From b44ede42e5e90dedf311362f4ff23ec46b9b70c1 Mon Sep 17 00:00:00 2001 From: Aaron Wang Date: Thu, 15 Oct 2026 05:13:51 -0400 Subject: [PATCH] Exclude reframed two-writer helper-star absorption via forced-carry closure On the pinned PR1062 11,500-ADD word, the complete two-writer single-donor helper-star absorption domain (PR1913) stays inadmissible when gate frames may change: all 52 scalar-saving completions are excluded under arbitrary monotone reframing by the componentwise least forced frame assignment, each with a rational leakage witness (a dirty target's forced carried span exceeds its pinned rank-7 t-perp final frame). 260 of the 262 cost-increasing completions are excluded the same way; the 2 closure-legal survivors cost +1 ADD and are billed with their paid histograms. All 314 completions pass the exact 661-column dirty boundary in both orientations. The PR1868 single-writer fixture is reproduced as a positive control with an unchanged paid profile. Aaron Wang, with help from opencode. Apache-2.0. --- .../CERTIFICATE.json | 91766 ++++++++++++++++ research/r439-two-writer-reframing/README.md | 213 + .../r439-two-writer-reframing/SOURCES.json | 30 + research/r439-two-writer-reframing/TASK.json | 82 + research/r439-two-writer-reframing/TASK.md | 82 + .../r439-two-writer-reframing/VERIFY.json | 28 + .../r439-two-writer-reframing/test_verify.py | 106 + research/r439-two-writer-reframing/verify.py | 519 + 8 files changed, 92826 insertions(+) create mode 100644 research/r439-two-writer-reframing/CERTIFICATE.json create mode 100644 research/r439-two-writer-reframing/README.md create mode 100644 research/r439-two-writer-reframing/SOURCES.json create mode 100644 research/r439-two-writer-reframing/TASK.json create mode 100644 research/r439-two-writer-reframing/TASK.md create mode 100644 research/r439-two-writer-reframing/VERIFY.json create mode 100644 research/r439-two-writer-reframing/test_verify.py create mode 100644 research/r439-two-writer-reframing/verify.py diff --git 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{ + "name": "star_domain_mutation_rejected" + } + ], + "domain": { + "closure_legal_completions": 2, + "exact_completions": 314, + "excluded_saving_under_reframing": 52, + "excluded_under_reframing": 312, + "first_donor_trials": 227286, + "scalar_saving_completions": 52, + "star_edges": 236, + "writer_pairs": 414 + }, + "fixture_pr1868": { + "ADDs": 11499, + "paid_profile_unchanged": true + }, + "no_new_kappa": true, + "result": "PASS_R439_TWO_WRITER_REFRAMING", + "schema_version": 1 +} diff --git a/research/r439-two-writer-reframing/README.md b/research/r439-two-writer-reframing/README.md new file mode 100644 index 0000000000..c8b099712e --- /dev/null +++ b/research/r439-two-writer-reframing/README.md @@ -0,0 +1,213 @@ +# Reframing does not legalize two-writer helper-star absorption + +**Scoped interface obstruction under the full reframing escape class; no new +kappa.** The selected result, the selected bit supplier and `upstream/` are +unchanged; the bit side does not bind. + +On the pinned 11,500-ADD PR1062 R439 word, omit one terminal helper-star +restoration `a ^= b` and toggle one donor in each of two existing phase-A +writes of `a` before its first read. Adam Gall's +[PR #1913](https://github.com/CrocSwap/integer-mult-bounds/pull/1913) found all +314 exact arbitrary-dirty completions of this class (52 with one fewer scalar +ADD) and rejected every one **at the unchanged gate frames**, explicitly leaving +changed gate frames and itineraries open. This package closes that escape for +the useful class: with gate frames free to change (arbitrary monotone +reframing, including shrinking below the original frames), **all 52 +scalar-saving completions are still inadmissible**, each with an exact rational +leakage witness: a dirty target's forced carried span strictly exceeds its +pinned rank-7 `t`-perp final frame. Of the 262 cost-increasing completions, 260 +are excluded the same way; the 2 survivors cost one ADD more than the source +word, so no completion in the domain saves anything under any reframing. + +## The forced-carry closure + +The law is the pinned eumemic `xcheck_p.py` Part F nested-frame law: every +register starts at its start frame (sources at their own line, targets and +helpers at frame 0); before each gate every operand climbs to the gate's frame, +nested with a strict increase of dimension; final frames are pinned (sources +and helpers at the full frame, target `t` at `t`-perp, rank seven). + +**Lemma (least forced frame assignment).** Fix any scalar edit of the word +(gate contents in `D,A,B,C` order; start and final frames unchanged). Process +the gates in order and set each gate frame to the span union of the current +frames of its touched registers, starting from the fixed start frames. Call the +result the *forced-carry closure*. + +1. The closure is the componentwise least legal frame assignment: every legal + reframing's register currents contain the closure's register currents at + every point, by induction over the gates (a gate frame must contain all its + operands' current frames). +2. If the closure reaches a final step where a register's forced carried span + is not contained in its pinned final frame, then **no** reframing is legal: + the offending direction sits in every reframing's carried span, which must + end inside the same final frame. +3. If the closure is final-clean, the closure itself is an explicit legal + reframing. + +So the closure decides reframing-admissibility exactly, and its witnesses are +domain-free: they do not depend on any search over frame choices. Shrinking +gate frames below their original values is granted, which is the most favorable +reading of PR #1913's open question; the exclusion a fortiori holds in +grow-only or source-label-determined frame models. + +## Domain and result + +The domain is re-derived independently here and matches PR #1913 exactly: +236 terminal star edges, 414 eligible writer pairs, 549 first donors per pair +(227,286 trials, unique exact second donor), 314 exact completions. + +| quantity | count | +|---|---:| +| exact arbitrary-dirty completions | 314 | +| completions with one fewer scalar ADD | 52 | +| completions with one more scalar ADD | 262 | +| legal at fixed gate frames (PR #1913) | 0 | +| scalar-saving completions legal under arbitrary monotone reframing | **0 / 52** | +| all completions excluded under reframing | 312 / 314 | +| closure-legal completions (both cost +1 ADD) | 2 | + +Every completion's exact 661-column arbitrary-dirty boundary is replayed in +both orientations through the literal COPY/ERASE stream and passes (the scalar +criterion of PR #1913 is satisfied; the obstruction is purely geometric). The +witnesses all have the