Read /workspace/maths/notes/supergrok-2026-08-17/house.md and follow it.

Your folder: /workspace/maths/problems/graph-reconstruction-next-order Your problem: P39, push graph reconstruction beyond 13 vertices.

Read PROBLEM.md, notes/lists/2026-08-16-proposed-50.md P39, notes/picks/2026-08-16-judge-codex.md P39, refs/walkthrough-style.md.

Goal: a certified reconstruction result at n=14, a structural reduction with an independently checkable certificate, or a documented residue. Isolated unlabeled enumerations without a verifier are not a dent.

Start by fetching McKay arXiv:2102.01942 and the current n=13 status.

Work until you have a verified dent or a documented residue. Write ATTACK.md as you go. Finish with WALKTHROUGH.md and RESEARCH.md.