diff --git a/research/anticipatory-lender-cleanup/README.md b/research/anticipatory-lender-cleanup/README.md new file mode 100644 index 0000000000..180acce9ec --- /dev/null +++ b/research/anticipatory-lender-cleanup/README.md @@ -0,0 +1,283 @@ +# PR2226 low lenders: exact cleanup and availability certificate + +**Finite certificate and scoped proof; no new supplier or κ.** For the +32 low lenders in Cinna Davis's [PR2226](https://github.com/CrocSwap/integer-mult-bounds/pull/2226), +all 48 retained early-tail operations are necessary to restore their original +arbitrary dirty inputs. The fixed cleanup consists of 32 subtractions and +16 negations. Its 32 distinct sources each require a rank-one promotion from +their last rank-three read to the rank-four cleanup frame. Those promotions +are already part of the predecessor's bill; this does not add 32 new charges. + +For **exactly k restored lender rows**, the minimum retained-operation count is + +\[ + C(k)=k+\max(0,k-16),\qquad 0\leq k\leq32. +\] + +This is a minimum within the **fixed 48-operation alphabet**, with the +subtraction before negation on a shared destination. It is not a minimum over +arbitrary circuits, changed coefficients, signed loan references, other +lenders, new observations or rewritten compensation. Partial subsets attain +the stated *row-restoration* contract; they are not asserted to form valid +partial suppliers or to preserve the other 48 loans. + +The second result is an exact interval certificate for retiming the **full** +cleanup while retaining the word's monotone frames and withdrawing each +physical operand at its recorded handoff. Five subtractions have a stricter +deadline than the low lender's handoff because their source is borrowed first. +The original earliest schedule and the latest permitted schedule have identical +frame endpoints and identical frame invoices through all 1,846 B events and +all 80 handoffs. Exact free-operator replay also gives identical complete rows +on all 624 arbitrary inputs, with `Y+=X` at the B endpoint. No defect in PR2226's original early schedule was found. + +## Reproduce and evidence + +Use Python 3.12 and its standard library; no numerical packages or network +access are needed. From the repository root: + +```sh +python3 -I -B scripts/research_package.py --package research/anticipatory-lender-cleanup --check-only +python3 -I -B scripts/research_package.py --package research/anticipatory-lender-cleanup +python3 -I -O -B research/anticipatory-lender-cleanup/verify.py +``` + +Expected direct output: + +```text +PASS_ANTICIPATORY_LENDER_CLEANUP lenders=32 subsets=281474976710656 tail_gates=48 rank1=32 source_deadlines=5 no_new_kappa +``` + +The direct checker takes approximately two seconds on a CPU. It writes no files +unless `--record NEW_PATH` is explicitly requested; that path must not exist. +No predecessor checker is imported. [RESULT.json](RESULT.json) contains: + +- All 64 relevant lender/source rows, independently reconstructed by forward + propagation on the 512 remaining non-target inputs and backward functional + propagation through the original 704-input prefix. The 112 Y inputs cannot + affect these non-target rows. The full borrowed word has 624 inputs. +- All 96 local subset outcomes, whose product covers **2^48** global subsets, + the complete 425-entry cost/restored-row distribution, and all 33 minima. +- Every actual last-read event, both endpoint frame bases, the 32 release + intervals, five source-limited deadlines, and the number of complete cut + assignments under the convention below. +- Chronological frame traces for both extreme schedules, including the actual + virtual-to-physical alias map and all 80 equal-dimensional handoffs. Both + complete scalar prefixes are also replayed over noncommuting loan operators; + all 624 output rows agree, all 32 low rows equal their original dirt at + handoff, and the 112 Y outputs equal `Y+X`. +- 136 rejecting semantic cases: 48 single omissions, 16 reversed subtraction/ + negation pairs, 32 early cuts, five missed source withdrawals, 32 + equal-rank wrong-subspace cases, one input-label mutation, and missing/wrong-sign + initial compensation. The 37 cut + mutations also fail the separate raw chronological frame executor. + Both extreme schedules and 32 equivalent frame-basis changes pass. + +`-O` does not disable any check. Source authentication checks SHA256 and Git +blob digests, including the decompressed word payload. Expected receipts use +typed canonical JSON, and duplicate JSON keys are rejected. + +## Exact sources and distinction from earlier work + +The scientific/task-selection base is main +`0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2`, priority revision 4. The only +mathematical data dependency is PR2226 head +`dacaf3d81f1936bb55b8454b1244e5d014272754`. Its word, witness, block certificate +and notice are retained byte-for-byte in `inputs/`; [SOURCE-PINS.json](SOURCE-PINS.json) +records original paths, commit, Git blobs and SHA256 hashes. The selected +word and block certificate descend from Ali Romman's +`complex-block-rank-optimum` at `697b00e5d36297563c22aac080dd5dee398c2624`. + +PR2226 already provides the 80-alias construction, the 48 early-tail gates, +positive lender-restoration checks, and full logical cleanup. This package +adds the **all-subset necessity proof, sharp partial row-restoration tradeoff, +and the exact pre-handoff retiming intervals**. Its positive checks independently +bind those statements to the original data; the original gate count, `Y+=X` +endpoint and construction are not claimed as new. +The new complete-prefix comparison checks their preservation under the +certified latest cleanup retiming. + +[PR2339](https://github.com/CrocSwap/integer-mult-bounds/pull/2339) and this +account's [PR2394](https://github.com/CrocSwap/integer-mult-bounds/pull/2394) +concern later T74 words and native initial compensation. They are context, +not inputs or a transfer of this certificate to those words. +[PR2573](https://github.com/CrocSwap/integer-mult-bounds/pull/2573) excludes +additional loans in a different ordinary retired-lender class; this result +fixes PR2226's low-lender cleanup. Source-partner substitutions and owner +repacking in PR2530/2571/2575/2588 are also different objects. + +The task card is [TASK.json](TASK.json): `complex-new-helper-inventory`, +scope key `f3b0895a4f9f1cc62e75`, changed from interface synthesis to this +necessary boundary check. It does not meet or claim the original card's +new-construction/packing-improvement acceptance gate. The selected result and +all predecessor packages remain unchanged. The