{"abstract":"The adapter reports an incorrect projected variance while other fields remain valid.","category":"Astronomical coordinate conventions","checks":6,"contract":"A tangent-plane catalog covariance has variances a,b and covariance c. Axis scale sx,sy includes signed orientation. A 90-degree basis rotation maps (x,y) to (-y,x). A projected RA coordinate supplied factor q converts covariance using a diagonal Jacobian. No confidence-level conversion is implied. Output fields are defined by: scaled_variance_x = d['a']*d['sx']**2; scaled_covariance = d['c']*d['sx']*d['sy']; rotated_covariance = -d['c']; projected_variance = d['a']*d['q']**2; projected_cross_term = d['c']*d['q']; determinant = d['a']*d['b']-d['c']**2","evaluation_group":"astro-catalog-error-ellipse","failed_approach":"A partial convention repair still uses d['a']/d['q']**2","family":"s3-astronomical-coordinate-conventions-catalog-error-ellipse-projected_variance","id":"FA-55246","implementations":{"attempt":{"sha256":"ca06693d84ea35ac7a08a17e383f2d1b40d1423cd9df4a4cef4ac83d2a7364a2","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    return {'scaled_variance_x': d['a']*d['sx']**2, 'scaled_covariance': d['c']*d['sx']*d['sy'], 'rotated_covariance': -d['c'], 'projected_variance': d['a']/d['q']**2, 'projected_cross_term': d['c']*d['q'], 'determinant': d['a']*d['b']-d['c']**2}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = {1: [({'a': 9, 'b': 16, 'c': 3, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 36, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 36, 'projected_cross_term': 6, 'determinant': 135}), ({'a': 9, 'b': 16, 'c': 3, 'sx': 1, 'sy': 1, 'q': 2}, {'scaled_variance_x': 9, 'scaled_covariance': 3, 'rotated_covariance': -3, 'projected_variance': 36, 'projected_cross_term': 6, 'determinant': 135}), ({'a': 9, 'b': 16, 'c': 0, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 36, 'scaled_covariance': 0, 'rotated_covariance': 0, 'projected_variance': 36, 'projected_cross_term': 0, 'determinant': 144}), ({'a': 9, 'b': 16, 'c': 3, 'sx': -2, 'sy': 3, 'q': 2}, {'scaled_variance_x': 36, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 36, 'projected_cross_term': 6, 'determinant': 135}), ({'a': 9, 'b': 16, 'c': 3, 'sx': 2, 'sy': -3, 'q': 1}, {'scaled_variance_x': 36, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 9, 'projected_cross_term': 3, 'determinant': 135}), ({'a': 4, 'b': 25, 'c': -2, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 16, 'scaled_covariance': 12, 'rotated_covariance': 2, 'projected_variance': 16, 'projected_cross_term': -4, 'determinant': 96})], 2: [({'a': 10, 'b': 16, 'c': 3, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 40, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 40, 'projected_cross_term': 6, 'determinant': 151}), ({'a': 10, 'b': 16, 'c': 3, 'sx': 1, 'sy': 1, 'q': 2}, {'scaled_variance_x': 10, 'scaled_covariance': 3, 'rotated_covariance': -3, 'projected_variance': 40, 'projected_cross_term': 6, 'determinant': 151}), ({'a': 10, 'b': 16, 'c': 0, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 40, 'scaled_covariance': 0, 'rotated_covariance': 0, 'projected_variance': 40, 'projected_cross_term': 0, 'determinant': 160}), ({'a': 10, 'b': 16, 'c': 3, 'sx': -2, 'sy': 3, 'q': 2}, {'scaled_variance_x': 40, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 40, 'projected_cross_term': 6, 'determinant': 151}), ({'a': 10, 'b': 16, 'c': 3, 'sx': 2, 'sy': -3, 'q': 1}, {'scaled_variance_x': 40, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 10, 'projected_cross_term': 3, 'determinant': 151}), ({'a': 5, 