{"data":{"id":"lf-exactly-105-length-2-mesh-pattern-distribution-classes","statement_oneline":"Mesh patterns of length 2 form exactly 105 equivalence classes under equality of their permutation distributions.","statement_full_latex":"Mesh patterns of length 2 form exactly 105 equivalence classes under equality of their permutation distributions. Open residue: Current bounds are 105 through 108.","source":{"title":"Equidistribution of mesh patterns of short length","arxiv":"2605.19429v1","url":"https://arxiv.org/abs/2605.19429","year":2026,"area":"Permutation patterns"},"renown":{"score":1,"rationale":"Recent research-paper conjecture; renown scored at catalog level per Rubric v1.","scored_by":"rubric-v1"},"attackability":{"score":5,"rationale":"The universe is finite and the paper already narrows the answer to 105–108, so exhaustive canonicalization can settle the last identifications.","scored_by":"rubric-v1","subscores":{"finite_witness":5,"oracle_cost":4,"freshness":5,"seedability":5}},"verification_tier":null,"ai_systems":[],"posed_by":null,"years_open":0,"notability":null,"source_trackers":[],"status":"open","ranking_score":5,"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 distributions to a provably sufficient permutation length and certify class merges with explicit bijections or generating functions. — 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":"2762","effective_status":"open","claims":[],"status_events":[{"id":"seed-lf-exactly-105-length-2-mesh-pattern-distribution-classes","conjecture_id":"lf-exactly-105-length-2-mesh-pattern-distribution-classes","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-exactly-105-length-2-mesh-pattern-distribution-classes/claim","verification":"email magic link"},{"name":"report_resolution","method":"POST","href":"/c/lf-exactly-105-length-2-mesh-pattern-distribution-classes/resolve","verification":"admin review"}],"resolutions":[]},"notice":"Status is community- and machine-tracked and may lag. Verify independently before investing effort."}