages remain unchanged. +""" +from pathlib import Path +import json +import shutil +import subprocess +import sys +import tempfile + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +RELATIVE = Path('research') / HERE.name +WORD = Path('research/p104-helper470-twin-rung-removal/WORD.json.gz') + + +def need(ok, why): + if not ok: + raise ValueError(why) + + +def replay(root, expected_failure=None): + process = subprocess.run([sys.executable, '-I', '-O', '-B', str(root / RELATIVE / 'verify.py')], + cwd=root, capture_output=True, text=True, timeout=240) + if expected_failure is None: + need(process.returncode == 0 and 'PASS_P104_FIXED_WORD_NEGATIVE_SCREENS' in process.stdout, + 'cold export failed: ' + process.stdout[-1000:] + process.stderr[-2000:]) + else: + need(process.returncode != 0 and expected_failure in process.stderr, + 'control did not reject for expected reason: ' + repr(expected_failure) + + '\n' + process.stdout[-1000:] + process.stderr[-2000:]) + + +def main(): + with tempfile.TemporaryDirectory(prefix='p104-negative-export-') as temporary: + root = Path(temporary) + destination = root / RELATIVE + shutil.copytree(HERE, destination, ignore=shutil.ignore_patterns('__pycache__', '*.pyc')) + word = root / WORD + word.parent.mkdir(parents=True, exist_ok=True) + shutil.copyfile(ROOT / WORD, word) + # No Git objects, scratch work, or network fetches are available here. + replay(root) + + original = word.read_bytes() + word.write_bytes(original + b'\x00') + replay(root, 'selected WORD bytes do not match') + word.write_bytes(original) + + vendor = destination / 'vendor/pr6045/leakfix.py' + original = vendor.read_bytes() + vendor.write_bytes(original + b'\n') + replay(root, 'vendored source drift') + vendor.write_bytes(original) + + expected = destination / 'EXPECTED.json' + value = json.loads(expected.read_text(encoding='utf-8')) + value['carrier']['leak_classes'] += 1 + expected.write_text(json.dumps(value), encoding='utf-8') + replay(root, 'semantic replay differs from EXPECTED.json') + print('PASS_P104_NEGATIVE_PACKAGE_CONTROLS cold_export word_drift vendor_drift semantic_receipt_drift') + + +if __name__ == '__main__': + main() diff --git a/research/p104-fixed-word-negative-screens/private_queries.py b/research/p104-fixed-word-negative-screens/private_queries.py new file mode 100644 index 0000000000..a5eaf873e4 --- /dev/null +++ b/research/p104-fixed-word-negative-screens/private_queries.py @@ -0,0 +1,75 @@ +"""Five private rank-four output-seam reconstructions on the pinned PR6030 word. + +Prepared by Jonathan Capalbo (jon314159), with OpenAI Codex assistance. +Apache-2.0. No query is removed or priced; the source and predecessor credits +remain with PR6030, PR5827 and the retained P104 lineage. +""" +from fractions import Fraction as Q +from endpoints import (advance, binary_span, encode, finish, initial_state, + need, span_solve) + + +CASES = {12805: (798, 267, 1091), 13495: (773, 1031, 597), + 13510: (781, 518, 240), 13563: (782, 517, 243), 13592: (779, 477, 1090)} + + +def controls(): + a, b = {0: Q(1), 1: Q(1)}, {0: Q(1), 1: Q(-1)} + positive = span_solve({0: Q(1)}, [('2', a), ('3', b)], fast=False) + need(positive['in_span'] and positive['witness'] == {'2': '1/2', '3': '1/2'}, + 'Dyadic two-donor positive') + need(not span_solve({2: Q(1)}, [('2', a), ('3', b)], fast=False)['in_span'], + 'Independent-column negative') + odd = span_solve({0: Q(1)}, [('3', {0: Q(3)})], fast=False) + need(odd['in_span'] and not odd['witness_dyadic'], 'Nondyadic witness is labeled') + target, rows, levels, receiver = {0: Q(1)}, [{0: Q(1)}, {1: Q(1)}], [0, 0], 0 + donors = [(str(r), row) for r, row in enumerate(rows) if r != receiver and levels[r] == 0] + need(not span_solve(target, donors, fast=False)['in_span'], 'Receiver cannot supply its own value') + need(span_solve(target, [('self', rows[receiver])], fast=False)['in_span'], 'Self-exclusion positive comparator') + need(binary_span([1, 2]) == binary_span([3, 2]), 'Distinct presentations of the same binary subspace') + need(binary_span([1, 2]) != binary_span([1, 4]), 'Different binary subspaces distinguished') + return {'dyadic_two_donor_positive': True, 'independent_column_negative': True, + 'nondyadic_witness_labeled': True, 'receiver_excluded': True, + 'duplicate_frame_presentations_recognized': True, 'different_frame_spans_distinguished': True} + + +def run(word): + """Return deterministic exact output-seam evidence; no I/O or source mutation.""" + control_results = controls() + public = word['public'] + frames = [binary_span(basis) for basis in word['frames']] + rows, levels = initial_state(word) + results, peak_live = [], 0 + for i, event in enumerate(word['program']): + advance(rows, levels, event, public) + peak_live = max(peak_live, sum(frame is not None for frame in levels[public:])) + if i not in CASES: + continue + r, a, b = CASES[i] + need(event == ['MOVE', r, a, b, True] and r >= public, 'Nominated private output seam') + need(frames[b] < frames[a] and len(word['frames'][a]) - len(word['frames'][b]) == 4, + 'Nominated nested private rank-four transport') + exact = [s for s, frame in enumerate(levels) if s != r and frame == b] + relaxed = [s for s, frame in enumerate(levels) + if s != r and frame is not None and frames[frame] == frames[b]] + exact_result = span_solve(rows[r], [(str(s), rows[s]) for s in exact], fast=False) + relaxed_result = span_solve(rows[r], [(str(s), rows[s]) for s in relaxed], fast=False) + results.append({'after_event_zero_based': i, 'role': r, 'source_frame': a, 'destination_frame': b, + 'target_row': encode(rows[r]), 'target_nonzero': bool(rows[r]), + 'exact_frame_donors': exact, 'exact_frame_result': exact_result, + 'same_span_donors': relaxed, 'same_span_result': relaxed_result, + 'donor_rows': {str(s): encode(rows[s]) for