Research

My research projects, current work and open questions.

1. Rule 30: the center column

   Open question

   Does Rule 30’s single-seed center column eventually become periodic? My notes and partial results on this open question.

2. SHA-256: structure and reduced-round models

   Work in progress

   I am studying the SHA-256 message schedule and reduced-round compression models; research notes will appear here as they are ready.

3. Schur number six: the published 536 certificate and a local distance bound at 537

   Work in progress

   For the published Fredricksen–Sweet six-color certificate on 1,...,536, any valid six-coloring through 537 would need at least 34 changes among the first 536 positions. This is a local distance bound for that specific certificate with fixed color labels; the known lower bound S(6) ≥ 536 is unchanged.

4. Zero-rotatability of equal-arm spider families

   Work in progress

   For every integer k≥19, all n≥2,m≥0 and any selected long arm of S(k^n,1^m), each depth 2≤d≤D8(k) can receive zero in a graceful labeling. Separate requests may use separate labelings. The explicit sufficient prefix includes both length parities and has limiting proportion 10/11; no optimality or historical priority is claimed.