[petalas]

Summary

Adds only research/p112-four-deletion-counterexample/, answering the C5 handoff in Discussion3156.

Five independent E8 directions, two six-dimensional label spaces
  separate deletion sets: at most 4 lines per direction
  one common deletion set: exactly 12 lines required

The p=2 span-four result does not extend to the p=4 per-direction relaxation. This does not refute the original common-P beta statement or C(P112) >= 64, determine every C5 cell's target, or improve kappa.

Credit DreamingOfClouds's PR3154 at 708f0ad8928c383de8294aea3c126e9461d2066d and its retained decoder lineage. Base is canonical main 997e6a9ca7b4f95d50e366f61412fd640d72a88a. Source pins, the literal witness, a short proof and reproduction instructions are included.

Evidence

• Before, C5's p=4 computation was unfinished. After, a literal rank-five minor has determinant -2; complete character-support enumeration proves the sharp common minimum of twelve.
• python3.12 -B scripts/research_package.py --package research/p112-four-deletion-counterexample passes, including 19 tests with twelve rejection controls.
• Separate rational label, Leibniz determinant, XOR-code and exhaustive deletion checks pass. Normal/optimized Python 3.12 and Python 3.13 agree.
• Exact source translation, three source-binding mutants, a Git-free read-only export, Ruff and all nine publication-byte comparisons pass locally.

Publication commit: 8e2167bac550bd653bb74c50c1f7c3f14b6c1f70. This is author-checked finite evidence, not independent human or proof-kernel review. No complete p=4 census, supplier replay or outer theorem audit is claimed.

Merge Danger

Door: two-way

Blast Radius: isolated

One opt-in research package. No shared code, frozen predecessor, selected record or frontier changes. The default replay needs only Python's standard library; predecessor data is optional for the additional source-translation check.