{"abstract":"Backtracked angles are computed from a pre-clamped ideal angle.","category":"Solar tracker geometry","checks":7,"contract":"Rows on terrain with cross-axis slope cross_tilt degrees. dist = 1/(gcr*cos(cross_tilt)); temp = dist*cos(ideal - cross_tilt). When temp < 1 the angle becomes ideal - sign(ideal)*acos(max(temp, -1)) degrees, else ideal. The result is then clamped to +-max_angle. Return the angle rounded to 3.","contract_signature":"ideal, gcr, cross_tilt, max_angle","evaluation_group":"w2-solar_tracker_geometry-cross-slope-backtracking","failed_approach":"Clamping only the positive side lets eastern angles pass the stop.","family":"w2-solar_tracker_geometry-cross-slope-backtracking-limit-applied-after-backtracking","id":"FA-93636","implementations":{"attempt":{"sha256":"7c014ece79e313c22ca19571b101b6d3d6d2785792c8739a89aee60d0593fc87","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(ideal, gcr, cross_tilt, max_angle):\n    dist = 1 / (gcr * math.cos(math.radians(cross_tilt)))\n    temp = dist * math.cos(math.radians(ideal - cross_tilt))\n    if temp < 1:\n        theta = ideal - math.copysign(math.degrees(math.acos(max(temp, -1.0))), ideal)\n    else:\n        theta = ideal\n    theta = min(max_angle, theta)\n    return round(theta, 3)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['normal: flat terrain matches plain backtracking', [-70, 0.4, 0, 60], -38.765],\n  ['boundary: slope-facing noon', [0, 0.4, 10, 60], 0],\n  ['boundary: clamp after backtracking', [80, 0.3, -10, 50], -10.0],\n  ['regression: limit applied after backtracking', [-80, 0.5, 0, 75], -10.322],\n  ['regression: limit applied after backtracking (partial repair)', [-60, 0.3, 10, 50], -50],\n  ['control 1', [-45, 0.5, -5, 50], -45], ['control 2', [-60, 0.3, 0, 60], -60]],\n [['normal: flat terrain matches plain backtracking', [-70, 0.4, 0, 60], -38.765],\n  ['boundary: slope-facing noon', [0, 0.4, 10, 60], 0],\n  ['boundary: clamp after backtracking', [80, 0.3, -10, 50], -10.0],\n  ['regression: limit applied after backtracking', [60, 0.5, -5, 55], 28.045],\n  ['regression: limit applied after backtracking (partial repair)', [-70, 0.3, -5, 60], -60],\n  ['control 1', [80, 0.4, 0, 60], 15.729], ['control 2', [-80, 0.4, 15, 75], 23.037]],\n [['normal: flat terrain matches plain backtracking', [-70, 0.4, 0, 60], -38.765],\n  ['boundary: slope-facing noon', [0, 0.4, 10, 60], 0],\n  ['boundary: clamp after backtracking', [80, 0.3, -10, 50], -10.0],\n  ['regression: limit applied after backtracking', [-70, 0.3, 15, 60], 2.496],\n  ['regression: limit applied after backtracking (partial repair)', [-70, 0.3, -5, 50], -50],\n  ['control 1', [0, 0.4, -5, 55], 0], ['control 2', [70, 0.4, -5, 75], 20.505]],\n [['normal: flat terrain matches plain backtracking', [-70, 0.4, 0, 60], -38.765],\n  ['boundary: slope-facing noon', [0, 0.4, 10, 60], 0],\n  ['boundary: clamp after backtracking', [80, 0.3, -10, 50], -10.0],\n  ['regression: limit applied after backtracking', [-80, 0.4, -10, 75], -50.255],\n  ['regression: limit applied after backtracking (partial repair)', [-60, 0.5, 0, 50], -50],\n  ['control 1', [-60, 0.4, -5, 50], -50], ['control 2', [0, 0.4, -5, 60], 0]],\n [['normal: flat terrain matches plain backtracking', [-70, 0.4, 0, 60], -38.765],\n  ['boundary: slope-facing noon', [0, 0.4, 10, 60], 0],\n  ['boundary: clamp after backtracking', [80, 0.3, -10, 50], -10.0],\n  ['regression: limit applied after backtracking', [-80, 0.4, 0, 75], -15.729],\n  ['regression: limit applied after backtracking (partial repair)', [-70, 0.3, -5, 60], -60],\n  ['control 1', [-80, 0.5, 0, 75], -10.322], ['control 2', [-45, 0.4, 15, 50], -45]]]\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":"da3f210b9bc8561c24bb682685ec3d7572ee5c9089b199cfecd3359d427a1033","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(ideal, gcr, cross_tilt, max_angle):\n    ideal = max(-max_angle, min(max_angle, ideal))\n    dist = 1 / (gcr * math.cos(math.radians(cross_tilt)))\n    temp = dist * math.cos(math.radians(ideal - cross_tilt))\n    if temp < 1:\n        theta = ideal - math.copysign(math.degrees(math.acos(max(temp, -1.0))), ideal)\n    else:\n        theta = ideal\n    return round(theta, 3)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['normal: flat terrain matches plain backtracking', [-70, 0.4, 0, 60], -38.765],\n  ['boundary: slope-facing noon', [0, 0.4, 10, 60], 0],\n  ['boundary: clamp after backtracking', [80, 0.3, -10, 50], -10.0],\n  ['regression: limit applied after backtracking', [-80, 0.5, 0, 75], -10.322],\n  ['regression: limit applied after backtracking (partial repair)', [-60, 0.3, 10, 50], -50],\n  ['control 1', [-45, 0.5, -5, 50], -45], ['control 2', [-60, 0.3, 0, 60], -60]],\n [['normal: flat terrain matches plain backtracking', [-70, 0.4, 0, 60], -38.765],\n  ['boundary: slope-facing noon', [0, 0.4, 10, 60], 0],\n  ['boundary: clamp after backtracking', [80, 0.3, -10, 50], -10.0],\n  ['regression: limit applied after backtracking', [60, 0.5, -5, 55], 28.045],\n  ['regression: