{"abstract":"Cosine decay remains above zero at the horizon.","category":"Learning rate schedules","checks":6,"contract":"For 0<=step<=total return base*(1+cos(pi*step/total))/2; clamp outside.","contract_signature":"step, base, total","evaluation_group":"lr-schedule-cosine-decay","failed_approach":"Removing amplitude normalization raises the initial rate to twice the base.","family":"w3-learning-rate-schedules-cosine-decay","id":"FA-99051","implementations":{"attempt":{"sha256":"6e28dfd01f622e7c0e808ad70f9bcd7deb88dadbed981a4e89680b419ab1320c","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(step, base, total):\n    import math\n    return base*(1+math.cos(math.pi*step/total)) if 0<=step<=total else (base if step<0 else 0)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('quarter',solve(1,8,4),8*(1+2**-0.5)/2); check('start',solve(0,6,3),6); check('middle',solve(2,10,4),5); check('end',solve(4,10,4),0); check('after',solve(5,9,4),0); check('negative',solve(-1,9,4),9)\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":"a539504f60fc1352257016703241120f7e00d379a9863a969e740c1ed831d7f4","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(step, base, total):\n    import math\n    return base*(1+math.cos(math.pi*step/(2*total)))/2 if 0<=step<=total else (base if step<0 else 0)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('quarter',solve(1,8,4),8*(1+2**-0.5)/2); check('start',solve(0,6,3),6); check('middle',solve(2,10,4),5); check('end',solve(4,10,4),0); check('after',solve(5,9,4),0); check('negative',solve(-1,9,4),9)\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":"These are toy scalar contracts with integer steps and finite parameters; they do not model framework defaults or optimizer state. 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":"w3-learning-rate-schedules-cosine-decay","generated_at":"2026-09-30T16:48:19.909886+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"A deterministic scalar schedule makes step-to-rate mapping explicit for a small training loop.","root_cause":"Dividing normalized progress by two runs only a quarter of the cosine cycle.","sha256":"f497d2eb3428e43dc820780026297f2fbde184f900add5f994b6f7d7178dcab2","title":"Cosine decay remains above zero at the horizon · case 01","variant":1,"variant_policy":"The same explicitly authored fixtures repeat across all five numbered records; runtime N is unused. These records share one mechanism and must remain together in evaluation splits.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":28.707,"exit_code":1,"observations":[{"actual":13.65685424949238,"check":"quarter","expected":6.82842712474619,"passed":false},{"actual":12.0,"check":"start","expected":6,"passed":false},{"actual":10.0,"check":"middle","expected":5,"passed":false},{"actual":0.0,"check":"end","expected":0,"passed":true},{"actual":0,"check":"after","expected":0,"passed":true},{"actual":9,"check":"negative","expected":9,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"quarter\", \"actual\": 13.65685424949238, \"expected\": 6.82842712474619, \"passed\": false}, {\"check\": \"start\", \"actual\": 12.0, \"expected\": 6, \"passed\": false}, {\"check\": \"middle\", \"actual\": 10.0, \"expected\": 5, \"passed\": false}, {\"check\": \"end\", \"actual\": 0.0, \"expected\": 0, \"passed\": true}, {\"check\": \"after\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"negative\", \"actual\": 9, \"expected\": 9, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":28.868,"exit_code":1,"observations":[{"actual":7.695518130045147,"check":"quarter","expected":6.82842712474619,"passed":false},{"actual":6.0,"check":"start","expected":6,"passed":true},{"actual":8.535533905932738,"check":"middle","expected":5,"passed":false},{"actual":5.0,"check":"end","expected":0,"passed":false},{"actual":0,"check":"after","expected":0,"passed":true},{"actual":9,"check":"negative","expected":9,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"quarter\", \"actual\": 7.695518130045147, \"expected\": 6.82842712474619, \"passed\": false}, {\"check\": \"start\", \"actual\": 6.0, \"expected\": 6, \"passed\": true}, {\"check\": \"middle\", \"actual\": 8.535533905932738, \"expected\": 5, \"passed\": false}, {\"check\": \"end\", \"actual\": 5.0, \"expected\": 0, \"passed\": false}, {\"check\": \"after\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"negative\", \"actual\": 9, \"expected\": 9, \"passed\": true}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}