[unpaidmoon]

Change and mathematical scope

Scoped verification. No new κ. The selected conditional exponent stays 781451/250000000 (0.003125804).

On the pinned PR5718 word, the input nuisance k and the output nuisance g = k - c are different covectors. The partner covector c is nonzero, so a contract that uses the same functional at both boundaries does not describe this split. The three early cleanup operations restore every scalar endpoint only in the published order. Moving 743 -= 146/2 ahead of the 126 and 188 restorations fails exactly rows 126 and 188. Changing only the sign of that 146 correction fails only row 743: the order is what couples the three registers.

The paid histogram is not changed by this audit, and no new conditional exponent is computed. Native maps, the physical caller, compiler closure, precision and the outer ledger remain the predecessor's obligations. Unknown costs there are not zero.

Task and overlap

Base commit 626e936ce4d61f2584316914fc71baf96940c512 on canonical CrocSwap/integer-mult-bounds main. Priority revision 8. Catalogue card p104-side-correction. Scope status: refined.

The card asks whether a legal helper split improves the complete invoice. This package does not search for another split. It answers the first open question of research/p104-two-boundary-helper-split: a separate reviewer checks the two boundary functionals and the early cleanup order.

Session selection, in first-mention order of open_questions from the TASK.json files of packages named by PR number in revision-8 docs/research/current-priorities.md, skipping #5599 because that PR is the selected frontier rather than an open assignment. Questions answered by a later merged package are dropped:

1. Split one G20 helper into independent rank4 jobs at ordinary BIT saving 0.003507410738409 #5679: Can a cut use a different physical role for the early output?
2. Split one G20 helper into independent rank4 jobs at ordinary BIT saving 0.003507410738409 #5679: Can the changed split word enable another paid-query removal?
3. Split one G20 helper into independent rank4 jobs at ordinary BIT saving 0.003507410738409 #5679: Can a stronger Gaussian caller consume the completed BIT component?
4. Raise G20 ordinary BIT saving to0.003507719059749 with scalar conjugations #5708: Can noncoordinate public input contracts give another split?
5. Raise G20 ordinary BIT saving to0.003507719059749 with scalar conjugations #5708: Can a stronger Gaussian caller consume this BIT component?
6. Improve P104 helper split with distinct input and output bases #5718: Can a separate reviewer verify the different input/output bases and early cleanup order?
7. Improve P104 helper split with distinct input and output bases #5718: Do other pairs of legal boundary functionals support profitable helper splits?
8. Improve P104 helper split with distinct input and output bases #5718: Can the retained framework assumptions be resolved?
9. Certify exact dyadic helper-channel capacity with Smith witnesses #5615: Does a current source cut gain a channel under the full dyadic criterion?
10. Independently audit P104 callers with explicit owned lifetimes #5717: Can the same explicit-inventory audit be rebound to a successor with a changed caller or helper ABI?

Item 6 is this package. Dropped before the list: #5708's longer-identity question, answered for one-to-three contacts by #6290 and for four or more fixed-frame contacts by #6305, and #5611's physical-target question, answered by #6297. The 19 October handoff index in discussion #1166 is already closed. The later H25 serializer handoffs are open engineering lanes on their own draft PRs and are not this finite scalar question.

The phrase "early cleanup order" occurs only in the #5718 README and task file. #5844 checks a different claim: the #5719 causal certificate does not transfer onto this word.

Validation

Python 3.12, standard library only, from the repository root:

python3 -B scripts/research_package.py --package research/p104-boundary-functional-review --check-only
python3 -I -B research/p104-boundary-functional-review/verify.py
python3 -I -O -B research/p104-boundary-functional-review/verify.py
python3 -B scripts/research_package.py --package research/p104-boundary-functional-review

Both direct runs and the registered replay print PASS_P104_BOUNDARY_FUNCTIONALS_DIFFER_AND_CLEANUP_ORDER carrier=88 input=87 output=118 partner=171 reversed=126,188 and PASS_REGISTERED_RESEARCH_PACKAGE.

Controls: the published order has no endpoint failure; inverse-first cleanup fails exactly rows 126 and 188; the opposite 146 sign fails only row 743; the recorded witness carrier, cleanup triple and 118-term output functional must match the replay.

Not run: the #5718 native maps, physical caller, pricing adapter, ordinary admission, Lean, Docker, and the selected-frontier cold replay.

Credit

The word, witness and source archive are flyingviper's research/p104-two-boundary-helper-split, following Ali Romman's PR5713 and Joel Pulikkan / GamingPuzzled's PR5684. No predecessor file is modified.

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

Open next questions

1. Do other legal boundary pairs at another coframed cut improve the signed bill? The first step is to write one new cut's input and output functionals before searching. This review does not supply that cut.
2. Does the scalar order obstruction still fail after native maps and the physical caller? The first step is to replay the predecessor caller on the three-instruction swap alone. Those engines were not run here.