{"abstract":"Squaring the total allows cancellation between samples.","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 energy squared norm. Exact operational definition: sum(v*v for v in values)","evaluation_group":"model-7e95710de5e6c117","failed_approach":"Magnitude sum is not quadratic energy.","family":"xn-discrete-energy-squared-norm","id":"FA-6466","implementations":{"attempt":{"sha256":"7dd3f5bfd57ad3c550c98d8b81d7157636826af31e4174f485b00637567e8d50","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 sum(abs(v) for v in values)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([2, -2],)', solve(*([2, -2],)), 8)\ncheck('fixture 2: ([1, 2, 3],)', solve(*([1, 2, 3],)), 14)\ncheck('fixture 3: ([0],)', solve(*([0],)), 0)\ncheck('fixture 4: ([],)', solve(*([],)), 0)\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":"c57058ca4a9bee9818150b77deb625f25878b00b2694d0745d1ead243eea3fa0","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 sum(values)**2\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([2, -2],)', solve(*([2, -2],)), 8)\ncheck('fixture 2: ([1, 2, 3],)', solve(*([1, 2, 3],)), 14)\ncheck('fixture 3: ([0],)', solve(*([0],)), 0)\ncheck('fixture 4: ([],)', solve(*([],)), 0)\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":"5da0a89029fab5d5331daa283748ec86573cd8259cd34cd3eebc3b7bd8079093","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 sum(v*v for v in values)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([2, -2],)', solve(*([2, -2],)), 8)\ncheck('fixture 2: ([1, 2, 3],)', solve(*([1, 2, 3],)), 14)\ncheck('fixture 3: ([0],)', solve(*([0],)), 0)\ncheck('fixture 4: ([],)', solve(*([],)), 0)\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-energy-squared-norm","generated_at":"2026-09-29T14:38:02.369070+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 sum(v*v for v in values)","root_cause":"Squaring the total allows cancellation between samples.","sha256":"17f6157cbdb66003949d8ada59300ebe165557c243476f90c797f7098611395b","title":"Discrete energy squared norm · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":47.375,"exit_code":1,"observations":[{"actual":4,"check":"fixture 1: ([2, -2],)","expected":8,"passed":false},{"actual":6,"check":"fixture 2: ([1, 2, 3],)","expected":14,"passed":false},{"actual":0,"check":"fixture 3: ([0],)","expected":0,"passed":true},{"actual":0,"check":"fixture 4: ([],)","expected":0,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([2, -2],)\", \"actual\": 4, \"expected\": 8, \"passed\": false}, {\"check\": \"fixture 2: ([1, 2, 3],)\", \"actual\": 6, \"expected\": 14, \"passed\": false}, {\"check\": \"fixture 3: ([0],)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: ([],)\", \"actual\": 0, \"expected\": 0, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":46.51,"exit_code":1,"observations":[{"actual":0,"check":"fixture 1: ([2, -2],)","expected":8,"passed":false},{"actual":36,"check":"fixture 2: ([1, 2, 3],)","expected":14,"passed":false},{"actual":0,"check":"fixture 3: ([0],)","expected":0,"passed":true},{"actual":0,"check":"fixture 4: ([],)","expected":0,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([2, -2],)\", \"actual\": 0, \"expected\": 8, \"passed\": false}, {\"check\": \"fixture 2: ([1, 2, 3],)\", \"actual\": 36, \"expected\": 14, \"passed\": false}, {\"check\": \"fixture 3: ([0],)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: ([],)\", \"actual\": 0, \"expected\": 0, \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":124.114,"exit_code":0,"observations":[{"actual":8,"check":"fixture 1: ([2, -2],)","expected":8,"passed":true},{"actual":14,"check":"fixture 2: ([1, 2, 3],)","expected":14,"passed":true},{"actual":0,"check":"fixture 3: ([0],)","expected":0,"passed":true},{"actual":0,"check":"fixture 4: ([],)","expected":0,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([2, -2],)\", \"actual\": 8, \"expected\": 8, \"passed\": true}, {\"check\": \"fixture 2: ([1, 2, 3],)\", \"actual\": 14, \"expected\": 14, \"passed\": true}, {\"check\": \"fixture 3: ([0],)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: ([],)\", \"actual\": 0, \"expected\": 0, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}