[unpaidmoon]

Change and mathematical scope

Partial frame-surrogate audit. No new κ. Selected κ stays 0.001672660197076918.

The added witness is one monotone decomposition of PR #2979 group V45. Sixty-one stage-one edits whose new frame lies in the declared V45 frame, and in no other declared group frame, replay on both PR #2942 parents. The measured profile cost is +78,512 with the four endpoints left unchanged and −8,388,172 with all four lowered. The weights are the published surrogate. STAGE-PRICES.json is not read. The four-helper margin on that walk is +22,972. Every 60-edit subset of the joint walk is nonmonotone.

The 29 edits that name helpers 249, 251, 265 or 267 are the same set identified by PR #3911. With or without the four endpoint changes they are nonmonotone at register 169. Adding any one of the other 32 partner-only edits to those 29 stays nonmonotone when the endpoints are unchanged.

Omitting restore index 137, or restore index 157, keeps the gate-only walk monotone and raises its cost from 78,512 to 83,508. With all four endpoints lowered, those omissions fail at registers 267 and 265.

Scalars, operators and the cleanup list stay fixed. The private-buffer count stays 86. The joint width inventory moves four units from width 8 to width 7.

Task and overlap

Base commit bb4bccbf42844d2801487450727c2f63e10d1d0f (canonical CrocSwap/integer-mult-bounds main, rechecked 2026-10-20). Priority revision 6. Task independent-moment. Scope is refined: one group, and only the decomposition that the open V45 audits do not already contain.

Already open, and not repeated here as the claim:

• Add independent V45 frame and ledger audit #3911 (1337isnot1337) rebuilds the frame walk and the stage-one ledger, prices all 15 nonempty V45 endpoint subsets on the full 139-edit word, and obtains +78,512 only as the pinned V45 joint_delta minus a measured endpoint delta of −4·c_1. It records that the 29 role edits are nonmonotone at register 169 and leaves the group price underived.
• Check the V45 rank-7 intersection and its declared subset margins #3543 (jwr404) checks the printed intersection and the declared subset margins from the price table.
• Record the V45 triple intersection #3823 (jwr404) records the 128-vector triple intersection.
• Record the printed V45 margin ladder #3841 (jwr404) records the printed margin ladder (difference 25,371) and the sum of the five joint prices.

The new delta is the 61-edit walk: exclusive new-frame containment supplies the 32 partner edits that the 29-edit refit omits, and the overhead is a profile cost of that walk.

Validation

Python 3.12, standard library, from the repository root:

python3 -B research/rank7-v45-group-audit/verify.py
python3 -B scripts/research_package.py --package research/rank7-v45-group-audit

Recorded result:

PASS_RANK7_V45_MONOTONE_SPLIT providers=2 containment_edits=61 role_edits=29 partner_only=32 sections=20+41 role_only_nonmonotone=169 measured_overhead=78512 joint_delta=-8388172 joint_margin=22972 single_margin=-53141 leave_one_out_joint=nonmonotone one_partner_extension=nonmonotone gate_only_omit_restore_137_or_157=83508
PASS_REGISTERED_RESEARCH_PACKAGE research/rank7-v45-group-audit outcome=partial

This is a finite replay of two parent words. It is not a proof that the 61-edit refit is the frame-search optimum, and it is not a multiplication theorem. Groups A–D, the physical invoice, idle packing and both supplier caps are unrun.

Credit

Marius-Paul Dumitrean (Dugongue / mdumitrean), PR #2979, for the words, the V45 claim and the published weights. Parent words descend from Mason Hale's PR #2917 and the PR #2942 extractions. Frame climb rules are Jeremy Kothe's, from the PR #2894 lineage. 1337isnot1337, PR #3911, for the frame and ledger audit whose open question this walk answers. jwr404, PRs #3543, #3823 and #3841, for the intersection and printed-ladder checks.

Prepared by unpaidmoon with substantial AI assistance (Cursor Grok). No independent human or formal-kernel review is claimed. Apache-2.0.

Open next questions

See research/rank7-v45-group-audit/README.md.

1. Is there a proper subset of the 61 edits, omitting at least two, that stays monotone for every endpoint subset and still measures +78,512 and −8,388,172? Every 60-edit subset fails the joint walk. The missing optimizer witness also leaves optimality open.
2. Do groups A–D have an exclusive-containment edit set that prices each group from profile costs?
3. Does the measured margin survive an independent enclosure of c_r at b = 0.001703676387993676 and the idle-width cap? Until then it does not move κ.

Workflow feedback (optional)

A title search for the rank-7 group missed #3911, whose title is "Add independent V45 frame and ledger audit". Searching the helper names together with "V45" would have found it before the first draft.