{"abstract":"Cosine decay ends at half the configured floor.","category":"Learning rate schedules","checks":6,"contract":"Return floor+(base-floor)*(1+cos(pi*progress))/2 for clamped progress.","contract_signature":"step, base, floor, total","evaluation_group":"lr-schedule-cosine-floor","failed_approach":"Removing amplitude normalization doubles the changing portion and can exceed the base rate.","family":"w3-learning-rate-schedules-cosine-floor","id":"FA-99136","implementations":{"attempt":{"sha256":"626250e73d73ab7126cd3af0b3be9fc269ff2528548a962b742863ca68838dc6","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(step, base, floor, total):\n    import math\n    progress=min(1,max(0,step/total))\n    return floor+(base-floor)*(1+math.cos(math.pi*progress))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('start',solve(0,10,2,4),10); check('quarter',solve(1,10,2,4),2+8*(1+2**-0.5)/2); check('mid',solve(2,10,2,4),6); check('end',solve(4,10,2,4),2); check('after',solve(7,10,2,4),2); check('flat',solve(2,5,5,4),5)\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":"301dc265ff2b37834e4b434e2c3b048320a846127b7a595271f431e96d7434b7","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(step, base, floor, total):\n    import math\n    progress=min(1,max(0,step/total))\n    return floor+(base-floor)*(1+math.cos(math.pi*progress))/2-floor/2\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('start',solve(0,10,2,4),10); check('quarter',solve(1,10,2,4),2+8*(1+2**-0.5)/2); check('mid',solve(2,10,2,4),6); check('end',solve(4,10,2,4),2); check('after',solve(7,10,2,4),2); check('flat',solve(2,5,5,4),5)\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-floor","generated_at":"2026-09-30T16:48:20.799100+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":"Subtracting half the floor after interpolation lowers the terminal rate below its target.","sha256":"5fa18bc475082af9576ed0080254888c280b7ad90cbf1dd4123309f9c4d2fc17","title":"Cosine decay ends at half the configured floor · 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":26.614,"exit_code":1,"observations":[{"actual":18.0,"check":"start","expected":10,"passed":false},{"actual":15.65685424949238,"check":"quarter","expected":8.82842712474619,"passed":false},{"actual":10.0,"check":"mid","expected":6,"passed":false},{"actual":2.0,"check":"end","expected":2,"passed":true},{"actual":2.0,"check":"after","expected":2,"passed":true},{"actual":5.0,"check":"flat","expected":5,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"start\", \"actual\": 18.0, \"expected\": 10, \"passed\": false}, {\"check\": \"quarter\", \"actual\": 15.65685424949238, \"expected\": 8.82842712474619, \"passed\": false}, {\"check\": \"mid\", \"actual\": 10.0, \"expected\": 6, \"passed\": false}, {\"check\": \"end\", \"actual\": 2.0, \"expected\": 2, \"passed\": true}, {\"check\": \"after\", \"actual\": 2.0, \"expected\": 2, \"passed\": true}, {\"check\": \"flat\", \"actual\": 5.0, \"expected\": 5, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":28.232,"exit_code":1,"observations":[{"actual":9.0,"check":"start","expected":10,"passed":false},{"actual":7.82842712474619,"check":"quarter","expected":8.82842712474619,"passed":false},{"actual":5.0,"check":"mid","expected":6,"passed":false},{"actual":1.0,"check":"end","expected":2,"passed":false},{"actual":1.0,"check":"after","expected":2,"passed":false},{"actual":2.5,"check":"flat","expected":5,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"start\", \"actual\": 9.0, \"expected\": 10, \"passed\": false}, {\"check\": \"quarter\", \"actual\": 7.82842712474619, \"expected\": 8.82842712474619, \"passed\": false}, {\"check\": \"mid\", \"actual\": 5.0, \"expected\": 6, \"passed\": false}, {\"check\": \"end\", \"actual\": 1.0, \"expected\": 2, \"passed\": false}, {\"check\": \"after\", \"actual\": 1.0, \"expected\": 2, \"passed\": false}, {\"check\": \"flat\", \"actual\": 2.5, \"expected\": 5, \"passed\": false}], \"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."}}