Prove uniform completion fails on the physical P104 encoding.

[unpaidmoon]

Change and mathematical scope

Scoped commutation obstruction. No new κ and no selected-frontier change. Selected κ stays 0.001672660197076918.

A uniform address operator U_C commutes with the scalar-bank encoding E0(r, w) = (D r + H w, w) for every C. It commutes with the physical encoding L(r, w) = (D r + H T w, w) if and only if C commutes with every active port chart T_p. The literal slot swap Pi commutes with every U_C, so Pi L fails for the same operators as L.

On the four-point translation model, Z_{e1} commutes with E0 and with C_{e2}, and it fails for C_{e1} on both L and Pi L. The address commutator [Z_{e1}, S_{e1}], with S_{e1} = 2 C_{e1}, has (0,1) entry 2-2i. Translation charts still commute with each other, so a uniform completion that stays in that family is not blocked.

This does not construct an adjacent completed-call pair, price a native caller, or change a supplier.

Task and overlap

• Base: bb4bccbf42844d2801487450727c2f63e10d1d0f (canonical CrocSwap/integer-mult-bounds main, rechecked unchanged before submission). Priority revision 6.
• Head: de25c6525aa866962309df5d107b32d55e6e5628.
• Task: p104-side-correction, scope changed. The card asks for a chronological side-correction word. This session does not draw a new card.

Ordered eligible handoffs, chronological on discussion #1166, after dropping tasks already delivered, matched by an open PR, or refined by this round's PRs #4107 and #4110–#4124:

1. Integer-shear payload subspace and encoder (comment 19032401).
2. Independent review of the research: certify local-first two-ADD obstruction on staged544 #3942 interaction/new-gap reduction (comment 19032637).
3. P104 adjacent completed-call pair (comment 19034066). The list has 11 entries, so item 25 is a distinct piece of this handoff.
4. One chronological row/column pair and fiber tags (comment 19034676).
5. Changed chronological caller after the research: derive P104 two-axis endpoint intertwiners and cost gate #3954 follow-ups (comment 19034741).
6. Fuse source-normalization with the full-output interface (comment 19035513).
7. Inspect the P104 tensor-word literal-index bridge (comment 19035716).
8. Pin one physical K/adjoint boundary (comment 19036235).
9. Review the fixed-tape prime producer at the encoded boundary (comment 19037887).
10. q2 event 58, target local 16 (comment 19039339).
11. Profile the P112 ten-deletion census.cpp hot path (comment 19045344).

The piece is the scalar-bank commutation sentence in comment 19034066, not the adjacent pair itself. Handoff: #1166 (comment)

Dropped before that cut: the #3605 wrapper replay (open #3681); typed actual-width H (#4123); the single-hub factorization (#4124); the L22 census refined by #4120; the six-tape bind (open #3932); the T385 replay (open #3936); the #3942 moved-ADD witness (#4122); tensor-pairing review (#4113); helpers 600/601 (open #4061).

Predecessor: PR #3954, head f1e2839819959cd0534d008be91ed5b79ec55a6a. Its checker is not imported. No open PR states this commutator. Sibling fork branch cursor/p104-uniform-commutation-gap-91e1 (discussion comment 19057062) certifies the separate C_u-versus-C_0 chart mismatch on the same handoff.

Validation

CPython 3.12.3, standard library. Registered replay:

python3.12 -B scripts/research_package.py --package research/p104-uniform-encoding-gap

Passed locally as PASS_REGISTERED_RESEARCH_PACKAGE research/p104-uniform-encoding-gap outcome=completed.

• verify.py multiplies the 16×16 Gaussian-integer matrices.
• independent.py does not import that file. It applies the maps to vectors.
• test_verify.py rejects the even-direction chart offered as an obstruction.

check_research_commit.py --check-source-history passed for commit de25c6525aa866962309df5d107b32d55e6e5628. The same checks pass under python3 -O.

Not run: Lean, Docker, a selected cold replay, the 104-port pivot matrix, and hosted CI. The argument is the block identity in PROOF.md. The finite model shows the hypothesis is realized. It is not a caller search.

Credit

Clear1nsight, PR #3954, for the scalar-bank positive control, the chart C_u, the literal swap Pi, and the normalization character, retaining the P104 and native lineage named there. New work by unpaidmoon with substantial Cursor Grok assistance. No independent human review is claimed. Apache-2.0.

Open next questions

1. Which operators does one actual completed P104 call apply uniformly? Translation charts commute, so this gap blocks only an operator outside that family. The retained caller text is not pinned here.
2. The adjacent completed-call pair from comment 19034066 remains open. This note does not build it and does not prove that no such pair exists.

Workflow feedback (optional)

Handoff-first selection against open PR titles separated this commutation check from the adjacent-pair construction. Link: #1200