[aliromman]

The complete actual restricted-C replay is 5.17x faster with exact quadratic states: median 57.62 to 11.15 seconds, over three alternating fresh-process rounds. Against Charles Bethin PR662's existing table accelerator, the median is 17.59 to 11.15 seconds, a 1.58x speedup. Every run returns the identical complete scientific result. No new kappa or physical-cost saving is claimed.

Algorithm and proof, exact engine, complete evidence, all-actual-state evidence, benchmark, verification, source pins, scope and limits. Exact head daa4d9dbd102d2a3677afc5614c56466bd2cf3a2.

The engine replaces the exponential state vector with independent binary support columns, a Z/4 quadratic phase and an exact Gaussian-dyadic scalar. An explicit elimination handles both kinds of dependent translation-root gate, including support reduction and absolute phase. The written induction covers every finite valid circuit in the retained P/D/X/C/phase grammar. Completed states have at most n support variables and polynomial storage. Full-support width-64 examples represent 2^64 nonzero amplitudes with 64 columns and 2048 phase terms; exact inverse and phase controls pass. This is a classical stabilizer method, with new repository-specific implementation and verification, not a new simulation theorem or a fastest-algorithm claim.

The named consumer is PR5698, head 024e43c. Explicit derived integration retains the whole source proof: both chronological words and independent-input checks, all 4268 native maps and 24 helper normalizers, all 408 helper debits, caps, paid profiles, four cut certificates, power/tail bounds and all eleven rejection controls. A complete syntax-tree comparison binds the integration to the frozen source, with only declared source paths and state-equality calls changed. Omitted grade and tail checks reject. Source files and classes are not patched at runtime.

python3.12 -B scripts/research_package.py --package research/exact-clifford-quadratic-replay

Expected: PASS_EXACT_CLIFFORD_QUADRATIC_REPLAY, PASS_ALL_ACTUAL_NATIVE_STATES and PASS_REGISTERED_RESEARCH_PACKAGE. Python 3.12 and the standard library suffice. Registered normal and optimized/warning-strict checks pass. The engine corpus checks 7322 states and 618544 amplitude entries, all basis inputs through width 4, 2728 affine lifts, 18724 twice-products, 6096 substitutions and 160 exact inverses. Thirteen malformed-input, five semantic and two omitted-proof controls pass. Valid constructor-derived full Pauli tableaus remain required: both a same-tableau wrong phase and a same-zero-column wrong operator reject.

A separate complete source cross-check covers 8634 state evaluations and 4420608 exact vector entries, including the phase mutation. It compares every numerator and denominator against the original literal evaluator, then the entire source result. Actual damaged-source and saved-receipt controls reject. The complete scientific JSON hash is a501b899b5f70e7cde6a10af4e4c2530cf9f4cb6ba53504828bf855ed3b74093 for every engine.

All 58 committed package files pass exact byte and official export checks. Sealed read-only Git-free optimized replay of both the new full verifier and the complete actual-state cross-check passes with empty PATH and all 59 exported files unchanged in bytes and modes. Thirty-five retained inputs and their notices remain byte-exact. Full-history ancestry preflight is unavailable in the shallow checkout; exact current source pins are checked. Hosted CI, independent human review and proof-kernel acceptance remain separate. The shared main navigation regression is outside this package.

The nine benchmark processes authenticate identical sources and compare identical complete results. All scientific stdout hashes match. The ranges are 50.95–73.75 seconds for literal vectors, 13.67–21.11 for tables and 10.96–15.88 for quadratic states. Host load varies and operating-system caches are warm. Timings include the complete source replay, not the additional independent corpus or literal cross-check. These measurements do not establish a speedup for a physical multiplier, another interpreter or another host.

Base and final canonical refresh: df0137efd35e11b4445734bf612bdd4c7ebc330c, priority revision 7; selected conditional .00310045 remains unchanged. Canonical claim. The final paginated overlap inventory covered 387 open PRs and 5029 Discussion records, supplemented by current PR delta and source-tree searches. Sparse local omissions and unpublished work remain outside that coverage. The verifier-engineering task is refined to the actual measured consumer.

The Gaussian construction, query bill, targets and local deficit 1680 are unchanged. Its compatible funded caller, uniform native/ROW, precision, storage, routes, compiler and full outer obligations remain open. Credit Charles Bethin PR662, Ali Romman PR5698, Dugongue PR5687, Cao Yifan, Cinna Davis and all retained native/frame/helper/ROW/controller/compiler notices; BigCactusLabs PR702 and Joshua Snider's quadratic-wrapper audit; and the classical Dehaene–De Moor and phase-sensitive stabilizer literature linked in the proof. New implementation, integration and checks: Ali Romman with substantial OpenAI Codex assistance; no subagents. Apache-2.0. No global literature priority is claimed.