[petalas]

Summary

PR3158's two fixed P112 label spaces
  separate four-line deletion sets: span exactly 5
  one common four-line deletion set: span at most 3, attained

Adds only research/p112-common-deletion-span/, with a proof, literal fixture, exact checker, receipt and reproduction instructions. E8 Weyl/parabolic coverage classifies every real direction, not just a predecessor catalogue. The proof also covers complex directions.

This answers the fixed-space common-set question in the C5 handoff. It does not settle other space pairs or the full C5 conjecture, supply a decoder, or improve kappa. The selected frontier and frozen inputs are unchanged.

Credit DreamingOfClouds/PR3154 at 708f0ad8928c383de8294aea3c126e9461d2066d, Nick Petalas/PR3158 at 8e2167bac550bd653bb74c50c1f7c3f14b6c1f70, and the retained decoder lineage. Canonical main is 997e6a9ca7b4f95d50e366f61412fd640d72a88a, priority revision 6.

Evidence

• Before: PR3158 establishes a twelve-line common minimum for five named directions, not the all-direction common-budget-four optimum. After: exact coverage leaves 248 orthogonality systems, ten separately admissible projective directions and six common-cut states; the sharp shared span is three.
• Registered CPython 3.12 replay and 15 behavioral tests pass. Normal Python 3.12 and optimized Python 3.13 agree. Separate normal-vector reflection, XOR-code and integer-rank checks pass, including direct checks of all 794 relevant subsets of size at most four.
• Semantic mutants, malformed inputs, capacity exhaustion and Git-free CLI fixture/receipt corruption controls reject. Ruff, formatting, warnings-as-errors compilation and 16 assignment tests pass.
• All ten published package files match the tested bytes at 9ab8c4cc2aed4a87293d7d04b2abfdf854ae43e2.

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

Development and internal checking used substantial automated assistance. This is author-checked evidence, not independent human or proof-kernel review. No native supplier or full selected-result replay is claimed; hosted CI is separate.

Merge Danger

Door: two-way.

Blast Radius: isolated.

One opt-in research package. No shared code, priorities, frozen predecessor, selected record or frontier changes.