{"abstract":"Rows backtrack at noon or never backtrack at all.","category":"Solar tracker geometry","checks":7,"contract":"Horizontal single-axis rows with ground coverage ratio gcr in (0, 1]. temp = |cos(ideal)|/gcr. When temp < 1 the rows would shade each other and the angle is corrected by -sign(ideal)*acos(temp) degrees (backtracking, flag True). gcr <= 0 disables backtracking. Return [angle rounded to 3, backtracking flag].","evaluation_group":"w2-solar_tracker_geometry-gcr-backtracking","failed_approach":"Dividing by the gap fraction 1-gcr models the wrong geometry.","family":"w2-solar_tracker_geometry-gcr-backtracking-coverage-ratio-scaling","id":"FA-93371","implementations":{"attempt":{"sha256":"e2d74ac93a1166ccb596b6ef31a922a93d9d09019783d79f33d15053f97740b9","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(ideal, gcr):\n    if gcr <= 0:\n        return [round(ideal, 3), False]\n    temp = abs(math.cos(math.radians(ideal))) / (1 - gcr)\n    if temp < 1:\n        corr = -math.copysign(1, ideal) * math.degrees(math.acos(temp))\n        return [round(ideal + corr, 3), True]\n    return [round(ideal, 3), False]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['boundary: noon never backtracks', [0, 0.4], [0, False]],\n  ['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],\n  ['regression: coverage ratio scaling', [-10, 0.4], [-10, False]],\n  ['regression: coverage ratio scaling (partial repair)', [-44.5, 0.25], [-44.5, False]],\n  ['control 1', [30, 0.25], [30, False]], ['control 2', [-29.5, 0.5], [-29.5, False]],\n  ['control 3', [-30, 0.4], [-30, False]]],\n [['boundary: noon never backtracks', [0, 0.4], [0, False]],\n  ['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],\n  ['regression: coverage ratio scaling', [-44.5, 0.6], [-44.5, False]],\n  ['regression: coverage ratio scaling (partial repair)', [-79.5, 0.4], [-16.603, True]],\n  ['control 1', [-80, 0.35], [-19.745, True]], ['control 2', [-10, 0.35], [-10, False]],\n  ['control 3', [75, 0.6], [10.554, True]]],\n [['boundary: noon never backtracks', [0, 0.4], [0, False]],\n  ['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],\n  ['regression: coverage ratio scaling', [-70, 0.4], [-38.765, True]],\n  ['regression: coverage ratio scaling (partial repair)', [-79.5, 0.3], [-26.905, True]],\n  ['control 1', [0, 0.25], [0, False]], ['control 2', [10.5, 0], [10.5, False]],\n  ['control 3', [70, 0.35], [57.742, True]]],\n [['boundary: noon never backtracks', [0, 0.4], [0, False]],\n  ['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],\n  ['regression: coverage ratio scaling', [-45, 0.25], [-45, False]],\n  ['regression: coverage ratio scaling (partial repair)', [60, 0.25], [60, False]],\n  ['control 1', [-45, 0.5], [-45, False]], ['control 2', [45, 0], [45, False]],\n  ['control 3', [-9.5, 0.35], [-9.5, False]]],\n [['boundary: noon never backtracks', [0, 0.4], [0, False]],\n  ['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],\n  ['regression: coverage ratio scaling', [60.5, 0.25], [60.5, False]],\n  ['regression: coverage ratio scaling (partial repair)', [85.5, 0.4], [6.812, True]],\n  ['control 1', [10, 0.35], [10, False]], ['control 2', [-60, 0.3], [-60, False]],\n  ['control 3', [70.5, 0.25], [70.5, False]]]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(*args), expected)\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":"467c41947a01144edc0d979e33cd678ea2dedd6126f137e4154ececb996abe23","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(ideal, gcr):\n    if gcr <= 0:\n        return [round(ideal, 3), False]\n    temp = abs(math.cos(math.radians(ideal))) * gcr\n    if temp < 1:\n        corr = -math.copysign(1, ideal) * math.degrees(math.acos(temp))\n        return [round(ideal + corr, 3), True]\n    return [round(ideal, 3), False]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['boundary: noon never backtracks', [0, 0.4], [0, False]],\n  ['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],\n  ['regression: coverage ratio scaling', [-10, 0.4], [-10, False]],\n  ['regression: coverage ratio scaling (partial repair)', [-44.5, 0.25], [-44.5, False]],\n  ['control 1', [30, 0.25], [30, False]], ['control 2', [-29.5, 0.5], [-29.5, False]],\n  ['control 3', [-30, 0.4], [-30, False]]],\n [['boundary: noon never backtracks', [0, 0.4], [0, False]],\n  ['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],\n  ['regression: coverage ratio scaling', [-44.5, 0.6], [-44.5, False]],\n  ['regression: coverage ratio scaling (partial repair)', [-79.5, 0.4], [-16.603, True]],\n  ['control 1', [-80, 0.35], [-19.745, True]], ['control 2', [-10, 0.35], [-10, False]],\n  ['control 3', [75, 0.6], [10.554, True]]],\n [['boundary: noon never backtracks', [0, 0.4], [0, False]],\n  ['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],\n  ['regression: coverage ratio scaling', [-70, 0.4], [-38.765, True]],\n  ['regression: coverage ratio scaling (partial repair)', [-79.5, 0.3], [-26.905, True]],\n  ['control 1', [0, 0.25], [0, False]], ['control 2', [10.5, 0], [10.5, False]],\n  ['control 3', [70, 0.35], [57.742, True]]],\n [['boundary: noon never backtracks', [0, 0.4], [0, False]],\n  ['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],\n  ['regression: coverage ratio scaling', [-45, 0.25], [-45, False]],\n  ['regression: coverage ratio scaling (partial repair)', [60, 0.25], [60, False]],\n  ['control 1', [-45, 0.5], [-45, False]], ['control 2', [45, 0], [45, False]],\n  ['control 3', [-9.5, 0.35], [-9.5, False]]],\n [['boundary: noon never backtracks', [0, 0.4], [0, False]],\n  ['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],\n  ['regression: coverage ratio scaling', [60.5, 0.25], [60.5, False]],\n  ['regression: coverage ratio scaling (partial repair)', [85.5, 0.4], [6.812, True]],\n  ['control 1', [10, 0.35], [10, False]], ['control 2', [-60, 0.3], [-60, False]],\n  ['control 3', [70.5, 0.25], [70.5, False]]]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(*args), expected)\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":"3f260ed14014fd55eb45bf364a8efb1081f7da6c2d8b966ae8bf060d432dfb90","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(ideal, gcr):\n    if gcr <= 0:\n        return [round(ideal, 3), False]\n    temp = abs(math.cos(math.radians(ideal))) / gcr\n    if temp < 1:\n        corr = -math.copysign(1, ideal) * math.degrees(math.acos(temp))\n        return [round(ideal + corr, 3), True]\n    return [round(ideal, 3), False]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['boundary: noon never backtracks', [0, 0.4], [0, False]],\n  ['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],\n  ['regression: coverage ratio scaling', [-10, 0.4], [-10, False]],\n  ['regression: coverage ratio scaling (partial repair)', [-44.5, 0.25], [-44.5, False]],\n  ['control 1', [30, 0.25], [30, False]], ['control 2', [-29.5, 0.5], [-29.5, False]],\n  ['control 3', [-30, 0.4], [-30, False]]],\n [['boundary: noon never backtracks', [0, 0.4], [0, False]],\n  ['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],\n  ['regression: coverage ratio scaling', [-44.5, 0.6], [-44.5, False]],\n  ['regression: coverage ratio scaling (partial repair)', [-79.5, 0.4], [-16.603, True]],\n  ['control 1', [-80, 0.35], [-19.745, True]], ['control 2', [-10, 0.35], [-10, False]],\n  ['control 3', [75, 0.6], [10.554, True]]],\n [['boundary: noon never backtracks', [0, 0.4], [0, False]],\n  ['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],\n  ['regression: coverage ratio scaling', [-70, 0.4], [-38.765, True]],\n  ['regression: coverage ratio scaling (partial repair)', [-79.5, 0.3], [-26.905, True]],\n  ['control 1', [0, 0.25], [0, False]], ['control 2', [10.5, 0], [10.5, False]],\n  ['control 3', [70, 0.35], [57.742, True]]],\n [['boundary: noon never backtracks', [0, 0.4], [0, False]],\n  ['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],\n  ['regression: coverage ratio scaling', [-45, 0.25], [-45, False]],\n  ['regression: coverage ratio scaling (partial repair)', [60, 0.25], [60, False]],\n  ['control 1', [-45, 0.5], [-45, False]], ['control 2', [45, 0], [45, False]],\n  ['control 3', [-9.5, 0.35], [-9.5, False]]],\n [['boundary: noon never backtracks', [0, 0.4], [0, False]],\n  ['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],\n  ['regression: coverage ratio scaling', [60.5, 0.25], [60.5, False]],\n  ['regression: coverage ratio scaling (partial repair)', [85.5, 0.4], [6.812, True]],\n  ['control 1', [10, 0.35], [10, False]], ['control 2', [-60, 0.3], [-60, False]],\n  ['control 3', [70.5, 0.25], [70.5, False]]]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(*args), expected)\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":"Deterministic stipulated toy contract for teaching; no claim of conformance with any standard, vendor protocol or production controller. 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":"w2-solar_tracker_geometry-gcr-backtracking-coverage-ratio-scaling","generated_at":"2026-09-29T14:51:54.472127+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Single-axis and dual-axis solar trackers turn a sun direction into actuator commands; a sign, frame or limit mistake points a whole plant away from the sun or into a mechanical stop.","repair":"Divide by gcr: temp = |cos(ideal)|/gcr.","root_cause":"The cosine is multiplied by the coverage ratio instead of divided by it.","sha256":"62ae164c4815f0d1e28c5425d17521469801d4213c46f3a9a185f74995a18c11","title":"Ground-coverage-ratio backtracking: coverage ratio scaling · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":40.54,"exit_code":1,"observations":[{"actual":[0,false],"check":"boundary: