[unpaidmoon]

Change and mathematical scope

Scoped partial result. No new κ and no selected-frontier change. The selected record stays κ = 781451/250000000.

The CrocSwap#6030 primary recorder is local.native in the PR5827 archive loaded by research/p104-helper470-twin-rung-removal. It stores lower_child records. Each phase field is a width-1 residue in {0,1,2,3}. The function builds no multiplicity-f recipe. Its returned proof sentence still says "frame induction at every positive tensor width"; that sentence is only a string in the summary.

The first rank-1 MOVE on the selected word is event 9896, MOVE 236 from frame 3 to frame 7. Its stored integer is p = 1. On all 512 basis inputs, deleting the phase gates and rotating by p recovers the operator, and rotating by p+1 does not. On all 512 × 512 input pairs,

(U|x>) ⊗ (U|y>) = i^{2} (U_0|x>) ⊗ (U_0|y>)

and one joint factor of i^1 disagrees. Copying the stored integer is the reading that fails. Executing the width-1 phase gate on every column is the reading that matches.

This does not recompute the registered payload hash, lower the other 2,921 chart records, or discharge native_all_columns.

Task and overlap

Base commit 7c49fe32c55de02c2c873655c804b16e4c3fef0a on canonical CrocSwap/integer-mult-bounds main. This fork draft is based on cursor/upstream-7c49fe32-pin-b561 at that commit, so the diff is one commit. A review against the fork's main includes unrelated history.

Task card uniform-transfer-audit, priority revision 8. Scope status: refined. The card asks for one assumption ID and one quantified implication at the actual caller. The assumption is native_all_columns. This implication is the phase integer stored by the selected primary, the first open question of research/move-chart-phase-power.

Session r102, item 5 of the ordered eligible list. Structured handoffs that are completed, answered on main, or whose artifact is an open pull request are excluded, including the 19 October index, the H25 requests and the 2 November review artifacts through CrocSwap#6396. The revision-8 next-decision table then orders the rows, and unnamed catalogue cards follow:

1. Complex helpers (p104-side-correction, coverage-law-change).
2. BIT (bit-helper-contract).
3. New decoders and interfaces.
4. Supplier audit.
5. All-size audit (this package). The scalar lifts Prove the selected #5599 scalar instructions lift at every column mul… CrocSwap/integer-mult-bounds#5837 and Prove the selected PR6030 scalar instructions lift at every column mu… CrocSwap/integer-mult-bounds#6635, the MOVE phase law Record that selected MOVE absolute phases scale as i^{p f} CrocSwap/integer-mult-bounds#6293, and the precision-envelope note Cursor/pr6030 precision envelope mass 7270 CrocSwap/integer-mult-bounds#6522 are different implications.
6. Verification tooling.
7. bit-new-register-model.
8. r437-carrier-integration.
9. complex-rank-shape-decoder.
10. complex-new-helper-inventory.

Nearest work:

• Merged Record that selected MOVE absolute phases scale as i^{p f} CrocSwap/integer-mult-bounds#6293 proves U^{(⊗)f} = i^{p f} U_0^{(⊗)f} for every MOVE on this word and leaves the primary payload unread.
• Open Prove the selected PR6030 scalar instructions lift at every column mu… CrocSwap/integer-mult-bounds#6635 lifts SCALE/ADD/COPY on this word. Not the MOVE phase integer.
• Open Bind optimal unbiased reversible rounding to the selected first native MOVE CrocSwap/integer-mult-bounds#6532 (Ali Romman) binds this same event 9896 to an unbiased rounding map and its tensor-power mean. It does not read local.native and does not compare a copied width-1 phase integer with p f.
• Add all-width native certificate for the selected #5599 word (native_all_columns; no new kappa) CrocSwap/integer-mult-bounds#5974 certifies factorwise phase i^{p f} for the older Raise conditional kappa to 0.00310045 with independent helper splits CrocSwap/integer-mult-bounds#5599 word.

No open upstream PR states this recorder inspection. Searches of open PR text for the proof sentence and for "copied width-1" had no match. Discussion CrocSwap#1166 was read in full (3,528 comments). The only post of this question is the CrocSwap#6293 finding, which leaves it open. Unexpired claims: none at 2026-11-08T13:14:09Z.

Validation

CPython 3.12, standard library, from the repository root:

python3 -B research/primary-move-phase-integer/verify.py
python3 -O -B research/primary-move-phase-integer/verify.py
python3 -B scripts/research_package.py --package research/primary-move-phase-integer
python3 -B scripts/check_research_commit.py --package research/primary-move-phase-integer --check-source-history
python3 -B scripts/research_selected_baseline.py

Observed PASS_PRIMARY_MOVE_PHASE_INTEGER event=9896 frames=3->7 phase=1 bases=512 pairs=262144 joint_recipe=false, PASS_REGISTERED_RESEARCH_PACKAGE with outcome partial, PASS_RESEARCH_COMMIT_BYTES, and PASS_RESEARCH_BASELINE_BINDINGS_ONLY. Checks raise exceptions, so -O does not disable them.

Failure controls: a planted phase * f line fails the source scan, and a wrong source frame on event 9896 is rejected. Width-1 off-by-one rotation fails. The copied integer fails on every width-2 basis pair.

Not run: the full 2,922-map native replay, payload-hash recomputation, make frontier6030-verify, Lean, and Docker.

Credit

DreamingOfClouds supplied the selected CrocSwap#6030 word and the verifier that loads this local.py. Ali Romman supplied that recorder in the PR5827 archive. The chart compiler is the retained clifford_exact.py / native_verify.py channel. CrocSwap#6293 left this payload question open. CrocSwap#6532 uses the same event for a rounding map.

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

Open next questions

1. Does the predecessor Conditional κ .003125282 (+5.22e-7 over #5827): remove helper 468's frame-593 rung with rerouted reads CrocSwap/integer-mult-bounds#5907 word, which has 3,454 MOVEs, carry the same phase histogram? First step: the same lower_child census on research/p104-helper470-twin-rung-removal/inputs/pr5907-WORD.json.gz. Not an input of this package.
2. Does one rank-0 main adapter stored by the same function fail when its width-1 phase is copied onto a joint state? First step: lower the first adapter and repeat the width-2 comparison. The source inspection already shows those records have no multiplicity field.

Workflow feedback (optional)

The handoff thread's structured HANDOFF blocks are mostly completion reports. The usable order for this session was the revision-8 next-decision table after dropping closed handoffs, with the first unanswered question inside the chosen row.