{"id":3,"slug":"edges-vs-triangles","repoId":"edges-vs-triangles","title":"Edges vs Triangles","status":"locked","mode":"construction","direction":"maximize","scoreName":"negative slope-3 area plus gap","seedBest":"-1/1","currentBest":"-16684282317138839/23437500000000000","optimum":"0/1","minImprovement":"1/1000000000000","bountyEth":"0.25","challengeWindowHours":72,"postingBondEth":"0.02","challengeBondEth":"0.02","verifierVersion":"0.1.0","verifierImage":"sha256:local-dev","verifierCommand":"make verify SOLUTION=path","repoPath":"problems/edges-vs-triangles","poolAddress":"base-sepolia:0x4242000000000000000000000000000000000003","donationWallet":{"chain":"Base Sepolia","asset":"ETH","address":"0x4242000000000000000000000000000000000003","status":"testnet-only","explorerUrl":"https://sepolia.basescan.org/address/0x4242000000000000000000000000000000000003","note":"Testnet deposit wallet for increasing the queued arena-board prize pool."},"tagline":"Rationalized slope-3 arena board with exact row normalization.","description":"A queued arena-derived board now packaged as a deterministic P42 verifier. It scores finite rational row distributions by exact edge/triangle moments, slope-3 area, and max-gap penalty; it stays locked until immutable image, N-host matrix, and external model review exist.","statement":"\\max\\ -\\left(\\operatorname{area}_{3}(P) + 10\\max_i (x_{i+1}-x_i)\\right), \\qquad x=1-\\sum_j p_j^2,\\quad y=1-3\\sum_j p_j^2+2\\sum_j p_j^3","statementCaveat":"This is a rationalized P42 package for the documented slope-3 verifier model, not a recovered copy of the missing historical Arena incumbent artifact. The exact scope is frozen in the package spec before any funding gate can open.","verifierStandard":["R1 Fraction-only density and area arithmetic","H1 fixed row-sum normalization","H3 all canonical slope-3 segments checked","H5 claimed-score trap","H6 historical artifact scope review pending"],"solutionSchema":{"type":"object","required":["atoms","row_sum","rows"]},"sampleSolution":{"atoms":20,"row_sum":1000,"rows":["up to 500 rows of 20 integers summing to 1000"]},"chainProvenance":{"settlementState":"local-only","chain":"Base Sepolia","chainId":84532,"donationWalletAddress":"0x4242000000000000000000000000000000000003","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."}}