[dillona]

The exact #7105 word admits one more independent helper split after a fully paid retiming. This raises the conditional claim from 0.00363216151 to 0.00363233825 (14529353/4000000000), a gain of 1.7674e-7. It changes the complete paid/target invoice; this is not a refinement of the same root.

At source cut 37420, retime role 533's contact-free MOVE 3→747 through frame 745, then split a rank-eight helper direction using pivot 1468. Per LOCAL, paid delta is {3:+2,6:−1} and target delta is {3:+1,5:+1,8:−1}. All eighteen LOCALs give strict margin gain 18(5^p+6^p−8^p−3^p)>0 for 0<p<1. The emitted word adds one MOVE and fourteen integer ADDs; owned lifetimes and ascent inventory stay fixed. Full ordinary bill 826,799,424<10^9. The raw fixed-invoice ceiling is bracketed at 0.00363233825927247587361768759941604…05, leaving about 9.27e-12 headroom above the claim.

Validation: two complete local CPython 3.14.7 runs, including frozen-receipt equality; exact source reconstruction, rational cut and all-input forward/adjoint checks, formal caller, full invoice, two rational root engines, ordinary cap, precision and compiler/54+4 outer gates, five exact 512-column phase/chart checks, negative controls and full width 512 physical replay. The registered Python 3.12 replay passed at exact public head 5b59588fbf54c392dfb90aa4a7e7e60f0c41c351; local Python 3.12 was unavailable. Metadata/provenance and committed-byte/mode checks passed. No Lean, Docker or historical replay sweep.

Scope remains conditional: all five framework assumptions and the source-specific caller, complete odd-return, provider and ordinary-tariff application obligations remain. The new #7000 review's conservative BIT cap 134 is acknowledged; the frozen BIT binding check does not itself discharge that supplement or the complete supplier application. No selected-result change or full rounded multiplier is claimed.

Credit: Ali Romman for helper basis splitting; Jerry Chen/CubeJerry for retiming, shared wires, caller/BIT and precision engines; DreamingOfClouds for the native chain; ToikY for #7003/#7004; #7105 for the immediate source. All predecessor notices are retained. Prepared for dillona with substantial OpenAI Codex assistance.

The package includes source pins, complete evidence, discovery limits and actionable next questions. Canonical investigation: #1166 (comment)

Publication provenance: scientific work was committed on canonical main f16923d4 as local research commit d5c519d02af0b94f1a1da368ef1d69f0a6a52d28. The published commit 5b59588fbf54c392dfb90aa4a7e7e60f0c41c351 has an identical package tree, transported onto existing fork main 66849e14 because the account token lacks workflow scope for unrelated upstream workflow history. Only this 25-file package is added. Canonical source-history preflight passed on the research commit; the publication parent is intentionally the older fork base. The PR merge checkout supplies current canonical history.