claim is in +[discussion #2615](https://github.com/CrocSwap/integer-mult-bounds/discussions/2615). + +The final refresh found main `b4560d9e7216f72b73c5aa940ac099c05e33ccf9` and +priority revision 5. Its new family-expansion guidance was read; the selected +record and PR2226 source head are unchanged. This package retains historical +revision-4 task provenance and is integrated on the refreshed main. The declared +milestone is **audit**. Decision: conclude this bounded audit, with no dependent +construction expansion inferred from the local result. Native restoration, +consumer/hosting and all-size costs remain unverified here; unknown costs are +not zero. TASK.json records the refresh and obligation ledger. + +## Proof of the subset classification + +Write `u_d` for lender d's own original arbitrary input and `v_s` for the +current value of its cleanup source s. Direct rational replay gives exactly +two component types: + +| Number of lenders | Before cleanup | Retained operations | After both/all operations | +| --- | --- | --- | --- | +| 16 | `u_d + v_s` | `d -= s` | `u_d` | +| 16 | `-u_d + v_s` | `d -= s; d = -d` | `u_d` | + +Each `v_s` is a nonzero rational combination of original X inputs, independent +of `u_d`. The coefficients and original input labels are recorded for every +component. No ordinary changed-B instruction writes any of these 64 roles +before its physical withdrawal. All 32 cleanup destinations differ, all +32 sources differ, and no cleanup source is a cleanup destination. The +source *values* need not be mutually independent: disjoint writes and +independence from each corresponding `u_d` suffice. + +For a one-operation component, omission leaves `u_d+v_s`, which is not the +required identity for arbitrary inputs. For a two-operation component, the +four retained-order subsets give + +\[ + -u_d+v_s,\quad -u_d,\quad u_d-v_s,\quad u_d. +\] + +Only the complete pair restores the input. Reversing the two operations gives +`u_d-2v_s`, also incorrect. No omissions in another component can change these +rows, because none of its writes targets d or s. This proves the classification +for all 2^48 subsets without treating successful single-omission tests as an +exhaustive proof. + +If x counts retained operations and y counts restored lender rows, the exact +subset enumerator is + +\[ + (1+xy)^{16}(1+2x+x^2y)^{16}. +\] + +To restore k rows, use at most the 16 one-operation components first. Every +additional restored row requires two operations. This proves the lower bound +`C(k)`, and choosing those complete components attains it. In particular, the +only subset restoring all 32 rows is the full 48-operation set. + +## Proof of the frame and deadline certificate + +A B cut c means **before B[c]**. All cleanup assigned to c executes first, +then all handoffs at c, then deferred/rewritten ordinary instructions and +B[c]. Within one cleanup component, subtraction precedes negation, including +when they share a cut. Different components commute. Cuts and operation +indices are zero-based. + +For each component the lender already has rank-four frame U and has no +ordinary B use. Its source follows a retained nested frame path ending with a +rank-three read in V strictly contained in U. The actual last-read indices +range from 719 to 855. The source row is unchanged by B before borrowing. +The cleanup subtraction requires both operands in U. + +Let L be one plus that last-read index. Any subtraction before cut L promotes +its source to U before the retained rank-three read. A monotone continuation +would then require `U ⊆ V`, which is false. Thus L is a **necessary** release +cut, even though the scalar subtraction would commute with ordinary reads. +At L the source can make the one-dimensional transition `V ⊂ U`; the lender +requires no promotion. There are 32 distinct sources, so the full cleanup +contains exactly 32 such rank-one transitions. Delaying the gates does not +merge them or remove their cost. + +Let H_d be the lender's handoff cut and H_s the source's handoff cut, with +`H_s = infinity` for a source not borrowed. The retained operand-identity +contract withdraws a field at its handoff. Therefore the subtraction can be +placed at precisely + +\[ + L\leq a\leq\min(H_d,H_s). +\] + +For a two-operation component, negation can then be placed at any cut + +\[ + a\leq b\leq H_d. +\] + +These are sufficient as well: there is no intervening write to either +unwithdrawn operand, all ordinary source reads are finished, and the lender +stays in U until its handoff. Once the subtraction has read the source, +negation no longer needs that source. The completed lender is `u_d` at +handoff. The changed source's frame is U in time for its own fixed handoff. +All subsequent source-bound frame transitions are identical. This is a proof +for every cut assignment, with the two extreme executions as source-bound +controls; it is not an inference from testing only two schedules. + +Five additions have `H_s < H_d`: + +| Lender d | Source s | Earliest addition L | Last addition H_s | Lender handoff H_d | +| --- | --- | --- | --- | --- | +| 277 | 281 | 720 | 1142 | 1150 | +| 282 | 285 | 722 | 1142 | 1150 | +| 346 | 349 | 801 | 1054 | 1070 | +| 357 | 361 | 817 | 1054 | 1142 | +| 362 | 365 | 819 | 1054 | 1070 | + +A scheduler checking only the lender's deadline would permit a stale source +read in these five cases. The original schedule satisfies all five bounds. +The remaining 27 addition deadlines equal the lender deadline; all component +rows and intervals are in RESULT.json. + +For one-operation components the number of cut assignments is `U-L+1`, where +`U=min(H_d,H_s)`. For two-operation components it is +`sum(a=L..U) (H_d-a+1)`. Their product, computed exactly in the receipt, counts +complete cut assignments with canonical commuting order at a shared cut; it +does not count arbitrary micro-orderings. The frame invoice through the end +of B, including COPY but **before final restoration**, is +`{1:2010,2:347,3:334,4:128,5:26,8:8}` for both extreme schedules. This prefix +profile must not be substituted for PR2226's complete local profile. + +## Limits + +The result fixes the source word, 48 cleanup gates and coefficients, original +input labels, rank-four cleanup frames, monotone ordinary frame paths, handoff +cuts and the requirement to restore the original signed dirty value. No new +read after physical withdrawal is allowed. More general reference changes, +nonmonotone adapters, alternative source combinations, copied observations, +changed compensation or other lenders are outside the theorem. + +The complete B prefix is checked, including `Y+=X`. This does not check final +non-target restoration, exact Gaussian phases, inverse-transpose execution, private inverse-cleanup buffers, full native +lowering, global ownership, precision/tape, all-size recursion or the outer +transfer. The original positive construction remains credited to PR2226; +its full verifier and the selected supplier cold replay were not rerun here. +No new paid-profile saving or κ follows from this scalar gate-count result. + +## Open next questions + +1. **Escape the fixed source/frame premise.