s in relaxed}, + 'donor_frames': {str(s): levels[s] for s in relaxed}}) + replay = finish(word, rows, levels) + need(len(results) == 5 and all(item['target_nonzero'] for item in results), 'Five nonzero private query values') + exact_candidates = sum(item['exact_frame_result']['in_span'] for item in results) + relaxed_candidates = sum(item['same_span_result']['in_span'] for item in results) + need(exact_candidates == relaxed_candidates == 0, 'Five exact negative private-query reconstructions') + return {'status': 'PASS_FIVE_PRIVATE_QUERY_OUTPUT_RECONSTRUCTION_SCREEN', + 'replay': replay, 'peak_live_owned': peak_live, 'cases': results, + 'exact_frame_candidates': exact_candidates, 'same_span_relaxed_candidates': relaxed_candidates, + 'controls': control_results, + 'scope': 'Only the five nominated immediate output seams. All other live same-chart rows are ' + 'available, with the receiver excluded. A further relaxation identifies duplicate ' + 'binary-subspace presentations for free. No changed continuation, new lifetime, ' + 'different native monomial, query deletion, paid improvement or global optimum is claimed.'} diff --git a/research/p104-fixed-word-negative-screens/review_controls.py b/research/p104-fixed-word-negative-screens/review_controls.py new file mode 100644 index 0000000000..cf6f855634 --- /dev/null +++ b/research/p104-fixed-word-negative-screens/review_controls.py @@ -0,0 +1,238 @@ +"""Independent exact certificate checks and scientific-boundary controls. + +Prepared by Jonathan Capalbo (jon314159), with substantial OpenAI Codex +assistance. Apache-2.0. This is a second AI/code review, not a human review or +a formal proof. It does not recompute the carrier reachability enclosure. +""" +from copy import deepcopy +from fractions import Fraction as Q +from itertools import permutations + + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def determinant(matrix): + """Direct permutation definition; no package elimination is imported.""" + size = len(matrix) + require(size <= 7 and all(len(row) == size for row in matrix), 'Small square review minor') + answer = Q(0) + for order in permutations(range(size)): + inversions = sum(order[i] > order[j] for i in range(size) for j in range(i + 1, size)) + term = Q(-1 if inversions % 2 else 1) + for i, j in enumerate(order): + term *= matrix[i][j] + answer += term + return answer + + +def independent_rows(rows): + """Choose a row minor using dense elimination in the small column space.""" + echelon, selected = {}, [] + for label, original in rows: + row = list(original) + for pivot in sorted(echelon): + coefficient = row[pivot] + row = [x - coefficient * y for x, y in zip(row, echelon[pivot])] + pivot = next((i for i, x in enumerate(row) if x), None) + if pivot is not None: + divisor = row[pivot] + echelon[pivot] = [x / divisor for x in row] + selected.append(label) + return selected + + +def suffix_column(word, cut, pivot): + """Independent dense scalar propagation of the uncorrected unit signal.""" + public = word['public'] + column = [Q(0)] * (public + word['owned_fields']) + require(-1 <= cut < len(word['program']) and 0 <= pivot < public, 'Review injection bounds') + column[pivot] = Q(1) + for event in word['program'][cut + 1:]: + operation, target = event[:2] + if operation in ('INIT', 'CLEAR'): + column[target] = Q(0) + elif operation == 'COPY': + column[target] = Q(event[3]) * column[event[2]] + elif operation == 'ADD': + column[target] += Q(event[3]) * column[event[2]] + elif operation == 'SCALE': + column[target] *= Q(event[2]) + else: + require(operation == 'MOVE', 'Review suffix opcode') + require(not any(column[public:]), 'Review terminal owned signal') + return column[:public] + + +def affine_certificate(word, result): + """Certify injective protected projection and membership of the offset.""" + case = result['case'] + basis = [{int(k): Q(v) for k, v in row.items()} for row in result['final_basis']] + public, dimension = word['public'], len(basis) + require(0 < dimension <= 7, 'Review terminal dimension') + require(all(0 <= k < public for row in basis for k in row), 'Review basis public coordinates') + protected = [r for r in range(public) if word['final'][r] != word['final'][case['pivot']]] + selected = independent_rows((r, [row.get(r, Q(0)) for row in basis]) for r in protected) + require(len(selected) == dimension, 'Review protected projection is not injective') + matrix = [[row.get(r, Q(0)) for row in basis] for r in selected] + divisor = determinant(matrix) + require(bool(divisor), 'Review protected determinant is zero') + offset = suffix_column(word, case['cut_after'], case['pivot']) + # Cramer's rule deliberately differs from the carrier module's solve_square. + coefficients = [] + for column in range(dimension): + substituted = [[offset[r] if j == column else matrix[i][j] + for j in range(dimension)] for i, r in enumerate(selected)] + coefficients.append(determinant(substituted) / divisor) + for r in range(public): + reconstructed = sum(q * row.get(r, Q(0)) for q, row in zip(coefficients, basis)) + require(reconstructed == offset[r], 'Review affine offset is not in correction span') + return {'cut_after': case['cut_after'], 'pivot': case['pivot'], + 'protected_rows': selected, 'determinant': str(divisor), + 'baseline_coefficients': [str(q) for q in coefficients], + 'checked_public_coordinates': public, + 'projection_injective': True, 'baseline_in_span': True, + 'conclusion': 'The only protected-zero point of this reported affine set is zero.'