[unpaidmoon]

Change and mathematical scope

Scoped proof of one implication of assumption native_all_columns for the selected #5599 word. No new κ. The selected conditional result stays κ = 62009/20000000.

Every SCALE, ADD and COPY in research/p104-helper-subspace-splits/WORD.json.gz acts on logical chart coordinates by the same rational matrix at every column multiplicity f ≥ 1, with the scalar coefficient outside the tensor power. The 342 events added to the pinned PR5565 word are 300 ADDs and 42 SCALEs, so the thirteen helper splits are inside that class. The 3,447 MOVEs remain inside the assumption.

If two charts differ by -I, the logical correction is (-1)^f. Width 2 then matches the width-free replay and widths 1 and 3 do not, so a finite width does not replace the common-chart hypothesis.

Status: proof of one caller-bound implication. This is not a paid-profile change, a κ improvement, or a discharge of the whole assumption.

Remaining obligations: MOVE chart operators with absolute phase; spectators, whole-job adapters and the fixed-tape tariff; owned_erasure, compiler, precision_tape and analytic_recovery.

Task and overlap

• Base: canonical main de5ec2e7a6074068452f45b1a191b5c72832df4a, priority revision 8.
• Task: uniform-transfer-audit, scope refined.
• Object: assumption ID native_all_columns, scalar instructions of the selected helper-subspace word, including the split delta against inputs/PR5565-WORD.json.gz.
• Ordered choice: revision-8 next-decision row 5, all-size audit, after checking Handoffs and requests for independent checks #1166.
• Nearest work: All-width certificate for the complete #5413 caller: group-algebra lifting lemma, 896 port identities, free body, abelian controller (no new kappa) #5442 (research/allwidth-caller-certificate) proves the group-algebra half for the older Complete coupled-output caller: conditional κ = 0.003027288235 (+5e-12 over #5400) #5413 caller and does not contain these scalar bases. research/final4610-independent-admission states the scalar-outside-tensor convention for the older Conditional κ = 0.0030217758: joint helper interfaces and Lean compiler tightening #4610 admission. 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. Overlap search at 2026-10-27T04:22:15Z covered 385 open PRs and 5,256 discussion records; the phrase "common scalar chart" hit no open PR.

Validation

Python 3.12, standard library. From the repository root:

python3 -B research/native-scalar-chart-lift/verify.py
python3 -O -B research/native-scalar-chart-lift/verify.py
python3 -B scripts/research_package.py --package research/native-scalar-chart-lift

Observed marker:

PASS_NATIVE_SCALAR_CHART_LIFT adds=21247 scales=757 copies=8 moves=3447 common_chart_violations=0 split_delta_add=300 split_delta_scale=42 split_delta_move=0
PASS_REGISTERED_RESEARCH_PACKAGE research/native-scalar-chart-lift outcome=partial

The all-f statement is the induction in PROOF.md. Widths 1–3 check the tensor implementation. The checker rejects a cross-chart synthetic ADD, a stale frame after MOVE, and a one-step retag of the first selected ADD.

Not run: make frontier5599-verify, native Clifford replay, Lean, Docker.

Credit

Ali Romman supplied the selected word (PR #5599). Pierre-Loic Doulcet / hexapode supplied the PR #5565 word. The caller lineage is credited in research/p104-helper-subspace-splits/README.md. The selected review is Douglas Colkitt's docs/research/pr-intake-evidence/pr5599-completion/PROOF-REVIEW.md. Mark / Matarener supplied #5442. #4610's admission note records the older scalar-outside-tensor convention.

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

Open next questions

Can the 3,447 retained MOVE chart changes of this same word be lifted by g ↦ g^{(⊗)f} with absolute phase, as group identities rather than width-1 recipe checks?

That is the remaining algebraic content of native_all_columns for this caller. Census one distinct frame pair through the pinned clifford_exact canonical frames and apply the #5442 lifting lemma, including the action on |0>. The selected native checker compares width-1 signed Pauli recipes only. A passing census would still leave spectators, adapters and the fixed-tape tariff open.