test(research): certify a complete P112 common-deletion slice

[petalas]

Summary

PR3160: both P112 label spaces fixed -> sharp common-cut span 3
This result: first space fixed, all 788,035 partners -> sharp span 4

Proves one complete rank-seven/common-four-deletion slice over all real and complex directions. Adds research/p112-common-deletion-slice/ and its dedicated native replay workflow only. The proof covers 4,560 normal lines and 1,120 normal planes, not just a direction catalogue.

This follows the C5 handoff. Concurrent #3161 reports a different global rank-six/eight-deletion theorem and closure of the historical (5,3) cell. This package does not claim another new exclusion for that cell. It retains a stronger-rank calibration slice and exact common-set checker, not a full C5 result or kappa improvement.

Credit DreamingOfClouds/#3154 at 708f0ad8928c383de8294aea3c126e9461d2066d, Nick Petalas/#3158 at 8e2167bac550bd653bb74c50c1f7c3f14b6c1f70 and #3160 at 9ab8c4cc2aed4a87293d7d04b2abfdf854ae43e2, with the retained E8 decoder lineage. Geometry is explicitly adapted from #3160. The scanner imports neither FINITE implementation nor its direction tables. Baseline is canonical main 997e6a9ca7b4f95d50e366f61412fd640d72a88a, priority revision 6, refreshed before submission.

Evidence

• Before: the fixed pair has sharp span three. After: all 788,035 partner spaces, 776,806 distinct live masks and 795,182 common-cut states give sharp span four. A literal four-direction witness attains it.
• Two complete partner-space enumerators agree on every mask and the full multiplicity histogram. Python separately checks all 197 nontrivial native rank decisions and their literal residual boundaries.
• Registered Python 3.12 replay and 15 behavioral groups pass, including three compiled semantic mutants. Optimized Python 3.13 replay of the read-only, Git-free committed export matches the same receipt.
• Strict native compiler diagnostics, Ruff/formatting, Python warnings-as-errors compilation, 16 assignment tests, metadata/pins and all 11 package publication-byte checks pass locally. All 12 published files, including the dedicated workflow, match their remote Git blobs at 89419106cd86896c366e853795978f1bc85f9112. Hosted CI is queued and is separate from local evidence.

python3.12 -B scripts/research_package.py --package research/p112-common-deletion-slice

Requires an x86-64 CPU with POPCNT, g++ and Boost.Multiprecision headers. The workflow installs native dependencies. Sources, proof, receipt, exact pins, resource bounds, remaining obligations and reproduction instructions are committed. No supplier/outer replay, proof-kernel review or selected-frontier change is claimed. Further rank-seven slices need a named remaining caller before expanding this census.

Development and internal checking used substantial automated assistance. This is author-checked evidence, not independent human review.

Merge danger

Door: two-way. One isolated research package and its path-scoped workflow.

Blast radius: research. Existing checkers, frozen inputs, priorities and the selected record are unchanged.