} + + +def independent_terminal(word, carrier_result): + dynamic = carrier_result['dynamic_screen'] + require(dynamic['tested'] == len(dynamic['results']) == 2, 'Review two terminal cases') + checks = [] + for result in dynamic['results']: + require(result['outcome'] == 'only_zero_signal', 'Review terminal outcome') + require(result['final_correction_rank'] == result['protected_projection_rank'] == 5, + 'Review reported terminal ranks') + require(result['zero_protected_dimension'] == 0 and not result['affine_remainder'], + 'Review reported affine conclusion') + checks.append(affine_certificate(word, result)) + return {'status': 'PASS_INDEPENDENT_TERMINAL_MINOR', 'checks': checks, + 'scope': 'Rechecks the reported terminal bases, protected projection and independently ' + 'propagated suffix offsets. Carrier census, kernel completeness and dynamic ' + 'enclosure induction require the separate source replay and mathematical proof.'} + + +def rejected(function, expected): + try: + function() + except ValueError as error: + require(str(error) == expected, 'Unexpected control rejection: ' + str(error)) + else: + raise ValueError('Boundary control was accepted: ' + expected) + + +def terminal_controls(): + # An actual scalar trace sends e0 to (1,1). Output 1 is protected. + word = {'public': 2, 'owned_fields': 0, 'initial': [0, 1], 'final': [0, 1], + 'program': [['MOVE', 1, 1, 0, False], ['ADD', 1, 0, '1', 0], + ['MOVE', 1, 0, 1, False]]} + result = {'case': {'cut_after': -1, 'pivot': 0}, 'final_basis': [{'0': '1', '1': '1'}]} + require(affine_certificate(word, result)['baseline_in_span'], 'Review terminal positive') + omission = deepcopy(result) + omission['final_basis'] = [{'1': '1'}] + rejected(lambda: affine_certificate(word, omission), 'Review affine offset is not in correction span') + zero_projection = deepcopy(result) + zero_projection['final_basis'] = [{'0': '1'}] + rejected(lambda: affine_certificate(word, zero_projection), 'Review protected projection is not injective') + duplicate = deepcopy(result) + duplicate['final_basis'] *= 2 + rejected(lambda: affine_certificate(word, duplicate), 'Review protected projection is not injective') + return {'terminal_positive': True, 'affine_offset_omission_rejected': True, + 'protected_kernel_rejected': True, 'dependent_basis_rejected': True} + + +def endpoint_boundary_controls(endpoints): + # Each summand is unavailable at both endpoints, but their true net is zero. + # A per-donor exclusion would incorrectly reject this cancellable interval. + word = {'program': [['MOVE', 0, 0, 1, False], ['ADD', 0, 1, '1', 1], + ['ADD', 0, 1, '-1', 1], ['MOVE', 0, 1, 0, False]]} + census, pairs, event_pair, requests = endpoints.enumerate_pairs(word) + require(len(pairs) == 1 and pairs[0]['incoming_events'] == [1, 2], 'Review endpoint interval census') + require(pairs[0]['windows'] == {'before': [0, 0], 'after': [4, 4]}, 'Review endpoint boundary slots') + donor, bank = {1: Q(1)}, [('other', {2: Q(1)})] + require(not endpoints.span_solve(donor, bank)['in_span'], 'Review unavailable individual donor') + net = {} + for i in pairs[0]['incoming_events']: + endpoints.add(net, donor, Q(word['program'][i][3])) + require(not net and endpoints.span_solve(net, bank)['in_span'], 'Review net cancellation is retained') + read = deepcopy(word) + read['program'].insert(2, ['ADD', 1, 0, '1', 1]) + require(not endpoints.enumerate_pairs(read)[1], 'Review intermediate receiver read must exclude interval') + scale = deepcopy(word) + scale['program'].insert(2, ['SCALE', 0, '2', 1]) + require(not endpoints.enumerate_pairs(scale)[1], 'Review receiver scaling must exclude interval') + # Two equal role numbers at different times must remain independent labels. + first, second = {0: Q(1), 1: Q(1)}, {1: Q(1)} + require(not endpoints.span_solve({0: Q(1)}, [('early:4', first)])['in_span'], 'Review one bank negative') + require(endpoints.span_solve({0: Q(1)}, [('early:4', first), ('late:4', second)])['in_span'], + 'Review accumulated distinct donor versions') + return {'net_cancellation_positive_despite_unavailable_summands': True, + 'intermediate_receiver_read_excluded': True, 'receiver_scaling_excluded': True, + 'word_boundary_slots_included': True, 'accumulated_distinct_versions_positive': True} + + +def separating_functional(target, donors): + """Return an explicit rational dual certificate; do not trust span_solve.""" + columns = sorted(set(target).union(*(set(row) for row in donors))) + position = {column: i for i, column in enumerate(columns)} + echelon = {} + for original in donors: + row = [original.get(column, Q(0)) for column in columns] + for pivot in sorted(echelon): + coefficient = row[pivot] + row = [x - coefficient * y for x, y in zip(row, echelon[pivot])] + pivot = next((i for i, value in enumerate(row) if value), None) + if pivot is not None: + divisor = row[pivot] + echelon[pivot] = [value / divisor for value in row] + residue = [target.get(column, Q(0)) for column in columns] + for pivot in sorted(echelon): + coefficient = residue[pivot] + residue = [x - coefficient * y for x, y in zip(residue, echelon[pivot])] + free = next((i for i, value in enumerate(residue) if value), None) + require(free is not None and free not in echelon, 'Review expected a separating functional') + functional = [Q(0)] * len(columns) + functional[free] = Q(1) + for pivot in sorted(echelon, reverse=True): + functional[pivot] = -sum(value * coefficient for value, coefficient + in zip(functional, echelon[pivot])) + for row in donors: + require(sum(value * functional[position[column]] for column, value in row.items()) == 0, + 'Review functional fails to annihilate donor') + pairing = sum(value * functional[position[column]] for column, value in target.items()) + require(bool(pairing), 'Review functional fails to separate target') + return {'functional': {str(column): str(functional[i]) for i, column in enumerate(columns) if functional[i]}, + 'target_pairing': str(pairing), 'donors_annihilated': len(donors)} + + +def private_dual_checks(word, private_module): + # Replaying this small module obtains the