[unpaidmoon]

Change and mathematical scope

Partial scalar bill, no new κ. Selected κ stays 0.001672660197076918.

One straight-line program applies (N-P) ⊗ M to one 104×104 bank. With B = B2/2 from the canonical P104 fixture,

(N-P)(v1, v2) = (-B v2, v2 - B^t v1 + B^t B v2).

The program uses 104 * 5 * 384 = 199680 additions of the ±1 entries of B2. It matches the matrix (N-P) X M on three banks. PR CrocSwap#3996's two-pair uncorrected Gram saving is 110592 unit additions, so paying this consumer once leaves a net of -89088. Both omitted sides, charged separately, cost 399360 additions, which already puts one coded pair above one 241280-addition reference pair.

This is not a lower bound, a native rank bill, a chronological flag program, or a multiplication theorem.

Task and overlap

Base bb4bccbf42844d2801487450727c2f63e10d1d0f, priority revision 6. Card p104-side-correction, scope changed: the card asks for a chronological endpoint correction; this prices the omitted identity side left open by discussion comment 19056819.

Item 16 of the chronological open-CrocSwap#1166 list recorded in the finding (sibling slots 1–10 left in place). Nearest overlap is PR CrocSwap#3996 (the algebra and the 110592 gap) and PR CrocSwap#4125 (the index bridge, which explicitly does not price the consumer). This package does not replay the 763,392 events.

Validation

CPython 3.12, standard library. python3.12 -B scripts/research_package.py --package research/p104-omitted-side-consumer returns PASS_P104_OMITTED_SIDE_CONSUMER and PASS_REGISTERED_RESEARCH_PACKAGE research/p104-omitted-side-consumer outcome=partial.

Checked: B2 digest and weights, A^2 = 13A, three banks, input-independent count 199680, dropped B^t B term rejected, flipped B2 entry rejected. Not run: literal-event replay, half/double invoice, native rank, a proof that 199680 is minimal.

Credit

ToikY / PR CrocSwap#3996, Chris R / Clear1nsight / PR CrocSwap#3979, and the retained P104 native-channel lineage for the fixture. Prepared by unpaidmoon with substantial Cursor Grok assistance. Apache-2.0.

Open next questions

1. A straight-line program for one bank with fewer than 110592 unit additions would put this factorization's cost back under the two-pair saving. None is known here.
2. Shared shears between (N-P) ⊗ M and M ⊗ (N-P) could make the separate 399360 charge too high.

Workflow feedback (optional)

CrocSwap#1200