** For one recorded component, + propose a phase-correct alternative which avoids the rank-four source + visit, then charge every new read, adapter and restoration operation. This + could improve the local bill; no such alternative is supplied here. +2. **Bind a complete native word.** Join these intervals with an explicitly + source-matched native initial-prefix implementation, then check both + orientations and full cleanup. This account's PR2394 is a starting point + on different successor words, so source comparison is required. Global + hosting and a favorable complete bill remain blockers. + +Structured next questions are also in TASK.json. + +## Credit + +Prepared for commdata2338 (@commdata2338), with substantial OpenAI Codex assistance. + +Cinna Davis (@1337isnot1337), PR2226: anticipatory borrowing, the fixed low-lender +construction, compensation and cleanup witness. Ali Romman: fixed-block +extraction and certificate. Thomas DiFiore: block discovery. Jeremy Kothe, +Rohan Arun, Hao Yan, Chafik Boukhalfa, icekylinx, Jonathan Capalbo and the +selected PR1042/1094 provider/frame/controller lineage retain credit. +The original [notice](inputs/NOTICE.md) is preserved; its references to the +predecessor's price engine describe that predecessor, not an imported engine. +New proof and checking code are Apache-2.0. OpenAI Codex performed the +derivation, implementation, checking and writing. No independent human +review, maintainer adoption or complete formal proof is claimed. diff --git a/research/anticipatory-lender-cleanup/RESULT.json b/research/anticipatory-lender-cleanup/RESULT.json new file mode 100644 index 0000000000..0b79294f6d --- /dev/null +++ b/research/anticipatory-lender-cleanup/RESULT.json @@ -0,0 +1,5692 @@ +{ + "all_restored": { + "full_restore_cut_assignments": 9467946087033230222697397748343316918234405131659192079965013748792863519964287333721372345723330950000000000000000, + "negations": 16, + "source_limited_deadlines": 5, + "source_rank_one_climbs": 32, + "subtractions": 32 + }, + "backward_original_inputs": 704, + "components": [ + { + "addition_deadline_B": 1158, + "full_restore_cut_assignments": 438, + "gate_count": 1, + "last_read": { + "B_index": 720, + "gate": [ + "add", + 100, + 12, + 1, + 1, + 535 + ] + }, + "lender": 273, + "lender_handoff_B": 1158, + "lender_row": [ + [ + 12, + "1" + ], + [ + 31, + "1" + ], + [ + 273, + "1" + ] + ], + "rank_four_basis": [ + 388, + 75, + 41, + 26 + ], + "rank_three_basis": [ + 388, + 41, + 26 + ], + "recipient": 697, + "release_B": 721, + "source": 12, + "source_climb_rank": 1, + "source_handoff_B": null, + "source_row": [ + [ + 12, + "1" + ], + [ + 31, + "1" + ] + ], + "subset_choices": [ + { + "gates": 0, + "mask": 0, + "restored": false, + "row": [ + [ + 12, + "1" + ], + [ + 31, + "1" + ], + [ + 273, + "1" + ] + ] + }, + { + "gates": 1, + "mask": 1, + "restored": true, + "row": [ + [ + 273, + "1" + ] + ] + } + ], + "tail_indices": [ + 40 + ] + }, + { + "addition_deadline_B": 1158, + "full_restore_cut_assignments": 436, + "gate_count": 1, + "last_read": { + "B_index": 722, + "gate": [ + "add", + 287, + 31, + 1, + 1, + 537 + ] + }, + "lender": 275, + "lender_handoff_B": 1158, + "lender_row": [ + [ + 12, + "-1/2" + ], + [ + 31, + "1/2" + ], + [ + 275, + "1" + ] + ], + "rank_four_basis": [ + 388, + 75, + 41, + 26 + ], + "rank_three_basis": [ + 463, + 41, + 26 + ], + "recipient": 696, 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"repository": "https://github.com/CrocSwap/integer-mult-bounds", + "source_pr": 2226, + "head": "dacaf3d81f1936bb55b8454b1244e5d014272754", + "files": [ + { + "path": "inputs/word.json.gz", + "source_path": "research/anticipatory-dirty-borrowing/inputs/selected-complex-word.json.gz", + "commit": "dacaf3d81f1936bb55b8454b1244e5d014272754", + "git_blob": "5f9ef680983b0b63a4c82a4ed909837b78e690cd", + "sha256": "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219", + "payload_sha256": "4ddb29fb9bc6f27e0c0fbfcf19a2a93a3496ad900d0f6d89059d0305c9576c0c" + }, + { + "path": "inputs/witness.json", + "source_path": "research/anticipatory-dirty-borrowing/WITNESS.json", + "commit": "dacaf3d81f1936bb55b8454b1244e5d014272754", + "git_blob": "62edbcce166f7cf388231078c2cd7f75939b97e2", + "sha256": "86392adde6992a08ae90f7a69c58cace1b52d942f4d2c96e82ca79e5d1e15235" + }, + { + "path": "inputs/blocks.json", + "source_path": "research/anticipatory-dirty-borrowing/inputs/selected-block-certificate.json", + "commit": "dacaf3d81f1936bb55b8454b1244e5d014272754", + "git_blob": "59a9863fa8d823524cd42b6845c548089b6ef694", + "sha256": "d3ada9ac84a74f72ce9364dd47ee2ab9f02d1a6513df135e81dad11d0e6c6958" + }, + { + "path": "inputs/NOTICE.md", + "source_path": "research/anticipatory-dirty-borrowing/NOTICE.md", + "commit": "dacaf3d81f1936bb55b8454b1244e5d014272754", + "git_blob": "5ea70357a04d083dba066fbc5c809a5736d8edd6", + "sha256": "f1d45d886926915531e3a59968abf0a4c974d7038f869848e71bd3a21b834422" + } + ] +} diff --git a/research/anticipatory-lender-cleanup/SOURCES.json b/research/anticipatory-lender-cleanup/SOURCES.json new file mode 100644 index 0000000000..392737aa2a --- /dev/null +++ b/research/anticipatory-lender-cleanup/SOURCES.json @@ -0,0 +1,18 @@ +{ + "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" + } + ] +} diff --git a/research/anticipatory-lender-cleanup/TASK.json b/research/anticipatory-lender-cleanup/TASK.json new file mode 100644 index 0000000000..8fd92c2f1b --- /dev/null +++ b/research/anticipatory-lender-cleanup/TASK.json @@ -0,0 +1,109 @@ +{ + "schema_version": 1, + "task_id": "complex-new-helper-inventory", + "priority_revision": 4, + "base_commit": "0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2", + "original_card": { + "id": "complex-new-helper-inventory", + "question": "Can a new local cost interface change the deficit-to-recursive-cost ratio beyond current packing?", + "starting_points": [ + "research/complex-local-word-ceiling/README.md", + "research/heterogeneous-owner-assembly/README.md", + "certificates/selected-result.json", + "research/selected-k8-unrestricted-ends/README.md" + ], + "methods": [ + "Propose a changed helper inventory and derive an optimistic exact moment.", + "Design a small completed instance and independently verify its endpoint and rank bill." + ], + "acceptance_gate": "A new physically realizable contract outside the frozen catalogue whose per-call profile, screened with ceiling.ceiling(), beats the selected word's packing ceiling; a lower cap does not establish identical circuitry or order attainable optima, and is insufficient to pass the stronger-budget target under this model.", + "first_step": { + "command": [ + "python3", + "-B", + "research/complex-local-word-ceiling/verify.py" + ], + "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING", + "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.", + "scope": "Positive control and planning budget only; this is not a new construction or full cold replay." + }, + "first_experiment": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin.", + "bottleneck_link": "Packing of the selected word is capped at +0.87% (ceiling model); only a lower local excess spend or a changed coverage law raises the cap.", + "allowed_variations": [ + "Narrow to one changed boundary or helper type with explicit counts.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "scope_change_triggers": [ + "Mixing only providers already inside the pinned catalogue.", + "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013." + ], + "overlap_terms": [ + "helper inventory", + "heterogeneous-owner", + "mutable leaver" + ] + }, + "scope_status": "changed", + "actual_scope": "PR2226: exact subset classification and sharp gate/availability tradeoff for its 32 low lenders and 48 early-tail operations, with monotone-frame release cuts and source-withdrawal deadlines.", + "scope_change_reason": "The selected helper-inventory card is narrowed from interface synthesis to an independent necessity and scheduling certificate for a fixed dirty-borrowing component. The predecessor checks one successful schedule; this proves a fixed-alphabet tradeoff and characterizes every full restoration cut assignment. No claim is made to meet the original construction or packing-cap gate.", + "bottleneck_link": "Native lowering of the low-lender borrowing mechanism must preserve its 32 source promotions and read-before-handoff dependencies; scalar omissions or recipient-only scheduling cannot discharge this boundary.", + "budget_minutes": 60, + "stop_rule": "Stop after exact row binding, finite component classification, frame/deadline certificate and meaningful controls; no full supplier or exponent claim.", + "outcome": "completed", + "evidence": "README.md proves the composition. RESULT.json binds all 64 observed rows, 96 local subsets covering 2^48 global choices, all 1846 B slots and 80 handoffs for both extreme schedules, all 624 complete free-operator rows and Y+=X at the B endpoint for both extreme schedules, and 136 rejecting/34 positive semantic cases.", + "author": "commdata2338", + "ai_assistance": "Substantial OpenAI Codex assistance in derivation, implementation, checking and writing; no independent human review claimed.", + "open_questions": [ + { + "question": "Can a changed cleanup alphabet or changed reference/compensation contract reduce the 32 required source promotions for low borrowing?", + "why_it_matters": "The present exclusion keeps the actual cleanup sources and rank-four gate frames fixed; changing one could remove a paid source promotion and improve the local supplier bill.", + "first_step": "Choose one component in RESULT.json and exhibit an arbitrary-input alternative that avoids its rank-three-to-four source visit; charge all new adapters, reads and restoration.", + "blocked_by": "No alternative native phase-correct word or complete cost comparison is supplied." + }, + { + "question": "Can a native compiler bind the complete 80-loan word to these exact cleanup intervals and the initial compensation lowering?", + "why_it_matters": "The scalar/frame certificate does not certify Clifford phases, inverse cleanup or global ownership.", + "first_step": "Join the five source-limited deadlines here with this account's PR2394 initial-prefix lowering, retaining exact predecessor pins and checking both orientations.", + "blocked_by": "PR2394 targets PR2339 successor words; transfer needs an explicit source comparison, full native execution and a favorable complete bill." + } + ], + "selection": { + "nonce": "a6f46cd88e711b738859e407ddbec9cd", + "track": "complex-mechanisms", + "scope_key": "f3b0895a4f9f1cc62e75", + "suggestion_index": 2, + "refined_scope": "PR2226/32-low-lenders/48-tail-subsets/monotone-frame-and-withdrawal-cuts" + }, + "predecessor": { + "pr": 2226, + "head": "dacaf3d81f1936bb55b8454b1244e5d014272754", + "status": "pending author-checked local component; not adopted as a supplier" + }, + "result_kind": "finite certificate and scoped proof", + "declared_milestone": "audit", + "unresolved_consumer_restoration_costs": { + "proved_here": [ + "32 fixed cleanup subtractions and 16 negations are necessary for all 32 low lender rows.", + "32 rank-one source promotions and the exact pre-withdrawal intervals are forced in the retained monotone-frame contract.", + "Both extreme schedules have the same frame prefix invoice and endpoints through all 1846 B events and 80 handoffs.", + "Both extreme complete B prefixes agree on all 624 arbitrary-input rows and satisfy Y+=X in the free operator algebra; final non-target inverse cleanup is not rerun." + ], + "unknown_here": [ + "Full native phase and inverse-transpose lowering, complete final restoration and private buffers.", + "Global hosting and idle invoice, precision/tape and all-size/compiler obligations.", + "Any improved complete supplier moment or kappa." + ] + }, + "family_expansion_decision": "Conclude the scoped audit; do not expand a construction campaign from this fixed-alphabet closure. Any proposed escape must change a named source/frame/reference premise and present its complete boundary and cost allowance; unknown consumer and restoration costs are not zero.", + "final_refresh": { + "utc": "2026-10-15T16:40:28Z", + "main_commit": "b4560d9e7216f72b73c5aa940ac099c05e33ccf9", + "priority_revision": 5, + "changed": "First refresh at 16:33 UTC advanced main from 0fdd7d82 to b4560d9e: AGENTS.md, autoresearch.md, task catalogue, bottleneck brief, priority log and new family-status page. Second fetch at 16:40 UTC found no additional change. Selected result and PR2226 input unchanged. Read revision5 guidance, conclude this audit, and rebase onto b4560d9e; retain historical revision4 task/catalogue