'b': 25, 'c': -2, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 20, 'scaled_covariance': 12, 'rotated_covariance': 2, 'projected_variance': 20, 'projected_cross_term': -4, 'determinant': 121})], 3: [({'a': 11, 'b': 16, 'c': 3, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 44, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 44, 'projected_cross_term': 6, 'determinant': 167}), ({'a': 11, 'b': 16, 'c': 3, 'sx': 1, 'sy': 1, 'q': 2}, {'scaled_variance_x': 11, 'scaled_covariance': 3, 'rotated_covariance': -3, 'projected_variance': 44, 'projected_cross_term': 6, 'determinant': 167}), ({'a': 11, 'b': 16, 'c': 0, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 44, 'scaled_covariance': 0, 'rotated_covariance': 0, 'projected_variance': 44, 'projected_cross_term': 0, 'determinant': 176}), ({'a': 11, 'b': 16, 'c': 3, 'sx': -2, 'sy': 3, 'q': 2}, {'scaled_variance_x': 44, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 44, 'projected_cross_term': 6, 'determinant': 167}), ({'a': 11, 'b': 16, 'c': 3, 'sx': 2, 'sy': -3, 'q': 1}, {'scaled_variance_x': 44, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 11, 'projected_cross_term': 3, 'determinant': 167}), ({'a': 6, 'b': 25, 'c': -2, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 24, 'scaled_covariance': 12, 'rotated_covariance': 2, 'projected_variance': 24, 'projected_cross_term': -4, 'determinant': 146})], 4: [({'a': 12, 'b': 16, 'c': 3, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 48, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 48, 'projected_cross_term': 6, 'determinant': 183}), ({'a': 12, 'b': 16, 'c': 3, 'sx': 1, 'sy': 1, 'q': 2}, {'scaled_variance_x': 12, 'scaled_covariance': 3, 'rotated_covariance': -3, 'projected_variance': 48, 'projected_cross_term': 6, 'determinant': 183}), ({'a': 12, 'b': 16, 'c': 0, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 48, 'scaled_covariance': 0, 'rotated_covariance': 0, 'projected_variance': 48, 'projected_cross_term': 0, 'determinant': 192}), ({'a': 12, 'b': 16, 'c': 3, 'sx': -2, 'sy': 3, 'q': 2}, {'scaled_variance_x': 48, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 48, 'projected_cross_term': 6, 'determinant': 183}), ({'a': 12, 'b': 16, 'c': 3, 'sx': 2, 'sy': -3, 'q': 1}, {'scaled_variance_x': 48, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 12, 'projected_cross_term': 3, 'determinant': 183}), ({'a': 7, 'b': 25, 'c': -2, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 28, 'scaled_covariance': 12, 'rotated_covariance': 2, 'projected_variance': 28, 'projected_cross_term': -4, 'determinant': 171})], 5: [({'a': 13, 'b': 16, 'c': 3, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 52, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 52, 'projected_cross_term': 6, 'determinant': 199}), ({'a': 13, 'b': 16, 'c': 3, 'sx': 1, 'sy': 1, 'q': 2}, {'scaled_variance_x': 13, 'scaled_covariance': 3, 'rotated_covariance': -3, 'projected_variance': 52, 'projected_cross_term': 6, 'determinant': 199}), ({'a': 13, 'b': 16, 'c': 0, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 52, 'scaled_covariance': 0, 'rotated_covariance': 0, 'projected_variance': 52, 'projected_cross_term': 0, 'determinant': 208}), ({'a': 13, 'b': 16, 'c': 3, 'sx': -2, 'sy': 3, 'q': 2}, {'scaled_variance_x': 52, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 52, 'projected_cross_term': 6, 'determinant': 199}), ({'a': 13, 'b': 16, 'c': 3, 'sx': 2, 'sy': -3, 'q': 1}, {'scaled_variance_x': 52, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 13, 'projected_cross_term': 3, 'determinant': 199}), ({'a': 8, 'b': 25, 