[1337isnot1337]

This adds a contact-search model that can leave ascending subspace chains while retaining a complete Gaussian rank invoice. It charges newly nonzero transitions and changed native warps, and allows both helper endpoints to move. Main, adapter and owned interfaces remain fixed. An additional paid-phase mode chooses a zero or common ambient symmetric form at each contact, charging every changed Gaussian rank. No new kappa or physical supplier is claimed.

The optional signed-cut MILP search uses exact four-state rank tables. The independent standard-library replay checks those ranks against 285 actual Clifford pairs, reconstructs both pinned #4610 source invoices, and certifies the fixed positive calibration with rational moment bounds. It reproduces #4672’s existing 49-contact / 13-helper change and full resulting invoice; that improvement belongs to #4672. Bounded coordinated searches on the stronger round-three word found no profitable candidate, and are not exact exclusion certificates.

The paid-phase implementation is checked against every symmetric form on every ordered subspace pair in dimensions one through three: 66,368 exact physical transition checks and 50,128 native-warp checks. All 511 rank-one common forms and 18 named compound forms returned zero candidate energy in bounded floating searches on round three. This is not an exact exclusion of arbitrary node forms. It explicitly changes #4665’s unchanged-paid-rank premise.

The Pauli-quarter-turn mode allows subspace and phase changes together. It prices every transition and warp using exact binary Lagrangian intersections. Literal Clifford circuits check all Pauli axes and ordered subspace pairs in dimensions 1..3 (66,060 transitions; 50,208 native warps with the same bounded map scope). Its pure-Z case agrees with the paid-phase model on every edge/helper of the complete nine-bit source. All 255 named tested axes returned zero candidate energy; this is a bounded sample, not the full 262,143-axis census or an exclusion of arbitrary Clifford gauges.

The scope, search receipts, precise unrun supplier obligations and open next questions are in research/general-gaussian-contact-search/README.md. Canonical main was refreshed at b58ad9e; selected conditional kappa remains 0.00302015. The narrow overlap check covered local notes, all reported open PR pages and discussion pages; predecessor work is explicitly retained.

Validation on final commit ddb7ead:

• python3.12 -B scripts/research_package.py --package research/general-gaussian-contact-search
• python3 -B scripts/check_research_commit.py --package research/general-gaussian-contact-search --check-source-history
• Package export and archive checks; Git-free CPython 3.12 isolated optimized replay with PATH=/nonexistent.
• Optional SciPy 1.18.1 discovery smoke reproduces the known positive calibration; every returned candidate is repriced from the complete invoice.

Credit Cao Yifan/#4610 for both native words; Cinna Davis/#4672 for the positive calibration and coordinated contact cuts; Dugongue/#4654 for the exact chart grammar; Cinna Davis/#4470 and its retained controller lineage, zxv, Jacob Alan Sussman and the retained E8/scalar/Clifford/native/compiler contributors. Prepared by Cinna Davis with substantial OpenAI Codex assistance; no subagents; Apache-2.0.