{"abstract":"Mirror elevations are wrong whenever sun and receiver are not aligned.","category":"Solar tracker geometry","checks":7,"contract":"mirror and receiver are [east, north, up] positions in metres. The mirror normal bisects the unit sun vector (east=cos(el)sin(az), north=cos(el)cos(az), up=sin(el)) and the unit vector from the mirror to the receiver. Return [normal azimuth 0..360 clockwise from north, normal elevation], rounded to 3; None when sun_el <= 0; 'invalid' when receiver equals mirror.","evaluation_group":"w2-solar_tracker_geometry-heliostat-bisector","failed_approach":"Halving the sum is only a unit vector when both inputs coincide.","family":"w2-solar_tracker_geometry-heliostat-bisector-bisector-normalisation","id":"FA-93506","implementations":{"attempt":{"sha256":"d2fb72e074493270fd8902e0b3016ccdf13fc2f77d788758c2ef1254a7b60204","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(sun_az, sun_el, mirror, receiver):\n    if sun_el <= 0:\n        return None\n    dx = [receiver[i] - mirror[i] for i in range(3)]\n    d = math.sqrt(sum(v * v for v in dx))\n    if d == 0:\n        return 'invalid'\n    t = [v / d for v in dx]\n    az = math.radians(sun_az)\n    el = math.radians(sun_el)\n    s = [math.cos(el) * math.sin(az), math.cos(el) * math.cos(az), math.sin(el)]\n    h = [s[i] + t[i] for i in range(3)]\n    m = math.sqrt(sum(v * v for v in h))\n    h = [v / 2 for v in h]\n    n_az = math.degrees(math.atan2(h[0], h[1])) % 360\n    n_el = math.degrees(math.asin(h[2]))\n    return [round(n_az, 3), round(n_el, 3)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['boundary: receiver at mirror', [180, 40, [0, 0, 0], [0, 0, 0]], 'invalid'],\n  ['boundary: night', [90, 0, [10, 10, 0], [0, 0, 50]], None],\n  ['regression: bisector normalisation', [270, 60, [6, -1, 1], [0, 5, 0]], [300.29, 28.278]],\n  ['regression: bisector normalisation (partial repair)', [270, 80, [-16, -19, 1], [0, 0, 0]],\n   [31.588, 46.473]],\n  ['control 1', [90, -3, [-12, 43, 1], [0, 0, 0]], None],\n  ['control 2', [180, -3, [-22, 14, 2], [0, 5, 0]], None],\n  ['control 3', [90, 40, [1, -24, 3], [0, -5, 0]], [35.903, 21.798]]],\n [['boundary: receiver at mirror', [180, 40, [0, 0, 0], [0, 0, 0]], 'invalid'],\n  ['boundary: night', [90, 0, [10, 10, 0], [0, 0, 50]], None],\n  ['regression: bisector normalisation', [270, 10, [38, -21, 0], [0, 0, 0]], [284.576, 5.163]],\n  ['regression: bisector normalisation (partial repair)', [90, 10, [31, -7, 0], [-10, 0, 30]],\n   [53.628, 73.122]],\n  ['control 1', [225, -3, [-22, -29, 0], [0, 5, 30]], None],\n  ['control 2', [225, 80, [-26, 5, 3], [10, 5, 0]], [97.999, 45.624]],\n  ['control 3', [225, 80, [-17, -20, 3], [0, 0, 0]], [39.385, 46.716]]],\n [['boundary: receiver at mirror', [180, 40, [0, 0, 0], [0, 0, 0]], 'invalid'],\n  ['boundary: night', [90, 0, [10, 10, 0], [0, 0, 50]], None],\n  ['regression: bisector normalisation', [315, 10, [-37, 26, 0], [0, -5, 60]], [323.691, 69.061]],\n  ['regression: bisector normalisation (partial repair)', [90, 25, [-2, -18, 2], [-10, 5, 0]],\n   [31.59, 17.138]],\n  ['control 1', [90, 10, [-6, -40, 0], [-10, 0, 30]], [48.617, 32.61]],\n  ['control 2', [30, 10, [-44, 5, 1], [-10, 0, 0]], [64.473, 5.033]],\n  ['control 3', [315, 80, [34, -46, 2], [0, 0, 0]], [322.271, 39.038]]],\n [['boundary: receiver at mirror', [180, 40, [0, 0, 0], [0, 0, 0]], 'invalid'],\n  ['boundary: night', [90, 0, [10, 10, 0], [0, 0, 50]], None],\n  ['regression: bisector normalisation', [180, 60, [10, 45, 1], [0, 0, 0]], [188.359, 29.509]],\n  ['regression: bisector normalisation (partial repair)', [315, 10, [22, 3, 2], [-10, 0, 0]],\n   [289.642, 3.557]],\n  ['control 1', [150, 40, [16, -12, 0], [0, 0, 0]], [261.353, 56.729]],\n  ['control 2', [90, 0, [46, -4, 0], [0, -5, 0]], None],\n  ['control 3', [45, 0, [36, -15, 0], [-10, -5, 30]], None]],\n [['boundary: receiver at mirror', [180, 40, [0, 0, 0], [0, 0, 0]], 'invalid'],\n  ['boundary: night', [90, 0, [10, 10, 0], [0, 0, 50]], None],\n  ['regression: bisector normalisation', [200, 10, [41, -47, 2], [0, 0, 30]], [255.744, 31.113]],\n  ['regression: bisector normalisation (partial repair)', [250, 80, [39, -38, 2], [10, 5, 0]],\n   [316.812, 41.896]],\n  ['control 1', [250, -3, [-49, 36, 3], [-10, 5, 60]], None],\n  ['control 2', [180, 60, [10, 45, 1], [0, 0, 0]], [188.359, 29.509]],\n  ['control 3', [315, 10, [22, 3, 2], [-10, 0, 0]], [289.642, 3.557]]]]\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":"2d7cfdcaf541887f190f53a729b239cbf511aad60adb22dccfcf172c16e6be35","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(sun_az, sun_el, mirror, receiver):\n    if sun_el <= 0:\n        return None\n    dx = [receiver[i] - mirror[i] for i in range(3)]\n    d = math.sqrt(sum(v * v for v in dx))\n    if d == 0:\n        return 'invalid'\n    t = [v / d for v in dx]\n    az = math.radians(sun_az)\n    el = math.radians(sun_el)\n    s = [math.cos(el) * math.sin(az), math.cos(el) * math.cos(az), math.sin(el)]\n    h = [s[i] + t[i] for i in range(3)]\n    m = math.sqrt(sum(v * v for v in h))\n    h = h\n    n_az = math.degrees(math.atan2(h[0], h[1])) % 360\n    n_el = math.degrees(math.asin(h[2]))\n    return [round(n_az, 3), round(n_el, 3)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['boundary: receiver at mirror', [180, 40, [0, 0, 0], [0, 0, 0]], 'invalid'],\n  ['boundary: night', [90, 0, [10, 10, 0], [0, 0, 50]], None],\n  ['regression: bisector normalisation', [270, 60, [6, -1, 1], [0, 5, 0]], [300.29, 28.278]],\n  ['regression: bisector normalisation (partial repair)', [270, 80, [-16, -19, 1], [0, 0, 0]],\n   [31.588, 46.473]],\n  ['control 1', [90, -3, [-12, 43, 1], [0, 0, 0]], None],\n  ['control 2', [180, -3, [-22, 14, 2], [0, 5, 0]], None],\n  ['control 3', [90, 40, [1, -24, 3], [0, -5, 0]], [35.903, 21.798]]],\n [['boundary: receiver at mirror', [180, 40, [0, 0, 0], [0, 0, 0]], 'invalid'],\n  ['boundary: night', [90, 0, [10, 10, 0], [0, 0, 50]], None],\n  ['regression: bisector normalisation', [270, 10, [38, -21, 0], [0, 0, 0]], [284.576, 5.163]],\n  ['regression: bisector normalisation (partial repair)', [90, 10, [31, -7, 0], [-10, 0, 30]],\n   [53.628, 73.122]],\n  ['control 1', [225, -3, [-22, -29, 0], [0, 5, 30]], None],\n  ['control 2', [225, 80, [-26, 5, 3], [10, 5, 0]], [97.999, 45.624]],\n  ['control 3', [225, 80, [-17, -20, 3], [0, 0, 0]], [39.385, 46.716]]],\n [['boundary: receiver at mirror', [180, 40, [0, 0, 0], [0, 0, 0]], 'invalid'],\n  ['boundary: night', [90, 0, [10, 10, 0], [0, 0, 50]], None],\n  ['regression: bisector normalisation', [315, 10, [-37, 26, 0], [0, -5, 60]], [323.691, 69.061]],\n  ['regression: bisector normalisation (partial repair)', [90, 25, [-2, -18, 2], [-10, 5, 0]],\n   [31.59, 17.138]],\n  ['control 1', [90, 10, [-6, -40, 0], [-10, 0, 30]], [48.617, 32.61]],\n  ['control 2', [30, 10, [-44, 5, 1], [-10, 0, 0]], [64.473, 5.033]],\n  ['control 3', [315, 80, [34, -46, 2], [0, 0, 0]], [322.271, 39.038]]],\n [['boundary: receiver at mirror', [180, 40, [0, 0, 0], [0, 0, 0]], 'invalid'],\n  ['boundary: night', [90, 0, [10, 10, 0], [0, 0, 50]], None],\n  ['regression: bisector normalisation', [180, 60, [10, 45, 1], [0, 0, 0]], [188.359, 29.509]],\n  ['regression: bisector normalisation (partial repair)', [315, 10, [22, 3, 2], [-10, 0, 0]],\n   [289.642, 3.557]],\n  ['control 1', [150, 40, [16, -12, 0], [0, 0, 0]], [261.353, 56.729]],\n  ['control 2', [90, 0, [46, -4, 0], [0, -5, 0]], None],\n  ['control 3', [45, 0, [36, -15, 0], [-10, -5, 30]], None]],\n [['boundary: receiver at mirror', [180, 40, [0, 0, 0], [0, 0, 0]], 'invalid'],\n  ['boundary: night', [90, 0, [10, 10, 0], [0, 0, 50]], None],\n  ['regression: bisector normalisation', [200, 10, [41, -47, 2], [0, 0, 30]], [255.744, 31.113]],\n  ['regression: bisector normalisation (partial repair)', [250, 80, [39, -38, 2], [10, 5, 0]],\n   [316.812, 41.896]],\n  ['control 1', [250, -3, [-49, 36, 3], [-10, 5, 60]], None],\n  ['control 2', [180, 60, [10, 45, 1], [0, 0, 0]], [188.359, 29.509]],\n  ['control 3', [315, 10, [22, 3, 2], [-10, 0, 0]], [289.642, 3.557]]]]\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":"b74b64b641a9fdbbe19789799af5584eb382765176bd99ebf3d21038c0f0f1cd","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(sun_az, sun_el, mirror, receiver):\n    if sun_el <= 0:\n        return None\n    dx = [receiver[i] - mirror[i] for i in range(3)]\n    d = math.sqrt(sum(v * v for v in dx))\n    if d == 0:\n        return 'invalid'\n    t = [v / d for v in dx]\n    az = math.radians(sun_az)\n    el = math.radians(sun_el)\n    s = [math.cos(el) * math.sin(az), math.cos(el) * math.cos(az), math.sin(el)]\n    h = [s[i] + t[i] for i in range(3)]\n    m = math.sqrt(sum(v * v for v in h))\n    h = [v / m for v in h]\n    n_az = math.degrees(math.atan2(h[0], h[1])) % 360\n    n_el = math.degrees(math.asin(h[2]))\n    return [round(n_az, 3), round(n_el, 3)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['boundary: receiver at mirror', [180, 40, [0, 0, 0], [0, 0, 0]], 'invalid'],\n  ['boundary: night', [90, 0, [10, 10, 0], [0, 0, 50]], None],\n  ['regression: bisector normalisation', [270, 60, [6, -1, 1], [0, 5, 0]], [300.29, 28.278]],\n  ['regression: bisector normalisation (partial repair)', [270, 80, [-16, -19, 1], [0, 0, 0]],\n   [31.588, 46.473]],\n  ['control 1', [90, -3, [-12, 43, 1], [0, 0, 0]], None],\n  ['control 2', [180, -3, [-22, 14, 2], [0, 5, 0]], None],\n  ['control 3', [90, 40, [1, -24, 3], [0, -5, 0]], [35.903, 21.798]]],\n [['boundary: receiver at mirror', [180, 40, [0, 0, 0], [0, 0, 0]], 'invalid'],\n  ['boundary: night', [90, 0, [10, 10, 0], [0, 0, 50]], None],\n  ['regression: bisector normalisation', [270, 10, [38, -21, 0], [0, 0, 0]], [284.576, 5.163]],\n  ['regression: bisector normalisation (partial repair)', [90, 10, [31, -7, 0], [-10, 0, 30]],\n   [53.628, 73.122]],\n  ['control 1', [225, -3, [-22, -29, 0], [0, 5, 30]], None],\n  ['control 2', [225, 