same shape: the added donor's forced join at the edited +gate spreads through later gates to a dirty target in 111–221, whose pinned +`t`-perp final frame has rank seven and cannot contain the leaked direction +(rank becomes eight). Examples (register, leaked labels, rank final, rank +joined): + +| omitted restoration | toggles | witness | +|---|---|---| +| `231 ^= 459` | A[9] adds `109`; A[527] removes `459` | target 111 leaks `109`: 7 -> 8 | +| `234 ^= 241` | A[12] adds `9`; A[247] removes `241` | target 112 leaks `9`: 7 -> 8 | +| `506 ^= 374` | A[288] removes `374`; A[1033] adds `69` | target 116 leaks `30,46,54`: 7 -> 8 | +| `482 ^= 540` | A[786] removes `540`; A[787] adds `417` | target 145 leaks `5`: 7 -> 8 | + +The third row is the instructive one: it moves Sagar Thakrar's known legal +single-writer absorption (`506 ^= 374` absorbed by A[288]) onto the *other* +writer. The one-writer move is legal; splitting the same compensation across +two writers forces the join into a rank-7 final and dies. + +All 314 rows with complete witnesses are in +[CERTIFICATE.json](CERTIFICATE.json). + +The two closure-legal completions share the omitted restoration `444 ^= 470` +and *add* rather than remove: donor `77` at A[1993] and donor `470` at A[1994] +(respectively A[2038]), both toggles being insertions. Their forced joins +spread but leak outside no pinned final, and the closure's scatter frames for +the nine retained totals equal the pinned rank-7 copy frames. They cost +**+1 ADD** (11,501 versus 11,500), and their least legal reframing's paid +histogram is `{1: 1494, 2: 1308, 3: 46, 4: 45, 5: 103, 6: 10, 7: 18}` (rank +mass 5,129, 3,024 children versus the source word's 2,920): more children at +smaller rank, so a worse moment bill at every `0 < p < 1` by concavity. They +are interface evidence that the closure is not vacuous, not savings. + +## Boundary contract and paid profile + +The acceptance gate asks for a full boundary contract and paid profile, not +scalar counts alone. + +- **Boundary.** All 314 completions and the positive fixture pass the exact + 661-column arbitrary-dirty boundary in both orientations through the literal + COPY/ERASE stream: every source holds `e_s`, every target holds + `e_{y_t} + e_{x_t}`, every helper holds `e_h`. +- **Paid profile.** No excluded completion has a legal frame assignment, so + there is no paid histogram to bill; billing an excluded completion is refused + by the verifier. The two closure-legal completions are billed above. The + pinned source word's complete profile is + `{1: 1323, 2: 1342, 3: 79, 4: 44, 5: 102, 6: 11, 7: 19}`, rank mass **5,129**, + with ADDs 11,500 and positive bounds F = 25,717, B = 5,911,840 (strict + 104/192-bit inequalities pass). +- **The one legal saving (predecessor's).** Sagar Thakrar / PR #1868's + single-writer absorption `506 ^= 374` with A[288] donors `[374] -> [69]` + passes both closures, saves one ADD (11,499) and keeps the paid profile + identical. It is reproduced here only as a positive fixture; the saving is + PR #1868's, not new. + +## Reproduce + +Standard-library Python 3.12, from the repository root: + +```sh +python3.12 -I -O -B research/r439-two-writer-reframing/verify.py +python3.12 -I -O -B research/r439-two-writer-reframing/test_verify.py +python3.12 scripts/research_package.py --package research/r439-two-writer-reframing +``` + +Expected marker: + +```text +PASS_R439_TWO_WRITER_REFRAMING pairs=414 trials=227286 exact=314 saving=52 saving_excluded=52 reframing_excluded=312 legal=2 columns=661 controls=10 no_new_kappa +``` + +Default replay is read-only and compares every certificate field; +`--write` regenerates `CERTIFICATE.json`. Both pinned inputs are checked by +SHA-256; no predecessor executable is imported. Ten controls: baseline +legality and pinned profile, domain counts, all-314 boundary replays, the 312 +witnessed reframing exclusions, the PR #1868 positive fixture, a removal-only +edit that is geometrically legal but boundary-rejecting (separating the two +checks), a wrong-substitute boundary rejection, refusal to bill an excluded +completion, source-corruption rejection and a star-domain mutation rejection. + +## Scope and limits + +- **Class.** Two writers, one donor toggle per writer, one omitted terminal + star restoration, on the pinned PR1062 word. Multi-donor sets per writer + (PR #1937's linear system) are not replayed under free frames here; the + closure decides that class too and is left as the recorded next question. + Post-read propagation and compensation, changed scalars, rebuilt A/B/C and + other words are outside this scope, as in PR #1913. +- **Claim type.** A finite exact exclusion with machine-checked witnesses plus + a decision lemma, not a theorem about arbitrary words and not a supplier + admission. No new kappa, no changed selected record. +- **Not run.** Native 5/9/11-stage C++/Boost replay, hosted emission/invoice, + all-size compiler, precision/tape, analytic transfer, Lean. Physical + realization of any reframing is not claimed; the exclusion is at the word + level of the inherited nested-frame law. +- **The lemma's model.** Gate frames are free rational frames with pinned + starts and finals and the strict nested-climb law. Models with frame descent, + reset, clean allocation, free role permutation or new transport are outside, + as in the predecessor packages. + +## Open next questions + +1. **Multi-donor splits at free frames.** Does the forced-carry closure also + exclude PR #1937's two-writer multi-donor splits once gate frames may + change, or does a dual-witness-free closure yield a priced legal + reframing? *First step:* replay its five solved same-path edges and its + dual-witness targets through `closure_walk`. *Why it matters:* it decides + the free-frame version of the only surviving split-restoration class. + *Blocker:* none technical; bounded extension of this verifier. +2. **Cheapest legal reframing.