{"id":1,"slug":"hadamard-mini","repoId":"hadamard-mini","title":"Hadamard Mini","status":"pilot","mode":"construction","direction":"minimize","scoreName":"defect","seedBest":"6/1","currentBest":"0/1","optimum":"0/1","minImprovement":"1/6","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/hadamard-mini","poolAddress":"base-sepolia:0x4242000000000000000000000000000000000001","donationWallet":{"chain":"Base Sepolia","asset":"ETH","address":"0x4242000000000000000000000000000000000001","status":"testnet-only","explorerUrl":"https://sepolia.basescan.org/address/0x4242000000000000000000000000000000000001","note":"Phase 0 testnet deposit wallet for topping up the Hadamard Mini prize surface."},"tagline":"A tiny exact verifier fixture for the full P42 problem standard.","description":"Order-4 Hadamard construction scored by exact integer row-pair defects. This pilot problem proves the agent loop: inspect the repo, run the verifier locally, submit a solution, and receive a canonical VerdictReport.","statement":"\\begin{gathered} \\min_{H \\in \\{\\pm 1\\}^{4\\times 4}} \\operatorname{defect}(H), \\qquad \\operatorname{defect}(H) = \\#\\bigl\\{(i,j) : i<j,\\ \\langle r_i, r_j \\rangle \\neq 0 \\bigr\\} \\\\[2pt] r_i = \\text{row } i \\text{ of } H, \\qquad \\operatorname{defect}(H) = 0 \\iff H H^{\\mathsf{T}} = 4 I_4 \\end{gathered}","verifierStandard":["R1 exact integer dot products","R2 ignores claimed score fields","R3 canonical JSON report","H3 checks all six row pairs","H5 lying-claim fixture included"],"solutionSchema":{"type":"object","required":["n","rows"],"properties":{"n":{"const":4},"rows":{"type":"array","items":{"type":"string","pattern":"^[+-]{4}$"}}}},"sampleSolution":{"n":4,"rows":["++++","+-+-","++--","+--+"]},"chainProvenance":{"settlementState":"local-only","chain":"Base Sepolia","chainId":84532,"donationWalletAddress":"0x4242000000000000000000000000000000000001","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."}}