exact recorded row bank. The + # independent part here is the checked dual witness, not donor enumeration. + result = private_module.run(word) + checks = [] + for case in result['cases']: + target = {int(k): Q(v) for k, v in case['target_row'].items()} + donors = [{int(k): Q(v) for k, v in row.items()} for row in case['donor_rows'].values()] + certificate = separating_functional(target, donors) + checks.append({'after_event_zero_based': case['after_event_zero_based'], + 'role': case['role'], 'same_span_bank': certificate}) + rejected(lambda: separating_functional({0: Q(1)}, [{0: Q(1)}]), + 'Review expected a separating functional') + positive = separating_functional({0: Q(1)}, [{0: Q(1), 1: Q(1)}]) + require(positive['target_pairing'] != '0', 'Review correlated dual positive') + return {'status': 'PASS_FIVE_EXPLICIT_DUAL_CERTIFICATES', 'checks': checks, + 'self_as_donor_mutation_rejected': True, 'correlated_span_dual_positive': True, + 'scope': 'Each displayed rational functional annihilates every reported same-span donor ' + 'and pairs nontrivially with the target. Source replay and exhaustive bank ' + 'enumeration remain the private-query module responsibility.'} + + +def run(word, carrier_result, endpoints_module, private_module): + return {'status': 'PASS_INDEPENDENT_CERTIFICATES_AND_BOUNDARY_CONTROLS', + 'terminal': independent_terminal(word, carrier_result), + 'terminal_controls': terminal_controls(), + 'endpoint_boundary_controls': endpoint_boundary_controls(endpoints_module), + 'private_dual_certificates': private_dual_checks(word, private_module), + 'review_type': 'Independent AI-assisted code and mathematical-scope review; not human or formal verification.'} diff --git a/research/p104-fixed-word-negative-screens/vendor/pr6045/inputs/shapesplit.py b/research/p104-fixed-word-negative-screens/vendor/pr6045/inputs/shapesplit.py new file mode 100644 index 0000000000..6eedc849e7 --- /dev/null +++ b/research/p104-fixed-word-negative-screens/vendor/pr6045/inputs/shapesplit.py @@ -0,0 +1,176 @@ +"""Exact census of PR5718-shape helper splits on a P104 word. Apache-2.0. Python 3.12, standard library only. + +Prepared by Nick Petalas. Extends the criterion and pure-subspace decision of Matarener's PR5994 census +(`research/p104-helper-split-exhaustion`, PR5599 PROOF.md section 1) to the shape of flyingviper's PR5718 split. + +Model (one helper p of a boundary group g = (U, V), cut after event i, strictly intermediate chart F holding p): + * input side: a combination a of the prefix rows of the fields at F with a_p != 0 and c = aP supported on the + group, on roles whose initial chart is U, or (in_kind='empty', PR5718's rule) on every role whose initial chart + is zero-dimensional; + * a new independent helper z replaces p after the cut (unit injection b = e_p, as in PR5718); its z-direction + reaches the outputs as d = S e_p (S = suffix columns of the original word); + * output normalisation only at V: every role whose final chart is V (other than p) may be corrected freely, so d + must vanish on O = {roles whose final chart is not V}; the pair needs a.b = c.d' != 0. +Classes whose d leaks into O are reported as `leak`: such a split needs a mid-word correction of that leak. +""" +from collections import defaultdict +from fractions import Fraction as Q +import gzip, json + + +def need(ok, why): + if not ok: + raise ValueError(why) + + +def read(path): + raw = open(path, 'rb').read() + return json.loads(gzip.decompress(raw) if str(path).endswith('.gz') else raw) + + +def spans(w): + out = [] + for basis in w['frames']: + s = {0} + for v in basis: + need(type(v) is int and 0 < v < 512 and v not in s, 'independent binary basis') + s |= {x ^ v for x in s} + out.append(frozenset(s)) + return out + + +def add(dst, src, q): + for k, v in src.items(): + x = dst.get(k, 0) + q * v + if x: + dst[k] = x + else: + dst.pop(k, None) + + +def groups_of(w): + n = w['public']; main = set(w['live']) | {r + 112 for r in w['live']} + g = defaultdict(set) + for r in range(n): + if r not in main: + g[(w['initial'][r], w['final'][r])].add(r) + return g + + +def pure_subspace(vecs, roles, support): + """Basis of {x : sum x_r vecs[r] supported in `support`} as (coefficients, image) pairs; kernel vectors included.""" + pivots, out = [], [] + for r in roles: + outside = {k: v for k, v in vecs[r].items() if k not in support} + coef = {r: Q(1)} + for key, prow, pcoef in pivots: + if key in outside: + s = -outside[key]; add(outside, prow, s); add(coef, pcoef, s) + if outside: + key = min(outside); s = 1 / outside[key] + pivots.append((key, {k: v * s for k, v in outside.items()}, {k: v * s for k, v in coef.items()})) + else: + img = {} + for x, q in coef.items(): + add(img, vecs[x], q) + out.append((coef, img)) + return out + + +def functional_witness(A, p, free, rho): + """Exact decision over the span of A. With L1 = a_p, L2 = c_p, L3 = c on the free coordinates and rho = d_p, a + split exists iff some a has L1 != 0 and (L3 != 0 or L1 = rho * L2): free coordinates of d' adjust c.d' at will, + otherwise c.d' = rho * c_p must equal a.b = a_p.""" + L1 = [coef.get(p, Q(0)) for coef, img in A] + L2 = [img.get(p, Q(0)) for coef, img in A] + L3 = [{k: v for k, v in img.items() if k in free} for coef, img in A] + if not any(L1): + return False + if any(L3): + return True + M = [L1[k] - rho * L2[k] for k in range(len(A))] # is L1 nonzero on ker M ? + if not any(M): + return True + j = next(k for k in range(len(A)) if M[k]) + return any(L1[k] * M[j] - L1[j] * M[k] for k in range(len(A))) + + +def census(w, in_kind='empty'): + """Returns (counts, classes). in_kind: 'boundary' (group + roles initial at U) or 'empty' (also every role + initial at a zero-dimensional chart).""" + n = w['public']; m = w.get('owned_fields', max(e[1] for e in w['program']) + 