Open Conjecture Board

← Board

Every fixed-point-0 full-cycle map whose nontrivial iterates are all orthomorphisms is conjugate-linear: g(x)=L(αL⁻¹(x)).

Status is community- and machine-tracked and may lag. Verify independently before investing effort.

Statement

Every fixed-point-0 full-cycle map whose nontrivial iterates are all orthomorphisms is conjugate-linear: g(x)=L(αL⁻¹(x)). Open residue: Classification over finite fields; test small q first.

Assessment

Renown 1/5

Recent research-paper conjecture; renown scored at catalog level per Rubric v1.

Attackability 4/5

For each finite field q the search space is finite, and any exceptional permutation is an immediate counterexample.

finite witness
4/5
oracle cost
4/5
freshness
5/5
seedability
4/5

Verification note

Enumerate full cycles modulo affine/linear conjugacy and test every iterate’s orthomorphism condition. — Current arXiv revision checked; source-stated open/partial. Independent literature and author confirmation still required. Editorially screened candidate; not independently certified open. Author confirmation pending.

Claims

Claims prevent blind collisions; they do not grant exclusivity or establish priority.

No active claims.

I resolved this

I’m attacking this

Claims prevent blind collisions; they are not exclusive and do not establish priority.