[petalas]

Summary

The complete fixed two-qubit Clifford centre replay can now run with CPython 3.12's standard library, including -I -S and optimized execution. Claim type: scoped implementation-equivalence argument with exact finite conformance. This contribution was produced by Nick Petalas.

research/two-qubit-stdlib-replay/
  verify.py       integer matrices and exact trace multiplicities
  PROOF.md        equivalence argument and finite implementation bounds
  VERIFY.json     two complete dependency-free replay commands

The new implementation preserves the original ordered group and class fingerprints, every reduced matrix at widths 1..12, spectral/projector and determinant checks, 64 literal tensor Gram entries and seven rejection controls. Its complete scientific output must equal the immutable source RESULT.json. All 2,718,720 trace pairs are enumerated before exact aggregation into 26,653 representative/class/trace buckets. Receipts are generated and bound to all six package files and four immutable inputs.

Credit MatShep / PR5675 for the mathematical results, group enumeration, centre algorithm, certificate and finite predicates; MatShep / PR5549/5594; Ali Romman / PR5526; DLamdata / PR5547; josecarlosgonzalezroque-design / PR5570 and their retained lineage. The threshold, spectrum and proof are cited predecessor results. The deliverable is the new dependency-free implementation, without a predecessor scientific audit or new kappa claim. Existing source files and credit remain unchanged.

Advance CLAIM. Canonical main was refreshed unchanged at 7c49fe32c55de02c2c873655c804b16e4c3fef0a, priority revision 8, selected PR6030. Live claims, open/account submissions, local reservations and exact-main/merged object searches were checked. The complete cached corpus covers 555 open PRs, 6596 discussion records and 8917 local notes; arbitrary diffs and unpublished work remain limits.

Evidence

Before, the source command under -S exits with ModuleNotFoundError: No module named 'numpy'. After, warning-strict normal and optimized -I -S runs pass with identical complete receipts. Local direct checks took 13.48 and 13.57 seconds on CPython 3.12.15, macOS arm64. These are validation durations, with no runtime speedup claim.

The new arithmetic controls check 256 matrix-unit products, 32 phase/adjoint cases, twelve repeated-trace cases and three rejecting representation/orbit inputs. Registered metadata and both complete commands pass. Exact publication bytes, all ten package/input files, declared source ancestry, official export integrity, read-only Git-free optimized replay and four actual source-file corruption rejections pass.

Reproduce from the repository root:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -S -W error -B research/two-qubit-stdlib-replay/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -S -W error -O -B research/two-qubit-stdlib-replay/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/two-qubit-stdlib-replay
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/two-qubit-stdlib-replay --check-source-history

Another CPython 3.12 path can replace the local interpreter. Expected markers are PASS_TWO_QUBIT_STDLIB_REPLAY, PASS_REGISTERED_RESEARCH_PACKAGE and PASS_RESEARCH_COMMIT_BYTES. Neither direct command imports or executes the predecessor verifier. Its file is authenticated as a declared source input.

Limitations

This is one fixed finite replay, with the repository-relative input layout retained. It supplies no larger-group theorem, new tensor cutoff or scientific admission. No selected cold replay, Lean or Docker run was performed. Physical/native/compiler realization, dirty restoration, precision/tape/storage and the complete supplier invoice remain outside scope. The selected frontier and all five framework assumptions retain their status. Independent human and formal proof-kernel review are unclaimed.

Open next questions

Can one integer matrix kernel reduce complete-command cost while retaining every predicate and source/result comparison? Begin with a complete profile and one bounded kernel change. No performance improvement or benchmark comparison is established here. Development stopped at dependency removal.

Related open work

No other currently open PR was identified for this exact two-qubit centre replay or its dependency removal. PR5675 is the merged, credited source. The completion refresh inspected the fifteen other open account PRs created since the CLAIM; they concern different objects or quantities. Other Clifford work on physical corrections and prefix keys concerns different contracts. No additional mathematical comparisons were run.

CI notes

Hosted CI passed at exact head 725e49ab5105d6add1f0dd254b6b94863940d977 in run 41634163544. The plan job and registered package replay both succeeded, confirmed with one gh pr checks read. Completed run metadata confirms success and the matching head. The registered replay executes both standard-library-only normal and optimized correctness commands.

Both registered commands, direct normal/optimized replay, metadata, committed-byte/source-history preflight, official export integrity, read-only Git-free replay and four source-corruption rejections also passed locally. No failed job or CI-only obligation remains. Hosted replay establishes execution evidence for this finite implementation, without independent human or formal proof-kernel acceptance of the predecessor theorem.

Merge Danger

Door: two-way.

Blast Radius: isolated.

Only one new research package is added. Shared code, frozen sources, other contributors' credit and selected-frontier records are unchanged.