{"abstract":"The center stencil coefficient lacks its factor of two.","category":"Discrete calculus","checks":4,"contract":"Integer sample values and compatible sample-array lengths. Rational results are reduced Fraction strings; spacing is positive unless explicitly stated otherwise. Discrete laplacian periodic. Exact operational definition: [values[i-1]-2*v+values[(i+1)%len(values)] for i,v in enumerate(values)]","evaluation_group":"model-13020d5959de9a08","failed_approach":"Zero boundary conditions replace periodic wraparound.","family":"xn-discrete-laplacian-periodic","id":"FA-6436","implementations":{"attempt":{"sha256":"9952c20926d4894ce7c8099947efea444974bd12f0af4fb48c784d8e9a57b3a4","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport calendar\nimport statistics\nimport itertools\nfrom fractions import Fraction\nfrom datetime import date, datetime, timedelta, timezone\nfrom decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR\n\nN = 1\nobservations = []\ndef solve(values):\n    return [(values[i-1] if i else 0)-2*v+(values[i+1] if i+1<len(values) else 0) for i,v in enumerate(values)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([1, 2, 3],)', solve(*([1, 2, 3],)), [3, 0, -3])\ncheck('fixture 2: ([4, 4, 4],)', solve(*([4, 4, 4],)), [0, 0, 0])\ncheck('fixture 3: ([5],)', solve(*([5],)), [0])\ncheck('fixture 4: ([],)', solve(*([],)), [])\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"60bdd74bc121a736409fa792b7e5fc73ab8bb82605e799cf503eb3d704305efe","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport calendar\nimport statistics\nimport itertools\nfrom fractions import Fraction\nfrom datetime import date, datetime, timedelta, timezone\nfrom decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR\n\nN = 1\nobservations = []\ndef solve(values):\n    return [values[i-1]-v+values[(i+1)%len(values)] for i,v in enumerate(values)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([1, 2, 3],)', solve(*([1, 2, 3],)), [3, 0, -3])\ncheck('fixture 2: ([4, 4, 4],)', solve(*([4, 4, 4],)), [0, 0, 0])\ncheck('fixture 3: ([5],)', solve(*([5],)), [0])\ncheck('fixture 4: ([],)', solve(*([],)), [])\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"fixed":{"sha256":"ea5bf33f06da4c345b8acaad85d2af367715d45e01f0b2299664b8ddd04bbe21","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport calendar\nimport statistics\nimport itertools\nfrom fractions import Fraction\nfrom datetime import date, datetime, timedelta, timezone\nfrom decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR\n\nN = 1\nobservations = []\ndef solve(values):\n    return [values[i-1]-2*v+values[(i+1)%len(values)] for i,v in enumerate(values)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([1, 2, 3],)', solve(*([1, 2, 3],)), [3, 0, -3])\ncheck('fixture 2: ([4, 4, 4],)', solve(*([4, 4, 4],)), [0, 0, 0])\ncheck('fixture 3: ([5],)', solve(*([5],)), [0])\ncheck('fixture 4: ([],)', solve(*([],)), [])\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":" This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"xn-discrete-laplacian-periodic","generated_at":"2026-09-29T14:38:01.852267+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Discrete calculus results depend on the stated convention.","repair":"Apply the specified mathematical contract directly, preserving all terms and boundary cases: return [values[i-1]-2*v+values[(i+1)%len(values)] for i,v in enumerate(values)]","root_cause":"The center stencil coefficient lacks its factor of two.","sha256":"d93425fba5ecbf84f6b9c686f5aafec4e4bbb38b8b60b36294ec731be01ac1df","title":"Discrete laplacian periodic · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":48.918,"exit_code":1,"observations":[{"actual":[0,0,-4],"check":"fixture 1: ([1, 2, 3],)","expected":[3,0,-3],"passed":false},{"actual":[-4,0,-4],"check":"fixture 2: ([4, 4, 4],)","expected":[0,0,0],"passed":false},{"actual":[-10],"check":"fixture 3: ([5],)","expected":[0],"passed":false},{"actual":[],"check":"fixture 4: ([],)","expected":[],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 2, 3],)\", \"actual\": [0, 0, -4], \"expected\": [3, 0, -3], \"passed\": false}, {\"check\": \"fixture 2: ([4, 4, 4],)\", \"actual\": [-4, 0, -4], \"expected\": [0, 0, 0], \"passed\": false}, {\"check\": \"fixture 3: ([5],)\", \"actual\": [-10], \"expected\": [0], \"passed\": false}, {\"check\": \"fixture 4: ([],)\", \"actual\": [], \"expected\": [], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":49.233,"exit_code":1,"observations":[{"actual":[4,2,0],"check":"fixture 1: ([1, 2, 3],)","expected":[3,0,-3],"passed":false},{"actual":[4,4,4],"check":"fixture 2: ([4, 4, 4],)","expected":[0,0,0],"passed":false},{"actual":[5],"check":"fixture 3: ([5],)","expected":[0],"passed":false},{"actual":[],"check":"fixture 4: ([],)","expected":[],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 2, 3],)\", \"actual\": [4, 2, 0], \"expected\": [3, 0, -3], \"passed\": false}, {\"check\": \"fixture 2: ([4, 4, 4],)\", \"actual\": [4, 4, 4], \"expected\": [0, 0, 0], \"passed\": false}, {\"check\": \"fixture 3: ([5],)\", \"actual\": [5], \"expected\": [0], \"passed\": false}, {\"check\": \"fixture 4: ([],)\", \"actual\": [], \"expected\": [], \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":42.857,"exit_code":0,"observations":[{"actual":[3,0,-3],"check":"fixture 1: ([1, 2, 3],)","expected":[3,0,-3],"passed":true},{"actual":[0,0,0],"check":"fixture 2: ([4, 4, 4],)","expected":[0,0,0],"passed":true},{"actual":[0],"check":"fixture 3: ([5],)","expected":[0],"passed":true},{"actual":[],"check":"fixture 4: ([],)","expected":[],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 2, 3],)\", \"actual\": [3, 0, -3], \"expected\": [3, 0, -3], \"passed\": true}, {\"check\": \"fixture 2: ([4, 4, 4],)\", \"actual\": [0, 0, 0], \"expected\": [0, 0, 0], \"passed\": true}, {\"check\": \"fixture 3: ([5],)\", \"actual\": [0], \"expected\": [0], \"passed\": true}, {\"check\": \"fixture 4: ([],)\", \"actual\": [], \"expected\": [], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}