[unpaidmoon]

Change and mathematical scope

Negative interface certificate. No new κ. Selected κ stays 0.001672660197076918.

On the PR #3954 two-axis scaffold, the literal correction Π P_enc Π, extended by identity on the 72 helper roles, does not give an adjacent completed-call pair:

• Data charts (T, I) and (F, E), with T = C_U, F = C_0 and E = F T^{-1}, agree on both banks only for the degenerate address u = v = 0. Every nonzero address mismatches. The literal correction intertwines one call's encoding A_T. It does not rewrite the exit pair (C_0, C_u^{-1}) into the next entrance (C_v, C_0).
• The same scaffold extends every compatibility map by identity on 14976 helper roles and charges 81 dimensions on each of them (1213056). The identity extension fixes a helper basis vector and adds no helper component to a data vector, so it does not turn the identity helper entrance into the full-F exit.
• Π swaps the 96 N-ports. That count is support size, not a native tariff. Under hypotheses (a)–(e), every nonnegative added rank-mass s leaves the excess equal to 44096 + s against capacity 2965248.

This is not a supplier, a global P104 obstruction, or a selected-frontier change. A different chart contract or a proved helper word needs its own gate.

Task and overlap

• Task p104-side-correction, scope refined.
• Base: canonical main 12fa8c5c844be21bfefb38a19503fbd867a11244, priority revision 7.
• Object: open question 1 of research/p104-literal-slot-defect, pinned to the research: derive P104 two-axis endpoint intertwiners and cost gate #3954 entrance, exit and gate. Discussion Handoffs and requests for independent checks #1166 comment 19034066 is the adjacent-pair request.
• Overlap at 2026-10-21 13:27 UTC: 458 open PRs and 3225 discussion records, complete pagination. No open PR states this helper-gate certificate. The scalar obstruction and the commutation gap do not price helpers. Split the R439 literal K defect into target reads and helper wraps across nine words (no new κ) #4216 is an R439 helper split, not this scaffold.
• Distinct from the unpaidmoon deliveries Certify the literal-slot defect that blocks a uniform P104 adjacent c… #4133, Certify that uniform P104 completion misses a port-dependent chart. #4136, Prove uniform completion fails on the physical P104 encoding. #4140, Certify the screened P104 source-chart shortcut misses the debt-free … #4153 and Record the P104 fiber-tag mismatch on one row/column pair. #4154: those record the slot, commutation, encoding, chart and fiber obstructions. This note starts from the literal intertwiner they leave unpriced and checks the helper entrance against the published gate.

Validation

Python 3.12, standard library, from the repository root:

python3 -B research/p104-literal-helper-gate/verify.py
python3 -B scripts/research_package.py --package research/p104-literal-helper-gate

Expected marker:

PASS_P104_LITERAL_HELPER_GATE charts=F2^4 nonzero_mismatch=true helper_extension=identity helper_progress=1213056 excess0=44096 ports_n=96 nonnegative_price=unfavorable no_new_kappa

Local run passed, including the registered -O command and PASS_REGISTERED_RESEARCH_PACKAGE. The chart check is finite on (F_2)^4; the gate arithmetic is the integer identity in PROOF.md. Not run: Lean, Docker, the #3954 native census, a selected cold replay, and hosted CI.

Credit

The entrance, exit, identity helper extension, N-port slot swap and the 44096 gate are Chris R / Clear1nsight's PR #3954. The adjacent-pair request is discussion #1166 comment 19034066. The question answered here is open question 1 of research/p104-literal-slot-defect. The chart formula is the one checked in research/p104-uniform-commutation-gap. Predecessor lineage named in those packages remains theirs, including Rohan Arun, Chafik Boukhalfa and Adam Gall.

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

Open next questions

1. Can one named helper word advance one of the 72 roles per fiber and be subtracted from the 1213056 helper-progress charge without a new nonnegative cost that restores the excess? First step: freeze one fiber and price that word. Blocker: the identity extension has no such word, and unknown physical costs are not negative rank-mass.
2. Is there an adjacent pair on charts other than (T, I) and (F, E) whose operator and helper schedule match under a freshly derived gate? First step: name the charts and recompute capacity. Blocker: the excess 44096 is not a theorem about a different coverage law.

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