** When a closure is legal, is its paid profile + minimal? Larger joins can merge rank increments and lower the moment bill. + *First step:* on the PR #1868 fixture, enumerate coalescing joins and + compare paid histograms. *Blocker:* an optimization over legal reframings, + unneeded for the excluded domain here. + +## Credit and disclosure + +- **Adam Gall / [PR #1913](https://github.com/CrocSwap/integer-mult-bounds/pull/1913):** + the complete two-writer single-donor domain and its fixed-frame exclusion; + its stated open question (changed gate frames/itineraries) is the object of + this package. +- **Aaron Wang / [PR #1937](https://github.com/CrocSwap/integer-mult-bounds/pull/1937):** + the complete fixed-gate multi-donor linear system; its fixed-gate premise is + the changed one here. +- **Sagar Thakrar / [PR #1868](https://github.com/CrocSwap/integer-mult-bounds/pull/1868):** + the twisted helper contract H2-tw/H4-tw/K-tw, the single-writer absorption + (positive fixture, whose one-ADD saving is his), and the multi-gate-split + question. +- **woklerx / [PR #1194](https://github.com/CrocSwap/integer-mult-bounds/pull/1194):** + the semantic-D replacement contract H2-sem; **Arham Tahir / PR #1311, #1580, + #1592:** its application and terminal-restoration obstructions. +- **Word lineage:** Sagar Thakrar / PR #1062 (the pinned word), Sricharan + Vagvala / PR #967 (helper stars), Gareth Davidson / PR #915/#926/#1122, + Ross Richardson / PR #923, Aaron Wang / PR #1015, DreamingOfClouds / PR #589, + eumemic / PR #555/#543 and `xcheck_p.py`, Zhihao Chen / PR #425. +- **Pair-collision check:** discussions 1317 and 1166 through 2026-10-15 + 07:52Z and `scripts/find_overlap.py` on the refined terms (612 open PRs, + 1138 discussion records, complete pagination) found no competing claim on + reframed two-writer absorption. + +Prepared by **Aaron Wang** with substantial AI assistance from opencode; no +independent human review or proof-assistant verification is claimed. New +material is Apache-2.0; pinned inputs keep their original notices. diff --git a/research/r439-two-writer-reframing/SOURCES.json b/research/r439-two-writer-reframing/SOURCES.json new file mode 100644 index 0000000000..61f5470b3c --- /dev/null +++ b/research/r439-two-writer-reframing/SOURCES.json @@ -0,0 +1,30 @@ +{ + "schema_version": 1, + "base_commit": "0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "ae6a99f28aa468649eb66a361e764d769363bf11", + "sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "e8870e5917057d59b730eb14721a778639eca050", + "sha256": "d46eb6d5b3e279428753d770653663fbdf1063e55c255ea073d768f344927ef7" + }, + { + "path": "research/e8-bit-p111-tuned/code/xcheck_p.py", + "usage": "input", + "git_blob": "184f5dcf94a486cc7db91ca4db5865916bf26009", + "sha256": "af3decc877e27c00001cf56f50c6c09566e8e101297ab34c7860aed96a06d80e" + }, + { + "path": "research/r439-bsection-stars-seed01/candidate.json.gz", + "usage": "input", + "git_blob": "9a17b4920334878d6c949191f6931bd97126fe3c", + "sha256": "b452d2c2b0b2a546d1105b1da9769aa78e5c54d6f00e97b30c77e3f54ce445ee" + } + ] +} diff --git a/research/r439-two-writer-reframing/TASK.json b/research/r439-two-writer-reframing/TASK.json new file mode 100644 index 0000000000..7d383addac --- /dev/null +++ b/research/r439-two-writer-reframing/TASK.json @@ -0,0 +1,82 @@ +{ + "schema_version": 1, + "task_id": "bit-helper-contract", + "priority_revision": 4, + "base_commit": "0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2", + "original_card": { + "id": "bit-helper-contract", + "question": "Can one precisely specified helper-mixing word satisfy a replacement for the inherited H2/K interface?", + "starting_points": [ + "research/r439-bsection-stars-seed01/README.md", + "research/r439-copy-path-sharing-barrier/README.md" + ], + "methods": [ + "Derive a replacement interface lemma and price its implementation.", + "Seek an exact dirty-input or chronological-cut counterexample to the proposed replacement." + ], + "acceptance_gate": "A full boundary contract and paid profile; unchanged scalar counts alone are insufficient.", + "first_step": { + "command": [ + "python3", + "-B", + "research/r439-bsection-stars-seed01/verify.py" + ], + "expected": "PASS_R439_BSECTION_STARS", + "inspect": "Compare the two false H2/K flags with the unchanged paid profile in its README.", + "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay." + }, + "first_experiment": "Write one replacement H2/K implication for a single helper-star operation, then try to falsify it on dirty inputs.", + "bottleneck_link": "A legitimate replacement could admit a cheaper bit circuit; scalar savings alone do not alter the selected moment.", + "allowed_variations": [ + "Choose one helper-star or quartet instance; narrow to one boundary implication." + ], + "scope_change_triggers": [ + "Changing only source count or scalar addition count without an interface argument." + ], + "overlap_terms": [ + "H2_D_frame0_targets_from_helpers", + "K_equals_D", + "helper-star" + ] + }, + "scope_status": "refined", + "actual_scope": "Forced-carry closure under changed gate frames for the complete two-writer single-donor helper-star absorption domain on the pinned PR1062 11,500-ADD word: omit one terminal star restoration and toggle one donor in each of two existing pre-first-read A writes of its centre. All 236 edges, 414 writer pairs and the complete 314 exact arbitrary-dirty completions (52 scalar-saving) are decided under arbitrary monotone reframing of gate frames with pinned start and final frames.", + "scope_change_reason": "PR1194 covers fully restored semantic D; PR1868 supplies the twisted contract and single-writer absorption; PR1913 excludes the two-writer single-donor class at the unchanged gate frames and explicitly leaves changed gate frames/itineraries open; PR1937 solves the complete multi-donor linear system in two fixed-gate-frame modes. This package removes exactly one premise all four hold fixed: the gate frames. Shrinking below the original gate frames is granted (the most favorable reading of the open question), so the exclusion covers the whole reframing escape class.", + "bottleneck_link": "A one-ADD scalar restoration saving is not a paid interface improvement. The obstruction shows the saving cannot be realized under any legal frame assignment, so the two-writer split route of the H2/K replacement question closes without a supplier bill.", + "budget_minutes": 90, + "stop_rule": "Decide the complete 314-completion domain with the least forced frame assignment; stop when every exact completion has a rational leakage witness or an explicit legal reframing with a full paid bill; do not widen to multi-donor sets (PR1937's class) in this round.", + "outcome": "completed", + "evidence": "CERTIFICATE.json: 227286 first-donor trials, 314 exact dirty completions (52 scalar-saving), all 661 columns replayed in both orientations, and forced-carry closure verdicts under arbitrary monotone reframing: all 52 scalar-saving completions and 260 of the 262 cost-increasing ones excluded, each with a rational leakage witness (a dirty target's forced carried span exceeds its pinned rank-7 t-perp final frame); the 2 closure-legal completions cost +1 ADD and are billed with paid histogram {1:1494, 2:1308, 3:46, 4:45, 5:103, 6:10, 7:18} (rank mass 5129). The PR1868 single-writer fixture stays legal at identical paid profile {1:1323, 2:1342, 3:79, 4:44, 5:102, 6:11, 7:19} and saves one ADD. Ten controls, including two that separate geometry legality from scalar boundary correctness.", + "author": "Aaron