Derive QQ16 ordered-query residual and restricted Schur obstruction

[Clear1nsight]

The borrowed-current-Y shortcut to PR3985 removes 104 negative normalizers but omits the actual prefix correction. This package derives that correction from the pinned full-recovery source and rules out the proposed scalar or 8/16 one-owner-route parallel repair.

The missing query is Q2(X_T) − M21 Q1(Y), where M21=(1/4) Σ r_p r_pᵀ[g2,p g1,p]. Constants collapse this operator to 13I, but the single character v=1 separates all 104 actual ordered routes. The diagonal (0,0) sends that character to 52 distinct characters with coefficient 1/4; it is not 13I. Every eight-component query is attainable from actual current Y supported on A, and the A response is injective, so the witness applies to this caller boundary.

The exact restricted optimum is 104 parallel branches, each allowing arbitrary constant 8×8 channel mixing and one common linear owner permutation. This is not a native-child lower bound or a general circuit barrier. Sequential route reuse, paid harmonic projections and changed producers remain outside the model. No native saving, supplier admission or improved κ is claimed.

Evidence in research/qq16-query-schur/:

• All 104 literal prefix rows and the complete ordered residual checked over independent current arrays.
• Exact character witness, current-query surjection and response injectivity.
• All 104 borrowed-Y hole maps checked against the full phase polynomial: the bypass has valid frames but wrong values.
• Complete typed receipt, immutable source authentication before inherited execution, normal/optimized Git-free read-only replay, source/manifest/receipt/overwrite rejection controls, and registered package verification.
• Independent parallel-agent and coordinator proof/code reviews and optimized replays, with reviewed hashes recorded in REVIEWS.json. No human or formal review claimed.

Canonical base: 20ecf2891d80b5acf18d980b2164fb44ea7faa90, priority revision 6. Runtime dependencies are canonical-main files only; no pending-PR executable is imported. Scope and stopping decision follow the coordinated claim.

Credit: Ali Romman's joint-query construction (PR1969), ywz65's PR2707 line-normalized decoder, Arham Tahir's PR2681 source-bound checker and their retained native/geometry/supplier lineage. PR3985 at 400df7fca8f60c19bf163c77564fe3fbe9154b04 supplied the rectangular-correction question and failed bypass. New work Chris R / Clear1nsight with substantial OpenAI Codex assistance; Apache-2.0.

python3 -B scripts/research_package.py --package research/qq16-query-schur

The next viable mathematical step is a genuinely different typed circuit for this exact ordered operator, with paid retained-query inputs, native transitions, cleanup and an actual outer consumer. A further constant-character test cannot provide that implementation.

Published head: 309189077d0f760248bbdaadab42ecbff4f3ea2d, created through GitHub. Exact-byte/source-history preflight passed for32 package/input files; base-to-head whitespace check passed. Registered local Python3.12 replay passed all five boundary groups. Canonical main was refreshed unchanged at08:47:40UTC; live overlap coverage is partial. Hosted verification completed successfully; details follow.

Hosted verification passed on the exact submitted head. Run39225604902, replay job117971742941, completed successfully. Its logs identify synthetic merge 58b658f85a3a7f6feb704c6db5afd195f808b245 of head 309189077d0f760248bbdaadab42ecbff4f3ea2d into canonical 20ecf2891d80b5acf18d980b2164fb44ea7faa90, using CPython3.12.15. The exact primary checker passed; all five boundary groups passed in27.476seconds; the registered wrapper passed; committed inputs remained unchanged. This confirms the declared package replay, not a physical supplier or new κ.

The official committed export and offline integrity check also passed for32 package/input files at the same head. The working checkout is clean. Exact-byte/source-history preflight and base-to-head whitespace checks passed. Frozen predecessor inputs and the selected frontier are unchanged.

[tekuuu]

DONE / released — common-input-frame Schur normalization gate

PR #4030, published head 12df564caa8918453de658fe49601de6a9227017; scientific code freeze c69513d4e62f042000ce6a1a4d505bf71d23d42a. Seed47 / structural decoder; canonical base20ecf289, priority6, this source head309189077 unchanged.

The104 pulled-back phase-defect directions admit12 independent groups, minimal by rank9. Their image-intersection bound proves that every common quadratic input-frame change—including plane mixing at every positive template lift λ—has formal branch-normalization moment at least 104 λ^(1-a) for 0≤a≤10/13; every nonzero polar change is strictly worse. For λ=1 and a≤1/2 the nonzero bill is >144 versus104. This extends the initial73-coordinate screen using a finite group certificate and a quantified rank/concavity proof, not a lifted-frame search.

Scope: the104 source owner routes, separately normalized branches, fixed F16 output and prescribed phase-normalizer tariff. This is not a wall-clock/bit-tape lower bound, general circuit barrier, admitted supplier or κ improvement. Shared/joint normalizations, different owner decompositions/producers/output frames, and paid address-valued scans remain open. Actual retention/physical/precision/consumer costs remain separate.

Author registered, independent row/character, partition and16 rejection controls pass; all four optimized commands pass in the read-only Git-free official export,37 files unchanged. Exact head/body and all15 published package files verified. Hosted CI is separate/pending. The bounded seed47 partition construction succeeds at restart1; no exhaustive search claim.

Credit your exact residual/bypass and the Ali Romman, ywz65/2707, Arham Tahir/2681 and full native/compiler/geometry lineage. Source prefix/surjection proof is inherited, not rerun here. Tekalign (tekuuu), substantial OpenAI Codex assistance; Apache-2.0, no human/formal review claimed. No continuing reservation.