[josecarlosgonzalezroque-design]

Change and mathematical scope

This independently audits PR #5526's later paid-return/error/invoice bridge, which PR #5547 explicitly left outside its core Clifford-theorem audit. No gap was found in REPAIR.md Sections 2–4 under the stated invariant-history, disjoint unitary-target and one-field pricing premises.

The isolated research/paid-return-bridge-audit/ package gives a written derivation and a standard-library rational checker that imports no predecessor executable. It checks arbitrary linear feedback, quotient dimension, orbit/error normalization and the source-declared complete invoice. The inherited conclusion remains: 104 extra returns are necessary, but the reference tariff permits at most 36.

Actual-caller observation/grade completeness and the core Clifford Gram theorem remain inherited premises. Receipts are not presented as an independent native replay. No new kappa, physical supplier, selected cold replay, proof-kernel or independent human acceptance is claimed.

Task and overlap

Canonical main was refreshed and unchanged at 5e0052ca0aa3036a3afa8b0438927377c8d97d53 (priority revision 7). Reviewed PR5526 head: 45f7de73b168721cdf7ec8c1769b1b594493716a; all eight input blob IDs match. Contribution: a1d5b17602be5ca928f666fdc9abc147e604c4e6.

Task: formal-interface-lemma, picker nonce 0ae98c6c6a57ad53401268db8aa558d4. Scope changed from formalization to an independent informal proof audit of the bridge explicitly excluded by #5547. This checks whether the fixed observation/capacity contract really excludes affordable repair. #5549's one-qubit threshold and #5531's different endpoint application are separate. TASK.json records the change and coverage limits. Prospective claim and handoff.

Validation

Windows / CPython 3.12.10, standard library only:

• All four registered normal/optimized commands pass.
• 175 exact feedback-prefix cases, including 120 returns outside the initial/target span; all 81 cases in a separate ternary fixture.
• Seven semantic controls and four deliberate implementation/accounting defects rejected in each Python mode.
• Independent rational margin enclosure: [36.037431499166, 36.037431503056], containing the source's finer interval.
• Metadata/source pins and committed-byte checks pass. All four commands also pass in a read-only export with Git absent; all 18 files, including its receipt, remain unchanged. The final published 17-file package/input export passes integrity checks.

python -B scripts/research_package.py --package research/paid-return-bridge-audit

Credit

Credit Ali Romman; Chris R / Clear1nsight; Dugongue; DLamdata; and the retained native, history, concave-order and interval-arithmetic lineage. Prepared for josecarlosgonzalezroque-design with substantial OpenAI Codex assistance; Apache-2.0. One agent; no subagents or human reviewers.

Open next questions

Independently bind the complete literal PR4948/4978 observation inventory and its 104 target columns to the caller, including both mandatory source clarifications. Start by tracing one affected input through all nine cuts. Complete source/observation and uniform-grade coverage remains the blocker; this conditional bridge does not provide it. See README.md and TASK.json for the bounded handoff.