[petalas]

Summary

 fixed literal P112 orthogonal-group fitting matrix K
- tariff 224 checked for its indicator queries
+ tariff 224 proved for every spanning query list in rowspace(K), over every field

Every rank-minimal factorization of this same K has sharp full-plane one-total tariff 224, including arbitrary dense query recoding. The theorem also covers redundant queries constrained to that row space, and applies conditionally to any even orthonormal partition of P112. The concrete replay binds PR3370's rank-32 fit. PR3345 and PR3370 already priced their literal indicators; this contribution closes the general recoding obligation.

Package: research/plane-fit-recoding-tariff/. Canonical investigation.

Evidence

• Before: the literal tariff was 224; a general scalar change of basis had no recorded lower-bound proof. After: a weighted spanning lemma proves the all-field minimum. The unchanged indicator basis attains it, while a dense exact recoding costs 288.
• Source-bound primary replay checks all 65,535 group closures, 11,392 forced mask entries and 37,632 dense factorization entries. A separate no-import checker verifies explicit-vector geometry and all 264,864 two-query invertible recodings. Seven behavioral groups include four actual CLI failures, a singular family and a query outside the row space.
• Python 3.12.15 registered replay, Python 3.15.0 optimized controls, read-only Git-free export, warning diagnostics, Ruff E/F/B/SIM/I/UP/PLW and formatting pass. Exact retained PR3370 certificate bytes and selected inputs are hash-bound. The pending source commit is not a runtime dependency.
• Replay: python3.12 -I -Werror -B scripts/research_package.py --package research/plane-fit-recoding-tariff. Standard library only. Proof, exact receipt, sources, limits and open questions are included.

Merge Danger

Door: two-way. This adds one isolated theorem package.

Blast radius: package. The result fixes the literal matrix and the full-plane additive tariff. Other fitting row spaces, overcomplete queries outside that space, changed readers and shared native operations remain open. Physical supplier, all-size and full multiplication theorem obligations are unrun. No new kappa or selected-frontier change is claimed. Frozen predecessors are unchanged.