{"id":6,"slug":"autoconvolution-c2-lower","repoId":"autoconvolution-c2-lower","title":"Autoconvolution C2 Lower","status":"locked","mode":"construction","direction":"maximize","scoreName":"C2 lower bound","seedBest":"47/50","currentBest":"140651861665566489683881393353250795846281833/146070932420211259869783468438333325818535926","optimum":"1/1","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/autoconvolution-c2-lower","poolAddress":"base-sepolia:0x4242000000000000000000000000000000000006","donationWallet":{"chain":"Base Sepolia","asset":"ETH","address":"0x4242000000000000000000000000000000000006","status":"testnet-only","explorerUrl":"https://sepolia.basescan.org/address/0x4242000000000000000000000000000000000006","note":"Testnet deposit wallet reserved for the Autoconvolution C2 lower-bound gate."},"tagline":"Large integer witness with exact L1/L2/Linf recomputation.","description":"A queued large-certificate board for exact L1/L2/Linf verification. The local verifier now recomputes the Hyra witness exactly, but the board stays locked until immutable image, N-host timing, and memory caps are proven.","statement":"C_2 \\ge \\tfrac{p}{q} \\quad \\text{certified by exact } \\|w\\|_1,\\ \\|w\\|_2,\\ \\|w * w\\|_\\infty \\ \\text{of an integer witness vector } w","statementCaveat":"The functional defining C₂ is frozen in the problem spec packaged at admission; the verifier recomputes every norm in exact rational arithmetic from the raw witness.","verifierStandard":["R1 exact integer norms","H3 all 1048575 coefficients checked","H5 claimed-score trap","N-host timing gate required"],"solutionSchema":{"type":"object","required":["n","values"]},"sampleSolution":{"n":524288,"values":["524288 nonnegative integers"]},"chainProvenance":{"settlementState":"local-only","chain":"Base Sepolia","chainId":84532,"donationWalletAddress":"0x4242000000000000000000000000000000000006","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."}}