research: speed up the complete selected P104 replay by 2.73x

research/selected-quadratic-replay/BENCHMARK.json

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+  "scope": "Complete selected scientific replay; fresh processes, warm OS caches, variable host load. Extra adapter corpus and literal cross-check are separate."
+}

research/selected-quadratic-replay/CROSS.json

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+{
+  "actual_state_calls": {
+    "amplitude_entries": 19988992,
+    "dense": 32777,
+    "evaluations": 39041,
+    "sparse": 6264
+  },
+  "amplitudes_per_literal_interpreter": 9037312,
+  "distinct_inputs": 17651,
+  "input_trace_sha256": "73ac04db73d83151efb474925d48298664cc7490d31bdec7a70dcf79b448f481",
+  "literal_interpreters": 2
+}

research/selected-quadratic-replay/NOTICE

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+New selected-caller integration, format adapter, bounded input cache and checks:
+Ali Romman with substantial OpenAI Codex assistance. Apache-2.0.
+The same assistant wrote the code and performed the author-side checks.
+
+The exact quadratic engine and its proof are retained from Ali Romman PR 5704,
+head daa4d9dbd102d2a3677afc5614c56466bd2cf3a2. Its NOTICE.md remains byte-exact
+and credits classical stabilizer simulation, Charles Bethin PR 662 and all
+native/compiler predecessors. This package does not claim that engine as new.
+
+The complete selected source is Ali Romman PR 5599, audited source head
+09dd0965711ca7eeb169057a420abab1c9052137. Its exact word, receipt, proof and
+NOTICE remain inputs. That notice retains Pierre-Loic Doulcet/hexapode,
+Joel Pulikkan/GamingPuzzled, DreamingOfClouds, thu-nmrc, Gareth Davidson/bitplane,
+David Arias, Cinna Davis, Jacob Alan Sussman, zxv, Cao Yifan and earlier geometry,
+BIT and analytic credit. The derived files retain their original module text.
+
+Classical deterministic memoization and exact affine-support enumeration are
+not new general algorithms. The new result is their checked integration into
+this complete source replay, with every scalar/native/invoice/compiler check,
+independent literal-state evidence and whole-replay measurements. No original
+source, selected record, native bill or kappa is changed. Archive inclusion,
+local replay and hosted CI are separate from independent mathematical review.
+
+Native-channel attribution from its pinned README: Rohan Arun PR 1972 supplied
+the scalar/frame channel; Adam Gall PR 1940 supplied the schedule. Josie Elliston
+PR 1071 supplied the P104 fixture/decoder, with Ali Romman PR 1125 and the retained
+PR 968/717/446/595/620 lineage. icekylinx's frame-sa504 retains the exact compiler;
+Ali Romman PR 1862/1931 retains the independent Gaussian interpreter. Native
+lowering and physical binding were prepared for Chafik Boukhalfa with OpenAI
+Codex assistance. These are predecessor contributions, not work of this adapter.
+Source: https://github.com/CrocSwap/integer-mult-bounds/blob/553d26d796fde9871ff2661a49ac7732e945410f/research/p104-native-channel/README.md

research/selected-quadratic-replay/PORTABILITY.json

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+{
+  "readonly_files_unchanged": 54,
+  "optimized_git_free": true,
+  "empty_path": true,
+  "source_corruption_rejected": true,
+  "python": "Python 3.12.14",
+  "science_commit": "83823449895cb1126c246570b92992d45157fe02",
+  "export_sha256": "7d9369a6870deb505aba75f53fcb5a08db2d2b95dec67d4946f58cc59b7b93f3",
+  "registered_commands": "Both VERIFY.json commands, serially, with -I -O -B and empty PATH",
+  "actual_input_controls": [
+    {
+      "path": "research/exact-clifford-quadratic-replay/quadratic.py",
+      "rejected": true,
+      "restored_sha256": "d406584aed1479b75c387bc964b9e797b2f4f75e5f8c6bbea00df07f7d590a91"
+    },
+    {
+      "path": "research/p104-helper-subspace-splits/WORD.json.gz",
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+      "restored_sha256": "bbb072bced5824a8d9094c49be2fc51fbfdd05fb2b7dab8106e1275053075099"
+    },
+    {
+      "path": "research/p104-native-channel/vendor/clifford_exact.py",
+      "rejected": true,
+      "restored_sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962"
+    }
+  ]
+}

