[ToikY]

Change and mathematical scope

NO VERIFIED GAIN (0% κ change). The comparable witness is #7161, κ = 0.003644890067940. At the fixed target 0.0040075385047236, the exact signed invoice needs 25,328 ideal equal-volume pairs. The most optimistic count is 33,991 pairs, including all 3,999 native rank-one MOVE occurrences at each of 17 stages. This is a price relaxation with free common clocks and coframing.

The scoped proof closes one rank-two child with uniformly bounded rectangular linear adapters and bounded-support bypass, including destructive scratch erasure. A separate support inequality covers arbitrary coefficients when the complete post-child state has a sparse left inverse. The exact projection control shows how a width-dependent reciprocal can return the map while using a priced bank expansion of at least 2^f, beyond the permitted 2^C.

Task and overlap

Changed selected-packing scope at canonical base e545235. The package pins #7161 e3f8d39, #7113 07a76c5, and the #7165 invoice extractor. #4932 gives the closest rectangular result in a fixed columnwise Clifford algebra. Here the hypotheses are support and norm bounds on arbitrary rectangular linear adapters. #4045 and #3989 provide earlier monomial and nonmonomial precedents.

Validation

python3.12 -B scripts/research_package.py --package research/p104-rectangular-clifford-adapter-bound

Tested with CPython 3.12.14. The exact native and caller replay checks all 512 signed columns of MOVE535 and 60 padded projection controls, reconstructs the 110,519 paid and 22,427 productive positions, and rejects an omitted paid MOVE, changed phase, missing reciprocal, duplicate source key, and altered pin or receipt. A clean independent replay and a second directed-price implementation agree. This branch includes the docs-only selected replay navigation prerequisite.

Credit and next question

Clear1nsight #7161 supplied the word and invoice. Rohan Arun #7113 supplied the signed caller and Gaussian replay closure. #7165 supplied the invoice reconstruction. The retained source notice credits the native lineage. Codex and subagents materially assisted. The next test is an exact pair with charged bank expansion below 2^C, including setup, tape, precision and returned ownership under the same contract.