Derive the reverse row coefficient of the two-window R437 carrier.

[unpaidmoon]

Change and mathematical scope

Finite coefficient certificate for the PR #4067 two-window R437 carrier. The cancellation-free reverse row-l1 coefficient rises from 1113998 to 1123650 (delta +9652). The forward coefficient stays 49347. Scalar ADDs on the word rise from 24208 to 24211. Forward children stay 2915.

The maximizing reverse ADD is register 158 += register 223 on both words, with source norm 8689. The whole +9652 is already in register 158 before that ADD. Both coefficients have bit length 21, so a 21-bit width cap covers 1123650. The composed-word integer 1113998 does not.

The published host moment reads the rank profile plus the bad-event surcharge 32*64*64*E/10^16. It does not read row-l1. Because E stays 2915, that surcharge is unchanged. The local moment improvement leaves the reverse precision coefficient unpaid.

This is a scoped replay, not an all-size transfer theorem, a pooled-compiler regeneration, or a new κ. Selected κ stays 0.001672660197076918.

Task and overlap

Base bb4bccbf42844d2801487450727c2f63e10d1d0f, priority revision 6. Task card uniform-transfer-audit. Scope status refined: one precision implication for this finite carrier.

Item 12 of the chronological open #1166 handoff list after dropping work already delivered or covered by an open PR through #4126. The piece is open question 2 of PR #4067, the coefficient half of the obligation named from Discussion #1166 comment 19040062. The vendored words are copied from PR #4067 head a95f11c52e3ca1e4c5171b3c20d8f4b0815aee2e and hashed in verify.py; they are not Git objects at the package base.

Ordered eligible list:

1. T488 literal-ownership invoice (comment 19022532 Q1).
2. Rank-8/u2 source and consumer contract (comment 19029639).
3. Integer-shear payload subspace and injective encoder (comment 19032401).
4. Review of the research: certify local-first two-ADD obstruction on staged544 #3942 interaction reduction (comment 19032637 task 1).
5. Adjacent completed-call pair for the P104 two-axis gate (comment 19034066).
6. Fiber-tagged row/column pair (comment 19034676).
7. Changed P104 caller with a compatible literal encoding (comment 19034741).
8. Source-normalization caller at the joint interface (comment 19035513).
9. Physical K/adjoint/frame boundary price (comment 19036235).
10. Many-axis prime producer at the encoded boundary (comment 19037887).
11. q2 event 58 target-local gap (comment 19039339).
12. This package.

Validation

Python 3.12, standard library only. Registered replay:

python3.12 -B scripts/research_package.py --package research/r437-reverse-row-coefficient

Author-checked output:

PASS_R437_REVERSE_ROW_COEFFICIENT {"add_delta": 3, "bit_width": 21, "bit_width_cap_covers": true, "children": 2915, "delta": 9652, "forward": 49347, "new_reverse": 1123650, "old_integer_coefficient_covers": false, "old_reverse": 1113998}
PASS_R437_REVERSE_ROW_COEFFICIENT_INDEPENDENT {"delta":9652,"new_reverse":1123650,"old_reverse":1113998,"peak":[158,223,8689]}
PASS_R437_REVERSE_ROW_COEFFICIENT_CONTROLS {"groups": 4, "mutated_reverse": 1132339}
PASS_REGISTERED_RESEARCH_PACKAGE research/r437-reverse-row-coefficient outcome=partial

independent.py does not import verify.py. The control rejects an unchanged candidate and a duplicated peak ADD, which moves the reverse coefficient to 1132339. Head 72e7bb797adf82aeb525a399f56ab8adbab8e93c matches the working tree (PASS_RESEARCH_COMMIT_BYTES).

Not run: Lean, Docker, the selected cold replay, hosted CI, host.py, and the pooled compiler. The published global +864 ADD events equal 3 * 288 only with the external call count; this package certifies the per-word +3.

Credit

The carrier and the stated coefficients are from Chris R / Clear1nsight, PR #4067, retaining ai-nanachi / PR #3647, Ali Romman / PR #1043, Sagar Thakrar / PR #3700 and PR #2423, and Rohan Arun. This package rederives the row-l1 identity and the coverage comparison.

New checks by unpaidmoon, with substantial Cursor Grok 4.7 assistance. Apache-2.0. No independent human review and no formal-kernel acceptance are claimed.

Open next questions

1. Regenerate the replica-indexed pooled codebook and native requests for this word, then price the physical caller. Start from the PR Construct a two-window R437 carrier exchange with a strictly better paid profile #4067 template and the early SOURCE 87 move. Blocker: the compiler is outside this package, and frozen request identifiers are not transferable.
2. Name one charged precision or stock envelope and test whether its reverse allowance is at least 1123650. Blocker: no named slack-bearing envelope is an input here.

Workflow feedback (optional)

Selecting item 12 required extending the chronological #1166 list past the truncated indexes in comments 19056694 and 19056827. The coefficient integers were already stated in PR #4067; the missing reviewable piece was the coverage comparison. Feedback discussion: #1200