1 - n); N = n + m + prog = w['program']; S = spans(w); dims = [len(f) for f in w['frames']] + groups = groups_of(w) + valid = {g: {f for f in range(len(S)) if S[g[0]] < S[f] < S[g[1]]} for g in groups} + insup = {} + for g, rs in groups.items(): + s = set(rs) | {r for r in range(n) if w['initial'][r] == g[0]} + if in_kind == 'empty': + s |= {r for r in range(n) if dims[w['initial'][r]] == 0} + insup[g] = s + rows = [{r: Q(1)} if r < n else {} for r in range(N)] + cur = list(w['initial']) + [None] * m + at = defaultdict(set) + for r in range(n): + at[cur[r]].add(r) + snaps = defaultdict(list); counts = defaultdict(int) + for i, e in enumerate(prog): + op, r = e[0], e[1] + if op == 'MOVE': + at[e[2]].discard(r); at[e[3]].add(r); cur[r] = e[3]; touched = (e[2], e[3]) + elif op == 'INIT': + rows[r] = {}; cur[r] = e[2]; at[e[2]].add(r); touched = (e[2],) + elif op == 'CLEAR': + rows[r] = {}; at[e[2]].discard(r); cur[r] = None; touched = (e[2],) + elif op == 'SCALE': + rows[r] = {k: v * Q(e[-2]) for k, v in rows[r].items()}; touched = (cur[r],) + elif op == 'COPY': + rows[r] = {k: v * Q(e[-2]) for k, v in rows[e[2]].items()}; touched = (cur[r],) + else: + add(rows[r], rows[e[2]], Q(e[-2])); touched = (cur[r],) + for F in set(touched): + if F is None or not at[F]: + continue + roles = sorted(at[F]) + for g in groups: + if F not in valid[g] or not (groups[g] & at[F]): + continue + counts['evaluations'] += 1 + A = pure_subspace(rows, roles, insup[g]) + hp = [p for p in sorted(groups[g] & at[F]) if any(coef.get(p) for coef, img in A)] + if not any(img for coef, img in A) or not hp: + counts['no_helper_prefix'] += 1 + continue + snaps[i].append((F, g, hp, A)) + pivots = {p for v in snaps.values() for (F, g, hp, A) in v for p in hp} + fin = {p: w['final'][p] for p in pivots} + outside = {p: {r for r in range(n) if w['final'][r] != fin[p]} for p in pivots} + keep = {p: outside[p] | {p} for p in pivots} + cols = [{r: Q(1)} if r < n else {} for r in range(N)] + classes = [] + for i in range(len(prog) - 1, -1, -1): + for (F, g, hp, A) in snaps.get(i, []): + for p in hp: + d = {k: x for k, x in cols[p].items() if k in keep[p]} + leak = sum(1 for k in d if k in outside[p]) + if leak: + counts['kind_leak'] += 1 + kind = 'leak' + else: + free = {r for r in range(n) if r not in keep[p]} + kind = 'witness' if functional_witness(A, p, free, d.get(p, Q(0))) else 'pairing' + counts['kind_' + kind] += 1 + classes.append({'cut_after': i, 'frame': F, 'group': list(g), 'pivot': p, + 'ranks': [dims[F] - dims[g[0]], dims[g[1]] - dims[F]], 'kind': kind, 'leak': leak}) + e = prog[i]; op, r = e[0], e[1] + if op in ('INIT', 'CLEAR'): + cols[r] = {} + elif op == 'COPY': + add(cols[e[2]], cols[r], Q(e[-2])); cols[r] = {} + elif op == 'SCALE': + cols[r] = {k: v * Q(e[-2]) for k, v in cols[r].items()} + elif op == 'ADD': + add(cols[e[2]], cols[r], Q(e[-2])) + counts['witnesses'] = sum(1 for c in classes if c['kind'] == 'witness') + counts['pivots'] = len(pivots) + return dict(counts), sorted(classes, key=lambda c: (c['cut_after'], c['frame'], c['pivot'])) diff --git a/research/p104-fixed-word-negative-screens/vendor/pr6045/leakfix.py b/research/p104-fixed-word-negative-screens/vendor/pr6045/leakfix.py new file mode 100644 index 0000000000..c54c16899a --- /dev/null +++ b/research/p104-fixed-word-negative-screens/vendor/pr6045/leakfix.py @@ -0,0 +1,377 @@ +"""Exact test of mid-word corrections for PR5718-shape helper-split leak classes. Apache-2.0. + +Python 3.12, standard library only. Extends Nick Petalas's PR6040 census (`inputs/shapesplit.py`, pinned), which +builds on Matarener's PR5994 census and flyingviper's PR5718 split shape. + +Setting (PR6040). A class is (cut after event i, chart F, helper p of a boundary group (U, V)). A new independent +helper z replaces p after the cut; its output column is d = S_i e_p (S = suffix columns of the original word). The +class "leaks" when d is nonzero on O = {public roles whose final chart is not V}. + +Corrections. Insert chart-local events ADD r' += q f after an event t >= i, where f is a field whose value in +the split word is a pure multiple of z (zero non-z part), and r' is any field at the same chart at time t. By the +product telescoping identity prod(I+D_k)A - prod A = sum_k (orig suffix after t_k) D_k (corrected state at t_k), +and because such an ADD only adds multiples of z (so every non-z part is unchanged), the corrected z-column is + + d' = d + sum_k mu_k v_k, v_k = S_{t_k} e_{r'_k} (suffix column of the ORIGINAL word), + +with mu_k = q_k * (z-coefficient of f_k at t_k in the corrected word). The non-z columns of the word are unchanged. +The non-z part of f in the split word is row_f(t) - zc_f(t) * row_p(i), where zc_f(t) is the coefficient with +which the content of field p at the cut reaches f at t (by linearity, the original word is the split word with +z := row_p(i)). Hence: + + * first-order sources: fields with zero non-z part and zc != 0 in the uncorrected split word; each correction + from such a source can take any mu (corrections in time order, each q chosen after the earlier ones); + * necessary superset: also fields whose whole split-word value is zero (zc = 0, row = 0), which can only carry z + after an earlier correction wrote into them. Any correction program whose sources are pure-z fields has its + v_k inside this superset span. + +Decision per class: is d_O in -span{(v_k)_O}? If so, the pairing of PR6040 (functional_witness) is tested with +rho = d'_p, which is either fixed by the solution or free (when a combination with zero O-part moves the p +coordinate). 