{"data":{"id":"lf-classification-of-full-cycle-orthomorphism-iterates","statement_oneline":"Every fixed-point-0 full-cycle map whose nontrivial iterates are all orthomorphisms is conjugate-linear: g(x)=L(αL⁻¹(x)).","statement_full_latex":"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.","source":{"title":"Note on the Equivalence of Costas Polynomials and Orthomorphisms","arxiv":"2606.07097v1","url":"https://arxiv.org/abs/2606.07097","year":2026,"area":"Finite fields / Costas arrays"},"renown":{"score":1,"rationale":"Recent research-paper conjecture; renown scored at catalog level per Rubric v1.","scored_by":"rubric-v1"},"attackability":{"score":4,"rationale":"For each finite field q the search space is finite, and any exceptional permutation is an immediate counterexample.","scored_by":"rubric-v1","subscores":{"finite_witness":4,"oracle_cost":4,"freshness":5,"seedability":4}},"verification_tier":null,"ai_systems":[],"posed_by":null,"years_open":0,"notability":null,"source_trackers":[],"status":"open","ranking_score":4,"last_verified_open":"2026-07-27","added":"2026-07-27","resolution_type":null,"resolver":null,"resolution_date":null,"evidence_url":null,"evidence_note":null,"method_note":null,"submitted_by":"Luke Francis","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.","openconjecture_id":"4038","effective_status":"open","claims":[],"status_events":[{"id":"seed-lf-classification-of-full-cycle-orthomorphism-iterates","conjecture_id":"lf-classification-of-full-cycle-orthomorphism-iterates","status":"open","date":"2026-07-27T00:00:00.000Z","actor":"human-admin","rationale":"Imported Tier 1 contributor candidate from Luke Francis.","note":"Editorially screened candidate; author confirmation pending."}],"public_actions":[{"name":"claim","method":"POST","href":"/c/lf-classification-of-full-cycle-orthomorphism-iterates/claim","verification":"email magic link"},{"name":"report_resolution","method":"POST","href":"/c/lf-classification-of-full-cycle-orthomorphism-iterates/resolve","verification":"admin review"}],"resolutions":[]},"notice":"Status is community- and machine-tracked and may lag. Verify independently before investing effort."}