Audit the composed T488 histogram against literal helper outputs.

[unpaidmoon]

Change and mathematical scope

Audit, no new κ. Selected κ stays 0.001672660197076918.

On both retimed canonical words from PR #3653 at 607a09ff441c79b215a8127a81f4cc70021d0d9b, every helper output width (final-frame rank minus start-frame rank) equals the corresponding literal provider width. The two frame tables differ only at index 300, both of rank 4, and that index is not a helper boundary. The published histogram

{1:10817496, 2:3179808, 3:1024434, 4:447984, 5:94794, 8:35136, 48:186782}

is exactly the predecessor owner-certificate profile plus 4392 * (-2 H1 - 2 H2 + 2 H3). The idle residual is unchanged: {1:114192, 3:31842, 5:6954, 48:186782}. Rank mass stays 65088 * 488 = 31762944. Physical count 437757 = 896 * 488 + 509.

This is not a supplier admission, a moment proof, or a selected-frontier change. The 1,791,936 literal rows were not regenerated.

Task and overlap

Base bb4bccbf42844d2801487450727c2f63e10d1d0f, priority revision 6. Item 2 of the chronological open #1166 list after dropping work delivered or refined through #4149: comment 19022532, question 1. Question 2 is PR #3796.

Card scalar-to-moment, scope changed: this audits an existing composition invoice instead of converting a new scalar simplification.

Nearest overlap: PR #3653 publishes the composition and its own owner replay; PR #3740 reproduces the arithmetic and leaves the ownership invoice open; PR #3796 shows the same histogram is the packing vertex. This check does not import those verifiers. It recomputes helper widths from the vendored frame tables and the histogram identity from the vendored certificate.

Validation

python3.12 -B scripts/research_package.py --package research/t488-ownership-invoice

Observed PASS_T488_OWNERSHIP_INVOICE with rows_regenerated=false and no_new_kappa=true. Metadata check passed. In-memory controls reject one incremented helper width and one incremented published count. Python 3.12, standard library only. No Lean, Docker, or full admission replay.

Credit

PR #3633 (owner certificate), PR #3642 (retimed words), PR #3653 (Rohan Arun / roger-sato, composed profile), PR #3740 (the open question), PR #3796 (saturation, not repeated). Prepared by unpaidmoon with substantial Cursor Grok assistance. Apache-2.0.

Open next questions

1. Sum residual capacities from a fresh FILL.json.gz without reading CANDIDATE.profile. Blocked by the several-minute integral-network expander.
2. Climb the canonical gate frames and compare that child histogram with the stored local bill. Helper output widths do not determine the local bill.