provenance.", + "dependency_head_rechecked": "dacaf3d81f1936bb55b8454b1244e5d014272754", + "overlap_prs_fetched_at": "2026-10-15T16:37:18.169440+00:00", + "overlap_discussions_fetched_at": "2026-10-15T16:27:10.714268+00:00", + "overlap_pr_files_fetched_at": "2026-10-15T15:59:04.742484+00:00" + }, + "discussion": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2615" +} diff --git a/research/anticipatory-lender-cleanup/VERIFY.json b/research/anticipatory-lender-cleanup/VERIFY.json new file mode 100644 index 0000000000..13b89f036f --- /dev/null +++ b/research/anticipatory-lender-cleanup/VERIFY.json @@ -0,0 +1,20 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-O", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 60, + "checks": "Pinned source bytes; independent forward/pullback row arithmetic; complete factored subset census; raw chronological frame and complete free-operator prefix traces; 136 rejecting semantic cases and 34 positive schedule/basis cases; typed canonical receipt." + } + ] +} diff --git a/research/anticipatory-lender-cleanup/inputs/NOTICE.md b/research/anticipatory-lender-cleanup/inputs/NOTICE.md new file mode 100644 index 0000000000..5ea70357a0 --- /dev/null +++ b/research/anticipatory-lender-cleanup/inputs/NOTICE.md @@ -0,0 +1,22 @@ +# Attribution and license + +New construction, proof text and checkers: Cinna Davis (@1337isnot1337), with +substantial OpenAI Codex assistance, Apache-2.0. + +The selected complex canonical word is the PR1042 ancestry retained in PR1094. +Jeremy Kothe, Rohan Arun, Hao Yan, Chafik Boukhalfa, icekylinx, Jonathan Capalbo +and the source package's full provider/frame/controller lineage retain credit. +Ali Romman supplied the source-bound fixed-block theorem and certificate; +Thomas DiFiore supplied the earlier block discovery. The borrowing construction +does not attribute its changed interface to those predecessor results. + +`price_engine.py` is an unchanged copy of the incorporated +`research/complex-local-word-ceiling/ceiling.py`: Douglas Colkitt, with Claude +(Anthropic) assistance; original SPDX/license context and docstring retained. +General Clifford frame and exact Gaussian normal forms are inherited from +`notes/general-clifford-frames.tex` and the repository's credited phase/compiler +lineage. The package independently checks its actual local Gaussian products. + +Source hashes, base commits and the copied engine's Git blob are in SOURCES.json. +No full native supplier, all-size compiler, precision theorem or new kappa is +claimed. 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a/research/anticipatory-lender-cleanup/inputs/word.json.gz b/research/anticipatory-lender-cleanup/inputs/word.json.gz new file mode 100644 index 0000000000..5f9ef68098 Binary files /dev/null and b/research/anticipatory-lender-cleanup/inputs/word.json.gz differ diff --git a/research/anticipatory-lender-cleanup/verify.py b/research/anticipatory-lender-cleanup/verify.py new file mode 100644 index 0000000000..1ebd62cf65 --- /dev/null +++ b/research/anticipatory-lender-cleanup/verify.py @@ -0,0 +1,591 @@ +#!/usr/bin/env python3 +"""Exact fixed-alphabet lender cleanup certificate; standard library only. + +Prepared for commdata2338, with substantial OpenAI Codex assistance. +Apache-2.0. No predecessor replay or arithmetic implementation is imported. +""" +from __future__ import annotations + +import argparse +from collections import Counter, defaultdict +from fractions import Fraction as Q +import gzip +import hashlib +import json +from pathlib import Path + +HERE = Path(__file__).resolve().parent + + +def need(condition, message): + if not condition: + raise ValueError(message) + + +def unique_object(pairs): + result = {} + for key, value in pairs: + need(key not in result, "duplicate JSON key: " + key) + result[key] = value + return result + + +def decode(data): + return json.loads(data, object_pairs_hook=unique_object) + + +def canonical(value): + # JSON encoding distinguishes integer 1 from boolean true. + return json.dumps(value, sort_keys=True, separators=(",", ":")) + + +def sources(): + pins = decode((HERE / "SOURCE-PINS.json").read_bytes()) + need(pins["source_pr"] == 2226 and pins["head"] == + "dacaf3d81f1936bb55b8454b1244e5d014272754", "predecessor head binding") + for entry in pins["files"]: + data = (HERE / entry["path"]).read_bytes() + need(hashlib.sha256(data).hexdigest() == entry["sha256"], + "source SHA256 mismatch: " + entry["path"]) + blob = b"blob " + str(len(data)).encode() + b"\0" + data + need(hashlib.sha1(blob).hexdigest() == entry["git_blob"], + "source Git blob mismatch: " + entry["path"]) + if "payload_sha256" in entry: + need(hashlib.sha256(gzip.decompress(data)).hexdigest() + == entry["payload_sha256"], "word payload mismatch") + return ( + decode(gzip.decompress((HERE / "inputs/word.json.gz").read_bytes())), + decode((HERE / "inputs/witness.json").read_bytes()), + decode((HERE / "inputs/blocks.json").read_bytes())["sources"][0]["blocks"], + ) + + +def incident(gate): + need(gate[0] in ("add", "scale"), "unknown scalar operation") + return gate[1:3] if gate[0] == "add" else gate[1:2] + + +def coefficient(gate): + return Q(gate[3], gate[4]) if gate[0] == "add" else Q(gate[2], gate[3]) + + +def plus(row, other, factor): + out = row.copy() + for index, value in other.items(): + new = out.get(index, Q(0)) + factor * value + if new: + out[index] = new + else: + out.pop(index, None) + return out + + +def scaled(row, factor): + return {index: factor * value for index, value in row.items() if factor * value} + + +def serial(row): + return [[index, str(value)] for index, value in sorted(row.items())] + + +def span(basis): + result = {0} + for vector in basis: + need(type(vector) is int and 0 <= vector < 512, "nonbinary frame label") + result |= {vector ^ value for value in tuple(result)} + need(len(result) == 1 << len(basis), "dependent frame basis") + return frozenset(result) + + +def strict_rank_one(before, after): + need(before < after and len(after) == 2 * len(before), + "rank-one climb must be a proper nested inclusion") + return 1 + + +def changed_slots(word, witness, blocks): + """Reconstruct virtual B instructions before physical alias resolution. + + High corrections move to first input; low early prefixes are replaced. + The cleanup under study is absent. Observations precede both handoffs. + """ + skipped = set() + deferred = defaultdict(list) + for block in blocks: + helpers = set(block["helpers"]) + for i in range(block["first_correction"], block["first_input"]): + gate = word["B"][i] + if set(incident(gate)) <= helpers: + need(i not in skipped, "overlapping deferred