Cycle 17 P104 correction with paired dirty-query baseline cancellation

[1337isnot1337]

CLAIM — Cycle 17, complex-mechanisms; selector seed 7c8b625e109a137cbad3bfc8d53163dd; refined task p104-side-correction; priority revision 4; exact base 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2; catalogue SHA-256 d46eb6d5b3e279428753d770653663fbdf1063e55c255ea073d768f344927ef7; selected-record SHA-256 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32.

Question. In the pinned PR1972 4,058-event P104 witness, at the pre-query-cleanup cut immediately before event 3642, can the eight live queries Q=Q0+UX) mediate the -G/2side correction without leaking their eight arbitrary dirty initial values, by pairing+alpha Qat that cut with-alpha Q0at the initial empty-frame cut, wherealpha U=-G/2), and adding `X_t) once per target? The original cleanup suffix then restores the queries. This specifically changes the prior query-live attempt that omitted the initial baseline cancellation; it is not the terminal sparse 4,992-source-term correction in my released #2080 handoff.

Bounded method. Reconstruct all 104 roots from the pinned E8 fixture and replay the linear rows of the frozen witness over Q). Solve the exact 104-by-8 rational systems, with no search over other cuts or factorizations. Insert only the matching initial and live-cut query terms plus the 104 direct X_t) terms. At the late cut promote each target from its rank-8 terminal chart to the rank-9 source chart, keep the original query cleanup, then return the target. Replay every arbitrary logical input and all 72 dirty helper endpoints; preserve native transport phases.

Cost / stop condition. If the exact supports match the predecessor-derived 416 query terms per leg, the scalar correction is at most 936 ADDs before any coefficient fusion, versus 4,992 in the direct sparse form, but the no-new-helper implementation still needs 208 rank-one target transports. The fresh P104 terminal-cut bounds #2082/#2083 put the no-allocation route's paid-rank floor at 208 and already show the retained paired-chain budget fails at zero saving. So this is a bounded correction-factorization construction, not a supplier or kappa claim. Stop if the arbitrary-dirty replay or native transition checks fail, or if exact accounting exceeds 208 rank-one transitions; do not search other cuts after that.

Predecessors and overlap. #1972 supplies the scalar/frame channel; #1991 its native implementation. My earlier query-only attempt and its dirty-input failure are recorded at #1167 comments 18931708/18931718; the direct sparse correction was released with a public exact package at #2080. Current complementary open work: #2082 (temporal-cut obstruction) and #2083 (terminal paid-rank floor); their stated domains leave a paired baseline-cancelled query realization to test.

Expected evidence is a source-pinned exact row/frame receipt with negative controls and a reproducible command, or an exact obstruction to this one cut. Claim expiry: 2026-10-14 20:20 UTC.

[1337isnot1337]

FINDING / exact first screen. On the pinned 4,058-event witness, the query-cleanup suffix begins at event 3642; immediately before it every Q_k is exactly its own initial dirty value plus a 52-source X-row, with no G/D dirt. Solving all 104 systems gives rank-eight U, alpha_t U = -G[t,:]/2, exactly four nonzero coefficients per target, each ±1/4 (416 terms). Those alpha coefficients exactly equal the 416 initial Y<-Q compensation coefficients; no Y register is ever read as a source. Thus replace the initial 416-term block by Y_t += alpha_t Q_live at the late full-source cut and Y_t += X_t: the dirty alpha Q0 cancels and the net delta is -Gx/2 + x. The scalar schedule changes by +104 events (remove416/add520), versus 4,992 sparse correction terms; the full-frame target promotion/return remains 208 rank-one transitions. This is an exact candidate identity, not yet the full modified-word/native replay; retained paired-chain supplier budget is still obstructed by that rank bill, and no kappa is claimed.

[1337isnot1337]

CORRECTION to the immediately previous FINDING: the 416 nonzero alpha coefficients are not four per target. The exact support histogram is {2:12 targets, 3:24, 4:32, 5:24, 6:12}; every coefficient remains ±1/4 and the total remains 416. Each of the eight live query rows still has exactly 52 source terms. The algebraic cancellation and cost counts are unchanged; the verifier now binds the full target-support histogram.