Certify the literal-slot defect that blocks a uniform P104 adjacent c…

[unpaidmoon]

Change and mathematical scope

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

With (H^2=H), (J_0=I-H), (K=T^{-1}) and arbitrary (D), the ordered commutator of the old correction (P) with (L_T) is
[
PL_T-L_TP=\begin{pmatrix}-HTK&0\K(D-I)&KHT\end{pmatrix}
]
with no assumption that (H) commutes with (T). When (HT=TH), the literal slot swap (\Pi) squares to (I) and
[
PA_T-A_TP=\begin{pmatrix}-HK&0\KJ_0(D-I)-H&KH\end{pmatrix},
\quad A_T=\Pi L_T.
]
On an N-port amplitude the first bank is (-Ka). If two N-port diagonal entries of (T) differ, no scalar (\lambda) cancels that defect for every such amplitude. A single scale (t) gives (\lambda=-1/t) on the image of (H) only. The ordered conjugate (L_T P L_T^{-1}) intertwines (L_T); the literal slots require the extra conjugation by (\Pi).

This is not an adjacent completed-call pair, a helper-role match, a native tariff, or a supplier. Linear rank is not a call lower bound.

Task and overlap

• Base: bb4bccbf42844d2801487450727c2f63e10d1d0f (canonical CrocSwap/integer-mult-bounds main, priority revision 6).
• Task: p104-side-correction, scope changed. The card asks for a chronological correction program and a complete bill. This package does not build one.
• Handoff refined: discussion Handoffs and requests for independent checks #1166 comment 19034066. The requested adjacent pair is left open. The piece taken is the commutator that pair must cancel if it reuses the old correction.
• Ordered eligible handoffs on Handoffs and requests for independent checks #1166, chronological from comment 19016211, after dropping work delivered or matched by an open PR through Add a typed one-round actual-width H and rounded return. #4123. The list has 17 items, so item index (21-1) mod 17 = 3 selects item 4 for a distinct refinement:
  1. Single-hub two-bearing factorization (19021149).
  2. Integer-shear supplier/recurrence inequality (19031016).
  3. Independent review of the research: certify local-first two-ADD obstruction on staged544 #3942 interaction reduction (19032637).
  4. Adjacent completed-call pair (19034066). Refined here, not constructed.
  5. Coupled source-normalization caller (19035513).
  6. Literal-index-to-tensor bridge (19035716).
  7. One physical K/adjoint/frame boundary (19036235).
  8. Encoded many-axis prime producer (19037887).
  9. q2 event 58 stock gap (19039339).
  10. R439 weakened-contract question (19046454).
  11. Exact rational stock-margin binding (19047276).
  12. Legal-versus-synthetic K hypothesis (19056041).
  13. V45 pairs among the 29 role edits (19056155).
  14. Two-point pair ceiling (19056233).
  15. Span-five eight-call case (19056267).
  16. Twelve cyclic lines at span six (19056337).
  17. Moved-ADD question on one pinned scalar segment (19056694).
• Dropped before that cut: the Reduce helpers 644/660 from width 8 to 7; conditional κ > 0.00173 #3605 replay (open Replay the complete PR3605 wrapper with a fresh retained bootstrap #3681), typed actual-width H (Add a typed one-round actual-width H and rounded return. #4123), the L22 census refined by Record the coset-wide one-point pair ceiling #4117 and Record that revisit 1 forbids joint length-4 and length-6 returns. #4120, the residual consumer (open research: consume P104 residuals in actual cleanup and price source return #3943), the T385 replay (open Replay T385 through release and audit R437 complete-stream COPY #3936), the QQ16 six-tape bind refined by Ledger intermediate F0 magnitudes on the L359 dirty ray. #4114, neutral-first retiming (Certify two neutral-first retiming domains on the pinned staged544 providers #3941 and Certify losing-first two-edit obstruction at displacement two on staged544 #3957), the tensor-pairing review (Review the common-map tensor-pairing bound independently. #4113), the A2 acceptance (Audit the separated A2 composition and cleanup split #4112), helpers 600/601 (Research: staged544 helpers 600 and 601 are not signed-proportional #4061), and the replay-runtime levers (perf(research): compile the P112 ten-deletion census with popcnt (2.69x, byte-identical receipts) #4090). Comment 19034676 is the same pair obligation as item 4.
• Nearest predecessor: PR research: derive P104 two-axis endpoint intertwiners and cost gate #3954, head f1e2839819959cd0534d008be91ed5b79ec55a6a, which already states these blocks for the P104 shapes and checks them inside its root census. This package does not import that code. The added result is the dimension-free identity, the scalar obstruction, and the two dropped-hypothesis controls.
• Bottleneck: the complex supplier binds. A uniform scalar repair of the adjacent-call mismatch is not a paid-profile improvement. No new κ.
• Head: 88666f1dee93fbd85b31fd5d6f91a219e111b5f4 on unpaidmoon/integer-mult-bounds, branch cursor/adjacent-call-scalar-defect-8aed.

Validation

CPython 3.12, standard library. Registered replay:

python3.12 -B scripts/research_package.py --package research/p104-literal-slot-defect

Observed:

PASS_P104_LITERAL_SLOT_DEFECT ordered=general literal=projection_and_commutation distinct_scales=no_scalar constant_scale=-1/2 pi_required=1 no_new_kappa
PASS_REGISTERED_RESEARCH_PACKAGE research/p104-literal-slot-defect outcome=negative-result

The direct verifier also passes under -O. Failure controls: a noncommuting (T) keeps the unsimplified ordered identity and rejects the simplified one; a non-projection breaks (\Pi^2=I); unequal N-port scales have no scalar; equal scales give (-1/2); a (J_0) component is not absorbed by that scalar.

Not run: Lean, Docker, a selected cold replay, the 10,816-line census, helper schedules, and hosted CI.

Credit

Chris R / Clear1nsight, PR #3954 and discussion comment 19034066, for the block shapes and the adjacent-pair question. That work retains PR #3882 / #3940 and the native P104 lineage (Rohan Arun, Chafik Boukhalfa, Adam Gall, and the contributors named there). The dimension-free expansion and these checks are by unpaidmoon, with substantial AI assistance (Cursor Grok 4.7). Apache-2.0. No independent human or formal-kernel review is claimed.

Open next questions

See research/p104-literal-slot-defect/README.md.

• Does one adjacent pair that uses (\Pi P_{\mathrm{enc}}\Pi), rather than (P), match every helper role as well as both data banks, and is the bill favorable? First step: pin one helper entrance and exit from PR research: derive P104 two-axis endpoint intertwiners and cost gate #3954 and price (\Pi) as a slot exchange. Blocker: this identity has no helper schedule, and linear rank is not a native tariff.
• Which portwise diagonal corrections other than (K) on the image of (H) cancel the first bank for every N-port amplitude? First step: name the diagonal alphabet and test two distinct N-port scales. Blocker: that alphabet is a different contract from the old correction.

Workflow feedback (optional)

Chronological handoffs on #1166, after the exclusions above, gave 17 items, so the session refined item 4 instead of redrawing a catalogue card. A machine-readable open-handoff list that drops requests already covered by an open PR would make parallel sessions agree without reconstructing that filter.