blocks") + skipped.add(i) + deferred[block["first_input"]].append(gate) + deleted, rewrites = set(), {} + for pair in witness["pairs"]: + need(not pair.get("handoff_echo_coefficients"), "unexpected handoff echo") + if pair["low"]: + deleted.update(pair.get("deleted_prefix_indices", pair["deleted_echo_indices"])) + for raw_i, gates in pair.get("early_prefix_rewrites", {}).items(): + i = int(raw_i) + need(i not in rewrites, "overlapping prefix rewrites") + rewrites[i] = gates + result = [] + for i, gate in enumerate(word["B"]): + events = deferred[i] + rewrites.get(i, []) + if i not in skipped and i not in deleted: + events = events + [gate] + result.append(events) + return result + + +def forward_rows(word, witness, slots): + """Forward propagation on all 512 remaining non-target inputs.""" + v = word["v"] + removed = {pair["register"] for pair in witness["pairs"]} + active = set(range(2 * v + word["R"])) - removed + non_target = active - set(range(v, 2 * v)) + rows = {r: {r: Q(1)} for r in non_target} + + def execute(gate): + d = gate[1] + if v <= d < 2 * v: + return + need(d in rows, "unallocated forward destination") + if gate[0] == "scale": + rows[d] = scaled(rows[d], coefficient(gate)) + else: + s = gate[2] + need(s in rows, "non-target reads removed helper or target") + rows[d] = plus(rows[d], rows[s], coefficient(gate)) + + for section in ("precondition", "compensation", "A", "cut"): + for gate in word[section]: + if section in ("precondition", "compensation") and gate[0] == "add" and gate[2] in removed: + need(v <= gate[1] < 2 * v, "removed compensation is not Y-only") + continue + execute(gate) + first_handoff = min(pair["handoff_B"] for pair in witness["pairs"]) + for events in slots[:first_handoff]: + for gate in events: + execute(gate) + return rows, first_handoff, len(active) + + +def backwards_row(register, raw_prefix): + """Independent functional pullback through the original 704-role prefix. + + No alias deletion, changed B compilation or forward row-add is used. + """ + weights = {register: Q(1)} + for gate in reversed(raw_prefix): + d = gate[1] + if d not in weights: + continue + if gate[0] == "scale": + weights[d] *= Q(gate[2], gate[3]) + else: + s = gate[2] + weights[s] = weights.get(s, Q(0)) + weights[d] * Q(gate[3], gate[4]) + if not weights[s]: + del weights[s] + return weights + + +def apply_subset(row, source_row, gates, mask): + for i, gate in enumerate(gates): + if mask & (1 << i): + if gate[0] == "add": + row = plus(row, source_row, coefficient(gate)) + else: + row = scaled(row, coefficient(gate)) + return row + + +def check_schedule(components, schedule): + for c in components: + times = schedule[c["lender"]] + need(len(times) == c["gate_count"], "schedule arity") + need(all(type(time) is int for time in times), "integer event cuts") + need(c["release_B"] <= times[0] <= c["addition_deadline_B"], + "addition violates frame release or source withdrawal") + if len(times) == 2: + need(times[0] <= times[1] <= c["lender_handoff_B"], + "negation violates dependency or lender withdrawal") + + +def trace_frames(word, witness, slots, schedule): + """Execute frame transitions in order, including all 80 physical loans. + + This does not use the derived release/deadline intervals. It checks the + actual before-handoff ordering and subspace inclusions, so an early or + late mutation is tested against the source event stream itself. + Logical scalar identities and exact Clifford phases are separate. + """ + v = word["v"] + F = list(map(span, word["frames"])) + removed = {p["register"] for p in witness["pairs"]} + cur = {r: F[f] for r, f in enumerate(word["start"]) if r not in removed} + aliases, withdrawn = {}, set() + profile, cleanup_profile = Counter(), Counter() + + def climb(r, space, cleanup=False): + need(r in cur and cur[r] <= space, "actual event has a nonnested frame") + gap = len(space).bit_length() - len(cur[r]).bit_length() + if gap: + profile[gap] += 1 + if cleanup: + cleanup_profile[gap] += 1 + cur[r] = space + + def event(gate, cleanup=False): + for r in incident(gate): + if cleanup: + need(r not in withdrawn, "cleanup reads a withdrawn physical role") + climb(aliases.get(r, r), F[gate[-1]], cleanup) + + target_pins = {r: word["start"][r] for r in range(v, 2 * v)} + for section in ("precondition", "compensation"): + for gate in word[section]: + for r in incident(gate): + if v <= r < 2 * v: + target_pins[r] = gate[-1] + if gate[0] == "add" and gate[2] in removed: + continue + event(gate) + for gate in word["A"]: + event(gate) + for r, f in target_pins.items(): + climb(r, F[f]) + for r, f in zip(word["centers"], word["center_frames"]): + need(cur[r] == F[f], "centre frame binding") + profile[len(F[f]).bit_length() - 1] += 1 + scheduled = defaultdict(list) + local_indices = Counter() + for entry in witness["early_tail_events"]: + d = entry["gate"][1] + j = local_indices[d] + local_indices[d] += 1 + scheduled[schedule[d][j]].append(entry["gate"]) + starts = defaultdict(list) + for pair in witness["pairs"]: + starts[pair["handoff_B"]].append(pair) + executed_cleanup = 0 + for i, events in enumerate(slots): + for gate in scheduled[i]: + event(gate, cleanup=True) + executed_cleanup += 1 + for pair in starts[i]: + old, new = pair["borrow_from"], pair["register"] + need(old not in withdrawn and new not in aliases, "duplicate physical loan") + need(cur[old] == F[pair["retirement_frame"]], "actual loan retirement frame") + entrance = span(pair["handoff_basis"]) + need(len(cur[old]) == len(entrance) and pair["handoff_paid_rank"] == 0, + "fixed rank-zero handoff") + aliases[new] = old + withdrawn.add(old) + cur[old] = entrance + for gate in events: + event(gate) + need(len(aliases) == 80, "all physical handoffs traced") + need(executed_cleanup == 48, "all scheduled cleanup operations executed") + payload = [[r, sorted(space)] for r, space in sorted(cur.items())] + return {"through_B_events": len(slots), "handoffs": len(aliases), + "profile_including_COPY": dict(sorted(profile.items())), + "cleanup_profile": dict(sorted(cleanup_profile.items())), + "final_frames_sha256": hashlib.sha256(canonical(payload).encode()).hexdigest()} + + +def trace_operator_rows(word, witness, slots, schedule): + """Whole B prefix over exact rationals and noncommuting loan symbols. + + This validates complete prefix equality after retiming, including every + arbitrary input and the Y endpoint, without asserting native phase or + final inverse-cleanup coverage. Reference operators are free generators. + """ + v = word["v"] + removed = {p["register"] for p in witness["pairs"]} + rows = {r: {(r, ()): Q(1)} for r in range(2 * v + word["R"]) if r not in removed} + aliases = {} + for term in