'single' = one correction suffices (some v_O proportional to d_O). + +Scope: the z-part necessary condition of PR6040 only. Corrections whose source carries non-z content, the non-z +part of the split normalization, native maps, caller, compiler and outer checks are not modelled. +""" +from collections import defaultdict +from fractions import Fraction as Q +import importlib.util, sys +from pathlib import Path + +HERE = Path(__file__).resolve().parent + + +def _load_shapesplit(): + name = 'pr6040_shapesplit' + if name in sys.modules: + return sys.modules[name] + spec = importlib.util.spec_from_file_location(name, HERE/'inputs'/'shapesplit.py') + mod = importlib.util.module_from_spec(spec); sys.modules[name] = mod; spec.loader.exec_module(mod) + return mod + + +SS = _load_shapesplit() +add, need = SS.add, SS.need + + +def leak_classes(w, in_kind='empty'): + """Re-run the PR6040 forward/backward census, keeping for each class its A, d (full column) and row_p(i). + Returns (classes, counts); counts must equal SS.census(w, in_kind)[0].""" + n = w['public']; m = w.get('owned_fields', max(e[1] for e in w['program']) + 1 - n); N = n + m + prog = w['program']; S = SS.spans(w); dims = [len(f) for f in w['frames']] + groups = SS.groups_of(w) + valid = {g: {f for f in range(len(S)) if S[g[0]] < S[f] < S[g[1]]} for g in groups} + insup = {} + for g, rs in groups.items(): + s = set(rs) | {r for r in range(n) if w['initial'][r] == g[0]} + if in_kind == 'empty': + s |= {r for r in range(n) if dims[w['initial'][r]] == 0} + insup[g] = s + rows = [{r: Q(1)} if r < n else {} for r in range(N)] + cur = list(w['initial']) + [None] * m + at = defaultdict(set) + for r in range(n): + at[cur[r]].add(r) + snaps = defaultdict(list); counts = defaultdict(int) + for i, e in enumerate(prog): + op, r = e[0], e[1] + if op == 'MOVE': + at[e[2]].discard(r); at[e[3]].add(r); cur[r] = e[3]; touched = (e[2], e[3]) + elif op == 'INIT': + rows[r] = {}; cur[r] = e[2]; at[e[2]].add(r); touched = (e[2],) + elif op == 'CLEAR': + rows[r] = {}; at[e[2]].discard(r); cur[r] = None; touched = (e[2],) + elif op == 'SCALE': + rows[r] = {k: v * Q(e[-2]) for k, v in rows[r].items()}; touched = (cur[r],) + elif op == 'COPY': + rows[r] = {k: v * Q(e[-2]) for k, v in rows[e[2]].items()}; touched = (cur[r],) + else: + add(rows[r], rows[e[2]], Q(e[-2])); touched = (cur[r],) + for F in set(touched): + if F is None or not at[F]: + continue + roles = sorted(at[F]) + for g in groups: + if F not in valid[g] or not (groups[g] & at[F]): + continue + counts['evaluations'] += 1 + A = SS.pure_subspace(rows, roles, insup[g]) + hp = [p for p in sorted(groups[g] & at[F]) if any(coef.get(p) for coef, img in A)] + if not any(img for coef, img in A) or not hp: + counts['no_helper_prefix'] += 1 + continue + snaps[i].append((F, g, hp, A, {p: dict(rows[p]) for p in hp})) + pivots = {p for v in snaps.values() for (F, g, hp, A, rp) in v for p in hp} + fin = {p: w['final'][p] for p in pivots} + outside = {p: {r for r in range(n) if w['final'][r] != fin[p]} for p in pivots} + keep = {p: outside[p] | {p} for p in pivots} + cols = [{r: Q(1)} if r < n else {} for r in range(N)] + classes = [] + for i in range(len(prog) - 1, -1, -1): + for (F, g, hp, A, rp) in snaps.get(i, []): + for p in hp: + d = {k: x for k, x in cols[p].items() if k in keep[p]} + leak = sum(1 for k in d if k in outside[p]) + free = {r for r in range(n) if r not in keep[p]} + if leak: + counts['kind_leak'] += 1; kind = 'leak' + else: + kind = 'witness' if SS.functional_witness(A, p, free, d.get(p, Q(0))) else 'pairing' + counts['kind_' + kind] += 1 + classes.append({'cut_after': i, 'frame': F, 'group': g, 'pivot': p, 'kind': kind, 'leak': leak, + 'ranks': [dims[F] - dims[g[0]], dims[g[1]] - dims[F]], + 'A': A, 'd': d, 'dall': dict(cols[p]), 'row_p': rp[p], 'outside': outside[p], 'free': free}) + e = prog[i]; op, r = e[0], e[1] + if op in ('INIT', 'CLEAR'): + cols[r] = {} + elif op == 'COPY': + add(cols[e[2]], cols[r], Q(e[-2])); cols[r] = {} + elif op == 'SCALE': + cols[r] = {k: v * Q(e[-2]) for k, v in cols[r].items()} + elif op == 'ADD': + add(cols[e[2]], cols[r], Q(e[-2])) + counts['witnesses'] = sum(1 for c in classes if c['kind'] == 'witness') + counts['pivots'] = len(pivots) + classes.sort(key=lambda c: (c['cut_after'], c['frame'], c['pivot'])) + return classes, dict(counts) + + +def source_intervals(w, cuts, superset=False, mode='carrier'): + """For each (cut i, pivot p) in `cuts` -> list of (field f, chart X, t0, t1): f has zero non-z part in the split + word at chart X after every event t in [t0, t1], and (unless superset) a nonzero z-coefficient. + One shared forward pass over the original word; z-coefficients zc are tracked per (i, p).""" + n = w['public']; m = w.get('owned_fields', max(e[1] for e in w['program']) + 1 - n); N = n + m + prog = w['program'] + rows = [{r: Q(1)} if r < n else {} for r in range(N)] + cur = list(w['initial']) + [None] * m + starts = defaultdict(list) + for key in cuts: + starts[key[0]].append(key) + zc = {} # key -> {field: coefficient} + rowp = {} # key -> row_p(i) + holders = defaultdict(set) # field -> keys with zc[key][field] != 0 + opened = {} # key -> {field: (chart, t0)} + out = defaultdict(list) + + def pure(key, f): + c = zc[key].get(f, 0) + if c == 0: + return superset and not rows[f] and cur[f] is not None + if mode == 'carrier': # original value zero: split value = c * (z - row_p(i)) + return not rows[f] + rp = rowp[key] + if len(rows[f]) != len(rp): + return False + return all(rows[f].get(k) == c * v for k, v in rp.items()) + + def refresh(key, f, t): + """Update the open interval of f for key after event t.""" + o = opened[key] + if f in o: + X, t0 = o[f] + if not pure(key, f) or cur[f] != X: + out[key].append((f, X, t0, t - 1)); del o[f] + if f not in o and cur[f] is not None and pure(key, f): + o[f] = (cur[f], t) + + for t, e in enumerate(prog): + op, r = e[0], e[1] + changed = {r} + if op == 'MOVE': + cur[r] = e[3] + elif op == 'INIT': + rows[r] = {}; cur[r] = e[2] + elif