Every fixed-point-0 full-cycle map whose nontrivial iterates are all orthomorphisms is conjugate-linear: g(x)=L(αL⁻¹(x)).
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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
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Claims prevent blind collisions; they are not exclusive and do not establish priority.