limit applied after backtracking (partial repair)', [-70, 0.3, -5, 60], -60],\n  ['control 1', [80, 0.4, 0, 60], 15.729], ['control 2', [-80, 0.4, 15, 75], 23.037]],\n [['normal: flat terrain matches plain backtracking', [-70, 0.4, 0, 60], -38.765],\n  ['boundary: slope-facing noon', [0, 0.4, 10, 60], 0],\n  ['boundary: clamp after backtracking', [80, 0.3, -10, 50], -10.0],\n  ['regression: limit applied after backtracking', [-70, 0.3, 15, 60], 2.496],\n  ['regression: limit applied after backtracking (partial repair)', [-70, 0.3, -5, 50], -50],\n  ['control 1', [0, 0.4, -5, 55], 0], ['control 2', [70, 0.4, -5, 75], 20.505]],\n [['normal: flat terrain matches plain backtracking', [-70, 0.4, 0, 60], -38.765],\n  ['boundary: slope-facing noon', [0, 0.4, 10, 60], 0],\n  ['boundary: clamp after backtracking', [80, 0.3, -10, 50], -10.0],\n  ['regression: limit applied after backtracking', [-80, 0.4, -10, 75], -50.255],\n  ['regression: limit applied after backtracking (partial repair)', [-60, 0.5, 0, 50], -50],\n  ['control 1', [-60, 0.4, -5, 50], -50], ['control 2', [0, 0.4, -5, 60], 0]],\n [['normal: flat terrain matches plain backtracking', [-70, 0.4, 0, 60], -38.765],\n  ['boundary: slope-facing noon', [0, 0.4, 10, 60], 0],\n  ['boundary: clamp after backtracking', [80, 0.3, -10, 50], -10.0],\n  ['regression: limit applied after backtracking', [-80, 0.4, 0, 75], -15.729],\n  ['regression: limit applied after backtracking (partial repair)', [-70, 0.3, -5, 60], -60],\n  ['control 1', [-80, 0.5, 0, 75], -10.322], ['control 2', [-45, 0.4, 15, 50], -45]]]\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-cross-slope-backtracking-limit-applied-after-backtracking","generated_at":"2026-09-29T14:51:56.910169+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.","root_cause":"The rotation limit is applied to the ideal angle before backtracking instead of to the result.","sha256":"3b9d6b5c13482456176e82f9f82b980adee6ff57e1bd8ffe3e0d8d915deddeff","title":"Cross-axis slope aware backtracking: limit applied after backtracking · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":39.572,"exit_code":1,"observations":[{"actual":-38.765,"check":"normal: flat terrain matches plain backtracking","expected":-38.765,"passed":true},{"actual":0,"check":"boundary: slope-facing noon","expected":0,"passed":true},{"actual":-10.0,"check":"boundary: clamp after backtracking","expected":-10.0,"passed":true},{"actual":-10.322,"check":"regression: limit applied after backtracking","expected":-10.322,"passed":true},{"actual":-60,"check":"regression: limit applied after backtracking (partial repair)","expected":-50,"passed":false},{"actual":-45,"check":"control 1","expected":-45,"passed":true},{"actual":-60,"check":"control 2","expected":-60,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"normal: flat terrain matches plain backtracking\", \"actual\": -38.765, \"expected\": -38.765, \"passed\": true}, {\"check\": \"boundary: slope-facing noon\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"boundary: clamp after backtracking\", \"actual\": -10.0, \"expected\": -10.0, \"passed\": true}, {\"check\": \"regression: limit applied after backtracking\", \"actual\": -10.322, \"expected\": -10.322, \"passed\": true}, {\"check\": \"regression: limit applied after backtracking (partial repair)\", \"actual\": -60, \"expected\": -50, \"passed\": false}, {\"check\": \"control 1\", \"actual\": -45, \"expected\": -45, \"passed\": true}, {\"check\": \"control 2\", \"actual\": -60, \"expected\": -60, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":39.285,"exit_code":1,"observations":[{"actual":-60,"check":"normal: flat terrain matches plain backtracking","expected":-38.765,"passed":false},{"actual":0,"check":"boundary: slope-facing noon","expected":0,"passed":true},{"actual":50,"check":"boundary: clamp after backtracking","expected":-10.0,"passed":false},{"actual":-16.174,"check":"regression: limit applied after backtracking","expected":-10.322,"passed":false},{"actual":-50,"check":"regression: limit applied after backtracking (partial repair)","expected":-50,"passed":true},{"actual":-45,"check":"control 1","expected":-45,"passed":true},{"actual":-60,"check":"control 2","expected":-60,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"normal: flat terrain matches plain backtracking\", \"actual\": -60, \"expected\": -38.765, \"passed\": false}, {\"check\": \"boundary: slope-facing noon\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"boundary: clamp after backtracking\", \"actual\": 50, \"expected\": -10.0, \"passed\": false}, {\"check\": \"regression: limit applied after backtracking\", \"actual\": -16.174, \"expected\": -10.322, \"passed\": false}, {\"check\": \"regression: limit applied after backtracking (partial repair)\", \"actual\": -50, \"expected\": -50, \"passed\": true}, {\"check\": \"control 1\", \"actual\": -45, \"expected\": -45, \"passed\": true}, {\"check\": \"control 2\", \"actual\": -60, \"expected\": -60, \"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."}}