[ToikY]

Result

NO VERIFIED GAIN. The κ change is exactly 0%. The comparable complete witness remains #7161, κ = 0.003644890067940, live head 7a607733a114689a60179898ab5ec9e30561daac.

For the fixed native scalar tape and paid calendar, an ordered-chart cut allows at most 48 independent equal-rank splits across distinct canonical charts, using the 24 old descending MOVEs. It allows arbitrary chart-local linear coding and side information. The predecessor cut granted 96. The full 17-stage directed saving is at most 118.54612795971228 against a 140.51726295091429 raw shortfall at κ = 0.0040075385047236. The exact directed margin upper is -54927837478005033828434093/2500000000000000000000000.

The cap counts one complete array per descending event and one split per original owner. The price grants all added ordinary charges free and all 73 pending direct chart capacities at their ideal values. All 24 timed descending checks and 104 direct chart checks were replayed. The result leaves changed scalar chronology, same-span detours, cross-stage sharing, larger payloads and per-owner rank redistribution open. No candidate or complete changed supplier was built.

Scope and overlap

Canonical e54523517d0f03e58352e647c403a5af3e525a57, changed p104-side-correction scope. #7161 scientific source supplies the native and invoice. #7113 supplies the signed caller at 07a76c5e2738882c0cb322278e56f6cae3c9885d. Exact bytes, paths, Git blobs, hashes and source notices are included. #2113 bounds eight private descents for an earlier disjoint-source-to-target identity. #7208 bounds a fixed-line preprocessing permutation. Here the endpoints can share charts across different lanes, so the proof uses a chart order to get a triangular full-rank submatrix. The separate CI navigation commit reuses the verified #7161 prerequisite.

Replay

From a clean repository checkout with CPython 3.12 and assertions:

python3.12 -B scripts/research_package.py --package research/p104-paid-cross-chart-stock

Local registered replay passed under CPython 3.12.14. It authenticates all 16 path-keyed inputs and receipts, reproduces the frozen census, independently rechecks all 128 contacts, and recounts all 110,519 paid positions and 22,427 productive fields. All 28 committed-byte, mode and source-history checks and six navigation tests passed. Source, duplicate-path and changed-ordered-receipt controls rejected. Finite triangularity controls corroborate the written rank proof. Hosted checks are pending. No selected cold replay or changed physical supplier replay ran.

Credit and next question

Credit Clear1nsight #7161, Rohan Arun #7113, #7165/#7166, the Round 11/13 directed-price and Round 18/19 coefficient and stock work in #7111, Jeremy Diviney and predecessors #2113, and Nick Petalas #7208. OpenAI Codex and subagents materially assisted. Apache-2.0.

A changed paid payload would need a full-construction capacity and price bound before a local prototype. A survivor must preserve exact arbitrary-input action and charge routing, ownership, restoration, precision and tape.