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Certify shared reverse centre phase with a charged precision guard - #1748
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Independent invoice audit of PR1748 at ea14f19. A separately written parser reconstructs the selected backward centre phase: 208 macros, 176 panel gathers, and eight distinct post-A sinks outside the target panel. It derives the quoted two-phase and shared invoices from these events and independently checks all 240 scalar dirty-input columns. The predecessor already supplies stronger Gaussian operator fixtures and the general guarded tariff inequality; those results remain credited to @ToikY. The added exact tariff certificate gives first passing widths 13, 25, 37 and 50 for common positive degree-1, 2, 3 and 4 width tariffs, respectively; it covers degrees 1 through 16 plus 3,072 mixed-tariff invoices. These illustrative prices are not actual native tariffs. In particular, 384 macros versus 416 does not itself establish a saving after increasing precision. Evidence: 923be15, research/shared-return-tariff-audit. Registered Python 3.12 replay and optimized Python 3.14 replay agree exactly; source and receipt corruption controls reject. Source archive SHA256/Git-blob pins, deterministic receipt and reproduction commands are retained. Next useful step: identify an eligible selected caller pair and instantiate the native child/scalar prices and all preparation, routing, restoration and hosting overhead. This audit does not establish that pair, actual 512-dimensional operators, rounded-prefix correctness, a full-call recurrence, cold replay or a new kappa. Credit @ToikY/PR1748, Cinna Davis/PR1708, Sagar Thakrar/PR751, Ryan Haines/PR830, Scratch-net, and the selected construction lineage. New audit prepared for woklerx with substantial OpenAI Codex assistance; Apache-2.0; no independent human or formal proof-assistant review. Exact committed audit artifact. Commit |
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Batch review at Merged to Reviewed scope: Common post-A sink and uninterrupted two-panel reverse phase yields 16 to8 rank8 returns, 368 to360 ADDs and32 to16 CLEARs. Full dirty input/zero scratch endpoint and local positive-envelope factor2 proof checked; one magnitude bit is not a rounding-error or native admission theorem. Real caller eligibility, tariffs and overhead remain open. The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions. Batch review, attribution and evidence. Thank you for the contribution. |
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Change and mathematical scope
This conditional interface certificate completes the reverse centre phase complementary to PR1708. For two disjoint 112-row panels sharing the same eight post-A sinks and corresponding exact native operators/charts, gathering both panels before each return preserves the signed persistent endpoint and returns the same eight arbitrary-input scratch rows to zero. It reduces the literal reverse-phase bill from 416 to 384 macros: 16→8 rank-8 children, 368→360 ADDs, and 32→16 CLEARs. All 352 panel reads remain charged.
The positive gather envelope doubles from 11/2 to 11. The written exact linear-prefix argument includes unchanged child-private dirt; one extra magnitude bit covers this local envelope comparison. Every fused primitive is therefore conservatively priced at mu+1, with additional preparation/routing/restoration/ownership/hosting overhead DeltaH. A saving requires 8 R8(mu+1)+360 ADD(mu+1)+16 CLEAR(mu+1)+DeltaH < 16 R8(mu)+368 ADD(mu)+32 CLEAR(mu). No native tariff, eligible selected-call pair, full-call recurrence or new kappa is admitted. CLEAR makes the full scratch map singular; the adjoint statement concerns the persistent block.
Task and overlap
Base: 0b1cccf. Revision-3 card: centre-path-sharing; nonce 1e94dbbfba8c1dc58dbab4dcba380ae3; scope key 184695337cedab03152e/selected-eight-centers/backward-two-panel-shared-return/weighted-guard. Scope is refined because PR1708, head 4d163c0, already covers the forward fanout. This adds the selected backward event binding and precision-sensitive invoice, without claiming new generic batching algebra. PR751 and PR830 are credited predecessors; their exact heads are in TASK.json.
Claim and handoff. Final overlap search covered 419 open PR bodies including drafts and 873 local records; relevant Discussions were read directly. Numbered pages are non-atomic, and no complete Discussion census or novelty certificate is claimed. Current main and PR1708's head were rechecked before submission.
Validation
Run:
Python 3.12.14, macOS arm64: registered replay passes, all 480 complex basis inputs match an independent closed-form endpoint, and seven semantic fault witnesses fail as required. Eight phase-bearing two-coordinate Gaussian unitary representatives exercise the abstract inverse-adjoint interface; this is not an actual 512-dimensional operator replay. Exact coefficients and all eight reverse blocks are pinned to selected-replay.tar.gz. Written linearity handles arbitrary exact common operators under the stated hypotheses.
All 18 repository onboarding tests pass. Standalone exports pass normally and under -O; input/receipt corruption and occupied-output controls reject safely. VALIDATION.json records evidence and limitations. No full frontier replay, Lean, native rounded precision theorem or hosting admission was run. Selected record and frozen sources are unchanged.
Credit
Credit Cinna Davis/1337isnot1337 (PR1708), Sagar Thakrar (PR751), Ryan Haines (PR830), Scratch-net (private-centre adjoint/CLEAR audit), Jeremy Kothe and the retained construction/auditor/compiler lineage listed in README and TASK. Generic adjoint/batching algebra is prior work. Prepared by @ToikY with substantial OpenAI Codex assistance in mathematics, implementation, bounded independent review, tests and writing. Apache-2.0; original notices retained. No independent human review.
Open next questions
README next questions: trace one actual caller pair to prove common post-A sinks, charts and uninterrupted ownership, then instantiate the native precision/tape prices and DeltaH. Those are blockers to a complete-call or frontier improvement. No merge or frontier update is requested.