[unpaidmoon]

Change and mathematical scope

This records one coupled handoff on the pinned PR5580 word. At cut 13762, frame 1053 and pivot 596, the dyadic row {592: 5/16, 593: 5/16, 594: 5/8, 596: 3/8} has no unit coordinate. The unit-pivot constructor rejects that row and the matching cut row with Dyadic basis pivot. The CrocSwap#5611 Euclidean compiler emits 36 ADD/SCALE operations at frame 3 and 34 at frame 1053. Substituting those schedules into the existing handoff adds public register 735.

Register 596 then runs from frame 3 to frame 1053 (rank 5). Register 735 runs from frame 1053 to frame 127 (rank 4). Those two lifetimes replace register 596's previous rank-9 lifetime from frame 3 to frame 127. Local replay keeps the paid MOVE histogram {1:2211, 2:459, 5:164, 4:94, 3:494, 7:14, 6:18}. Helper ranks change from {9:424, 4:83, 5:5, 8:15} to {9:423, 4:84, 5:6, 8:15}. The scalar allowance rises from 217428 to 218564 (+1136). Events go from 25140 to 25280, and public width from 735 to 736. Endpoint identity, peak owned fields 1, and all eight owned lifetimes hold.

The +1136 allowance is the cost of this feasible Euclidean schedule and its inverse. It is not a proved minimum. The paid histogram does not improve. This is not a κ result. The selected frontier is unchanged. Native maps, the physical caller, compiler closure and the outer ledger remain unrun; those unknown costs are not zero.

Task and overlap

Base commit: 2485805a6d47f36ea83ddde6327d453ac82d44dc on canonical CrocSwap/integer-mult-bounds main. Priority revision 8. Catalogue card p104-side-correction. Scope status: changed.

The card asks whether a legal split improves the complete P104 invoice, starting from the selected CrocSwap#5599 word. This package answers the open question left by CrocSwap#5611: whether a newly admitted dyadic pair gives an additional physical helper target. The object is one cut on the PR5580 constructor word, which is the word that constructor consumes. The local answer is yes, and the local scalar bill consumes the step.

Session selection, in first-mention order of open-next questions from the packages named in revision-8 docs/research/current-priorities.md:

1. Split one G20 helper into independent rank4 jobs at ordinary BIT saving 0.003507410738409 CrocSwap/integer-mult-bounds#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 CrocSwap/integer-mult-bounds#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 CrocSwap/integer-mult-bounds#5679: Can a stronger Gaussian caller consume the completed BIT component?
4. Raise G20 ordinary BIT saving to0.003507719059749 with scalar conjugations CrocSwap/integer-mult-bounds#5708: Can longer scalar identities improve this emitted word?
5. Raise G20 ordinary BIT saving to0.003507719059749 with scalar conjugations CrocSwap/integer-mult-bounds#5708: Can noncoordinate public input contracts give another split?
6. Raise G20 ordinary BIT saving to0.003507719059749 with scalar conjugations CrocSwap/integer-mult-bounds#5708: Can a stronger Gaussian caller consume this BIT component?
7. Improve P104 helper split with distinct input and output bases CrocSwap/integer-mult-bounds#5718: Can a separate reviewer verify the different input/output bases and early cleanup order?
8. Improve P104 helper split with distinct input and output bases CrocSwap/integer-mult-bounds#5718: Do other pairs of legal boundary functionals support profitable helper splits?
9. Improve P104 helper split with distinct input and output bases CrocSwap/integer-mult-bounds#5718: Can the retained framework assumptions be resolved?
10. Complete dyadic helper bases without an individual unit pivot CrocSwap/integer-mult-bounds#5611: Does a newly admitted dyadic pair give an additional physical helper target?

Item 10 is this package. CrocSwap#5615's capacity question is the next item and is not answered here. CrocSwap#5718 stays on the list because its boundary-functional questions are a different object from this dyadic row.