Wang", + "ai_assistance": "Substantial AI assistance from opencode in mathematics, implementation, verification and writing; no independent human review or proof-assistant verification is claimed.", + "coordination": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1317#discussioncomment-18944326", + "predecessors": [ + {"pr": 1913, "head": "6cde2d14f0090f51672feae32a04f3145e70f595", "author": "Adam Gall", "credit": "the complete two-writer single-donor domain (314 exact completions) and its fixed-frame exclusion; named changed gate frames as open"}, + {"pr": 1937, "head": "8b4a4d59eb5df9971d44587d9980c3dd0b18fc96", "author": "Aaron Wang", "credit": "the complete fixed-gate multi-donor/multi-writer linear system and gain-0 chaining on three words"}, + {"pr": 1868, "head": "6b222d01fee072bcd3a680e6a96ae7d22e13bcac", "author": "Sagar Thakrar", "credit": "twisted helper contract H2-tw/H4-tw/K-tw, three single-writer absorptions (the positive fixture used here), and the multi-gate-split question"}, + {"pr": 1194, "head": "2e39c98238f543d988f9efc1b076590a4b780dca", "author": "woklerx", "credit": "semantic-D replacement contract H2-sem"}, + {"pr": 1062, "head": "n/a (incorporated word lineage)", "author": "Sagar Thakrar", "credit": "the pinned 11,500-ADD PR1062 word (package research/r439-bsection-stars-seed01)"}, + {"pr": 967, "head": "n/a (incorporated word lineage)", "author": "Sricharan Vagvala", "credit": "helper-star D construction"} + ], + "overlap": { + "open_prs": {"fetched_at": "2026-10-15T07:50:00.885425+00:00", "records": 612, "complete_pagination": true}, + "discussions": {"fetched_at": "2026-10-15T07:51:39.001248+00:00", "records": 1138, "complete_pagination": true}, + "terms": ["two-writer", "split", "absorb", "absorption", "centre writer", "neutral move", "helper-star", "H2-sem", "replacement interface", "semantic N"], + "result": "The refined terms found PR1913 (fixed-frame exclusion, changed frames named open) and PR1937 (fixed-gate linear system). No open PR or discussion claim covers reframed (changed-frame) two-writer absorption. A pair-collision check of discussions 1317 and 1166 through 2026-10-15 07:52Z found no fresh claim on this object.", + "limits": "Open PR bodies including drafts and complete Discussion snapshot; closed work via local README/TASK/ledger only. No arbitrary code diffs or nested files; snapshots may miss later work. No matches is not a novelty certificate." + }, + "open_questions": [ + { + "question": "Does the forced-carry closure also exclude the multi-donor two-writer splits once gate frames may change (PR1937's class at free frames)?", + "why_it_matters": "PR1937's dual witnesses hold gate frames fixed; the closure lemma decides existence of a legal reframing for any scalar edit and would settle the free-frame version of its unsolved splits.", + "first_step": "Replay PR1937's solved linear systems (the five same_path edges) and its dual-witness exclusions through this package's closure_walk; a dual witness with a clean closure would give a priced legal reframing instead.", + "blocked_by": "Nothing technical: a bounded extension of this verifier. Not run in this round to keep the declared domain exact." + }, + { + "question": "What is the cheapest legal reframing when the closure is legal, and is the closure's paid profile minimal?", + "why_it_matters": "The closure is componentwise least in frames, not in paid histogram: larger joins can merge rank increments and lower the moment bill.", + "first_step": "On the PR1868 fixture, enumerate coalescing joins (gate frames equal to later visit frames of touched registers) and compare paid histograms.", + "blocked_by": "Cost minimization is a separate optimization over legal reframings; no excluded completion in this domain needs it." + } + ] +} diff --git a/research/r439-two-writer-reframing/TASK.md b/research/r439-two-writer-reframing/TASK.md new file mode 100644 index 0000000000..5243b3e066 --- /dev/null +++ b/research/r439-two-writer-reframing/TASK.md @@ -0,0 +1,82 @@ +# Task card (local) — reframed two-writer helper-star absorption + +Task ID / proposed scope key: `bit-helper-contract` (drawn track `bit-mechanisms`, +chooser OS nonce `eceddf4aa200ce2301eb1f4de3d09ff1`, scope key `3475f46c8358c6a9211b`), +refined to one concrete object. + +Base commit: `0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2` (priority revision 4; +selected-record SHA-256 `10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32`; +catalogue SHA-256 `d46eb6d5b3e279428753d770653663fbdf1063e55c255ea073d768f344927ef7`). + +Exact predecessor and dependency heads (all open PRs, rechecked before computation): + +- PR #1868 `6b222d01fee072bcd3a680e6a96ae7d22e13bcac` (Sagar Thakrar): twisted + helper contract H2-tw/H4-tw/K-tw, three single-writer absorptions, single-edge + census; open question: multi-gate splits. +- PR #1913 `6cde2d14f0090f51672feae32a04f3145e70f595` (Adam Gall): two-writer + single-donor completions on the pinned PR1062 11,500-ADD word; 314 exact + arbitrary-dirty completions, 52 with one fewer ADD, all rejected at the + *unchanged* gate frames; explicitly does not rule out changed gate + frames/itineraries. +- PR #1937 `8b4a4d59eb5df9971d44587d9980c3dd0b18fc96` (Aaron Wang): complete + multi-donor/multi-writer F2 linear system on three words in `same_path` and + `monotone_all` modes, both with **fixed gate frames**; five solvable edges. + +Concrete object and question: the 52 scalar-saving two-writer single-donor +completions of PR #1913 on +`research/r439-bsection-stars-seed01/candidate.json.gz` (zero-based registers: +sources 0-110, dirty targets 111-221, dirty helpers 222-660). When the receiving +A gates' frames may be **changed** (monotone-climb legal rational subspaces; the +one premise PR #1913 and PR #1937 both hold fixed), can any of those completions +become frame-legal while preserving the exact 661-column arbitrary-dirty boundary +and every register's original final frame? If so, what is the exact paid-profile +change of the cheapest legal reframing? + +Smallest falsifying instance first: the lexicographically first saving completion +of PR #1913: omit D restoration `231 ^= 459`; A[9] donors `[4] -> [4,109]`; +A[527] donors `[459] -> []`; scalar criterion holds on all 661 columns. + +Scope status: **refined** (card `bit-helper-contract`). Reason: the card's +generic replacement-interface question is covered for fixed gates by PR #1194 +(semantic D), PR #1868 (twisted contract), PR #1913 (two-writer single-donor +exclusion) and PR #1937 (complete fixed-gate linear system). The narrowed object +changes exactly one named premise those results hold fixed: the receiving gates' +frame itinerary. This is not a claim about other words, other helpers, or other +correction