Independent exact forward-basis audit of PR1611 helper450

[ToikY]

Change and mathematical scope

PR1611 certifies helper450's scalar restoration using sparse rational row/column propagation. This independently corroborates that scalar premise by pushing every input basis vector forward with a separately written exact dyadic implementation. No discrepancy was found. Only research/k8-hpe450-forward-audit/ is added: eight files, including the checker, deterministic receipt, source pins and review/validation records.

Both pinned local orientations have 24,767 events and 19,693 scalar operations. All 1,424 basis executions confirm the unit helper output row, its isolated dirt column and zero coefficients from all eight arbitrary private inputs. Six malformed programs reject with explicit exact coefficient witnesses. A dirt-leaking read preserves the row but leaks 1/2 to L230 forward and 1 to L27 backward. This is finite corroboration, not a new identity, Lean theorem, supplier admission or kappa.

The retained conditional C7 conclusion still needs exact event recipes and JSON-to-Lean correspondence. COPY/CLEAR lifetimes, other recipes, hosting/footprints, all-size compilation, precision/tape, complete costs and analytic transfer remain open. Selected sources/frontier and predecessor packages are unchanged.

Task and overlap

Base current main 0b1cccf86e2f5132ed286a26ef0a681a495740ea; contribution a2078691245ff8d2825def7048680759b695cb49. Task formal-interface-lemma, scope key e3ffea67887eeb4c396c, nonce 9c92a140d6ff014ccc0bdd30a86e9981, revision 3. Scope refined to the scalar premise of one existing theorem-to-emission binding; exact card and stop rule are in TASK.json. Claim.

• PR1611, exact head 156cc788b5a8122b19686f015e5654b117e4389d: construction/binding predecessor; the new algorithm obtains the row by forward basis execution rather than reverse covector propagation. Its published verifier separately passes all 28 controls. No pending checker code is imported.
• PR1415, 0d8d2c3a96346756f02563b401a042ab97198e20: retained complex operator semantics, not repeated.
• PR1697: parallel all-511 cold-hyperplane operator binding, a distinct domain.

Final overlap at 07:25 UTC read 393 open PR bodies, including drafts, through an empty numbered page; the helper also searched 875 local records. Discussions1163/1166/1394 and the active board were read live. Full Discussion pagination was unavailable, the helper warns about its absent Discussion cache, and concurrent merges make numbered pagination non-atomic. No-match output is not a novelty certificate.

Validation

python3.12 -B scripts/research_package.py --package research/k8-hpe450-forward-audit

Registered replay passes on CPython3.12.14/macOS in 5.72s. Also passed: metadata/source pins, unchanged selected-record check, 18 repository onboarding tests, a read-only optimized source export without Git, source-drift and receipt-corruption rejection, and occupied-output preservation. Exact arithmetic is compared with Fraction over 4,624 operand pairs; a four-input dirty echo checks destructive COPY/CLEAR and inverse scales. Two bounded agent static reviews found no actionable issue. VALIDATION.json records actual commands/environment and separates negative exit codes from success.

No fresh Lean/Mathlib build, general serialization proof, physical hosting replay, full selected cold replay, hosted CI success or independent human review is claimed.

Credit

Hanson Sun/@bbMisk (PR1611); Jeremy Kothe (HPE/k8); DreamingOfClouds (wrappers/Lemmas A/G); icekylinx (compiler); Rohan Arun (packing); Josie Elliston and Sagar Thakrar (word/audit lineage); @commdata2338 (PR1415); Aaron Wang/navinor (distinct cold audit); Chafik Boukhalfa, Zhihao Chen and all retained realization contributors. New work by @ToikY with substantial OpenAI Codex assistance in research, implementation, verification and writing, including bounded subagents. Apache-2.0; original notices unchanged.

Open next questions

README records the smallest useful follow-ups: translate this one helper into an actual Lean event word with private COPY/CLEAR lifetimes, or trace it through actual T16 hosted invocations. Scalar agreement does not discharge either missing correspondence or physical footprint proof.

[Mister-Meeseeks]

Batch review at a2078691245ff8d2825def7048680759b695cb49.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Independent forward dyadic replay checks all 712 entries of helper450 output row and its dirt column in both orientations, corroborating PR1611. Source producers are shared; event-to-Lean correspondence and physical hosting remain unproved by this scalar audit.

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.