noon never backtracks","expected":[0,false],"passed":true},{"actual":[-10.554,true],"check":"normal: steep morning angle backtracks","expected":[-25.319,true],"passed":false},{"actual":[-10,false],"check":"regression: coverage ratio scaling","expected":[-10,false],"passed":true},{"actual":[-26.49,true],"check":"regression: coverage ratio scaling (partial repair)","expected":[-44.5,false],"passed":false},{"actual":[30,false],"check":"control 1","expected":[30,false],"passed":true},{"actual":[-29.5,false],"check":"control 2","expected":[-29.5,false],"passed":true},{"actual":[-30,false],"check":"control 3","expected":[-30,false],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"boundary: noon never backtracks\", \"actual\": [0, false], \"expected\": [0, false], \"passed\": true}, {\"check\": \"normal: steep morning angle backtracks\", \"actual\": [-10.554, true], \"expected\": [-25.319, true], \"passed\": false}, {\"check\": \"regression: coverage ratio scaling\", \"actual\": [-10, false], \"expected\": [-10, false], \"passed\": true}, {\"check\": \"regression: coverage ratio scaling (partial repair)\", \"actual\": [-26.49, true], \"expected\": [-44.5, false], \"passed\": false}, {\"check\": \"control 1\", \"actual\": [30, false], \"expected\": [30, false], \"passed\": true}, {\"check\": \"control 2\", \"actual\": [-29.5, false], \"expected\": [-29.5, false], \"passed\": true}, {\"check\": \"control 3\", \"actual\": [-30, false], \"expected\": [-30, false], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":37.675,"exit_code":1,"observations":[{"actual":[-66.422,true],"check":"boundary: noon never backtracks","expected":[0,false],"passed":false},{"actual":[9.058,true],"check":"normal: steep morning angle backtracks","expected":[-25.319,true],"passed":false},{"actual":[56.801,true],"check":"regression: coverage ratio scaling","expected":[-10,false],"passed":false},{"actual":[35.229,true],"check":"regression: coverage ratio scaling (partial repair)","expected":[-44.5,false],"passed":false},{"actual":[-47.496,true],"check":"control 1","expected":[30,false],"passed":false},{"actual":[34.703,true],"check":"control 2","expected":[-29.5,false],"passed":false},{"actual":[39.732,true],"check":"control 3","expected":[-30,false],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"boundary: noon never backtracks\", \"actual\": [-66.422, true], \"expected\": [0, false], \"passed\": false}, {\"check\": \"normal: steep morning angle backtracks\", \"actual\": [9.058, true], \"expected\": [-25.319, true], \"passed\": false}, {\"check\": \"regression: coverage ratio scaling\", \"actual\": [56.801, true], \"expected\": [-10, false], \"passed\": false}, {\"check\": \"regression: coverage ratio scaling (partial repair)\", \"actual\": [35.229, true], \"expected\": [-44.5, false], \"passed\": false}, {\"check\": \"control 1\", \"actual\": [-47.496, true], \"expected\": [30, false], \"passed\": false}, {\"check\": \"control 2\", \"actual\": [34.703, true], \"expected\": [-29.5, false], \"passed\": false}, {\"check\": \"control 3\", \"actual\": [39.732, true], \"expected\": [-30, false], \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":41.844,"exit_code":0,"observations":[{"actual":[0,false],"check":"boundary: noon never backtracks","expected":[0,false],"passed":true},{"actual":[-25.319,true],"check":"normal: steep morning angle backtracks","expected":[-25.319,true],"passed":true},{"actual":[-10,false],"check":"regression: coverage ratio scaling","expected":[-10,false],"passed":true},{"actual":[-44.5,false],"check":"regression: coverage ratio scaling (partial repair)","expected":[-44.5,false],"passed":true},{"actual":[30,false],"check":"control 1","expected":[30,false],"passed":true},{"actual":[-29.5,false],"check":"control 2","expected":[-29.5,false],"passed":true},{"actual":[-30,false],"check":"control 3","expected":[-30,false],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"boundary: noon never backtracks\", \"actual\": [0, false], \"expected\": [0, false], \"passed\": true}, {\"check\": \"normal: steep morning angle backtracks\", \"actual\": [-25.319, true], \"expected\": [-25.319, true], \"passed\": true}, {\"check\": \"regression: coverage ratio scaling\", \"actual\": [-10, false], \"expected\": [-10, false], \"passed\": true}, {\"check\": \"regression: coverage ratio scaling (partial repair)\", \"actual\": [-44.5, false], \"expected\": [-44.5, false], \"passed\": true}, {\"check\": \"control 1\", \"actual\": [30, false], \"expected\": [30, false], \"passed\": true}, {\"check\": \"control 2\", \"actual\": [-29.5, false], \"expected\": [-29.5, false], \"passed\": true}, {\"check\": \"control 3\", \"actual\": [-30, false], \"expected\": [-30, false], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}