{"id":12,"slug":"distinct-subset-sums-a11","repoId":"distinct-subset-sums-a11","title":"Distinct Subset Sums a(11)","status":"locked","mode":"construction","direction":"minimize","scoreName":"max element","seedBest":"594/1","currentBest":"594/1","optimum":"310/1","minImprovement":"1/1","bountyEth":"0.00","challengeWindowHours":72,"postingBondEth":"0.00","challengeBondEth":"0.00","verifierVersion":"0.1.0","verifierImage":"sha256:local-dev","verifierCommand":"make verify SOLUTION=path","repoPath":"problems/distinct-subset-sums-a11","tagline":"Shrink the largest element of an 11-set whose 2048 subset sums are all distinct.","description":"Erdos problem #1 / OEIS A276661. The seed is the Conway-Guy-lineage set with max 594; the verifier exhaustively checks all 2^11 = 2048 subset sums for distinctness. a(11) is open with the bracket 310 <= a(11) <= 594, so any valid witness scoring below 594 improves the published upper bound. The board stays locked until an immutable image and N-host admission evidence exist.","verifierStandard":["R1 exact integer subset sums","R2 ignores claimed score fields","H3 all 2048 subset sums enumerated","H5 lying-claim fixture included"],"solutionSchema":{"type":"object","required":["set"]},"sampleSolution":{"set":[285,433,510,550,570,581,587,590,592,593,594]},"statement":"a(11) = \\min\\ \\max(S) \\quad \\text{over } S = \\{s_1 < \\cdots < s_{11}\\} \\subset \\mathbb{Z}_{\\ge 1} \\text{ with all } 2^{11} \\text{ subset sums distinct}, \\qquad 310 \\le a(11) \\le 594","statementCaveat":"The lower bound 310 (optimum) is the prefix lemma over the closed value a(10) = 309 (Dyson 2025); it is metadata, not a verifier check. Validity is decided solely by exact recomputation of the 2048 subset sums.","source":"local-phase-0","pool":null,"funding":null,"chainProvenance":{"settlementState":"local-only","reconciliationOk":false,"source":"static-portal-data","note":"Phase 0 portal state only: no deployed registry manifest or indexer reconciliation is attached to this problem yet.","fundingTargetDeployed":false}}