Research: transport terminal centre-error kernels through causal feedback

[tekuuu]

PR2799 gives a 149-dimensional terminal-Y error kernel in the selected scalar projection. Its 21 noncoordinate directions change later centre inputs, so their cancellation cannot simply be carried over to changed centre operators. This package computes the exact causal correction and implements one fully charged repair. Research interface / independent verification; no new κ or native supplier.

For the complete selected 144-call schedule, let K map insertion errors to later centre inputs and Δ=diag(H_j-I). Strict causality proves

R_H = R (I-ΔK)^(-1)
ker(P_Y R_H) = (I-ΔK) ker(P_Y R).

The kernel retains dimension 149 per payload coordinate even for noncommuting linear centre operators. Exactly 128 directions remain operator-independent. The other 21 need corrections at 546 sites / 1,913 rational coefficients. Both orientation-specific correction matrices have rank 21. An exact reciprocal derivative has rank 21 on those directions: it detects a rotating kernel, not a loss of kernel dimension.

The generated repair assumes read-only access to 21 parameters and initially zero work. Its entire word, including source access and cleanup, uses 43 work fields, 42 H calls, 42 H-inverse calls, 4,969 signed additions and 2,838 rational scales. A free-Laurent replay checks arbitrary invertible H and arbitrary dirty injection targets. A restricted one-pass linear batch needs at least 42 oracle queries before cleanup; no adaptive/native recursive-call lower bound is claimed. This construction does not fund a free 21-call saving.

Only research/centre-kernel-feedback/ is added: 12 files, about 2,200 text lines and 115 KB including compressed, byte-exact predecessor receipts. Frozen inputs and the selected frontier are unchanged.

Validation

python3.12 -B scripts/research_package.py --package research/centre-kernel-feedback

Expected: PASS_REGISTERED_RESEARCH_PACKAGE research/centre-kernel-feedback outcome=completed.

Passed locally on Linux / CPython 3.12.14:

• Exact independent forward reconstruction of every original local/global response coefficient, all 149 kernel directions, strict causality and matching rational/prime-field rank evidence.
• A separate literal interpreter executes all 2,835,792 scalar instructions, checks all chronological correction coefficients, 1,152 noncommuting operator repairs, private cleanup and every coefficient of the rational derivative witness. Wrong signs fail at 435 sites.
• The complete symbolic repair word and its invoice; omitted-cleanup and wrong-oracle controls.
• Three behavioral test groups, including assignment/determinant oracles, optimized Git-free replay, source/reference/correction corruption, bool/int substitution and output refusal.
• Post-rebase metadata/source checks and git diff --check.

The general operator statement follows from the written causal proof; finite probes are not a formal proof of the multiplication theorem. Physical frames/cover routing, a real caller providing the parameters and clean fields, movement/hosting/precision, complementary X restoration, supplier admission and all-size obligations remain open. Full cold replay, hosted CI, human review and a proof assistant were not run locally.

Scientific base 28f54620ff770dd051d5df35882bd84303d13c6f; rebased onto canonical main d9b24831174325cad2e04e34da2068d7acb02938. Guidance, selected inputs and runner are unchanged. Final open-PR metadata covers 722 PRs through #2813, with live targeted Discussion2791 and unchanged PR2799 head. The package records the earlier broad-refresh timeout. A subsequent pre-submission refresh completed across 1,458 Discussion records with no warnings; no targeted term match was returned. These metadata searches do not cover arbitrary code diffs or establish novelty.

Credit Arham Tahir / #2799 (3401bcfce70ad5b692cd4d89e92955229f56c819) for the terminal kernels and ywz65 / #2622 (4ffb893a08e8868057a30a065642d0b5f647f742) for the complete response and handoff; retain #2763's separate source-history audit, Sagar Thakrar/#2199, Adam Gall/#1918, commdata2338/#2048, Aaron Wang/#2391 and the selected construction/compiler lineage. No predecessor implementation is imported. New work by Tekalign with substantial OpenAI Codex assistance; no subagents or independent human review this round. Apache-2.0.

Canonical claim/result. TASK.json records seed 75, the three candidates, the first-order test, the evidence-driven kernel-transport refinement and the stopping decision. The next useful step is an actual consumer for the 128 terminal directions or already-available HZ values that evade this direct repair's extra queries.