[ToikY]

Result

Independently derives PR #6353's complete finite formal recursive-job invoice, under its declared frame-rank tariff and frozen PR6348 caller interface. Separate span-based and pivot-based implementations agree on all old/new local and complete paid/productive coefficients and all four delta vectors.

All nine target contractions are debited at each of nineteen calls: 171 debit records, 70,656 paid jobs, 14,214 productive fields, rank-mass surplus808. Local scalar work rises127,088→128,694. At the author's fixed saving315057/100000000, rigorous rational bounds certify new margin>0.00306055749 and same-caller source margin<−0.19287557317.

This resolves a finite billing gate, not native/physical tariff applicability, the caller Laurent endpoint/contacts, erasure, complete ordinary funding, compiler/outer admission, or a newκ. All five framework assumptions and selected6030 remain.

Evidence

• Python3.12.14 metadata and four registered normal/optimized commands pass.
• Six counterfactual ledger vectors expose concrete coefficient errors; an inconsistent literal output declaration rejects. These are not claimed as six physical-program mutation replays.
• An independent rational atanh/exponential enclosure proves the one-point signs; no crossing search.
• Read-only Git-free/empty-PATH replay passes; six source-corruption and two typed-receipt controls reject.
• Exact committed bytes/modes, declared source ancestry and self-contained export pass.

Scope, proof, commands, full receipts and next questions. Hosted CI and human acceptance remain separate.

Task and credit

Refined independent-moment card, taking handoff19343304 and source request19342830. Canonical claim. Complements PR6355's rational gate.

Exact source6353 db2a20bc50bc7a8a4db931af85ce7f012ae7c3c3, on source6349 and fixedcaller6348. Canonical main refreshed unchanged at7c49fe32c55de02c2c873655c804b16e4c3fef0a; priority8. Fresh323-open-PR pagination and visible source handoffs checked; bounded overlap is not novelty proof.

Construction/interval/recursion credit stays with Ali Romman, PR6349/6348/6350, DreamingOfClouds/6314, Cinna Davis, David Arias, Gareth Davidson, Jacob Alan Sussman, zxv, Cao Yifan and the complete retained NOTICE chain. New recount/oracle/proof: ToikY with substantial OpenAI Codex assistance and three bounded agents.

Next: exact native normalizers and actual caller/funding admission. No merge, closure or frontier change; maintainer edits disabled.