'c': -2, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 32, 'scaled_covariance': 12, 'rotated_covariance': 2, 'projected_variance': 32, 'projected_cross_term': -4, 'determinant': 196})]}\nfor i, (record, expected) in enumerate(fixtures[N]):\n    check('astronomical fixture %s' % i, solve(record), 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":"976fac8d2c9d3a34298b7d57e9af07cf630c4407b7f3783dfc7d1ba6d5bcd7d4","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    return {'scaled_variance_x': d['a']*d['sx']**2, 'scaled_covariance': d['c']*d['sx']*d['sy'], 'rotated_covariance': -d['c'], 'projected_variance': d['a']*d['q'], 'projected_cross_term': d['c']*d['q'], 'determinant': d['a']*d['b']-d['c']**2}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = {1: [({'a': 9, 'b': 16, 'c': 3, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 36, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 36, 'projected_cross_term': 6, 'determinant': 135}), ({'a': 9, 'b': 16, 'c': 3, 'sx': 1, 'sy': 1, 'q': 2}, {'scaled_variance_x': 9, 'scaled_covariance': 3, 'rotated_covariance': -3, 'projected_variance': 36, 'projected_cross_term': 6, 'determinant': 135}), ({'a': 9, 'b': 16, 'c': 0, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 36, 'scaled_covariance': 0, 'rotated_covariance': 0, 'projected_variance': 36, 'projected_cross_term': 0, 'determinant': 144}), ({'a': 9, 'b': 16, 'c': 3, 'sx': -2, 'sy': 3, 'q': 2}, {'scaled_variance_x': 36, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 36, 'projected_cross_term': 6, 'determinant': 135}), ({'a': 9, 'b': 16, 'c': 3, 'sx': 2, 'sy': -3, 'q': 1}, {'scaled_variance_x': 36, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 9, 'projected_cross_term': 3, 'determinant': 135}), ({'a': 4, 'b': 25, 'c': -2, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 16, 'scaled_covariance': 12, 'rotated_covariance': 2, 'projected_variance': 16, 'projected_cross_term': -4, 'determinant': 96})], 2: [({'a': 10, 'b': 16, 'c': 3, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 40, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 40, 'projected_cross_term': 6, 'determinant': 151}), ({'a': 10, 'b': 16, 'c': 3, 'sx': 1, 'sy': 1, 'q': 2}, {'scaled_variance_x': 10, 'scaled_covariance': 3, 'rotated_covariance': -3, 'projected_variance': 40, 'projected_cross_term': 6, 'determinant': 151}), ({'a': 10, 'b': 16, 'c': 0, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 40, 'scaled_covariance': 0, 'rotated_covariance': 0, 'projected_variance': 40, 'projected_cross_term': 0, 'determinant': 160}), ({'a': 10, 'b': 16, 'c': 3, 'sx': -2, 'sy': 3, 'q': 2}, {'scaled_variance_x': 40, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 40, 'projected_cross_term': 6, 'determinant': 151}), ({'a': 10, 'b': 16, 'c': 3, 'sx': 2, 'sy': -3, 'q': 1}, {'scaled_variance_x': 40, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 10, 'projected_cross_term': 3, 'determinant': 151}), ({'a': 5, 'b': 25, 'c': -2, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 20, 'scaled_covariance': 12, 'rotated_covariance': 2, 'projected_variance': 20, 'projected_cross_term': -4, 'determinant': 121})], 3: [({'a': 11, 'b': 16, 'c': 3, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 44, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 44, 'projected_cross_term': 6, 'determinant': 167}), ({'a': 11, 'b': 16, 'c': 3, 'sx': 1, 'sy': 1, 'q': 2}, {'scaled_variance_x': 11, 'scaled_covariance': 3, 'rotated_covariance': -3, 'projected_variance': 44, 'projected_cross_term': 6, 'determinant': 167}), ({'a': 11, 'b': 16, 'c': 0, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 