80, [-26, 5, 3], [10, 5, 0]], [97.999, 45.624]],\n  ['control 3', [225, 80, [-17, -20, 3], [0, 0, 0]], [39.385, 46.716]]],\n [['boundary: receiver at mirror', [180, 40, [0, 0, 0], [0, 0, 0]], 'invalid'],\n  ['boundary: night', [90, 0, [10, 10, 0], [0, 0, 50]], None],\n  ['regression: bisector normalisation', [315, 10, [-37, 26, 0], [0, -5, 60]], [323.691, 69.061]],\n  ['regression: bisector normalisation (partial repair)', [90, 25, [-2, -18, 2], [-10, 5, 0]],\n   [31.59, 17.138]],\n  ['control 1', [90, 10, [-6, -40, 0], [-10, 0, 30]], [48.617, 32.61]],\n  ['control 2', [30, 10, [-44, 5, 1], [-10, 0, 0]], [64.473, 5.033]],\n  ['control 3', [315, 80, [34, -46, 2], [0, 0, 0]], [322.271, 39.038]]],\n [['boundary: receiver at mirror', [180, 40, [0, 0, 0], [0, 0, 0]], 'invalid'],\n  ['boundary: night', [90, 0, [10, 10, 0], [0, 0, 50]], None],\n  ['regression: bisector normalisation', [180, 60, [10, 45, 1], [0, 0, 0]], [188.359, 29.509]],\n  ['regression: bisector normalisation (partial repair)', [315, 10, [22, 3, 2], [-10, 0, 0]],\n   [289.642, 3.557]],\n  ['control 1', [150, 40, [16, -12, 0], [0, 0, 0]], [261.353, 56.729]],\n  ['control 2', [90, 0, [46, -4, 0], [0, -5, 0]], None],\n  ['control 3', [45, 0, [36, -15, 0], [-10, -5, 30]], None]],\n [['boundary: receiver at mirror', [180, 40, [0, 0, 0], [0, 0, 0]], 'invalid'],\n  ['boundary: night', [90, 0, [10, 10, 0], [0, 0, 50]], None],\n  ['regression: bisector normalisation', [200, 10, [41, -47, 2], [0, 0, 30]], [255.744, 31.113]],\n  ['regression: bisector normalisation (partial repair)', [250, 80, [39, -38, 2], [10, 5, 0]],\n   [316.812, 41.896]],\n  ['control 1', [250, -3, [-49, 36, 3], [-10, 5, 60]], None],\n  ['control 2', [180, 60, [10, 45, 1], [0, 0, 0]], [188.359, 29.509]],\n  ['control 3', [315, 10, [22, 3, 2], [-10, 0, 0]], [289.642, 3.557]]]]\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-heliostat-bisector-bisector-normalisation","generated_at":"2026-09-29T14:51:55.715986+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":"Normalise the bisector by its Euclidean length.","root_cause":"The sum vector is used without normalising it to unit length.","sha256":"2bb80e2c7eb735e3056a364888c007e09882bf7663b0c0d32b73f27b2345f27e","title":"Heliostat mirror normal aiming: bisector normalisation · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":42.987,"exit_code":1,"observations":[{"actual":"invalid","check":"boundary: receiver at mirror","expected":"invalid","passed":true},{"actual":null,"check":"boundary: night","expected":null,"passed":true},{"actual":[300.29,21.993],"check":"regression: bisector normalisation","expected":[300.29,28.278],"passed":false},{"actual":[31.588,28.183],"check":"regression: bisector normalisation (partial repair)","expected":[31.588,46.473],"passed":false},{"actual":null,"check":"control 1","expected":null,"passed":true},{"actual":null,"check":"control 2","expected":null,"passed":true},{"actual":[35.903,14.094],"check":"control 3","expected":[35.903,21.798],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"boundary: receiver at mirror\", \"actual\": \"invalid\", \"expected\": \"invalid\", \"passed\": true}, {\"check\": \"boundary: night\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression: bisector normalisation\", \"actual\": [300.29, 21.993], \"expected\": [300.29, 