{"id":2,"slug":"erdos-min-overlap","repoId":"erdos-min-overlap","title":"Erdos Min-Overlap","status":"locked","mode":"hybrid","direction":"minimize","scoreName":"upper bound","seedBest":"380926853433087/1000000000000000","currentBest":"1424992289798782609633201801352767458976314440679252577/3741444197802851304404516484910431627947663875649308401","optimum":"0/1","minImprovement":"1/1000000000000","bountyEth":"0.50","challengeWindowHours":72,"postingBondEth":"0.02","challengeBondEth":"0.02","verifierVersion":"0.1.0","verifierImage":"sha256:local-dev","verifierCommand":"make verify SOLUTION=path","repoPath":"problems/erdos-min-overlap","poolAddress":"base-sepolia:0x4242000000000000000000000000000000000002","donationWallet":{"chain":"Base Sepolia","asset":"ETH","address":"0x4242000000000000000000000000000000000002","status":"testnet-only","explorerUrl":"https://sepolia.basescan.org/address/0x4242000000000000000000000000000000000002","note":"Testnet deposit wallet reserved for the Erdos Min-Overlap verifier packaging gate."},"tagline":"Exact upper-bound witness packaged from the certified Erdos note.","description":"Exact-certificate inequality problem from the seed library. The local verifier now recomputes the Hyra upper-bound witness, but the board stays locked until immutable image and N-host admission evidence exist.","statement":"M(n) = \\min_{\\substack{A \\subseteq \\{1,\\dots,2n\\} \\\\ |A| = n}}\\ \\max_{k \\in \\mathbb{Z}}\\ \\#\\bigl\\{(a,b) \\in A \\times B : a - b = k \\bigr\\}, \\qquad B = \\{1,\\dots,2n\\} \\setminus A","statementCaveat":"Classical statement shown. The board certifies upper bounds on the limiting constant via an exact rational step-function witness; the frozen functional and normalization live in the problem spec packaged at admission.","verifierStandard":["R1 integer/rational arithmetic","H1 exact normalization","H3 all 4799 lags checked","H6 reduction lemma review pending"],"solutionSchema":{"type":"object","required":["n","denominator_power","values"]},"sampleSolution":{"n":2400,"denominator_power":82,"values":["2400 dyadic integer numerators"]},"chainProvenance":{"settlementState":"local-only","chain":"Base Sepolia","chainId":84532,"donationWalletAddress":"0x4242000000000000000000000000000000000002","poolAddress":null,"registryAddress":null,"problemRegistryId":null,"verifierImageHash":"sha256:local-dev","admissionMatrixHash":null,"deploymentCommit":null,"indexedThroughBlock":null,"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."}}