{"id":8,"slug":"mertens-lp-ceiling-k12000","repoId":"mertens-lp-ceiling-k12000","title":"Mertens LP Ceiling K12000","status":"locked","mode":"proof","direction":"minimize","scoreName":"certified ceiling","seedBest":"1/1","currentBest":"249371902576813203926437/250000000000000000000000","optimum":"0/1","minImprovement":"1/1000000000000","bountyEth":"0.50","challengeWindowHours":96,"postingBondEth":"0.03","challengeBondEth":"0.03","verifierVersion":"0.1.0","verifierImage":"sha256:local-dev","verifierCommand":"make verify SOLUTION=path","repoPath":"problems/mertens-lp-ceiling-k12000","poolAddress":"base-sepolia:0x4242000000000000000000000000000000000008","donationWallet":{"chain":"Base Sepolia","asset":"ETH","address":"0x4242000000000000000000000000000000000008","status":"testnet-only","explorerUrl":"https://sepolia.basescan.org/address/0x4242000000000000000000000000000000000008","note":"Testnet deposit wallet reserved for the Mertens LP ceiling certificate gate."},"tagline":"Dyadic LP dual certificate with interval-enclosed log residuals.","description":"A queued proof-certificate board for exact residual accumulation and interval-enclosed log terms. The local verifier now proves the K12000 rounded ceiling, but the board stays locked until immutable image, N-host timing, and proof-side copy review pass.","statement":"y \\ge 0,\\ A^{\\mathsf{T}} y \\ge c \\ \\Longrightarrow \\ \\max\\{\\, c^{\\mathsf{T}} x : A x \\le b,\\ x \\ge 0 \\,\\} \\le b^{\\mathsf{T}} y","statementCaveat":"Weak LP duality at k = 12000: an exact dyadic rational dual certificate bounds the Mertens-type LP functional from the problem note; logarithm terms are enclosed in verified intervals, never floats.","verifierStandard":["R1 dyadic rational arithmetic","R6 interval log audit","H3 all k=2..12000 residuals checked","H5 one-ULP vault fixture"],"solutionSchema":{"type":"object","required":["K","M","denom_pow","m","Y"]},"sampleSolution":{"K":12000,"M":120000,"denom_pow":48,"m":["dual rows"],"Y":["dyadic weights"]},"chainProvenance":{"settlementState":"local-only","chain":"Base Sepolia","chainId":84532,"donationWalletAddress":"0x4242000000000000000000000000000000000008","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."}}