{"abstract":"Staircase decay applies before the first interval boundary.","category":"Learning rate schedules","checks":6,"contract":"Return base*gamma**(step//interval) for nonnegative steps.","contract_signature":"step, base, gamma, interval","evaluation_group":"lr-schedule-staircase-decay","failed_approach":"Shifting the step before integer division still crosses some interval boundaries early, including unit intervals.","family":"w3-learning-rate-schedules-staircase-decay","id":"FA-99061","implementations":{"attempt":{"sha256":"843ae8f272eeb312badcf9b9599f38ed7275285511e064f678c1b6ccb32c2803","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(step, base, gamma, interval):\n    return base*gamma**((step+1)//interval)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('before edge',solve(2,16,0.5,3),16); check('edge',solve(3,16,0.5,3),8); check('next interval',solve(6,16,0.5,3),4); check('zero',solve(0,7,0.2,4),7); check('negative clamp',solve(-1,9,0.5,3),9); check('unit interval',solve(2,8,0.5,1),2)\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":"8d390de9a5f8cb927bfd697a24c3e450235c387109f6ae3cf16bc0c427e52c41","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(step, base, gamma, interval):\n    return base*gamma**(step//interval+1)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('before edge',solve(2,16,0.5,3),16); check('edge',solve(3,16,0.5,3),8); check('next interval',solve(6,16,0.5,3),4); check('zero',solve(0,7,0.2,4),7); check('negative clamp',solve(-1,9,0.5,3),9); check('unit interval',solve(2,8,0.5,1),2)\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-staircase-decay","generated_at":"2026-09-30T16:48:19.909763+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":"The interval quotient is incremented before exponentiation, so every step is one decay level early.","sha256":"ab21ad33db4e3fce079d53364f8834097decb1407902747d53396adcd20dda83","title":"Staircase decay applies before the first interval boundary · 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":28.587,"exit_code":1,"observations":[{"actual":8.0,"check":"before edge","expected":16,"passed":false},{"actual":8.0,"check":"edge","expected":8,"passed":true},{"actual":4.0,"check":"next interval","expected":4,"passed":true},{"actual":7.0,"check":"zero","expected":7,"passed":true},{"actual":9.0,"check":"negative clamp","expected":9,"passed":true},{"actual":1.0,"check":"unit interval","expected":2,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"before edge\", \"actual\": 8.0, \"expected\": 16, \"passed\": false}, {\"check\": \"edge\", \"actual\": 8.0, \"expected\": 8, \"passed\": true}, {\"check\": \"next interval\", \"actual\": 4.0, \"expected\": 4, \"passed\": true}, {\"check\": \"zero\", \"actual\": 7.0, \"expected\": 7, \"passed\": true}, {\"check\": \"negative clamp\", \"actual\": 9.0, \"expected\": 9, \"passed\": true}, {\"check\": \"unit interval\", \"actual\": 1.0, \"expected\": 2, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":28.505,"exit_code":1,"observations":[{"actual":8.0,"check":"before edge","expected":16,"passed":false},{"actual":4.0,"check":"edge","expected":8,"passed":false},{"actual":2.0,"check":"next interval","expected":4,"passed":false},{"actual":1.4000000000000001,"check":"zero","expected":7,"passed":false},{"actual":9.0,"check":"negative clamp","expected":9,"passed":true},{"actual":1.0,"check":"unit interval","expected":2,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"before edge\", \"actual\": 8.0, \"expected\": 16, \"passed\": false}, {\"check\": \"edge\", \"actual\": 4.0, \"expected\": 8, \"passed\": false}, {\"check\": \"next interval\", \"actual\": 2.0, \"expected\": 4, \"passed\": false}, {\"check\": \"zero\", \"actual\": 1.4000000000000001, \"expected\": 7, \"passed\": false}, {\"check\": \"negative clamp\", \"actual\": 9.0, \"expected\": 9, \"passed\": true}, {\"check\": \"unit interval\", \"actual\": 1.0, \"expected\": 2, \"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."}}