Live inputs, pinned in research/dyadic-rejected-dual-target/SOURCES.json:

• research/p104-coupled-helper-bases/inputs/pr5580-WORD.json.gz, sha256 b2a98c4bd0dbe86c09e9d15ee060dcf1aab09dbef90aa1e2127676f4039f406b
• research/p104-coupled-helper-bases/construct.py
• research/p104-coupled-helper-bases/local.py
• research/dyadic-helper-basis-completion/basis.py

CrocSwap#5611 (research/dyadic-helper-basis-completion, discussion #5125 comment 19184390) supplies the compiler and leaves the physical-target question open, with no new channel claimed for the constructor itself. An offline local overlap search matches many other p104-side-correction packages by card id. Remote PR and discussion coverage was not refreshed. No exhaustive novelty claim is made.

Validation

Environment: Python 3.12.3, standard library only. From the repository root:

python3 -B scripts/research_package.py --package research/dyadic-rejected-dual-target --check-only
python3 -B scripts/research_package.py --package research/dyadic-rejected-dual-target

Both registered commands passed, including the optimized (-O) command. The verifier prints PASS_DYADIC_REJECTED_DUAL_TARGET. The launcher prints PASS_REGISTERED_RESEARCH_PACKAGE with outcome partial.

The verifier recomputes the prefix and suffix images from the word. Prefix supports 595 and 597 cancel, so the source functional equals the cut row. Suffix supports 193, 199 and 204 cancel, leaving helper register 188 in the output direction. Both pairings equal 1. The helper group with frames (3, 127) has 424 members, and no owned field is live at the cut. Direct matrix checks give a R = e_596^T and R e_596 = b for both pairs. Compiled coefficients lie in {±1, ±5, ±10, ±1/16, 16} and satisfy the 2^16 growth bound; every SCALE is a dyadic unit. The 140 inserted events account for the +1136 allowance.

Failure controls: the old constructor rejects both exhibited pairs; a nearby row with a unit coordinate is still accepted; a non-dyadic pair and a pair whose product is not 1 are rejected by the compiler; scaling the cut row by 3, pivot 0, group (3, 126), and a forged output witness are rejected by the handoff; coefficient 2^16 fails the growth bound; SCALE by 3 fails the unit-SCALE check. The input word is left unchanged.

Not run: native(), the physical caller, the PR5545 capsule, outer predicates, other pivots, other cuts, and any coefficient-minimal schedule. The nine published unit-pivot handoffs remain the CrocSwap#5611 receipt. A locating search outside this verifier is not part of the receipt.

Credit

Ali Romman's PR CrocSwap#5611 and PR CrocSwap#5602 supply the Euclidean compiler and the coupled handoff. PR CrocSwap#5599 is the reviewed helper-subspace construction named by the priority prose. Nick Petalas's PR CrocSwap#5115 uses Euclidean row preparation for a different single-hub contract. The PR5580 word and local.py retain David Arias, Cinna Davis, Gareth Davidson and Ali Romman's source credit. Prepared by unpaidmoon with substantial Cursor Grok assistance. Apache-2.0. No independent human or formal-kernel acceptance is claimed.

Open next questions

The structured questions are in research/dyadic-rejected-dual-target/TASK.json and the package README.

1. Does this rank-9 to rank-5-plus-rank-4 split improve the complete signed moment once the scalar allowance, native maps and physical caller are charged? First step: replay the coupled caller and native maps on this one-step word and charge the +1136 allowance. Blocked by the PR5545 capsule and outer predicates, which were not run.
2. Is there a shorter ADD and dyadic-unit SCALE schedule than 36 operations at frame 3 and 34 at frame 1053? First step: search for a shorter factorization of the same two matrices inside the growth bound. Blocked here by the lack of a coefficient-minimal compiler.
3. Does another pivot in {592, 593, 594, 596}, or another legal rejected pair on this word, produce a lower local scalar allowance? First step: recompile those pivots and compare local replay. A frame-597 locating hit is not a packaged witness.

Workflow feedback (optional)

On this base commit, certificates/selected-result.json records κ = 781451/250000000 while docs/research/current-priorities.md still describes the CrocSwap#5599 checkpoint κ = 0.00310045. This package leaves both files untouched. Feedback discussion: CrocSwap#1200