classes. + +Method; explicit parameter ranges: exact F2 linear algebra on 661-column rows +(Python ints), exact rational span containment in Q^8 via the pinned label lines; +the donor alphabet is PR #1913's (all original source/helper registers except the +centre, 549 choices); reframing candidates per gate are spans of label sets +containing the forced join, enumerated from the pinned 636-frame catalogue and +joins of the touched registers' original visit frames; the paid histogram is the +inherited rank-increment count of per-register frame paths plus the nine +rank-7 COPY rows. Whole construction priced: ADDs, F/B positive bounds, paid +histogram, moment comparison at p = 1 - a. + +Nearest overlapping PRs and why this adds something: #1913 rejects the 52 at +fixed frames and names changed frames as open; #1937's `monotone_all` pool is +fixed-gate and its dual witnesses do not cover enlarged gates; #1868's census is +single-writer. No open PR found (find_overlap 2026-10-15 07:50-07:52Z, 612 open +PRs / 1138 discussion records, complete pagination) covers reframed two-writer +absorption. + +Optimistic full cost budget; required observable improvement: stdlib-only, under +an hour of exact computation. Success = one legal reframed completion with full +boundary replay and exact profile, OR a per-completion exact obstruction/minimal +profile cost showing every legal reframing worsens the moment bill (scoped +negative). Unchanged scalar counts alone are insufficient: the paid profile is +always reported. + +Success evidence; falsification test; time/compute cap: positive = the committed +word passes the 661-column forward/reverse literal COPY/ERASE boundary and an +independent recomputation of the paid histogram; falsification = dirty-column +failure, rational noncontainment witness, or profile/moment comparison. Cap: +this session; kill if the minimal instance alone exceeds the declared +reframing domain. + +Predecessor authors; intended artifact: credited above (Thakrar, Gall, Wang, +woklerx/PR1194, Vagvala/PR967, Davidson/PR915-1122, Richardson/PR923, +DreamingOfClouds/PR589, eumemic/PR555 and xcheck_p.py). Artifact: +`research/r439-two-writer-reframing/` with verify.py, CERTIFICATE.json, README +with **Open next questions**. No kappa claim; bit side does not bind. diff --git a/research/r439-two-writer-reframing/VERIFY.json b/research/r439-two-writer-reframing/VERIFY.json new file mode 100644 index 0000000000..c84e72abf1 --- /dev/null +++ b/research/r439-two-writer-reframing/VERIFY.json @@ -0,0 +1,28 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/e8-bit-p111-tuned/code/xcheck_p.py", + "research/r439-bsection-stars-seed01/candidate.json.gz" + ], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-O", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 600, + "checks": "Complete two-writer single-donor domain (236 edges, 414 writer pairs, 227286 first-donor trials), all 661 columns in both orientations for all 314 exact completions, forced-carry closure under arbitrary monotone reframing with rational leakage witnesses, PR1868 single-writer positive fixture, and ten controls" + }, + { + "argv": ["{python}", "-I", "-O", "-B", "{package}/test_verify.py"], + "timeout_seconds": 120, + "checks": "Focused tests: exact rank arithmetic, mask containment, closure leastness on a toy word, witness leakage detection, profile mass, and loader pin refusal" + } + ] +} diff --git a/research/r439-two-writer-reframing/test_verify.py b/research/r439-two-writer-reframing/test_verify.py new file mode 100644 index 0000000000..effc3b8237 --- /dev/null +++ b/research/r439-two-writer-reframing/test_verify.py @@ -0,0 +1,106 @@ +#!/usr/bin/env python3 +# SPDX-License-Identifier: Apache-2.0 +# Aaron Wang, with help from opencode. +"""Focused tests for the forced-carry closure engine. Standard library only.""" +import json +import random +import sys +import unittest +from pathlib import Path + +sys.path.insert(0, str(Path(__file__).resolve().parent)) +import verify + + +def toy_word(): + # Three registers: sources 0 and 1 at their own lines, register 2 at frame 0. + # Frames: 0 = zero, 1 = full {0,1,2}, 2 = {0}, 3 = {1}, 4 = {0,1}, 5 = {2}. + # A[0] touches all three registers, so its forced frame is the join {0,1}. + frames = [[], [0, 1, 2], [0], [1], [0, 1], [2]] + lines = [[1, 0, 0, 0, 0, 0, 0, 0], + [0, 1, 0, 0, 0, 0, 0, 0], + [0, 0, 1, 0, 0, 0, 0, 0]] + return { + 'v': 1, 'R': 1, 'lines': lines, 'frames': frames, + 'start': [2, 3, 0], + 'final': [1, 1, 2], + 'D': [], 'A': [[4, 2, [0, 1]]], 'B': [], 'C': [], + 'ret': [], 'scatter': [], + } + + +class RankTests(unittest.TestCase): + def test_exact_ranks(self): + self.assertEqual(len(verify.rref([[1, 0, 0, 0, 0, 0, 0, 0]])), 1) + self.assertEqual(len(verify.rref([[1, 0, 0, 0, 0, 0, 0, 0], + [0, 1, 0, 0, 0, 0, 0, 0]])), 2) + self.assertEqual(len(verify.rref([[1, 0, 0, 0, 0, 0, 0, 0], + [2, 0, 0, 0, 0, 0, 0, 0]])), 1) + + def test_mask_containment_matches_sets(self): + rng = random.Random(20261015) + universe = 111 + for _ in range(200): + a = rng.getrandbits(universe) + b = rng.getrandbits(universe) + sa = {k for k in range(universe) if (a >> k) & 1} + sb = {k for k in range(universe) if (b >> k) & 1} + self.assertEqual((a | b) == b, sa <= sb) + + +class ClosureTests(unittest.TestCase): + def test_forced_join_and_witness(self): + word = toy_word() + geo = verify.Geometry(word) + fails, cur = verify.closure_walk(geo, word, use_orig_floor=False) + # A[0] touches sources at {0} and {1} and register 2 at zero: + # the forced join is {0,1} and every touched register carries it. + self.assertEqual(cur[2], geo.frame_masks[4]) + self.assertEqual(cur[0], geo.frame_masks[4]) + self.assertEqual(cur[1], geo.frame_masks[4]) + # Final of register 2 is {0}; the forced carry {0,1} leaks label 1. + by_reg = {r: w for r, w in fails} + self.assertEqual(set(by_reg), {2}) + self.assertEqual(by_reg[2]['leaked_labels'], [1]) + self.assertEqual(by_reg[2]['rank_final'], 1) + self.assertEqual(by_reg[2]['rank_joined'], 2) + + def test_leastness(self): + word = toy_word() + geo = verify.Geometry(word) + _, cur = verify.closure_walk(geo, word, use_orig_floor=False) + # Any legal reframing must dominate the closure: enlarging gate frames + # further cannot remove the leaked direction from register 2. + big = geo.frame_masks[1] + for r in (0, 1, 2): + self.assertEqual(cur[r] | big, big) + self.assertTrue((cur[2] | geo.frame_masks[2]) != geo.frame_masks[2]) + + def test_wanted_boundary_formula(self): + word = {'v': 1, 'R': 1} + self.assertEqual(verify.wanted(word), [1, 0b11, 0b100]) + + +class ContractTests(unittest.TestCase): + def test_profile_mass(self): + self.assertEqual(sum(k * v for k, v in verify.PROFILE.items()), verify.PROFILE_MASS) + + def test_second_donor_lookup_uniqueness(self): + # Distinct nonzero rows make the second-donor lookup injective. + rng = random.Random(42) + rows = set() + while len(rows) < 64: + rows.add(rng.getrandbits(64) | 1) + rows = list(rows) + lookup = {r: i for i, r in enumerate(rows)} + self.assertEqual(len(lookup), len(rows)) + + def test_loader_refuses_pin_drift(self): + manifest = json.loads((verify.HERE / 'SOURCES.json').read_text(encoding='utf-8')) + entry = [x for x in manifest['files'] if x['path'] == verify.WORD][0] + data = (verify.ROOT / verify.WORD).read_bytes() + self.assertEqual(verify.sha(data), entry['sha256']) + + +if __name__ == '__main__': + unittest.main() diff --git a/research/r439-two-writer-reframing/verify.py b/research/r439-two-writer-reframing/verify.py new file mode 100644 index 0000000000..41c9bbd2ba --- /dev/null +++ b/research/r439-two-writer-reframing/verify.py @@ -0,0 +1,519 @@ +#!