{"data":{"id":"lf-optimal-modulus-for-unique-multiset-sums","statement_oneline":"Every valid n-residue set needs modulus N≥2^n−2^floor(log2 n); the super-increasing construction is optimal.","statement_full_latex":"Every valid n-residue set needs modulus N≥2^n−2^floor(log2 n); the super-increasing construction is optimal. Open residue: Exact proposed optimum for every n≥2.","source":{"title":"Minimum modulus for the unique multiset-sum problem","arxiv":"2607.08366v2","url":"https://arxiv.org/abs/2607.08366","year":2026,"area":"Additive combinatorics"},"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 n this is a finite modular subset/multiset-sum search, and violations have tiny explicit certificates.","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":"CP-SAT/exhaustive search over residue sets and collision constraints; export a set or a proof of infeasibility. — 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":"4435","effective_status":"open","claims":[],"status_events":[{"id":"seed-lf-optimal-modulus-for-unique-multiset-sums","conjecture_id":"lf-optimal-modulus-for-unique-multiset-sums","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-optimal-modulus-for-unique-multiset-sums/claim","verification":"email magic link"},{"name":"report_resolution","method":"POST","href":"/c/lf-optimal-modulus-for-unique-multiset-sums/resolve","verification":"admin review"}],"resolutions":[]},"notice":"Status is community- and machine-tracked and may lag. Verify independently before investing effort."}