44, 'scaled_covariance': 0, 'rotated_covariance': 0, 'projected_variance': 44, 'projected_cross_term': 0, 'determinant': 176}), ({'a': 11, 'b': 16, 'c': 3, 'sx': -2, 'sy': 3, 'q': 2}, {'scaled_variance_x': 44, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 44, 'projected_cross_term': 6, 'determinant': 167}), ({'a': 11, 'b': 16, 'c': 3, 'sx': 2, 'sy': -3, 'q': 1}, {'scaled_variance_x': 44, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 11, 'projected_cross_term': 3, 'determinant': 167}), ({'a': 6, 'b': 25, 'c': -2, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 24, 'scaled_covariance': 12, 'rotated_covariance': 2, 'projected_variance': 24, 'projected_cross_term': -4, 'determinant': 146})], 4: [({'a': 12, 'b': 16, 'c': 3, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 48, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 48, 'projected_cross_term': 6, 'determinant': 183}), ({'a': 12, 'b': 16, 'c': 3, 'sx': 1, 'sy': 1, 'q': 2}, {'scaled_variance_x': 12, 'scaled_covariance': 3, 'rotated_covariance': -3, 'projected_variance': 48, 'projected_cross_term': 6, 'determinant': 183}), ({'a': 12, 'b': 16, 'c': 0, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 48, 'scaled_covariance': 0, 'rotated_covariance': 0, 'projected_variance': 48, 'projected_cross_term': 0, 'determinant': 192}), ({'a': 12, 'b': 16, 'c': 3, 'sx': -2, 'sy': 3, 'q': 2}, {'scaled_variance_x': 48, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 48, 'projected_cross_term': 6, 'determinant': 183}), ({'a': 12, 'b': 16, 'c': 3, 'sx': 2, 'sy': -3, 'q': 1}, {'scaled_variance_x': 48, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 12, 'projected_cross_term': 3, 'determinant': 183}), ({'a': 7, 'b': 25, 'c': -2, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 28, 'scaled_covariance': 12, 'rotated_covariance': 2, 'projected_variance': 28, 'projected_cross_term': -4, 'determinant': 171})], 5: [({'a': 13, 'b': 16, 'c': 3, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 52, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 52, 'projected_cross_term': 6, 'determinant': 199}), ({'a': 13, 'b': 16, 'c': 3, 'sx': 1, 'sy': 1, 'q': 2}, {'scaled_variance_x': 13, 'scaled_covariance': 3, 'rotated_covariance': -3, 'projected_variance': 52, 'projected_cross_term': 6, 'determinant': 199}), ({'a': 13, 'b': 16, 'c': 0, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 52, 'scaled_covariance': 0, 'rotated_covariance': 0, 'projected_variance': 52, 'projected_cross_term': 0, 'determinant': 208}), ({'a': 13, 'b': 16, 'c': 3, 'sx': -2, 'sy': 3, 'q': 2}, {'scaled_variance_x': 52, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 52, 'projected_cross_term': 6, 'determinant': 199}), ({'a': 13, 'b': 16, 'c': 3, 'sx': 2, 'sy': -3, 'q': 1}, {'scaled_variance_x': 52, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 13, 'projected_cross_term': 3, 'determinant': 199}), ({'a': 8, 'b': 25, 'c': -2, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 32, 'scaled_covariance': 12, 'rotated_covariance': 2, 'projected_variance': 32, 'projected_cross_term': -4, 'determinant': 196})]}\nfor i, (record, expected) in enumerate(fixtures[N]):\n    check('astronomical fixture %s' % i, solve(record), 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":"30f9cef590d4ff4d2c51d56855b322849b12831759c4cba531ae0ecb8efa3dfd","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    return {'scaled_variance_x': d['a']*d['sx']**2, 'scaled_covariance': d['c']*d['sx']*d['sy'], 'rotated_covariance': -d['c'], 'projected_variance': d['a']*d['q']**2, 'projected_cross_term': d['c']*d['q'], 