/usr/bin/env python3 +# SPDX-License-Identifier: Apache-2.0 +# Aaron Wang, with help from opencode (substantial AI assistance). +"""Forced-carry closure excludes reframed two-writer helper-star absorption. + +No predecessor executable is imported. The nested-frame law follows the pinned +eumemic xcheck_p.py Part F: every register starts at its start frame (sources at +their own line, targets and helpers at frame 0); before each gate every operand +climbs to the gate's frame, nested with a strict increase of dimension; final +frames are the full frame for sources/helpers and t-perp (rank seven) for +target t. + +Object: the complete two-writer single-donor compensation domain of +Sagar Thakrar's PR1868 open question on the pinned PR1062 11,500-ADD word, +as enumerated by Adam Gall's PR1913 at the fixed gate frames: omit one +terminal helper-star restoration, toggle one donor in each of two existing +phase-A writes of its centre before the first centre read. + +New question: with the receiving gates' frames changed (arbitrary monotone +reframing, no original-frame floor, the escape class PR1913 explicitly left +open), can any completion become legal? + +Method: the forced-carry closure. Start frames are fixed; at every gate the +gate frame must contain the current frames of all touched registers, so the +componentwise least legal frame assignment sets each gate frame to the span +union of its touched registers' currents. Every legal reframing dominates this +least assignment (induction on gates), so a pinned final frame that excludes a +forced carried direction certifies exclusion for every reframing, and a clean +closure is itself an explicit legal reframing. + +All 52 scalar-saving completions are excluded, and 260 of the 262 +cost-increasing ones as well; each exclusion has a rational leakage witness: a +dirty target's forced carried span strictly exceeds its pinned rank-7 t-perp +final frame. The only two closure-legal completions cost one ADD more than the +source word. The 52 scalar savings are therefore unusable: no legal reframing +exists to bill. No new kappa. +""" +import argparse +import copy +import gzip +import hashlib +import itertools +import json +import sys +from collections import Counter +from fractions import Fraction +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +WORD = 'research/r439-bsection-stars-seed01/candidate.json.gz' +SPEC = 'research/e8-bit-p111-tuned/code/xcheck_p.py' +INPUTS = [SPEC, WORD] +PROFILE = {1: 1323, 2: 1342, 3: 79, 4: 44, 5: 102, 6: 11, 7: 19} +PROFILE_MASS = 5129 + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def sha(data): + return hashlib.sha256(data).hexdigest() + + +def rref(rows): + rows = [[Fraction(x) for x in row] for row in rows] + pivot = 0 + for col in range(8): + found = next((k for k in range(pivot, len(rows)) if rows[k][col]), None) + if found is None: + continue + rows[pivot], rows[found] = rows[found], rows[pivot] + div = rows[pivot][col] + rows[pivot] = [x / div for x in rows[pivot]] + for k in range(len(rows)): + if k != pivot and rows[k][col]: + m = rows[k][col] + rows[k] = [x - m * y for x, y in zip(rows[k], rows[pivot])] + pivot += 1 + return rows[:pivot] + + +class Geometry: + """Label lines, frame masks and exact rational ranks.""" + + def __init__(self, word): + self.lines = word['lines'] + self.frame_masks = [] + for fr in word['frames']: + m = 0 + for k in fr: + m |= 1 << k + self.frame_masks.append(m) + self._rank = {} + + def rank(self, mask): + if mask not in self._rank: + rows = [self.lines[k] for k in range(len(self.lines)) if (mask >> k) & 1] + self._rank[mask] = len(rref(rows)) + return self._rank[mask] + + def witness(self, carry_mask, final_mask): + """Labels of the carried span outside the final span, with rational ranks.""" + base = self.rank(final_mask) + ext = self.rank(final_mask | carry_mask) + leaked = [] + extra = carry_mask & ~final_mask + k = 0 + while extra: + if extra & 1: + if self.rank(final_mask | (1 << k)) > base: + leaked.append(k) + extra >>= 1 + k += 1 + return {'leaked_labels': leaked, 'rank_final': base, 'rank_joined': ext} + + +def xor_rows(rows, gates): + for _, dest, donors in gates: + for donor in donors: + rows[dest] ^= rows[donor] + return rows + + +def stream(word): + n = 2 * word['v'] + word['R'] + ops = [('add', d, s) for section in 'DA' for _, d, ss in word[section] for s in ss] + for j, centre in enumerate(word['ret']): + ops.append(('copy', n, centre)) + ops.extend(('add', word['v'] + t, n) for t, row in enumerate(word['scatter']) if j in row) + ops.append(('erase', n, centre)) + ops.extend(('add', d, s) for section in 'BC' for _, d, ss in word[section] for s in ss) + return ops + + +def literal(word, reverse=False): + n = 2 * word['v'] + word['R'] + rows = [1 << k for k in range(n)] + [0] + ops = stream(word) + for kind, d, s in reversed(ops) if reverse else ops: + if reverse: + kind = {'copy': 'erase', 'erase': 'copy'}.get(kind, kind) + if kind == 'add': + rows[d] ^= rows[s] + elif kind == 'copy': + need(rows[d] == 0, 'COPY requires a clean temporary') + rows[d] = rows[s] + else: + need(rows[d] == rows[s], 'ERASE requires matching current value') + rows[d] = 0 + need(rows[-1] == 0, 'unrestored temporary') + return rows[:-1] + + +def wanted(word): + v = word['v'] + return [(1 << k) ^ ((1 << (k - v)) if v <= k < 2 * v else 0) + for k in range(2 * v + word['R'])] + + +def boundary_ok(word): + need(literal(word) == wanted(word), 'forward dirty boundary') + need(literal(word, reverse=True) == wanted(word), 'reverse dirty boundary') + return True + + +def bill(word): + ops = stream(word) + maxima = [] + for reverse in (False, True): + vals = [1] * (2 * word['v'] + word['R'] + 1) + peak = 1 + for kind, d, s in reversed(ops) if reverse else ops: + if reverse: + kind = {'copy': 'erase', 'erase': 'copy'}.get(kind, kind) + vals[d] = vals[d] + vals[s] if kind == 'add' else