op == 'CLEAR': + rows[r] = {}; cur[r] = None + elif op == 'SCALE': + rows[r] = {k: v * Q(e[-2]) for k, v in rows[r].items()} + elif op == 'COPY': + rows[r] = {k: v * Q(e[-2]) for k, v in rows[e[2]].items()} + else: + add(rows[r], rows[e[2]], Q(e[-2])) + # z-coefficient propagation, same linear action on the scalar zc[key][*] + aff = set(holders.get(r, ())) + if op in ('ADD', 'COPY'): + aff |= holders.get(e[2], set()) + for key in aff: + z = zc[key]; old = z.get(r, 0) + if op in ('INIT', 'CLEAR'): + new = 0 + elif op == 'SCALE': + new = old * Q(e[-2]) + elif op == 'COPY': + new = Q(e[-2]) * z.get(e[2], 0) + elif op == 'ADD': + new = old + Q(e[-2]) * z.get(e[2], 0) + else: + new = old + if new: + z[r] = new; holders[r].add(key) + else: + z.pop(r, None); holders[r].discard(key) + # interval bookkeeping for keys whose purity of r may have changed + check = aff if not superset else set(opened) + for key in check: + refresh(key, r, t) + # new cuts start after event t + for key in starts.get(t, ()): + i, p = key + zc[key] = {p: Q(1)}; holders[p].add(key); rowp[key] = dict(rows[p]); opened[key] = {} + if superset: + for f in range(N): + if cur[f] is not None and not rows[f] and f != p: + opened[key][f] = (cur[f], t) + refresh(key, p, t) + T = len(prog) - 1 + for key, o in opened.items(): + for f, (X, t0) in o.items(): + out[key].append((f, X, t0, T)) + return out + + +class Span: + """Incremental exact row-echelon basis over Q for sparse dict vectors; coordinate order given by `order`.""" + def __init__(self, order): + self.rank = {k: j for j, k in enumerate(order)} + self.piv = {} # pivot coordinate -> normalized vector + + def reduce(self, v): + v = dict(v) + while v: + k = min(v, key=self.rank.__getitem__) + if k not in self.piv: + return v, k + add(v, self.piv[k], -v[k]) + return v, None + + def insert(self, v): + v, k = self.reduce(v) + if k is None: + return False + s = 1 / v[k] + self.piv[k] = {x: y * s for x, y in v.items()} + return True + + +def correction_spans(w, classes, intervals): + """One backward pass. For every class, the span of v = S_t e_{r'} restricted to O + {p}, over insertion times t + in a source interval and r' at the source's chart. Also flags a single-correction (v_O proportional to d_O).""" + n = w['public']; m = w.get('owned_fields', max(e[1] for e in w['program']) + 1 - n); N = n + m + prog = w['program'] + # chart membership after each event, reconstructed forward then walked backward + cur = list(w['initial']) + [None] * m + for e in prog: + if e[0] == 'MOVE': cur[e[1]] = e[3] + elif e[0] == 'INIT': cur[e[1]] = e[2] + elif e[0] == 'CLEAR': cur[e[1]] = None + at = defaultdict(set) + for f in range(N): + if cur[f] is not None: + at[cur[f]].add(f) + byclass = {} + active_at = defaultdict(list) # t1 -> list of (class index, f, X, t0) + for ci, c in enumerate(classes): + key = (c['cut_after'], c['pivot']) + O = c['outside']; p = c['pivot'] + order = sorted(O) + sorted(r for r in range(n) if r not in O) + byclass[ci] = {'span': Span(order), 'seen': set(), 'single': None, 'n_vectors': 0, 'O': O, + 'dO': {k: x for k, x in c['d'].items() if k in O}, 'd': c['dall']} + for (f, X, t0, t1) in intervals.get(key, ()): + active_at[t1].append((ci, f, X, t0)) + live = [] # currently open (ci, f, X, t0) + version = [0] * N + cols = [{r: Q(1)} if r < n else {} for r in range(N)] + for t in range(len(prog) - 1, -1, -1): + # state: cols = suffix after event t, membership = after event t + live.extend(active_at.get(t, ())) + still = [] + for item in live: + ci, f, X, t0 = item + if t < t0: + continue + still.append(item) + B = byclass[ci] + for r2 in at[X]: + tag = (r2, version[r2]) + if tag in B['seen']: + continue + B['seen'].add(tag) + v = cols[r2] + if not v: + continue + B['n_vectors'] += 1 + O = B['O']; vO = {k: x for k, x in v.items() if k in O} + dO = B['dO'] + if B['single'] is None and vO and set(vO) == set(dO): + k0 = next(iter(dO)); s = -dO[k0] / vO[k0] + if all(dO[k] + s * vO[k] == 0 for k in dO): + rest = dict(B['d']); add(rest, v, s) + if rest: # z must still reach a V-final role (no erasure of the new helper) + B['single'] = {'after_event': t, 'target': r2, 'source': f, 'chart': X, 'mu': str(s)} + B['span'].insert(v) + live = still + e = prog[t]; op, r = e[0], e[1] + # reverse membership of event t + if op == 'MOVE': + at[e[3]].discard(r); at[e[2]].add(r) + elif op == 'INIT': + at[e[2]].discard(r) + elif op == 'CLEAR': + at[e[2]].add(r) + # suffix columns before event t + if op in ('INIT', 'CLEAR'): + cols[r] = {}; version[r] += 1 + elif op == 'COPY': + add(cols[e[2]], cols[r], Q(e[-2])); cols[r] = {}; version[r] += 1; version[e[2]] += 1 + elif op == 'SCALE': + cols[r] = {k: v * Q(e[-2]) for k, v in cols[r].items()}; version[r] += 1 + elif op == 'ADD': + add(cols[e[2]], cols[r], Q(e[-2])); version[e[2]] += 1 + return byclass + + +def decide(c, B): + """Return (kind, rho) for one leak class. 'unreachable': no correction combination clears d on O; + 'erased': only by removing z from every V-final output (the new helper would have no target); otherwise the + PR6040 pairing outcome ('witness' / 'pairing') with rho = d'_p fixed or 'free'.""" + p = c['pivot']; O = c['outside']; sp = B['span'] + r, k = sp.reduce(c['dall']) # O coordinates come first in the elimination order + if k is not None and k in O: + return 'unreachable', None + W = [v for piv, v in sp.piv.items() if piv not in O] # zero O-part: free moves of d' on V-final roles + if not r and not W: + return 'erased', None + rho_free = any(v.get(p) for v in W) + A = c['A']; free = c['free'] + if rho_free: + L1 = [coef.get(p, Q(0)) for coef, img in A] + L2 = [img.get(p, Q(0)) for coef, img in A] + L3 = [{k2: v for k2, v in img.items() if k2 in free} for coef, img in A] + ok = any(L1) and (any(L3) or any(L2)) + return ('witness' if