'determinant': d['a']*d['b']-d['c']**2}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = {1: [({'a': 9, 'b': 16, 'c': 3, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 36, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 36, 'projected_cross_term': 6, 'determinant': 135}), ({'a': 9, 'b': 16, 'c': 3, 'sx': 1, 'sy': 1, 'q': 2}, {'scaled_variance_x': 9, 'scaled_covariance': 3, 'rotated_covariance': -3, 'projected_variance': 36, 'projected_cross_term': 6, 'determinant': 135}), ({'a': 9, 'b': 16, 'c': 0, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 36, 'scaled_covariance': 0, 'rotated_covariance': 0, 'projected_variance': 36, 'projected_cross_term': 0, 'determinant': 144}), ({'a': 9, 'b': 16, 'c': 3, 'sx': -2, 'sy': 3, 'q': 2}, {'scaled_variance_x': 36, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 36, 'projected_cross_term': 6, 'determinant': 135}), ({'a': 9, 'b': 16, 'c': 3, 'sx': 2, 'sy': -3, 'q': 1}, {'scaled_variance_x': 36, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 9, 'projected_cross_term': 3, 'determinant': 135}), ({'a': 4, 'b': 25, 'c': -2, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 16, 'scaled_covariance': 12, 'rotated_covariance': 2, 'projected_variance': 16, 'projected_cross_term': -4, 'determinant': 96})], 2: [({'a': 10, 'b': 16, 'c': 3, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 40, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 40, 'projected_cross_term': 6, 'determinant': 151}), ({'a': 10, 'b': 16, 'c': 3, 'sx': 1, 'sy': 1, 'q': 2}, {'scaled_variance_x': 10, 'scaled_covariance': 3, 'rotated_covariance': -3, 'projected_variance': 40, 'projected_cross_term': 6, 'determinant': 151}), ({'a': 10, 'b': 16, 'c': 0, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 40, 'scaled_covariance': 0, 'rotated_covariance': 0, 'projected_variance': 40, 'projected_cross_term': 0, 'determinant': 160}), ({'a': 10, 'b': 16, 'c': 3, 'sx': -2, 'sy': 3, 'q': 2}, {'scaled_variance_x': 40, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 40, 'projected_cross_term': 6, 'determinant': 151}), ({'a': 10, 'b': 16, 'c': 3, 'sx': 2, 'sy': -3, 'q': 1}, {'scaled_variance_x': 40, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 10, 'projected_cross_term': 3, 'determinant': 151}), ({'a': 5, 'b': 25, 'c': -2, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 20, 'scaled_covariance': 12, 'rotated_covariance': 2, 'projected_variance': 20, 'projected_cross_term': -4, 'determinant': 121})], 3: [({'a': 11, 'b': 16, 'c': 3, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 44, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 44, 'projected_cross_term': 6, 'determinant': 167}), ({'a': 11, 'b': 16, 'c': 3, 'sx': 1, 'sy': 1, 'q': 2}, {'scaled_variance_x': 11, 'scaled_covariance': 3, 'rotated_covariance': -3, 'projected_variance': 44, 'projected_cross_term': 6, 'determinant': 167}), ({'a': 11, 'b': 16, 'c': 0, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 44, 'scaled_covariance': 0, 'rotated_covariance': 0, 'projected_variance': 44, 'projected_cross_term': 0, 'determinant': 176}), ({'a': 11, 'b': 16, 'c': 3, 'sx': -2, 'sy': 3, 'q': 2}, {'scaled_variance_x': 44, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 44, 'projected_cross_term': 6, 'determinant': 167}), ({'a': 11, 'b': 16, 'c': 3, 'sx': 2, 'sy': -3, 'q': 1}, {'scaled_variance_x': 44, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 11, 'projected_cross_term': 3, 'determinant': 167}), ({'a': 6, 'b': 25, 'c': -2, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 24, 'scaled_covariance': 12, 'rotated_covariance': 