Certify that uniform P104 completion misses a port-dependent chart.

[unpaidmoon]

Change and mathematical scope

Partial certificate. No new κ. Selected κ stays 0.001672660197076918.

On address space (F_2)^4, with C_u = ((1+i)I + (1-i)X_u)/2:

• C_0 = I. For u ≠ 0, C_u acts by i on an odd half of size 8, and X_u - X_v differs on exactly 8 characters when u ≠ v.
• The same chart on both banks fixes every character-diagonal encoding. Exit C_u matches entrance C_u.
• Exit C_u for u ≠ 0 does not match entrance C_0. F T^{-1} acts by -i on the odd half, not by 1. All 15 nonzero labels fail. One data role already fails the every-role condition. Helper roles are not in the model.
• In ordered coordinates, PL - LP = [[-H, 0], [K(D-I), H]] when H commutes with T and K = T^{-1}. With H = I, the first-bank image of (A, 0) is -A. The literal factor -T^{-1} acts by i on the odd character, not by -1. The bookkeeping permutation Pi is not applied.
• The published scaffold arithmetic is reproduced and not re-proved: lower mass 3009344, capacity 2965248, excess 44096. At a = 0 the ratio is already greater than 1.

This does not construct an adjacent completed-call pair, a chronological correction, or a supplier.

Task and overlap

• Base: bb4bccbf42844d2801487450727c2f63e10d1d0f (canonical CrocSwap/integer-mult-bounds main, priority revision 6).
• Head: 281ce601a8be9db470de630759179c23e1dfaa88.
• Task: p104-side-correction, scope changed. The card asks for a chronological correction program. Eligible handoffs on Handoffs and requests for independent checks #1166, after dropping delivered work and open PRs through Add a typed one-round actual-width H and rounded return. #4123, numbered 12. Item index (18-1) mod 12 = 5 (0-based) is comment 19034066, the adjacent completed-call pair. This package does not build that pair. It certifies the uniform-commutation gap the request says is not a matched caller.
• Handoff: Handoffs and requests for independent checks #1166 (comment)
• Predecessor formulas and scaffold integers: PR research: derive P104 two-axis endpoint intertwiners and cost gate #3954, not imported.
• Not redone: the pair search, helper roles, PR research: derive P104 two-axis endpoint intertwiners and cost gate #3954 hypotheses (a)–(e), or a κ calculation.

Ordered eligible handoffs used for this index, chronological on #1166 from comment 19016211 through 2026-10-20T02:32Z. A comment is kept when it states a smallest/next useful task that is not performed by an open PR numbered at most 4123 and is not in this round's delivered set. One comment, one item. Later text on the same thread replaces the earlier task.

1. Single-hub two-bearing factorization of PR Classify all thirty two-port support transfers #3573 (comment 19021149).
2. QQ16 adjacent event pair after the delivered F0 bind (comment 19030049; the bind itself is Ledger intermediate F0 magnitudes on the L359 dirty ray. #4114).
3. Integer-shear payload subspace and dirty return (comment 19032401, replacing 19031016).
4. Independent review of the research: certify local-first two-ADD obstruction on staged544 #3942 interaction reduction (comment 19032637, task 1).
5. Match the research: consume P104 residuals in actual cleanup and price source return #3943 legacy-return adapter with research: price P104 encoded-source return at a retained inverse-shear caller #3940 (comment 19032700, task 1).
6. Adjacent completed-call pair (comment 19034066). This session refines a different piece of that request.
7. Chronological row/column tag reconciliation (comment 19034676).
8. Source-normalization fusion caller (comment 19035513).
9. Literal-index-to-tensor bridge (comment 19035716).
10. One physical K/adjoint/frame boundary (comment 19036235).
11. Hypothesis separating the three legal R439 words from the synthetic edge (comment 19056041).
12. Smaller V45 joint witness among the 29 role edits (comment 19056155).

Dropped before that list: the #3605 full wrapper (open #3681), typed actual-width H (#4123), the L22 split census after its cheap pair step (#4117), the residual consumer (open #3943), the T385 wrapper (open #3936), neutral-first retiming (open #3941), tensor-pairing review (#4113), moved-ADD (#4122), and separated A2 acceptance (#4112).

Validation

CPython 3.12.3. Registered replay:

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

Passed locally as PASS_REGISTERED_RESEARCH_PACKAGE research/p104-uniform-commutation-gap outcome=partial. Both the normal command and -O print PASS_P104_UNIFORM_COMMUTATION_GAP. Failures are raised exceptions, so -O does not skip them.

Not run: check_research_commit.py --check-source-history (this clone has no full Git history), Lean, Docker, a selected cold replay, and any search for a matching pair.

Credit

Chris R / Clear1nsight, PR #3954, for the ordered encoding, the commutator, and the scaffold integers. Discussion #1166 comment 19034066 for the adjacent-pair request and the warning that uniform commutation is not that pair. Rohan Arun, Chafik Boukhalfa, and Adam Gall retain the lineage named there.

Prepared by unpaidmoon with substantial Cursor Grok assistance. No independent human or formal-kernel review is claimed. Apache-2.0.

Open next questions

1. Is there one adjacent pair, port-dependent charts allowed, whose exit matches the next entrance on every data role and every helper role? First step: write the charts on one data line and its helper block. Blocker: this model has no helper roles and does not search pairs.
2. Do hypotheses (a)–(e) of the published 44,096-excess scaffold hold for one actual producer? First step: bind one local call to mass 2,576 and progress 2,312. Blocker: those hypotheses were not replayed.

Workflow feedback (optional)

Handoff-first selection left 12 explicit next tasks after the delivered round and open PRs through #4123, so item 18 is a refinement of item 6 rather than a new card. #1200