ok else 'pairing'), 'free' + rho = r.get(p, Q(0)) + if not any(v for v in W) and not {x for x in r if x != p} and rho == 0: + return 'erased', None + return ('witness' if SS.functional_witness(A, p, free, rho) else 'pairing'), str(rho) + + +def run(w, in_kind='empty', superset=False, only_leak=True, mode='carrier', select=None): + """mode 'carrier': sources whose ORIGINAL value is zero while carrying p's cut content (their split value is a + multiple of z - row_p(i), the full defect direction); mode 'purez': sources whose split value is a multiple of z + (PR6040's suggested r += q*new; fixes only the z-part).""" + classes, counts = leak_classes(w, in_kind) + todo = [c for c in classes if c['kind'] == 'leak'] if only_leak else classes + if select: + todo = [c for c in todo if select(c)] + cuts = sorted({(c['cut_after'], c['pivot']) for c in todo}) + iv = source_intervals(w, cuts, superset, mode) + spans = correction_spans(w, todo, iv) + res = [] + for ci, c in enumerate(todo): + B = spans[ci] + kind, rho = decide(c, B) + res.append({'cut_after': c['cut_after'], 'frame': c['frame'], 'pivot': c['pivot'], 'group': list(c['group']), + 'ranks': c['ranks'], 'leak': c['leak'], 'sources': len(iv.get((c['cut_after'], c['pivot']), ())), + 'vectors': B['n_vectors'], 'span_rank': len(B['span'].piv), 'kind': kind, 'rho': rho, + 'single': B['single']}) + return counts, res, iv + diff --git a/research/p104-fixed-word-negative-screens/verify.py b/research/p104-fixed-word-negative-screens/verify.py new file mode 100644 index 0000000000..2ab3a7ffb2 --- /dev/null +++ b/research/p104-fixed-word-negative-screens/verify.py @@ -0,0 +1,103 @@ +#!/usr/bin/env python3 +"""Reproduce scoped P104 negative screens; Python 3.12, standard library. + +Jonathan Capalbo (jon314159), with substantial OpenAI Codex assistance. +Apache-2.0. No new kappa, supplier admission, or general optimality claim. +""" +import argparse +import gzip +import hashlib +import importlib.util +import json +from pathlib import Path +import sys +import tempfile + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +WORD_PATH = 'research/p104-helper470-twin-rung-removal/WORD.json.gz' +WORD_PIN = '7834725d9e34ee846a9ccc615221ea81e0201613938afa185d2eda0c9a6c232f' +VENDOR_PINS = { + 'vendor/pr6045/leakfix.py': 'dbbdc9ff9ebb55f1b9e832dcbe1aa5e407e7932a8d958a006bdaca6055e7f4ee', + 'vendor/pr6045/inputs/shapesplit.py': '11e8ef691b28fb4f401a8c2e97b6d462e7a004f0e215a28579d6a654b4ca3304', +} + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def digest(raw): + return hashlib.sha256(raw).hexdigest() + + +def authenticated_inputs(): + raw = (ROOT / WORD_PATH).read_bytes() + need(digest(raw) == WORD_PIN, 'selected WORD bytes do not match the pinned PR6030 input') + vendor = json.loads((HERE / 'VENDOR.json').read_text(encoding='utf-8')) + declared = {row['path']: row['sha256'] for row in vendor['files']} + need(declared == VENDOR_PINS, 'vendor declaration differs from frozen input set') + for path, expected in VENDOR_PINS.items(): + need(digest((HERE / path).read_bytes()) == expected, 'vendored source drift: ' + path) + decoded = gzip.decompress(raw) + word = json.loads(decoded) + need((word['public'], word['owned_fields'], len(word['program'])) == (770, 29, 22803), + 'unexpected selected-word dimensions') + return word, dict(word_path=WORD_PATH, word_sha256=WORD_PIN, + decoded_sha256=digest(decoded), vendor_sha256=VENDOR_PINS) + + +def load(name): + spec = importlib.util.spec_from_file_location(name, HERE / (name + '.py')) + need(spec is not None and spec.loader is not None, 'cannot load package module ' + name) + module = importlib.util.module_from_spec(spec) + sys.modules[name] = module + spec.loader.exec_module(module) + return module + + +def compute(): + word, sources = authenticated_inputs() + # -B prevents writes but not stale bytecode reads. Isolate both before any + # research module or frozen dependency is imported, including direct runs. + with tempfile.TemporaryDirectory(prefix='p104-negative-pycache-') as cache: + old_cache, old_write = sys.pycache_prefix, sys.dont_write_bytecode + sys.pycache_prefix, sys.dont_write_bytecode = cache, True + try: + endpoints = load('endpoints') + private_queries = load('private_queries') + carrier = load('carrier') + review_controls = load('review_controls') + print('Checking fixed-word carrier programs...', flush=True) + c = carrier.run(word, HERE / 'vendor/pr6045') + print('Checking both endpoint windows...', flush=True) + e = endpoints.run(word) + print('Checking five private-query output seams...', flush=True) + p = private_queries.run(word) + print('Checking independent certificate and controls...', flush=True) + review = review_controls.run(word, c, endpoints, private_queries) + return dict(schema_version=1, sources=sources, carrier=c, endpoints=e, + private_queries=p, independent_review=review) + finally: + sys.pycache_prefix, sys.dont_write_bytecode = old_cache, old_write + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--output', type=Path, help='write the checked semantic receipt to this new file') + args = parser.parse_args() + expected_path = HERE / 'EXPECTED.json' + need(expected_path.is_file(), 'missing committed EXPECTED.json') + expected = json.loads(expected_path.read_text(encoding='utf-8')) + actual = compute() + canonical = json.dumps(actual, sort_keys=True, separators=(',', ':'), ensure_ascii=True) + need(actual == expected, 'semantic replay differs from EXPECTED.json; do not silently regenerate a claim') + if args.output: + need(not args.output.exists(), 'refusing to overwrite receipt') + args.output.write_text(json.dumps(actual, indent=2, sort_keys=True) + '\n', encoding='utf-8') + print('PASS_P104_FIXED_WORD_NEGATIVE_SCREENS', digest(canonical.encode('utf-8'))) + + +if __name__ == '__main__': + main()