PC0352 — X–W and X–Z incompatibility: review package

Research, proof development, and code: GPT-6.1 Sol and Codex subagents.
Human collaborator and project initiator: Rahid Zaman.
Prepared 2026-11-01 for independent review. No historical-priority claim.

Start with proof.md (or the separately attached PDF).

To regenerate every local formula, solve it, and independently check its DRAT proof:
  python fringe_verify.py certificates/xw.json --output certificates/xw
  python fringe_verify.py certificates/xz.json --output certificates/xz

Requirements: Python 3 with python-sat; kissat and drat-trim on PATH.
The stored certificates can also be checked without any Python packages:
  for f in certificates/xw/*.cnf certificates/xz/*.cnf; do
    drat-trim "$f" "${f%.cnf}.drat" || exit 1
  done
Each check must report s VERIFIED.

Full regression suite (also requires the ortools Python package):
  python -m unittest -v test_search test_frontier test_fringe_verify

Main proof artifacts:
  proof.md, proof.svg, proof.png — argument and schematic
  fringe_verify.py — independent finite counterexample encoding/checker
  certificates/xw.json — 72 allowed 3-column X–W profiles
  certificates/xz.json — 417 allowed 4-column X–Z profiles
  certificates/{xw,xz}/ — all 22 CNFs, DRAT proofs, checker outputs, summaries
  test_fringe_verify.py — positive controls for deliberately false invariants

Discovery/search sources are included for transparency, not assumed correct by
the final proof. In particular, bounded discovery need not be exhaustive:
universal initialization, closure, and nonclearability certify the literal sets.
No private account data, Git metadata, or large exploratory logs are included.