witness["initial_corrections"]: + key = (term["source"], tuple(term["operator_word"])) + rows[term["target"]] = plus(rows[term["target"]], {key: Q(1)}, Q(term["coefficient"])) + + def execute(gate): + d = aliases.get(gate[1], gate[1]) + need(d in rows, "unallocated operator destination") + if gate[0] == "scale": + rows[d] = scaled(rows[d], coefficient(gate)) + else: + s = aliases.get(gate[2], gate[2]) + need(s in rows, "unallocated operator source") + rows[d] = plus(rows[d], rows[s], coefficient(gate)) + + for section in ("precondition", "compensation", "A", "cut"): + for gate in word[section]: + if section in ("precondition", "compensation") and gate[0] == "add" and gate[2] in removed: + continue + execute(gate) + scheduled, local_index = defaultdict(list), Counter() + for entry in witness["early_tail_events"]: + d = entry["gate"][1] + scheduled[schedule[d][local_index[d]]].append(entry["gate"]) + local_index[d] += 1 + starts = defaultdict(list) + for token, pair in enumerate(witness["pairs"], 1): + starts[pair["handoff_B"]].append((token, pair)) + low_checks = 0 + for i, events in enumerate(slots): + for gate in scheduled[i]: + execute(gate) + for token, pair in starts[i]: + old = pair["borrow_from"] + if pair["low"]: + need(rows[old] == {(old, ()): Q(1)}, "actual low-lender row at handoff") + low_checks += 1 + transformed = {} + for (variable, operators), value in rows[old].items(): + reduced = operators[1:] if operators and operators[0] == -token else (token,) + operators + transformed[variable, reduced] = value + rows[old] = transformed + aliases[pair["register"]] = old + for gate in events: + execute(gate) + need(low_checks == 32 and len(aliases) == 80, "complete scalar loan coverage") + for y in range(v, 2 * v): + need(rows[y] == {(y, ()): Q(1), (y - v, ()): Q(1)}, "Y endpoint in free operator algebra") + return rows + + +def operator_rows_digest(rows): + data = [[r, [[var, list(ops), str(value)] for (var, ops), value in sorted(row.items())]] + for r, row in sorted(rows.items())] + return hashlib.sha256(canonical(data).encode()).hexdigest() + + +def rejected(function, message): + try: + function() + except ValueError: + return + raise ValueError("negative control accepted: " + message) + + +def analyze(word, witness, blocks): + v, n = word["v"], 2 * word["v"] + word["R"] + need((word["h"], v, n) == (9, 112, 704), "source dimensions") + pairs = witness["pairs"] + loans = {pair["borrow_from"]: pair for pair in pairs} + need(len(pairs) == len(loans) == 80, "distinct loan inventory") + low = {pair["borrow_from"]: pair for pair in pairs if pair["low"]} + need(len(low) == 32, "low lender inventory") + tails = witness["early_tail_events"] + need(len(tails) == 48, "fixed tail alphabet") + groups, indices = defaultdict(list), set() + for entry in tails: + index, gate = entry["old_tail_index"], entry["gate"] + need(index not in indices and gate == word["tail"][index], "tail source binding") + indices.add(index) + groups[gate[1]].append(entry) + need(set(groups) == set(low), "exact cleanup destinations") + source_registers = {entries[0]["gate"][2] for entries in groups.values()} + need(len(source_registers) == 32 and source_registers.isdisjoint(low), + "independent cleanup components") + observed = set(low) | source_registers + frames = list(map(span, word["frames"])) + slots = changed_slots(word, witness, blocks) + rows, first_handoff, active_count = forward_rows(word, witness, slots) + need(active_count == 624 and first_handoff == 1054, "actual prefix boundary") + raw_prefix = sum((word[s] for s in ("precondition", "compensation", "A", "cut")), []) + # B only reads these roles until physical withdrawal. This proves that + # omitted tails in one component cannot affect another component. + for events in slots: + for gate in events: + need(gate[1] not in observed, "B writes a cleanup component") + for r in sorted(observed): + need(rows[r] == backwards_row(r, raw_prefix), "forward/backward row disagreement") + cur = word["start"].copy() + for section in ("precondition", "compensation", "A"): + for gate in word[section]: + for r in incident(gate): + cur[r] = gate[-1] + # The cut is logical and unframed in the pinned source contract. + histories = {r: [] for r in observed} + for i, events in enumerate(slots): + for gate in events: + for r in incident(gate): + if r in observed: + histories[r].append((i, gate[-1], gate)) + components, distribution = [], Counter({(0, 0): 1}) + time_assignments = 1 + for d in sorted(low): + entries = groups[d] + gates = [entry["gate"] for entry in entries] + s = gates[0][2] + need(gates[0][0] == "add" and coefficient(gates[0]) == -1, "cleanup subtraction") + need(len(gates) in (1, 2), "component size") + if len(gates) == 2: + need(gates[1][0] == "scale" and coefficient(gates[1]) == -1, "cleanup negation") + need(all(gate[-1] == gates[0][-1] for gate in gates), "common cleanup frame") + U = frames[gates[0][-1]] + need(len(U) == 16 and frames[cur[d]] == U and not histories[d], + "lender stays at rank four before borrowing") + h = histories[s] + need(bool(h), "source has no last ordinary read") + previous = frames[cur[s]] + for _, frame_id, _ in h: + after = frames[frame_id] + need(previous <= after <= U, "ordinary source frame is not nested") + previous = after + release = h[-1][0] + 1 + need(all(entry["before_B"] == release for entry in entries), "earliest witness cut") + need(h[-1][2] == word["B"][release - 1], "raw last-read binding") + need(len(previous) == 8, "last source read must have rank three") + strict_rank_one(previous, U) + need(release < first_handoff, "prefix must cover cleanup release") + need(not U <= previous, "early-frame obstruction disappeared") + unit = {d: Q(1)} + sign = 1 if len(gates) == 1 else -1 + need(rows[d] == plus(rows[s], unit, Q(sign)), "lender row normal form") + need(rows[s] and all(r < v for r in rows[s]), "source is nonzero pure X data") + need(d not in rows[s], "source depends on lender dirt") + own_deadline = low[d]["handoff_B"] + source_deadline = loans[s]["handoff_B"] if s in loans else None + upper = min(own_deadline, source_deadline or own_deadline) + need(release <= upper, "no legal restoration window") + need(frames[low[d]["retirement_frame"]] == U, "lender retirement frame") + if s in loans: + need(frames[loans[s]["retirement_frame"]] == U, "source retirement frame") + choices, local = [], Counter() + for mask in range(1 << len(gates)): + out = apply_subset(rows[d], rows[s], gates, mask) + restored = out == unit + need(restored == (mask == (1 << len(gates)) - 1), "non-full local restoration") + local[mask.bit_count(), int(restored)] += 1 + choices.append({"mask": mask, "gates": mask.bit_count(), + "restored": restored, "row": serial(out)}) + nxt = Counter() + for (cost, restored), count in distribution.items(): + for (dc, dr), multiplicity in local.items(): + nxt[cost + dc, restored + dr] += count * multiplicity + distribution = nxt + count = upper - release + 1 + if len(gates) == 2: + count = count * (own_deadline + 1) - (release + upper) * count // 2 + time_assignments *= count + components.append({ + "lender": d, "recipient": low[d]["register"], "source": s, + "gate_count": len(gates), "tail_indices": [e["old_tail_index"] for e in entries], + "release_B": release, "addition_deadline_B": upper, + "lender_handoff_B": own_deadline, "source_handoff_B": source_deadline, + "last_read": {"B_index": release - 1, "gate": h[-1][2]}, + "rank_three_basis": word["frames"][h[-1][1]], + "rank_four_basis": word["frames"][gates[0][-1]], + "source_climb_rank": 1, "lender_row": serial(rows[d]), + "source_row": serial(rows[s]), "subset_choices": choices, + "full_restore_cut_assignments": count, + }) + need(Counter(c["gate_count"] for c in components) == {1: 16, 2: 16}, "component census") + minimum = [min(cost for cost, number in distribution if number == k) for k in range(33)] + need(minimum == [k + max(0, k - 16) for k in range(33)], "sharp local tradeoff") + need(sum(distribution.values()) == 2 ** 48 and distribution[48, 32] == 1, + "complete subset product") + early = {c["lender"]: [c["release_B"]] * c["gate_count"] for c in components} + late = {c["lender"]: [c["addition_deadline_B"]] + + ([c["lender_handoff_B"]] if c["gate_count"] == 2 else []) for c in components} + check_schedule(components, early) + check_schedule(components, late) + early_trace = trace_frames(word, witness, slots, early) + late_trace = trace_frames(word, witness, slots, late) + need(early_trace == late_trace, "retiming changes the actual prefix frame bill") + need(early_trace["cleanup_profile"] == {1: 32}, "32 actual cleanup source climbs") + early_rows = trace_operator_rows(word, witness, slots, early) + late_rows = trace_operator_rows(word, witness, slots, late) + need(early_rows == late_rows, "retiming changes a complete free-operator prefix row") + controls = Counter() + for c in components: + d = c["lender"] + gates = [e["gate"] for e in groups[d]] + full_mask = (1 << len(gates)) - 1 + for j in range(len(gates)): + need(apply_subset(rows[d], rows[c["source"]], gates, full_mask ^ (1 << j)) != {d: Q(1)}, + "omission control missed") + controls["single_gate_omission"] += 1 + if len(gates) == 2: + wrong = apply_subset(rows[d], rows[c["source"]], list(reversed(gates)), 3) + need(wrong != {d: Q(1)}, "reversed dependency control missed") + controls["negation_before_subtraction"] += 1 + bad = {r: ts[:] for r, ts in early.items()} + bad[d][0] -= 1 + rejected(lambda: check_schedule(components, bad), "before last rank-three read") + rejected(lambda: trace_frames(word, witness, slots, bad), "actual early frame event") + controls["early_frame_cut"] += 1 + if c["addition_deadline_B"] < c["lender_handoff_B"]: + bad = {r: ts[:] for r, ts in late.items()} + bad[d][0] += 1 + rejected(lambda: check_schedule(components, bad), "source borrowed first") + rejected(lambda: trace_frames(word, witness, slots, bad), "actual source withdrawal") + controls["source_withdrawal_cut"] += 1 + U = span(c["rank_four_basis"]) + basis = c["rank_three_basis"][:] + basis[0] = next(x for x in range(1, 512) if x not in U) + wrong_space = span(basis) + need(len(wrong_space) == 8, "wrong-axis control must preserve dimension") + rejected(lambda: strict_rank_one(wrong_space, U), "same rank, wrong subspace") + controls["equal_rank_wrong_axis"] += 1 + basis = c["rank_three_basis"][:] + basis[0] ^= basis[1] + need(span(basis) == span(c["rank_three_basis"]), "equivalent basis control") + strict_rank_one(span(basis), U) + controls["equivalent_basis_positive"] += 1 + need(controls["source_withdrawal_cut"] == 5, "source-limited deadlines") + d = components[0]["lender"] + wrong = {r + 704: q for r, q in rows[d].items()} + need(wrong != backwards_row(d, raw_prefix), "input-role binding control") + controls["wrong_input_roles"] += 1 + changed = decode(canonical(witness)) + changed["initial_corrections"] = [] + rejected(lambda: trace_operator_rows(word, changed, slots, late), "missing initial compensation") + controls["missing_initial_compensation"] += 1 + changed = decode(canonical(witness)) + changed["initial_corrections"][0]["coefficient"] = str(-Q(changed["initial_corrections"][0]["coefficient"])) + rejected(lambda: trace_operator_rows(word, changed, slots, late), "wrong initial compensation sign") + controls["wrong_initial_compensation_sign"] += 1 + return { + "status": "PASS_ANTICIPATORY_LENDER_CLEANUP", + "scope": "PR2226 fixed cleanup alphabet, monotone frames, and pre-handoff operand identity; no supplier or kappa claim", + "source_pr": 2226, "source_head": "dacaf3d81f1936bb55b8454b1244e5d014272754", + "remaining_inputs": active_count, "forward_non_target_inputs": len(rows), + "backward_original_inputs": n, "independently_bound_rows": len(observed), + "lenders": 32, "local_subsets_checked": 96, "global_subsets_certified": 2 ** 48, + "minimum_gates_for_exactly_k_restored": minimum, + "all_restored": {"subtractions": 32, "negations": 16, "source_rank_one_climbs": 32, + "source_limited_deadlines": 5, "full_restore_cut_assignments": time_assignments}, + "subset_polynomial": "(1+x*y)^16 * (1+2*x+x^2*y)^16", + "earliest_and_latest_full_B_frame_trace": early_trace, + "earliest_and_latest_full_B_operator_trace": { + "arbitrary_input_columns": 624, "output_rows": len(early_rows), + "low_handoff_row_checks_per_schedule": 32, "Y_endpoint": "Y+=X", + "complete_rows_sha256": operator_rows_digest(early_rows), + "scope": "before final inverse cleanup; symbolic operators, not native Gaussian phases"}, + "subset_distribution": [[cost, restored, count] for (cost, restored), count in sorted(distribution.items())], + "components": components, "controls": dict(sorted(controls.items())), + } + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--record", type=Path, help="write a new result file exclusively") + args = parser.parse_args() + result = analyze(*sources()) + if args.record: + with args.record.open("x") as stream: + json.dump(result, stream, indent=2, sort_keys=True) + stream.write("\n") + else: + expected = decode((HERE / "RESULT.json").read_bytes()) + need(canonical(result) == canonical(expected), "typed canonical receipt mismatch") + print("PASS_ANTICIPATORY_LENDER_CLEANUP lenders=32 subsets=281474976710656 " + "tail_gates=48 rank1=32 source_deadlines=5 no_new_kappa") + + +if __name__ == "__main__": + main()