[unpaidmoon]

Change and mathematical scope

Partial invoice certificate. No new κ. Selected conditional κ stays 836330098538459/500000000000000000 (0.001672660197076918).

On the vendored PR CrocSwap#3653 numerics inputs at head 607a09ff441c79b215a8127a81f4cc70021d0d9b, the published admission histogram is the literal-owner histogram plus the retiming move -2 H_1 - 2 H_2 + 2 H_3 on all 4,392 calls. Both providers carry that same move. Its rank mass is 0, so the global rank mass stays 31,762,944 = 65,088 * 488. The idle histogram {1:114192, 3:31842, 5:6954, 48:186782} is common to both bills. With live = 488 * 896,

73 * live - 31762944 = live - 64 * 4392 = 156160.

Sections A, cut, restore, warps, center_frames, helper_final, removed and start_extra are unchanged. B and cleanup change. This is not a literal-row replay, a moment bracket, a native admission, or a multiplication theorem.

Task and overlap

• Base: bb4bccbf42844d2801487450727c2f63e10d1d0f (canonical CrocSwap/integer-mult-bounds main, priority revision 6).
• Task: scalar-to-moment, scope refined. The card asks whether one scalar simplification becomes a paid-profile improvement. This package does not propose a simplification. It checks the histogram bridge the retimed composition already claims.
• Handoff: discussion Handoffs and requests for independent checks CrocSwap/integer-mult-bounds#1166 comment 19022532, question 1. Question 2, the saturation check, is open PR Audit (no new kappa): the composed T488 profile is exactly PR3642's optimal packing vertex CrocSwap/integer-mult-bounds#3796.
• Ordered eligible handoffs, chronological from the twelve-item list in fork PR Prove codimension-one L/2 substitution soundness on double transversals #39 (comments from 19016211, one remaining next task per marker, after dropping work delivered or matched by an open PR at or below Research (no κ claim): Gaussian E8 c = 20 exact certificates; local-rewrite census on #4088's T360 words CrocSwap/integer-mult-bounds#4121). Items answered or refined by this round's PRs Price flag 9's head-step co-host at exactly +2 rank mass CrocSwap/integer-mult-bounds#4107 and Rebind central-factor-packed pins so community-batch952 can admit sou… CrocSwap/integer-mult-bounds#4111–Price the cut58 ADDRESS swap against the separable response menu. CrocSwap/integer-mult-bounds#4149 are then removed. Six items remain, so item 8 is the refinement at 0-based index (8-1) mod 6 = 1:
  1. (7,18) / (7,20) functional census (comment 19021170, question 1).
  2. T488 literal ownership/output invoice (comment 19022532, question 1). This piece.
  3. Physical rank-8/u2 contract (comment 19029639).
  4. Fiber-dependent chronological row/column pair (comment 19034676).
  5. Coupled source-normalization caller (comment 19035513).
  6. Physical K/adjoint/frame boundary (comment 19036235).
• Dropped from that twelve after the exclusion list: single-hub factorization (Prove the exceptional single-hub literal charge is 48. CrocSwap/integer-mult-bounds#4124, Record the three-hub extremal actual-reader charge. CrocSwap/integer-mult-bounds#4145), integer-shear (Prove faithful integer-shear words fail the supplier moment test. CrocSwap/integer-mult-bounds#4126, research: stop the one-XOR shear carrier on a lossless integer payload CrocSwap/integer-mult-bounds#4135, Price integer transvections on the shear target B^k. CrocSwap/integer-mult-bounds#4146), the research: certify local-first two-ADD obstruction on staged544 CrocSwap/integer-mult-bounds#3942 review (Review the staged544 fixed-frame new-gap reduction. CrocSwap/integer-mult-bounds#4134), the adjacent completed-call pair (Certify the literal-slot defect that blocks a uniform P104 adjacent c… CrocSwap/integer-mult-bounds#4133, Certify that uniform P104 completion misses a port-dependent chart. CrocSwap/integer-mult-bounds#4136, Prove uniform completion fails on the physical P104 encoding. CrocSwap/integer-mult-bounds#4140), the A1858 challenge (Audit the separated A2 composition and cleanup split CrocSwap/integer-mult-bounds#4112, and open Certify current-provider A2 transfer and unchanged owner-cone allowance CrocSwap/integer-mult-bounds#4041), and the many-axis encoded review (Review the encoded many-axis production_axis guard. CrocSwap/integer-mult-bounds#4142).
• The piece taken is the histogram identity. The 1,791,936 literal rows and report.local_profile event recount stay open.
• Nearest overlap: PR Compose retimed T488 suppliers: conditional kappa 0.00173041889976 CrocSwap/integer-mult-bounds#3653 states the profile; PR Independent arithmetic audit (no kappa): PR3653's conditional T488 composition root, released string and PR3642 delta reproduce CrocSwap/integer-mult-bounds#3740 reproduces the root and leaves the invoice comparison; PR Audit (no new kappa): the composed T488 profile is exactly PR3642's optimal packing vertex CrocSwap/integer-mult-bounds#3796 shows the unretimed profile is the packing vertex. None of those is this independent bridge. No predecessor checker is imported.

Validation

CPython 3.12.3. Registered replay:

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

Observed PASS_REGISTERED_RESEARCH_PACKAGE research/t488-owner-invoice-identity outcome=partial and PASS_T488_OWNER_INVOICE_IDENTITY. The same marker passed under -O -I.

Checked: SHA256 of the nine vendored inputs; the four old histograms agree; both providers have the stated delta; published profile equals literal profile plus that move; coverage deficit 156160; role count 4392 * 408. Controls reject a short call count, a bumped literal rank-1 count, a nonzero rank-mass move, and a changed A section.

Not run: literal FILL row replay, event-level recount of the local bills, PR CrocSwap#3653 moment engines, native admission, the fresh bootstrap wrapper, Lean, Docker, and the selected cold replay.

Credit

Rohan Arun, PR CrocSwap#3653, for the composition and recorded admission profile. roger-sato, PR CrocSwap#3642, for the retimed words. hexapode, PR CrocSwap#3633, for the literal-owner package as vendored by CrocSwap#3653. Nick Petalas, PR CrocSwap#3740, for the arithmetic audit that left this comparison open. Prepared by unpaidmoon with substantial Cursor Grok assistance. No independent human or formal-kernel review is claimed. New work is Apache-2.0.

Open next questions

Linked from research/t488-owner-invoice-identity/TASK.json:

1. Does the literal FILL payload, not OWNER-EXPECTED.json, sum to the old histogram? First step: materialize FILL.json.gz at SHA256 20662cc64df34cab409fdf31ed0f0222462530922a01308a46964d661d2374cf. Blocker: that payload is not vendored here.
2. Can the local bills be recounted from the B and cleanup events? First step: one child-rank rule that reproduces both base bills. Blocker: the event rank slot is not the child histogram.

Workflow feedback (optional)

CrocSwap#1200