[unpaidmoon]

Change and mathematical scope

Scoped proof of one implication of assumption native_all_columns for the selected #6030 word. No new κ. The selected conditional result stays κ = 781451/250000000.

A MOVE from frame a to frame b is the width-1 operator U = chart(a)† chart(b). Its global phase is i^p with p ∈ {0,1,2,3}. At every column multiplicity f ≥ 1,

U^{(⊗)f} = i^{p f} U_0^{(⊗)f}.

i^{p f} = i^p for every f ≥ 1 if and only if p = 0. On this word, 1,809 of 2,886 distinct MOVE operators (2,117 of 3,453 events) have p ≠ 0. Width 2 separates them: i^2 = -1, i^4 = 1, and i^6 = -1.

Per-column execution of the width-1 circuit is the tensor power, so it matches the identity. The obstructed reading is a joint recipe that copies the width-1 phase integer unchanged.

Status: proof of one caller-bound implication, plus an exhaustive phase census. This is not a paid-profile change, a κ improvement, or a discharge of native_all_columns.

Remaining obligations: width-1 equality of U with the frame formula (already recorded by the primary, not re-proved here); spectators, whole-job adapters and the fixed-tape tariff; owned_erasure, compiler, precision_tape and analytic_recovery.

Task and overlap

• Base: canonical main 2485805a6d47f36ea83ddde6327d453ac82d44dc, priority revision 8. Selected record κ = 781451/250000000.
• Task: uniform-transfer-audit, scope refined.
• Ordered choice: revision-8 next-decision row 5, all-size audit, after checking Handoffs and requests for independent checks #1166. Rows 1–4 and 6 were left for the sibling sessions. Recent Handoffs and requests for independent checks #1166 posts in the fetched window are claims and released results, not an open request for this implication. The 19 October handoff index is already delivered or closed, including unpaidmoon Add a typed one-round actual-width H and rounded return. #4123/Price one typed actual-width physical H and its toward-zero return #4127 on the typed actual-width handoff.
• Object: assumption ID native_all_columns, MOVE chart changes of research/p104-helper470-twin-rung-removal/WORD.json.gz.
• Prove the selected #5599 scalar instructions lift at every column mul… #5837 lifts SCALE/ADD/COPY on the older Raise conditional kappa to 0.00310045 with independent helper splits #5599 word and leaves MOVE open. Add all-width native certificate for the selected #5599 word (native_all_columns; no new kappa) #5974 certifies factorwise tensor lift, including the monomial factor i^{p f}, for that Raise conditional kappa to 0.00310045 with independent helper splits #5599 word (3,447 MOVEs, 2,887 pairs). This word shares 2,808 pairs, drops 79, and adds 78 (103 events; phases 23/17/20/18). All-width certificate for the complete #5413 caller: group-algebra lifting lemma, 896 port identities, free body, abelian controller (no new kappa) #5442 is the group-algebra lift for the older Complete coupled-output caller: conditional κ = 0.003027288235 (+5e-12 over #5400) #5413 caller. Close paid CRT source updates for uninterrupted row execution #5625 and Lower minimum root prefixes to physical Count tapes and complete root callers #5707 are partial interfaces of other callers. GitHub search on 2026-10-30 found no open PR for native_all_columns on Conditional κ .003125804 (+5.22e-7 over #5907): remove helper 470's frame-593 rung, the twin of #5907's removal #6030.
• The fork draft is based on cursor/upstream-2485805-pin-c6a3, the pin of canonical main, so the diff is this package. Upstream review should use CrocSwap main at the same commit.

Validation

Python 3.12, standard library. From the repository root:

python3 -B research/move-chart-phase-power/verify.py
python3 -O -B research/move-chart-phase-power/verify.py
python3 -B scripts/research_package.py --package research/move-chart-phase-power

Observed marker, in the registered replay and under -O:

PASS_MOVE_CHART_PHASE_POWER pairs=2886 events=3453 phase0_pairs=1077 phase0_events=1336 nontrivial_pairs=1809 nontrivial_events=2117 only_new_pairs=78 only_new_events=103
PASS_REGISTERED_RESEARCH_PACKAGE research/move-chart-phase-power outcome=partial

python3 -B scripts/research_selected_baseline.py returned PASS_RESEARCH_BASELINE_BINDINGS_ONLY.

Controls reject a MOVE whose source frame is not current, a non-nested destination, and an off-by-one global phase. The width-2 congruence 2p ≡ p (mod 4) holds exactly for p = 0. Lemmas B and C in PROOF.md are the all-f argument. The four state comparisons are controls.

Not run: the #6030 primary native replay, make frontier6030-verify, Lean, and Docker. The Clifford census takes about two minutes.

Credit

DreamingOfClouds supplied the selected #6030 word. Ali Romman supplied the #5599 word used as the predecessor pair set. The chart compiler is the retained native channel. #5837 is unpaidmoon's scalar lift. #5974 and #5442 are Mark / Matarener's all-width certificates for earlier callers. The selected review is Douglas Colkitt's docs/research/pr-intake-evidence/pr6030-audit/PROOF-REVIEW.md.

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

Open next questions

Does any joint recipe in the #6030 primary copy a nontrivial width-1 phase integer p instead of p f? Compare one lowered recipe with p ≠ 0 against the f-column operator. The primary payload is not a live input here.

Separately, does the predecessor #5907 word, which has 3,454 MOVEs, carry the same phase histogram? Run the same census on research/p104-helper470-twin-rung-removal/inputs/pr5907-WORD.json.gz.