{"abstract":"Triangular schedule descends before reaching its peak.","category":"Learning rate schedules","checks":6,"contract":"Repeat a triangular cycle with value base* (1-abs(phase-peak)/peak), phase=step%period, peak=period//2.","contract_signature":"step, base, period","evaluation_group":"lr-schedule-cyclic-triangle","failed_approach":"Adding one to the distance denominator lowers the peak below base.","family":"w3-learning-rate-schedules-cyclic-triangle","id":"FA-99091","implementations":{"attempt":{"sha256":"5963dbe205d53a72cd1329fc675f65989b0afecbe0a9077f1fe7c9ec022f2e91","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(step, base, period):\n    phase=step%period\n    peak=period//2\n    return base*(1-abs(phase-peak)/(peak+1))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('start',solve(0,10,6),0); check('ascending',solve(1,12,6),4); check('peak',solve(3,8,6),8); check('descending',solve(3,8,4),4); check('cycle reset',solve(6,9,6),0); check('second peak',solve(9,5,6),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":"a202a51b15b2ff90330d96953dde449110a8a0964b737ff35a9d9a61956595a9","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(step, base, period):\n    phase=step%period\n    peak=period//2\n    return base*abs(phase-peak)/peak\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('start',solve(0,10,6),0); check('ascending',solve(1,12,6),4); check('peak',solve(3,8,6),8); check('descending',solve(3,8,4),4); check('cycle reset',solve(6,9,6),0); check('second peak',solve(9,5,6),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-cyclic-triangle","generated_at":"2026-09-30T16:48:20.351926+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":"Distance from the peak is returned directly, inverting the intended triangle.","sha256":"2c0ce5af123237d0f13223944eb825f956ee259aa3709266e0b29fb777e8e2e8","title":"Triangular schedule descends before reaching its peak · 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":27.478,"exit_code":1,"observations":[{"actual":2.5,"check":"start","expected":0,"passed":false},{"actual":6.0,"check":"ascending","expected":4,"passed":false},{"actual":8.0,"check":"peak","expected":8,"passed":true},{"actual":5.333333333333334,"check":"descending","expected":4,"passed":false},{"actual":2.25,"check":"cycle reset","expected":0,"passed":false},{"actual":5.0,"check":"second peak","expected":5,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"start\", \"actual\": 2.5, \"expected\": 0, \"passed\": false}, {\"check\": \"ascending\", \"actual\": 6.0, \"expected\": 4, \"passed\": false}, {\"check\": \"peak\", \"actual\": 8.0, \"expected\": 8, \"passed\": true}, {\"check\": \"descending\", \"actual\": 5.333333333333334, \"expected\": 4, \"passed\": false}, {\"check\": \"cycle reset\", \"actual\": 2.25, \"expected\": 0, \"passed\": false}, {\"check\": \"second peak\", \"actual\": 5.0, \"expected\": 5, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":27.336,"exit_code":1,"observations":[{"actual":10.0,"check":"start","expected":0,"passed":false},{"actual":8.0,"check":"ascending","expected":4,"passed":false},{"actual":0.0,"check":"peak","expected":8,"passed":false},{"actual":4.0,"check":"descending","expected":4,"passed":true},{"actual":9.0,"check":"cycle reset","expected":0,"passed":false},{"actual":0.0,"check":"second peak","expected":5,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"start\", \"actual\": 10.0, \"expected\": 0, \"passed\": false}, {\"check\": \"ascending\", \"actual\": 8.0, \"expected\": 4, \"passed\": false}, {\"check\": \"peak\", \"actual\": 0.0, \"expected\": 8, \"passed\": false}, {\"check\": \"descending\", \"actual\": 4.0, \"expected\": 4, \"passed\": true}, {\"check\": \"cycle reset\", \"actual\": 9.0, \"expected\": 0, \"passed\": false}, {\"check\": \"second peak\", \"actual\": 0.0, \"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."}}