DONE: two-image-volume-independent-proof

[JoyboyBrian]

DONE (scoped result) / 2026-10-23T07:14:31.732132+00:00 / priority revision 7

A code-disjoint audit corroborates the original/repaired two-image all-width nonsingular complex-coefficient volume classification and supplies its separate singular-coefficient rank-drop implication. Exact source phase/spectrum bindings and a compensated-partner boundary control pass. The conclusion is restricted to the fixed finite word and arbitrary dirty-return model.

Public artifact: #5038, exact head 8039f5db835f26b92694e349ebc535bae7104be8, package research/two-image-volume-independent-audit. Scientific base f259dabc7d70e0db8d6d36bfda888f008bbfecc1.

Evidence status: author-checked with a separate AI-assisted read-only source/logic review; normal and optimized registered checks, source pins, committed bytes/history and package export checks pass. Exact commands, environments and unrun obligations are in the package. Hosted CI status is separate and is not implied by DONE.

Scope: Independently audit PR4991's all-width dirty-helper volume invariant and its classification for every fixed nonzero complex coefficient pair at the actual original and phase-repaired two-image prefixes. Reconstruct the order-four character multiplicities and normalized log-determinant implication without importing the predecessor verifier; produce a scoped proof corroboration or exact missing implication.

Next work: see the package's Open next questions and explicit remaining contracts. No new selected frontier, complete multiplication theorem, independent human review or proof-kernel acceptance is asserted. This claim is released.

Credit: Cinna Davis PR4991/4998; lee-phys PR4688; Yiyang/Lyy-iiis PR4710; Dugongue PR4743; Jacob Alan Sussman PR4628 with eumemic and Swapnil Jain; retain exact notices. Substantial OpenAI Codex assistance. Prepared by JoyboyBrian with substantial OpenAI Codex assistance.

{
  "schema": "integer-mult-coordination/v1",
  "kind": "DONE",
  "task": "formal-interface-lemma",
  "scope": "Independently audit PR4991's all-width dirty-helper volume invariant and its classification for every fixed nonzero complex coefficient pair at the actual original and phase-repaired two-image prefixes. Reconstruct the order-four character multiplicities and normalized log-determinant implication without importing the predecessor verifier; produce a scoped proof corroboration or exact missing implication.",
  "base": "f259dabc7d70e0db8d6d36bfda888f008bbfecc1",
  "expiry": null,
  "artifact": "https://github.com/CrocSwap/integer-mult-bounds/pull/5038"
}