2, 'projected_variance': 24, 'projected_cross_term': -4, 'determinant': 146})], 4: [({'a': 12, 'b': 16, 'c': 3, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 48, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 48, 'projected_cross_term': 6, 'determinant': 183}), ({'a': 12, 'b': 16, 'c': 3, 'sx': 1, 'sy': 1, 'q': 2}, {'scaled_variance_x': 12, 'scaled_covariance': 3, 'rotated_covariance': -3, 'projected_variance': 48, 'projected_cross_term': 6, 'determinant': 183}), ({'a': 12, 'b': 16, 'c': 0, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 48, 'scaled_covariance': 0, 'rotated_covariance': 0, 'projected_variance': 48, 'projected_cross_term': 0, 'determinant': 192}), ({'a': 12, 'b': 16, 'c': 3, 'sx': -2, 'sy': 3, 'q': 2}, {'scaled_variance_x': 48, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 48, 'projected_cross_term': 6, 'determinant': 183}), ({'a': 12, 'b': 16, 'c': 3, 'sx': 2, 'sy': -3, 'q': 1}, {'scaled_variance_x': 48, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 12, 'projected_cross_term': 3, 'determinant': 183}), ({'a': 7, 'b': 25, 'c': -2, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 28, 'scaled_covariance': 12, 'rotated_covariance': 2, 'projected_variance': 28, 'projected_cross_term': -4, 'determinant': 171})], 5: [({'a': 13, 'b': 16, 'c': 3, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 52, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 52, 'projected_cross_term': 6, 'determinant': 199}), ({'a': 13, 'b': 16, 'c': 3, 'sx': 1, 'sy': 1, 'q': 2}, {'scaled_variance_x': 13, 'scaled_covariance': 3, 'rotated_covariance': -3, 'projected_variance': 52, 'projected_cross_term': 6, 'determinant': 199}), ({'a': 13, 'b': 16, 'c': 0, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 52, 'scaled_covariance': 0, 'rotated_covariance': 0, 'projected_variance': 52, 'projected_cross_term': 0, 'determinant': 208}), ({'a': 13, 'b': 16, 'c': 3, 'sx': -2, 'sy': 3, 'q': 2}, {'scaled_variance_x': 52, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 52, 'projected_cross_term': 6, 'determinant': 199}), ({'a': 13, 'b': 16, 'c': 3, 'sx': 2, 'sy': -3, 'q': 1}, {'scaled_variance_x': 52, 'scaled_covariance': -18, 'rotated_covariance': -3, 'projected_variance': 13, 'projected_cross_term': 3, 'determinant': 199}), ({'a': 8, 'b': 25, 'c': -2, 'sx': 2, 'sy': -3, 'q': 2}, {'scaled_variance_x': 32, 'scaled_covariance': 12, 'rotated_covariance': 2, 'projected_variance': 32, 'projected_cross_term': -4, 'determinant': 196})]}\nfor i, (record, expected) in enumerate(fixtures[N]):\n    check('astronomical fixture %s' % i, solve(record), 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":"Explicitly stipulated finite algebraic adapter; no standards conformance, physical accuracy, or production-library claim. Inputs are the documented finite valid model domain. 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":"s3-astronomical-coordinate-conventions-catalog-error-ellipse-projected_variance","generated_at":"2026-09-29T14:45:55.882689+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Catalog, detector, sky-coordinate, and spectroscopy adapters must preserve the association between numeric coordinates and their declared reference conventions.","repair":"Preserve the declared model convention at this site: d['a']*d['q']**2","root_cause":"Projected RA variance uses a linear rather than squared Jacobian. Faulty expression: d['a']*d['q']","sha256":"f780e86eb442d9fe189b54a9cf27fff255d210fe2efc8808a1145d7c6263ba7e","title":"Catalog error ellipse: Projected RA variance uses a linear rather than squared Jacobian · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":41.585,"exit_code":1,"observations":[{"actual":{"determinant":135,"projected_cross_term":6,"projected_variance":2.25,"rotated_covariance":-3,"scaled_covariance":-18,"scaled_variance_x":36},"check":"astronomical fixture 0","expected":{"determinant":135,"projected_cross_term":6,"projected_variance":36,"rotated_covariance":-3,"scaled_covariance":-18,"scaled_variance_x":36},"passed":false},{"actual":{"determinant":135,"projected_cross_term":6,"projected_variance":2.25,"rotated_covariance":-3,"scaled_covariance":3,"scaled_variance_x":9},"check":"astronomical fixture 1","expected":{"determinant":135,"projected_cross_term":6,"projected_variance":36,"rotated_covariance":-3,"scaled_covariance":3,"scaled_variance_x":9},"passed":false},{"actual":{"determinant":144,"projected_cross_term":0,"projected_variance":2.25,"rotated_covariance":0,"scaled_covariance":0,"scaled_variance_x":36},"check":"astronomical fixture 2","expected":{"determinant":144,"projected_cross_term":0,"projected_variance":36,"rotated_covariance":0,"scaled_covariance":0,"scaled_variance_x":36},"passed":false},{"actual":{"determinant":135,"projected_cross_term":6,"projected_variance":2.25,"rotated_covariance":-3,"scaled_covariance":-18,"scaled_variance_x":36},"check":"astronomical fixture 3","expected":{"determinant":135,"projected_cross_term":6,"projected_variance":36,"rotated_covariance":-3,"scaled_covariance":-18,"scaled_variance_x":36},"passed":false},{"actual":{"determinant":135,"projected_cross_term":3,"projected_variance":9.0,"rotated_covariance":-3,"scaled_covariance":-18,"scaled_variance_x":36},"check":"astronomical fixture 4","expected":{"determinant":135,"projected_cross_term":3,"projected_variance":9,"rotated_covariance":-3,"scaled_covariance":-18,"scaled_variance_x":36},"passed":true},{"actual":{"determinant":96,"projected_cross_term":-4,"projected_variance":1.0,"rotated_covariance":2,"scaled_covariance":12,"scaled_variance_x":16},"check":"astronomical fixture 5","expected":{"determinant":96,"projected_cross_term":-4,"projected_variance":16,"rotated_covariance":2,"scaled_covariance":12,"scaled_variance_x":16},"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"astronomical fixture 0\", \"actual\": {\"scaled_variance_x\": 36, \"scaled_covariance\": -18, \"rotated_covariance\": -3, \"projected_variance\": 2.25, \"projected_cross_term\": 6, \"determinant\": 135}, \"expected\": {\"scaled_variance_x\": 36, \"scaled_covariance\": -18, \"rotated_covariance\": -3, \"projected_variance\": 36, \"projected_cross_term\": 6, \"determinant\": 135}, \"passed\": false}, {\"check\": \"astronomical fixture 1\", \"actual\": {\"scaled_variance_x\": 9, \"scaled_covariance\": 3, \"rotated_covariance\": -3, \"projected_variance\": 2.25, \"projected_cross_term\": 6, \"determinant\": 135}, \"expected\": {\"scaled_variance_x\": 9, \"scaled_covariance\": 3, \"rotated_covariance\": -3, \"projected_variance\": 36, \"projected_cross_term\": 6, \"determinant\": 135}, \"passed\": false}, {\"check\": \"astronomical fixture 2\", \"actual\": {\"scaled_variance_x\": 36, \"scaled_covariance\": 0, \"rotated_covariance\": 0, \"projected_variance\": 2.25, \"projected_cross_term\": 0, \"determinant\": 144}, \"expected\": {\"scaled_variance_x\": 36, \"scaled_covariance\": 0, \"rotated_covariance\": 0, \"projected_variance\": 36, \"projected_cross_term\": 0, \"determinant\": 144}, \"passed\": false}, {\"check\": \"astronomical fixture 3\", \"actual\": {\"scaled_variance_x\": 36, \"scaled_covariance\": -18, \"rotated_covariance\": -3, \"projected_variance\": 