[petalas]

Summary

The selected MOVE24472 left binary map has a 25-CNOT word, improving the 27-gate word in CubeJerry's #7430 at 39b40c465f7636a4bb6d70af28595fe8f70f4f3f. Its adjacent gates 5 and 6 are both x1 ^= x0 and cancel.

- left map: 27 coordinate CNOTs
+ same map: 25 coordinate CNOTs

Claim type: exact finite certificate and scoped written all-column proof. The new word implements rows (3,5,9,17,32,65,129,1,256) for every positive column count f, saving exactly 2f elementary column CNOT calls. Coordinate 8 and untouched spectators are fixed. Classical cancellation is not claimed as a new theorem. This contribution was produced by Nick Petalas; #7430 supplies the matrix/source binding and comparison word, with its credited #3834/#5188/#6992 native/compiler lineage.

Evidence

• Before: Implement both selected Gaussian linear maps as fixed tape programs with every column and complete owner return #7430 records 27 left CNOTs.
• After: PASS_SELECTED_LINEAR_CNOT_CANCELLATION, new count 25; exact nine-row identity; all 512 one-column and 262,144 two-column addresses match an explicit coordinate oracle, including inverse and spectator checks. Three malformed implementations are distinguished.
• CPython 3.12.15, macOS arm64: normal and optimized warning-strict direct checks passed in 0.4534s and 0.4583s. Both registered commands passed; their combined package invocation took 1.118s. Committed-byte/source-history preflight passed for all six files at 060749f4000e71dba9b1cfcc12a6b91c887e2cb3. AST inspection found no recursion and a longest function of 16 physical lines.

From the repository root, reproduce with:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/selected-linear-cnot-cancellation/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -O -W error -B research/selected-linear-cnot-cancellation/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/selected-linear-cnot-cancellation
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/selected-linear-cnot-cancellation --check-source-history

Another CPython 3.12 path can replace the local interpreter. Direct checks emit generated receipts bound to all six package hashes and write nothing. No predecessor executable is imported or replayed. The explicit new word and target require no pending Git commit at replay time.

Limitations

No shortest-word claim, updated literal tape graph, exact instruction saving, physical supplier admission, new kappa or complete multiplication theorem. Literal compiler integration, full tape execution and history receipts are unrun. The all-f statement is proved by independent column action; finite tests corroborate it. All five selected framework assumptions remain. Independent human and formal proof-kernel review are unclaimed.

Open next questions

• Integrate the shorter word into Implement both selected Gaussian linear maps as fixed tape programs with every column and complete owner return #7430's literal compiler and regenerate its complete graph, array and historical-storage evidence before quoting instruction savings.
• Determine whether 25 is optimal for this exact matrix. This package stops at its first strict improvement.

Related open work

• Implement both selected Gaussian linear maps as fixed tape programs with every column and complete owner return #7430 studies these same binary maps and supplies the cited 27-gate baseline and literal compiler; this contribution supplies a shorter left word without rerunning that implementation.
• Lower the current selected quadratic Gaussian phase to a fixed tape table with complete owner return #7426 implements the quadratic phase of the same selected MOVE; its phase recipe is a separate composition obligation and is not changed here.
• Implement the positive rank-one native C tensor leaf with complete literal control and retained workspace accounting #7429 implements the selected positive C tensor leaf; joining it to both monomial boundaries remains outside this gate certificate.

The completion check inspected this account's other open PRs created since the advance CLAIM: #7461, #7463, #7464, #7465 and #7466. They concern quadratic-refinement widths, an A1 projector denominator, compiler plateau widths, mixed line/hyperplane recharts and robust pairing capacity. None studies this exact left binary map or computes a competing gate count. No extra mathematical computations were run to check them.

CI notes

CI did not certify this package. At unchanged head 060749f4000e71dba9b1cfcc12a6b91c887e2cb3, run 43279348945, plan job 131396171336, failed in Onboarding helper tests. I read the actual job log: 760 tests, exactly one failure, 24 skipped. The failing test is test_research_current_status.CurrentCiNavigationTests.test_current_ci_section_matches_selected_record; its AssertionError says `make frontier7000-verify` was not found in the CI verification document.

This mismatch is already present on base main e54523517d0f03e58352e647c403a5af3e525a57: certificates/selected-result.json names make frontier7000-verify, while docs/ci-verification.md still describes #6030 and make frontier6030-verify. I inspected both base files and the relevant test. This PR changes none of them. The package replay job was skipped because plan failed.

I also read the failed-job logs of run 42905094314 and run 42903313790. Both report the same sole failing test, missing-command assertion, 760-test total and 24 skips. These establish the shared repository-level CI blocker; they supply no hosted mathematical coverage for this package. All verification evidence above remains local.

No fix, retrigger commit, push or workflow rerun was made. Repair of main remains with maintainers.

Merge Danger

Door: two-way

Blast Radius: isolated

Six new package files; shared code and the selected frontier are unchanged.