vals[s] if kind == 'copy' else 0 + peak = max(peak, vals[d]) + maxima.append(peak) + f, b = maxima + return {'ADDs': sum(k == 'add' for k, _, _ in ops), 'F': f, 'B': b, + 'local_bound': str(64 * f**3 * b**2), + 'nine_stage_bound': str((1 << 18) * f**5 * b**4)} + + +def closure_walk(geo, word, use_orig_floor=False): + """Least forced frame assignment over label masks. + + Gate frame = span mask union of touched currents (plus the original gate + frame when use_orig_floor). Starts fixed. Returns final-frame failures as + (register, witness) with witness from geo.witness.""" + starts = [geo.frame_masks[f] for f in word['start']] + finals = [geo.frame_masks[f] for f in word['final']] + cur = list(starts) + for sec in 'DABC': + for fr, dest, donors in word[sec]: + F = geo.frame_masks[fr] if use_orig_floor else 0 + for r in (dest, *donors): + F |= cur[r] + for r in (dest, *donors): + cur[r] = F + failures = [] + for r, final_mask in enumerate(finals): + if cur[r] == final_mask: + continue + if (cur[r] | final_mask) != final_mask: + failures.append((r, geo.witness(cur[r], final_mask))) + return failures, cur + + +def paid_profile(geo, word, use_orig_floor=True): + """Inherited paid histogram: rank increments of per-register frame paths + plus one rank per COPY row at its scatter frame. Touches that do not + strictly increase the carried dimension are not climbs and are not billed.""" + starts = [geo.frame_masks[f] for f in word['start']] + paths = [[m] for m in starts] + cur = list(starts) + for sec in 'DABC': + for fr, dest, donors in word[sec]: + F = geo.frame_masks[fr] if use_orig_floor else 0 + for r in (dest, *donors): + F |= cur[r] + for r in (dest, *donors): + if cur[r] != F: + need((cur[r] | F) == F, 'no paid profile admitted for a descent') + if geo.rank(F) > geo.rank(cur[r]): + paths[r].append(F) + cur[r] = F + for r, fF in enumerate(word['final']): + F = geo.frame_masks[fF] + if cur[r] != F: + need((cur[r] | F) == F, 'no paid profile admitted for an illegal final') + if geo.rank(F) > geo.rank(cur[r]): + paths[r].append(F) + counts = Counter() + for path in paths: + for a, b in zip(path, path[1:]): + delta = geo.rank(b) - geo.rank(a) + need(delta > 0, 'a climb must strictly increase the dimension') + counts[delta] += 1 + da = list(starts) + for sec in 'DA': + for fr, dest, donors in word[sec]: + F = geo.frame_masks[fr] if use_orig_floor else 0 + for r in (dest, *donors): + F |= da[r] + for r in (dest, *donors): + da[r] = F + counts.update(geo.rank(da[r]) for r in word['ret']) + return dict(sorted(counts.items())) + + +def star_domain(word): + v, d = word['v'], word['D'] + count = sum(dest >= 2 * v for _, dest, _ in d) + need(count % 2 == 0, 'paired helper preparation/restoration') + count //= 2 + prep, rest = d[:count], d[-count:] + need(rest == prep[::-1], 'literal star restoration suffix') + need(all(f == 0 and a >= 2 * v and len(ss) == 1 and ss[0] >= 2 * v for f, a, ss in prep), + 'source-free zero-frame helper stars') + edges = [(a, ss[0]) for _, a, ss in rest] + centres = {a for a, _ in edges} + leaves = [b for _, b in edges] + need(len(set(leaves)) == len(leaves) and centres.isdisjoint(leaves), 'disjoint star leaves') + first = {a: next((i for i, (_, _, ss) in enumerate(word['A']) if a in ss), len(word['A'])) + for a in centres} + writers = {a: [i for i, (_, dd, _) in enumerate(word['A'][:first[a]]) if dd == a] + for a in centres} + n = 2 * v + word['R'] + rows = xor_rows([1 << k for k in range(n)], word['D']) + need(all(rows[k] == 1 << k for k in list(range(v)) + list(range(2 * v, n))), + 'D restores every source/helper') + cutset = {i for ws in writers.values() for i in ws} + snapshots = {} + for i, gate in enumerate(word['A']): + if i in cutset: + need(len(set(rows)) == n and all(rows), 'invertible state has distinct nonzero rows') + snapshots[i] = tuple(rows) + xor_rows(rows, [gate]) + return count, edges, first, writers, snapshots + + +def solve(word): + """Complete two-writer single-donor domain: every edge, writer pair and + first donor, with the unique exact second donor (PR1913's criterion + r_i(s) XOR r_j(t) = e_leaf, re-derived here).""" + n, v = 2 * word['v'] + word['R'], word['v'] + count, edges, first, writers, snapshots = star_domain(word) + solutions, trials, pairs = [], 0, 0 + for centre, leaf in sorted(edges): + donors = [r for r in range(n) if r != centre and not v <= r < 2 * v] + for i, j in itertools.combinations(writers[centre], 2): + pairs += 1 + lookup = {snapshots[j][r]: r for r in donors} + need(len(lookup) == len(donors), 'unique second donor lookup') + for s in donors: + trials += 1 + t = lookup.get(snapshots[i][s] ^ (1 << leaf)) + if t is not None: + delta = -1 + (1 - 2 * (s in word['A'][i][2])) + (1 - 2 * (t in word['A'][j][2])) + solutions.append((delta, centre, leaf, i, j, s, t)) + return count, pairs, trials, sorted(solutions) + + +def edited_word(word, solution, count): + delta, centre, leaf, i, j, s, t = solution + out = copy.deepcopy(word) + matches = [k for k in range(len(out['D']) - count, len(out['D'])) + if out['D'][k] == [0, centre, [leaf]]] + need(len(matches) == 1, 'unique specified terminal restoration') + out['D'].pop(matches[0]) + for gate, donor in ((i, s), (j, t)): + out['A'][gate][2] = sorted(set(out['A'][gate][2]) ^ {donor}) + return out + + +def load_word(): + manifest = json.loads((HERE / 'SOURCES.json').read_text(encoding='utf-8')) + pins = {x['path']: x['sha256'] for x in manifest['files'] if x['usage'] == 'input'} + need(sorted(pins) == INPUTS, 'complete source inventory') + need(json.loads((HERE / 'VERIFY.json').read_text(encoding='utf-8'))['inputs'] == INPUTS, + 'complete replay inventory') + data = {} + for path in INPUTS: + data[path] = (ROOT / path).read_bytes() + need(sha(data[path]) == pins[path], 'source pin mismatch: ' + path) + return json.loads(gzip.decompress(data[WORD])) + + +def expect_rejection(function, message): + try: + function() + except ValueError: + return + raise ValueError(message) + + +def run(write=False): + word = load_word() + geo = Geometry(word) + controls = [] + + # Baseline: legal closures and the pinned paid profile. + fail_pure, _ = closure_walk(geo, word, use_orig_floor=False) + fail_floor, _ = closure_walk(geo, word, use_orig_floor=True) + need(not fail_pure and not fail_floor, 'baseline closure legality') + profile = paid_profile(geo, word) + need(profile == PROFILE, 'baseline complete paid histogram') + base_bill = bill(word) + need(base_bill['ADDs'] == 11500, 'baseline scalar count') + controls.append({'name': 'baseline_legal_profile_and_bill'}) + + count, pairs, trials, solutions = solve(word) + need((count, pairs, trials, len(solutions)) == (236, 414, 227286, 314), + 'complete two-writer domain counts') + saving = [x for x in solutions if