Open search tooling for paired-cube complex words (no κ claim)

[GamingPuzzled]

Tooling only. No new κ is claimed, and no certificate or verification group changes.

Stacked on #161 at d14e29157bc905be1ced0776dd893d0714013f3a. Its word, modules, gauges and physical checker are prerequisites, not contributions of this PR.

What this adds

The physical frame descents and compensated reuse pairs of the paired-cube complex words are shipped as frozen inputs (references/paired-cube/physical/{frames,pairs}.json); no producer is included in the repository. New modules also need frozen carrier arcs. research/paired-cube-open-search/ supplies open producers for both:

• generator.py: physical frame descent (alternating passes; each operation moves to the lower or upper nested bound when cheaper) and maximum-weight donor→recipient reuse pairs. It runs PR161's unchanged scripts/paired_cube_physical.py on its own output.
• frames_open.py: PR161's compiler plus open maximum carrier matching (Hopcroft–Karp) when no frozen arcs are given.
• modules_open.py: all-but-one variants (cyclic intervals, prefix/suffix, tree split).
• search.py: a parallel genetic search over triple coordinates and all-but-one module.

Reproduction

python3 -m pip install -r research/paired-cube-open-search/requirements.txt
python3 -B research/paired-cube-open-search/reproduce.py     # about 40 s

Every line passes PR161's checker, including its exact aliased dirty-scratch replay:

Word	Pairs	W	Complex saving (float)	vs PR161
PR161 frozen plan (asserted equal to its certificate)	2,970	15,681	5.8856699e-4	—
PR161 word, open generator	2,970	15,681	5.8905532e-4	+0.083%
Cyclic all-but-one, open matching + generator	2,970	14,361	5.9306799e-4	+0.765%

A two-generation search smoke run reached 5.9334228e-4 in 65 s on 6 workers.

These are complex-supplier discovery scores. Since #163/#164/#165 the bit supplier binds, so they do not raise κ alone. They are offered for the next stacked word. Any κ still needs the usual exact supplier, bit and assembly certificates.

Speed

One configuration takes about 7 s with warm caches, against about 74 s for the straightforward loop:

• basis() returns the unique reduced echelon form, so it is memoized exactly and shared with the selector and checker.
• Donor-in-gauge containment is computed for all distinct frame pairs as one F2 parity matrix in numpy.

Each worker uses about 2.6 GB.

CI: .github/workflows/paired-cube-open-search.yml runs reproduce.py and a one-configuration search on Python 3.13, with pinned numpy and scipy.

Credits: icekylinx (#144 paired cubes; frames_open.py is a modified copy of the Apache-2.0 compiler, with notice retained), eumemic (#157/#161 word and physical checker; #131/#143), jamesyc (#124), and the #130 frame lemma. Prepared by Joel Pulikkan with Anthropic Claude assistance; Apache-2.0.

🤖 Generated with Claude Code

[Mister-Meeseeks]

Thank you @GamingPuzzled. This contribution is now retained on main in the scoped 100-PR review and contributor credits.

Contribution: Open, reproducible search tooling for paired-cube complex words.

Review and limits: Fresh reproduction passed with scientific dependencies installed; the initial stdlib-only environment lacked NumPy. Candidate-generation scores are not certificates or a new kappa.

The complete original source, notices and relevant execution evidence are retained through the pinned source archive. The review distinguishes fresh local runs, source-bound historical Linux CI and prior exact-head review; it does not claim 100 fresh full mathematical audits. Closing this historical PR as reconciled. This preserves parallel and cumulative credit without replacing the selected frontier or promoting priced research targets to completed constructions.

Reviewed head: 3540326866af459ef28ee23252e3c54d2ac49017. Publication: 50d768818f579d4e165b4c257c6ee25bca300802.