[unpaidmoon]

Change and mathematical scope

Negative result. No new κ. The selected conditional exponent stays 605457647/200000000000.

The recording-only theorem for the fused five-bank producer leaves one escape: the raw state after gate 11, whose grade-3 channel has image dimension 5d. This package prices that state as a child that must be exposed, continued and cleaned. On the predecessor moment, for every exponent t in [0, 1],

gap(t) = 2 * 3^t - 8 <= -2.

Replacing the two cleanup letters inside D by one new grade-2 letter still gives 2 * 3^t - 2^t - 6 <= -2.

The exposed owner is B x0 + D x1, with B = M C2 + 2 K a. No left-linear image of the live owners can drop D x1 and keep 2 K a x0. A fresh D costs two source rank-1 calls, and M C2 costs one more. Keeping the later fused banks costs the hybrid profile 5 H1 + 3 H3 before that cleanup, and 8 H1 + 3 H3 after it. Five rank-3 jobs are credited, which is generous: the off-diagonal grade-3 terms already in the final rows are not charged.

The moment does not charge monomials, field additions, the factor 1/2, or a field copy of the exposed owner. Charging any of them widens the deficit. Precision, compiler reserve, outer transfer and feedback into a live owner are further nonnegative charges on a gap that is already negative. They are not decided here.

Task and overlap

Base: 32890bc5de034ab8fc93ac88ead7279a6a416d04 (upstream CrocSwap/integer-mult-bounds main).

Task: complex-rank-shape-decoder, scope refined. The catalogue card asks for a larger-rank decoder profile. The request taken is open handoff item 3 after exclusions: the changed-resource invoice after the fixed-producer completion ceiling, discussion comment 19133451.

Nearest overlap is open PR #5491, which proves that this raw cut raises the grade-3 image dimension from 4d to 5d and leaves the cleanup bill open. This package does not replay that image proof. It prices the bill. The predecessor gate list and operators are pinned from research/block3-shared-port-composition and are not modified.

Eligible-list note for the parallel session: open #1166 HANDOFF blocks in comment order, excluding the typed actual-width handoff (unpaidmoon CrocSwap#4123/CrocSwap#4127) and the height-1 truncated-source handoff (unpaidmoon CrocSwap#5273). Item 3 is this completion-ceiling successor.

Validation

Python 3.12, standard library only. From the repository root:

python3 -B scripts/research_package.py --package research/shared-port-raw-cut-invoice --check-only
python3 -B scripts/research_package.py --package research/shared-port-raw-cut-invoice

Both registered commands passed here, normal and -O, each printing PASS_SHARED_PORT_RAW_CUT_INVOICE with gap_t1=-2 and widened_gap_t1=-2. Metadata and pins passed. The verifier rejects a missing aligning rank-1 call, an add-sign fault, a wrong pivot operator, and a grade-2 letter hiding in the source schedule.

Not run: native suite, Lean build, selected cold replay, compiler/outer replay. The derivative comparison 2 < 9 is the all-real argument for the widened gap; the in-alphabet gap is also checked on the uniform 64-step grid by the integer comparison 3^k < 4^64.

Credit

The gate list and operators are the PR4813 / block3 schedule retained in research/block3-shared-port-composition, including the hexapode, Dugongue, Yiyang / Lyy-iiis, lee-phys, Jacob Alan Sussman and Cinna Davis / 1337isnot1337 lineage recorded there. The recording-only 4d bound and the raw-cut 5d witness are Chris R / Clear1nsight and JoyboyBrian's open CrocSwap#5491.

Prepared by unpaidmoon with substantial Cursor Grok assistance. Apache-2.0.

Open next questions

1. Can a feedback write into the live owner separate D x1 from K a x0 with fewer than two extra rank-1 letters? That is the only Gaussian saving large enough to make gap(1) positive. First step: one explicit feedback word and its paid profile. Blocker: every pure source letter is invertible, and the recording-only interface forbids the write.

2. Do the off-diagonal grade-3 terms in the final rows need their own cleanup before those four jobs are legal children? The reward here already credits all four. First step: price one off-diagonal class on final row 3. Blocker: a consumer contract that says whether image dimension 4d is itself a legal child.

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