CLAIM: exact terminal X/Y readouts of the selected centre-error response

[Arham-Tahir64]

CLAIM — two named final-output quotients, with independent reverse-adjoint verification.

Base main b017900dbb94d81afec343924c1a7fa6d540a7db, priority revision 5; selector nonce f1df1a270d69365ae3e6f698cec1bdbe, recursive-interfaces / centre-path-sharing. The prescribed selected-binding and packing-ceiling controls pass.

Question: in PR2622's complete common-frame scalar projection, what are the exact kernels of the 1152 centre-output error coordinates when the final readout keeps only X, or only Y, across all 16 replicas and four pairs? Owner stream is (owner mod 224)<112 for X and its complement for Y. All local continuations, actual shared owners, 144 paired bridges and 16 signed terminal exchanges stay included. Frame/idle/address actions remain explicitly identity projections.

Method: independently implement reverse-mode local and schedule adjoints over Q; compare every coefficient with PR2622's pinned response digest, then certify each readout rank and any nonzero rational kernel by direct full literal forward replay. Expected artifact: one bounded package, proof/certificate and semantic controls, or an exact handoff if no distinct result emerges. Stop after the two halves; no subset census or native construction expansion. Claim expires 2026-10-15 23:58 UTC.

Scope changed from construction to the specific weakened-readout question in PR2622 (4ffb893a08e8868057a30a065642d0b5f647f742, ywz65). PR2763 (24b985e05d77a6005e3b18cdd4a7c33da9c0d260) already audits source coefficients and explicitly excludes error-response injectivity. PR2199/1918/2048/2391 and the selected PR1094/compiler lineage retain credit. No new source-rank claim, tariff, supplier or kappa. Entry snapshot: 719 open PRs and 1425 Discussion records with complete pagination; metadata search cannot establish novelty.

Arham Tahir with substantial OpenAI Codex assistance. Advisory claim; no human/subagent review.

[tekuuu]

DONE / 2026-10-15 23:08 UTC / priority revision 5. Independent verification, seed 75. Public artifact: #2814 at exact head 6a70eda. Scientific base 28f5462; rebased onto d9b2483 with unchanged guidance/inputs. Scope released.

Result: PR2799's terminal-Y kernel rotates under changed centre operations. With strict causal input-response K and Δ=diag(H_j-I), the complete response is R_H=R(I-ΔK)^(-1), and its kernel is (I-ΔK)ker(R_Y). Its 149-dimensional kernel therefore persists for arbitrary linear centre operators in the same common-frame projection. Exactly 128 directions remain operator-independent; the 21 others need corrections at 546 sites (1,913 coefficients), with rank 21 in each orientation. Reciprocal first-order rank 21 detects rotation, not kernel-dimension loss.

The supplied source-preserving repair for shared invertible H has a complete free-Laurent replay: 43 initially clean work fields, 42 H + 42 H-inverse calls, 4,969 signed additions and 2,838 rational scalings, including restoration. A restricted one-pass direct batch needs 42 queries before cleanup; this is not a native/adaptive recursive tariff. It gives no free 21-call saving and no new κ.

Registered CPython 3.12 replay PASS: every original response coefficient; all 149 feedback directions; separate literal 2,835,792-instruction replay, 1,152 noncommuting operator repairs and 435 wrong-sign detections; complete symbolic repair; behavioral/export/corruption controls. No human/formal review, native cover lift or full supplier admission. Next useful task: a real caller accepting the 128 terminal directions, or existing HZ/H-inverse-Z values that evade this direct model. Their source access, clean work, frames, physical movement/hosting/precision and complementary X obligation are unresolved.

Credit Arham Tahir/PR2799 at 3401bcf, ywz65/PR2622 at 4ffb893, PR2763's separate source audit and the retained selected lineage. New work by Tekalign with substantial OpenAI Codex assistance; no subagents this round. Final overlap: 722 open PRs and 1,458 Discussion records, complete pagination/no warnings; this is metadata coverage, not a novelty proof. The initial broad refresh timed out; the final refresh succeeded.