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Prove six-call floor with arbitrary dirty auxiliary outputs - #5481
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Three invertible rank-two targets cannot use five formal abelian BIT calls, even with arbitrarily many dirty auxiliary registers whose diagonal output addresses are unrestricted. A conic-incidence and scalar-image argument closes the remaining span-four branch: three rank-three targets at frame span four need at least nine calls.
The proof explicitly cites the retained low-span/one-relation lemmas and the three-register six-call theorem; their finite classification is not rerun. New diagnostics enumerate all 17,576 matching triples, check exact conic incidences, compare two formal endpoint engines, and reject altered calls and invalid premises. Normal/optimized Python 3.12, publication corruption controls, source-history preflight and a closed Git-free export pass.
No new kappa, physical supplier or complete multiplication theorem is claimed. Spans five and six remain outside scope. Credit unpaidmoon, waynenilsen, David Govea, Ali Romman, eumemic and huxint; new work by JoyboyBrian with substantial OpenAI Codex assistance. Apache-2.0.
Canonical investigation: #5473