research/selected-quadratic-replay/PROOF.md

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+# Exact selected-state adapter
+
+This package reuses the quadratic-state engine and proof from PR 5704. It does
+not change the native compiler, controller, local word or invoice. Its new
+claims concern the state-format conversion, bounded cache and complete source
+integration.
+
+## State-format conversion
+
+The retained engine returns `(n,o,C,p,a,b,d)`. Its nonzero support is
+`o + span(C)` over F2. The columns C are independent. For a coefficient vector
+z, the amplitude at `o + C*z` is `(a+ib)*i^p(z)/2^d`. Its proof covers each gate
+in the retained P/D/X/C/phase grammar and includes the absolute phase.
+
+The adapter enumerates every z in `{0,1}^len(C)`. Independence makes each address
+unique, so assignment to the output map cannot overwrite another amplitude.
+All other addresses have amplitude zero. The dense result fills those addresses
+with `(0,0)`; the sparse result omits them. Both use the same denominator d.
+The engine divides the scalar pair by every common factor of two. Every nonzero
+amplitude is a rotation of that pair, so it has the same common factor of two.
+Thus this denominator is the same minimal denominator used by both original
+literal interpreters. The returned vectors and maps are exactly equal to the
+original representations, not merely scalar multiples or the same support.
+
+The selected native width is 9. Dense conversion therefore retains all 512
+entries. This adapter does not claim polynomial storage for its dense public
+interface. The reused engine avoids literal state evolution at each gate;
+the final dense result remains available to every original caller check.
+
+## Bounded cache and invalidation
+
+Each key contains width, the complete ordered circuit, and the initial basis
+address. The key builder copies lists and tuples to nested immutable tuples.
+Its only scalar types are exact integers and strings. It rejects booleans,
+floats and other objects before cache lookup, so Python numeric aliases cannot
+turn a malformed input into a hit on a valid integer key.
+
+On a miss, the unchanged engine validates and evaluates that exact key. The
+result contains only immutable tuples and integers. The function is pure with
+respect to these inputs, so a hit has the same value as another evaluation.
+Changing a gate, gate order, matrix entry, width or initial address changes the
+key. Equal list and tuple forms have the same gate semantics. Each output vector
+or map is constructed anew; a caller cannot mutate the cached signature.
+
+The process holds at most 8192 keys. Eviction removes only a reusable answer;
+a later request recomputes it. No entry is saved between processes. The cache
+contains neither a selected result nor a claimed invoice. Source authentication
+runs before the scientific replay. Every caller check still executes and every
+new exact state input is evaluated. This is checked reuse of a pure function,
+not reuse of a scientific acceptance decision.
+
+## Complete source binding
+
+`binding.py` constructs the expected syntax tree from four exact retained files.
+It changes only these sites:
+
+- The compiler's `Op.zero_state` calls the dense adapter.
+- The independent native interpreter's `state` calls the sparse adapter.
+- The local verifier loads those two explicit derived modules.
+- The top-level verifier uses the derived local module, keeps all original input
+  paths, accepts an explicit argument list, and rejects its source-write option.
+- Every remaining assertion becomes `if not condition: raise AssertionError`.
+  Its condition and optional message stay unchanged. This retains the check
+  when Python runs with `-O`.
+
+All other source syntax must match. A missing native-phase check, a missing
+public-row check and an omitted complete pricing call each fail this binding.
+The only 13 assertions in the declared Python input closure are in the retained
+Clifford compiler. All 13 are retained as explicit failures in its derived copy.
+The original files and classes are never patched at runtime. Comments are not
+part of the syntax comparison; source files and attribution stay in the export.
+
+The derived main runs the same selected scientific obligations and compares
+both the complete RESULT and regenerated WORD with the retained artifacts.
+It preserves all 13 helper cuts, arbitrary rational input rows, dense reverse
+columns, native maps and phases, productive target checks, physical contacts,
+query and idle work, two moment engines, compiler and all outer inequalities.
+The original rejected input/output/target/cost mutations still run.
+
+## Independent checks and claim boundary
+
+The small adapter corpus compares 1522 exact states and 22700 amplitude entries
+with the original interpreters. Separate controls check type aliases, key
+invalidation, mutable outputs, bounded capacity, eviction and source-proof
+omissions. `cross.py` reruns the complete selected check and collects every
+actual state input. It then compares each distinct input against both original
+literal interpreters, including every numerator, zero and denominator.
+Repeated equal inputs need one independent comparison; the fresh full replay
+still records every call. The trace hash and counts are checked on replay.
+
+The source's signed Pauli checks stay unchanged. Equality of a valid Clifford
+operator's signed Pauli action and one nonzero state fixes its absolute phase;
+the adapter does not substitute a zero-column test for those Pauli checks.
+The saved selected receipt must stay identical. This retains the existing
+conditional kappa statement and its five assumptions. It proves no new supplier,
+physical runtime improvement, precision theorem or selected-frontier change.
+The engine proof and scientific predecessor results remain credited dependencies.