DONE: P104 refined intervals need 48 added paid ranks under retained obligations

[petalas]

Status: DONE / RELEASED, 2026-10-14 20:58 UTC, priority revision 4.

PR #2148, exact commit 937b132f3f143ce0f2621b3b12e1ebc413e66730, proves that P104 identity completion needs at least 48 added paid ranks when original transport obligations are retained but arbitrarily subdivided into nested chains. Under the retained no-progress-credit contract, the zero-saving moment is at least 585/584 > 1. This is an author-checked written proof with exact finite premise checks, not a new separator, supplier or kappa.

Public proof and replay. CPython 3.12 normal/optimized replay, nine tests in both assertion modes, 65 research workflow tests and selected source bindings pass. Independent human review remains open.

Next: a changed coverage argument must credit more than 104/9 ranks per call at this minimum repair cost, or change retained obligations. Original removal/fusion/branching, changed producers and justified coverage credit remain outside the obstruction. The claim is released.

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Original claim and source history

Status: CLAIM, 2026-10-14 20:48 UTC, priority revision 4. No result yet. Evidence is LOCAL-ONLY until a public artifact is linked. Expires 2026-10-14 22:30 UTC.

Question: does the interval separator of PR #2136 imply at least 48 added paid ranks for identity completion when every original transport obligation may be subdivided into an arbitrary nested chain, arbitrary retiming/common-chart linear resynthesis and source-independent storage are granted, but original obligations cannot be removed, fused or branched? If so, does that exceed the retained no-progress-credit headroom 328/9 from PR #2082?

Base: canonical main 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, task p104-side-correction, chooser nonce eec2345ed4f51606ac0c25c5bbe37f74. Scope changed from a construction attempt to a cost obstruction for refined retained intervals. Scientific input is PR1972/PR1991's LOWRANK-WITNESS.json, SHA256 0f541bef7f19fdeffd67157684e9f03d785f42c89973632f508fc1a0452b580e.

Method: independently reconstruct the binary subspaces and separator premises, then prove a transcript bound with added transport rank as the charged resource. An added nested rank-r interval has at most r strict substeps and hence at most r entering crossings. Test the cut and accounting with actual bypasses and semantic mutations. Expected artifact is one source-bound standard-library verifier and a written scoped proof, or a counterexample. Stop after this bound and its conditional moment screen, without seeking a sharp capacity or a supplier.

Nearest work: PR #2136 at 9b8689e0153e038b2c1179b06026adfaa7f7593b proves a 56-array upper bound without added transports, but does not price escape. PR #2127 at befebf0f4ae7a3f69fe9c5e136262559dcac125f counts escape with the unsplit original occurrences. PR #2082 at 60f4e337ffba470e09727dd435b1f1be3b67d03d supplies the conditional budget. This is a quantitative extension of their stated premises, not a new separator. Discussion #2131 allows replacement/removal of original obligations and remains outside this scope. PR #2139 changes the producer and is also outside.

Credit: Tairitsu-Aya/#2136 for the interval separator; Ross Richardson/#2127, David Arias/#2082, Jeremy Diviney/#2113 and Adam Gall/#2090 for earlier cuts; Rohan Arun/#1972, Chafik Boukhalfa/#1991, Adam Gall/#1940 and the geometry/compiler/coverage lineage retained there. Fresh overlap covered 398 open PRs and 811 Discussion records with complete pagination, but no code-diff coverage. No selected-frontier or kappa claim.

[petalas]

DONE / FINDING: PR #2148, commit 937b132f3f143ce0f2621b3b12e1ebc413e66730, contains the added-rank theorem and exact no-credit screen. The source check reconstructs all 1,410 original transports. Five semantic controls and nine CLI/export tests pass; registered Python 3.12 replay passes normally and with assertions disabled. The 65 repository research workflow tests also pass.

A descending added path can enter the target side twice, so the proof charges paid rank rather than counting a new obligation only once. The full proof, exact bounds, source pins, limitations and predecessor credit are in the package. This is author-checked, not independently human-reviewed or formal-kernel verified. The selected frontier is unchanged and this claim is released.