28.278], \"passed\": false}, {\"check\": \"regression: bisector normalisation (partial repair)\", \"actual\": [31.588, 28.183], \"expected\": [31.588, 46.473], \"passed\": false}, {\"check\": \"control 1\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"control 2\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"control 3\", \"actual\": [35.903, 14.094], \"expected\": [35.903, 21.798], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":40.598,"exit_code":1,"observations":[{"actual":"invalid","check":"boundary: receiver at mirror","expected":"invalid","passed":true},{"actual":null,"check":"boundary: night","expected":null,"passed":true},{"actual":[300.29,48.502],"check":"regression: bisector normalisation","expected":[300.29,28.278],"passed":false},{"actual":[31.588,70.836],"check":"regression: bisector normalisation (partial repair)","expected":[31.588,46.473],"passed":false},{"actual":null,"check":"control 1","expected":null,"passed":true},{"actual":null,"check":"control 2","expected":null,"passed":true},{"actual":[35.903,29.146],"check":"control 3","expected":[35.903,21.798],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"boundary: receiver at mirror\", \"actual\": \"invalid\", \"expected\": \"invalid\", \"passed\": true}, {\"check\": \"boundary: night\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression: bisector normalisation\", \"actual\": [300.29, 48.502], \"expected\": [300.29, 28.278], \"passed\": false}, {\"check\": \"regression: bisector normalisation (partial repair)\", \"actual\": [31.588, 70.836], \"expected\": [31.588, 46.473], \"passed\": false}, {\"check\": \"control 1\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"control 2\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"control 3\", \"actual\": [35.903, 29.146], \"expected\": [35.903, 21.798], \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":40.561,"exit_code":0,"observations":[{"actual":"invalid","check":"boundary: receiver at mirror","expected":"invalid","passed":true},{"actual":null,"check":"boundary: night","expected":null,"passed":true},{"actual":[300.29,28.278],"check":"regression: bisector normalisation","expected":[300.29,28.278],"passed":true},{"actual":[31.588,46.473],"check":"regression: bisector normalisation (partial repair)","expected":[31.588,46.473],"passed":true},{"actual":null,"check":"control 1","expected":null,"passed":true},{"actual":null,"check":"control 2","expected":null,"passed":true},{"actual":[35.903,21.798],"check":"control 3","expected":[35.903,21.798],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"boundary: receiver at mirror\", \"actual\": \"invalid\", \"expected\": \"invalid\", \"passed\": true}, {\"check\": \"boundary: night\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression: bisector normalisation\", \"actual\": [300.29, 28.278], \"expected\": [300.29, 28.278], \"passed\": true}, {\"check\": \"regression: bisector normalisation (partial repair)\", \"actual\": [31.588, 46.473], \"expected\": [31.588, 46.473], \"passed\": true}, {\"check\": \"control 1\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"control 2\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"control 3\", \"actual\": [35.903, 21.798], \"expected\": [35.903, 21.798], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}