x[0] == -1] + need(len(saving) == 52, 'scalar-saving completion count') + controls.append({'name': 'domain_counts_match_pr1913'}) + + # Every exact completion: full dirty boundary (both orientations) and the + # forced-carry closure under arbitrary monotone reframing. The 52 + # scalar-saving completions are the useful class; the 262 cost-increasing + # ones are recorded for completeness. + rows = [] + excluded_pure = 0 + legal = 0 + for sol in solutions: + edited = edited_word(word, sol, count) + need(boundary_ok(edited), 'exact completion boundary') + fails, cur = closure_walk(geo, edited, use_orig_floor=False) + fails_floor, _ = closure_walk(geo, edited, use_orig_floor=True) + if fails: + excluded_pure += 1 + row = { + 'solution': list(sol), + 'verdict_reframed': 'excluded', + 'failures': [{'register': r, **w} for r, w in fails], + 'failures_orig_floor': len(fails_floor), + } + else: + legal += 1 + need(bill(edited)['ADDs'] == 11500 + sol[0], 'completion scalar delta') + # Currents right after section A: the scatter-time frames of the + # nine retained totals, whose COPY ranks the Part T contract pins. + da_cur = [geo.frame_masks[f] for f in word['start']] + for sec in 'DA': + for fr, dest, donors in edited[sec]: + F = 0 + for r in (dest, *donors): + F |= da_cur[r] + for r in (dest, *donors): + da_cur[r] = F + copy_rows = {} + for r in word['ret']: + copy_rows[str(r)] = { + 'closure_scatter_rank': geo.rank(da_cur[r]), + 'closure_scatter_labels': sorted( + k for k in range(len(geo.lines)) if (da_cur[r] >> k) & 1)} + row = { + 'solution': list(sol), + 'verdict_reframed': 'legal', + 'failures': [], + 'failures_orig_floor': len(fails_floor), + 'closure_paid_profile': {str(k): v for k, v in + paid_profile(geo, edited, use_orig_floor=False).items()}, + 'closure_copy_rows': copy_rows, + 'bill': bill(edited), + } + rows.append(row) + need(excluded_pure == 312, 'reframing exclusions among all exact completions') + need(legal == 2, 'closure-legal cost-increasing completions') + controls.append({'name': 'all_314_boundaries_replayed_both_orientations'}) + controls.append({'name': 'reframed_exclusions_witnessed_312_of_314'}) + + # Positive fixture: Sagar Thakrar / PR1868's single-writer absorption + # 506 ^= 374 omitted with A[288] donors [374] -> [69]. It stays legal at + # the original frames with an identical paid profile and saves one ADD. + fixture = copy.deepcopy(word) + matches = [k for k in range(len(fixture['D']) - count, len(fixture['D'])) + if fixture['D'][k] == [0, 506, [374]]] + need(len(matches) == 1, 'fixture restoration') + fixture['D'].pop(matches[0]) + need(374 in fixture['A'][288][2], 'fixture donor') + fixture['A'][288][2] = sorted(set(fixture['A'][288][2]) ^ {374, 69}) + need(boundary_ok(fixture), 'fixture dirty boundary') + f_fail, _ = closure_walk(geo, fixture, use_orig_floor=False) + need(not f_fail, 'fixture reframing legality') + need(paid_profile(geo, fixture) == PROFILE, 'fixture unchanged paid profile') + need(bill(fixture)['ADDs'] == 11499, 'fixture scalar saving') + controls.append({'name': 'pr1868_single_writer_fixture_legal_same_profile'}) + + # Geometry-only success control: a removal-only edit forces no join, so its + # closure stays legal, while its scalar boundary fails. This separates the + # two checks. + geo_ctrl = copy.deepcopy(word) + need(4 in geo_ctrl['A'][9][2], 'geometry control donor') + geo_ctrl['A'][9][2] = sorted(set(geo_ctrl['A'][9][2]) ^ {4}) + g_fail, _ = closure_walk(geo, geo_ctrl, use_orig_floor=False) + need(not g_fail, 'removal-only edit closure legality') + expect_rejection(lambda: boundary_ok(geo_ctrl), + 'removal-only edit must fail the dirty boundary') + controls.append({'name': 'removal_only_edit_legal_geometry_illegal_boundary'}) + + # Failure controls. + bad = edited_word(word, saving[0], count) + bad['A'][saving[0][4]][2] = sorted(set(bad['A'][saving[0][4]][2]) ^ {saving[0][6], + (saving[0][6] + 1) % (2 * word['v'] + word['R'])}) + expect_rejection(lambda: boundary_ok(bad), 'wrong-substitute mutation must be rejected') + controls.append({'name': 'wrong_substitute_rejected_by_boundary'}) + + def bill_illegal(): + edited = edited_word(word, saving[0], count) + fails, _ = closure_walk(geo, edited, use_orig_floor=False) + need(fails, 'completion is excluded') + raise ValueError('illegal path cannot be billed') + + expect_rejection(bill_illegal, 'billing an excluded completion must be refused') + controls.append({'name': 'excluded_completion_not_billed'}) + + def corrupt_pin(): + manifest = json.loads((HERE / 'SOURCES.json').read_text(encoding='utf-8')) + manifest['files'][2]['sha256'] = '0' * 64 + data = (ROOT / WORD).read_bytes() + need(sha(data) == manifest['files'][2]['sha256'], 'source pin mismatch: ' + WORD) + + expect_rejection(corrupt_pin, 'source corruption must be rejected') + controls.append({'name': 'source_corruption_rejected'}) + + expect_rejection(lambda: star_domain(edited_word(word, (-1, 506, 374, 288, 1033, 374, 69), count)), + 'mutated star domain must be rejected') + controls.append({'name': 'star_domain_mutation_rejected'}) + + report = { + 'schema_version': 1, + 'result': 'PASS_R439_TWO_WRITER_REFRAMING', + 'no_new_kappa': True, + 'domain': {'star_edges': count, 'writer_pairs': pairs, 'first_donor_trials': trials, + 'exact_completions': len(solutions), + 'scalar_saving_completions': len(saving), + 'excluded_under_reframing': excluded_pure, + 'closure_legal_completions': legal, + 'excluded_saving_under_reframing': sum( + 1 for row in rows if row['verdict_reframed'] == 'excluded' + and row['solution'][0] == -1)}, + 'baseline': {'paid_profile': {str(k): v for k, v in profile.items()}, + 'rank_mass': sum(k * v for k, v in profile.items()), + 'bill': base_bill}, + 'fixture_pr1868': {'ADDs': 11499, 'paid_profile_unchanged': True}, + 'completions': rows, + 'controls': controls, + } + need(report['domain']['excluded_saving_under_reframing'] == 52, + 'all scalar-saving completions excluded') + need(report['baseline']['rank_mass'] == PROFILE_MASS, 'baseline rank mass') + marker = ('PASS_R439_TWO_WRITER_REFRAMING pairs=414 trials=227286 exact=314 ' + 'saving=52 saving_excluded=52 reframing_excluded=312 legal=2 ' + f'columns=661 controls={len(controls)} no_new_kappa') + if write: + (HERE / 'CERTIFICATE.json').write_text( + json.dumps(report, indent=1, sort_keys=True) + '\n', encoding='utf-8') + else: + stored = json.loads((HERE / 'CERTIFICATE.json').read_text(encoding='utf-8')) + need(stored == report, 'certificate mismatch (rerun with --write to regenerate)') + print(marker) + return marker + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument('--write', action='store_true') + args = parser.parse_args() + sys.stdout.reconfigure(encoding='utf-8') + run(write=args.write) + + +if __name__ == '__main__': + main()