Projects / Published artifact
Certified Small Signed Difference Sets Census
A computer-assisted census resolving the frozen set of 68 small signed-difference-set cases recorded as open, with explicit constructions and certified nonexistence results.
The project studies signed arrangements on finite groups. For every nonidentity shift, the arrangement must have the same periodic autocorrelation. The census answers the 68 cases recorded as open in a frozen upstream snapshot, for abelian groups of order at most 36.
Principal classifications
- For signed
(32,20,4)difference sets, a construction exists exactly for the six noncyclic abelian groups of order 32. A complete quotient refinement rules out the cyclic groupC32. - No abelian group of order 36 admits a signed
(36,29,4)difference set. The project checks all four groups; theC6 × C6case also has a solver-free direct enumeration.
Evidence and scope
The census contains 16 existence results and 52 nonexistence results. Existence witnesses pass two independently implemented validators. Nonexistence claims rely on complete finite arguments or checked solver proofs; timeouts and unsuccessful searches do not count as evidence.
The documented novelty screen distinguishes 58 independently replicated entries from 10 entries for which no exact public predecessor was found in the reviewed sources. A literature and repository search is not a proof of novelty.
Publication status
Version 1.1.0 was released publicly on GitHub on 23 September 2026. It contains a revised manuscript and a reproducibility package. The earlier v1.0 proof archive remains available on Zenodo.
The work received independent expert review. Daniel Gordon encouraged journal submission; this is not an acceptance. No journal submission or acceptance has been identified in the available correspondence. The public release is a citable research artifact, not a peer-reviewed journal article.