Prove sharp P112 COPY power for the right-space free-correction extension

[ywz65]

PR2398's ten-term boundary leaves the minimal P112 right factor space and attains eight rank-eight COPY charges using free correction terms. This contribution proves that this is sharp throughout the enlarged free-correction class: left factors in col_C(X,e0), right factors in col_C(X,e0,e1), any finite number of mixed terms, and COPY zero for every pure-projection term. The minimum is 8*8^q for every real 0<q<=1. Positive-COPY pure terms remain explicitly outside the eight-mixed-term theorem.

The new support catalogue covers all 1,022 binary-character kernels. Rational nullspaces are independently certified by integer annihilation and modular rank lower bounds. The all-length proof uses a rank-three bound for cost-seven contributions when there are at least nine mixed terms. With exactly eight, dual-basis coefficient comparison forces alpha*(beta-1)=1 and excludes every cost-seven exceptional class. The existing ten-term attainer is credited; four nontrivial free-correction family witnesses and a redundant mixed-pair example check every 12,544 matrix entry. Eight controls include a valid algebraic factorization with charged pure terms, rejected only at the stated scope boundary.

Registered optimized CPython 3.12.14 replay passed, including unchanged Git-free export, source and full-receipt drift controls, exact regeneration and exclusive output. The prescribed ceiling and selected baseline binding controls passed. Separate AI-assisted proof review found no actionable issue; no human/formal-kernel review, selected cold replay or hosted-CI pass is claimed.

Base and refreshed canonical main: 0fdd7d8, priority 4. Fresh complex-mechanisms/new-helper-inventory selection is explicitly changed to PR2398's algebraic handoff; no physical-inventory acceptance is claimed. Submission overlap covers 710 open PRs and 1,207 Discussion records with complete pagination at 13:17–13:18 UTC. Exact source pins, limits and next questions are included. Advance claim: #2398 (comment).

Only research/p112-free-right-extension/ is added. No physical supplier, native implementation, new kappa or selected-record change. Credit commdata2338/PR2021/PR2398, Hanhong Zhao/PR2321 and the retained root/support lineage. Prepared for ywz65 with substantial OpenAI Codex assistance; Apache-2.0.