CLAIM: commuting interval transport in the target-dependent PR1054 precision budget (seed 64)

[mightyOil]

CLAIM

Adversarial audit, OS seed 64. Base dadfea6.

Question: substitute PR1278’s squarefree commuting interval bound and PR1085’s sharp prefix count into PR1054’s actual target-dependent rounded leaf error contract, preserving the negative-leaf preimage and signed integer guard.

Pins: PR1278 06b8c00; PR1085 82b99c7; PR1054 6bc675b.

Expected deliverable: explicit sufficient fractional/integer precision formulas, exact source-bound budget comparison and meaningful nonlinear rounded controls. This follows PR1278’s stated next question; it does not claim a sharp interval coefficient, physical supplier adoption, runtime gain or new kappa. All movement, preparation and leaf calls remain paid.

Claim expires 2026-10-13 22:25 UTC; expected finish 22:20 UTC. Prepared for Philipp (@mightyOil) with substantial OpenAI Codex assistance. Independent implementations mean separate code paths, not independent human review.

[mightyOil]

DONE: PR #1295, #1295

Completed the conditional PR1054 rounded-contract substitution using pinned PR1085/1278 lemmas. At r=64,p=128,m=20, sufficient fractional width is 1,162,598 versus 1,420,902; beta^-8 inverse-preimage reserve remains, with the same 4,000 leaves, six scratch arrays and preparation. No supplier/kappa or optimal-precision claim.

Written all-size proof, 5,220 exact uniform budgets, 216 generic cases, 78 literal dispatcher comparisons, 80 actual signed rounded words/2,336 leaves, meaningful noncommuting/target-dependent controls, source/receipt corruption and read-only relocation are included. Python3.12 registered replay and all25 selected tests pass. The large radix64 row is a budget calculation, not a million-bit execution; full supplier, factorizer and physical admission remain open.

Credit Ali Romman #1054, Hanson Sun #1085/#1244, Charles Bethin #1278 and retained lineage. Concurrent #1294 universal local algebra audit is complementary and credited. Prepared for Philipp (@mightyOil) with substantial OpenAI Codex / GPT-6 Astra assistance.