Certify minimum rank for paid connector chart repair

[ywz65]

The retained connector chart interface requires equal kernels when no additional source information is allowed. This module permits one paid residual injection and determines its exact minimum rank over invertible row charts:

min_R rank(B1-R B0) = max(rank B0,rank B1) - dim(row B0 intersect row B1).

The written proof covers every field, singular maps and unequal ranks, and constructs an attaining chart by adapted row bases. It also bounds the total injected rank of any internal sequence of invertible charts and additive source corrections. This is a rank optimum, not a native chart or scalar-price optimum. Woklerx's equal-kernel chart interface, Ross Richardson's dirty-query accounting and the standard row-space argument retain credit.

A literal binary example pays its source correction, chart and final inverse:26 scalar XORs versus34 for separately closed queries, on the same12 arbitrary dirty bits. The source and connector restore, and the first output is delivered before the chart and never rewritten. The declared fixed-port tariff is498 versus614. An11-XOR direct-matrix control is cheaper outside this fixed-call alphabet and is explicitly retained; no general circuit-optimality claim is made. The complete symbolic invoice includes preparation, admission, instruction work and all query/chart/repair prices. Rank alone never makes an observation or implementation free.

Validation: all262,144 binary3-by-3 map pairs agree with an independently enumerated complete chart-orbit oracle;8,192 constructive charts attain the predicted rank. All4,096 dirty pilot inputs/inverses/delivery cuts pass. A separate F3 control checks6,561 dirty banks and inverses with noncommuting readers and rejects the wrong closing sign. Four program mutations fail semantically. Native CPython3.12.7 registered checks and four export/source/typed-receipt groups pass; optimized3.14.5 primary passes. Separate OpenAI Codex proof/chronology review and independently minimized4,454 smaller pairs plus all168 pilot charts found no material issue. No predecessor executable is imported.

python3.12 scripts/research_package.py --package research/connector-chart-rank-repair

The round began from current main0fdd7d82 under revision4 and preserved its assigned card when guidance advanced. The clean checkout fast-forwarded to revision5 main b4560d9e7216f72b73c5aa940ac099c05e33ccf9; scientific predecessor blobs were unchanged. TASK.json records the five-point expansion decision: narrow to one local module, then stop. General native repair/chart costs, selected hosting, precision and a concrete selected consumer remain unknown. No supplier, recursive contraction, physical compiler, selected-result change or new kappa is asserted.

Final main refresh at16:54UTC was unchanged. Overlap includes817 open PRs and1,279 Discussion records with complete pagination, supplemented by the latest80 PRs and canonical claim comments; metadata coverage is not a novelty guarantee. Claim: #943 (comment). New questions require an actual caller and strict complete cost allowance before another dependent optimization.

Prepared by ywz65 with substantial OpenAI Codex assistance. Apache-2.0. No human/formal-kernel review, hosted CI or selected cold replay is claimed.