2.25, \"projected_cross_term\": 6, \"determinant\": 135}, \"expected\": {\"scaled_variance_x\": 36, \"scaled_covariance\": -18, \"rotated_covariance\": -3, \"projected_variance\": 36, \"projected_cross_term\": 6, \"determinant\": 135}, \"passed\": false}, {\"check\": \"astronomical fixture 4\", \"actual\": {\"scaled_variance_x\": 36, \"scaled_covariance\": -18, \"rotated_covariance\": -3, \"projected_variance\": 9.0, \"projected_cross_term\": 3, \"determinant\": 135}, \"expected\": {\"scaled_variance_x\": 36, \"scaled_covariance\": -18, \"rotated_covariance\": -3, \"projected_variance\": 9, \"projected_cross_term\": 3, \"determinant\": 135}, \"passed\": true}, {\"check\": \"astronomical fixture 5\", \"actual\": {\"scaled_variance_x\": 16, \"scaled_covariance\": 12, \"rotated_covariance\": 2, \"projected_variance\": 1.0, \"projected_cross_term\": -4, \"determinant\": 96}, \"expected\": {\"scaled_variance_x\": 16, \"scaled_covariance\": 12, \"rotated_covariance\": 2, \"projected_variance\": 16, \"projected_cross_term\": -4, \"determinant\": 96}, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":43.431,"exit_code":1,"observations":[{"actual":{"determinant":135,"projected_cross_term":6,"projected_variance":18,"rotated_covariance":-3,"scaled_covariance":-18,"scaled_variance_x":36},"check":"astronomical fixture 0","expected":{"determinant":135,"projected_cross_term":6,"projected_variance":36,"rotated_covariance":-3,"scaled_covariance":-18,"scaled_variance_x":36},"passed":false},{"actual":{"determinant":135,"projected_cross_term":6,"projected_variance":18,"rotated_covariance":-3,"scaled_covariance":3,"scaled_variance_x":9},"check":"astronomical fixture 1","expected":{"determinant":135,"projected_cross_term":6,"projected_variance":36,"rotated_covariance":-3,"scaled_covariance":3,"scaled_variance_x":9},"passed":false},{"actual":{"determinant":144,"projected_cross_term":0,"projected_variance":18,"rotated_covariance":0,"scaled_covariance":0,"scaled_variance_x":36},"check":"astronomical fixture 2","expected":{"determinant":144,"projected_cross_term":0,"projected_variance":36,"rotated_covariance":0,"scaled_covariance":0,"scaled_variance_x":36},"passed":false},{"actual":{"determinant":135,"projected_cross_term":6,"projected_variance":18,"rotated_covariance":-3,"scaled_covariance":-18,"scaled_variance_x":36},"check":"astronomical fixture 3","expected":{"determinant":135,"projected_cross_term":6,"projected_variance":36,"rotated_covariance":-3,"scaled_covariance":-18,"scaled_variance_x":36},"passed":false},{"actual":{"determinant":135,"projected_cross_term":3,"projected_variance":9,"rotated_covariance":-3,"scaled_covariance":-18,"scaled_variance_x":36},"check":"astronomical fixture 4","expected":{"determinant":135,"projected_cross_term":3,"projected_variance":9,"rotated_covariance":-3,"scaled_covariance":-18,"scaled_variance_x":36},"passed":true},{"actual":{"determinant":96,"projected_cross_term":-4,"projected_variance":8,"rotated_covariance":2,"scaled_covariance":12,"scaled_variance_x":16},"check":"astronomical fixture 5","expected":{"determinant":96,"projected_cross_term":-4,"projected_variance":16,"rotated_covariance":2,"scaled_covariance":12,"scaled_variance_x":16},"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"astronomical fixture 0\", \"actual\": {\"scaled_variance_x\": 36, \"scaled_covariance\": -18, \"rotated_covariance\": -3, \"projected_variance\": 18, \"projected_cross_term\": 6, \"determinant\": 135}, \"expected\": {\"scaled_variance_x\": 36, \"scaled_covariance\": -18, \"rotated_covariance\": -3, \"projected_variance\": 36, \"projected_cross_term\": 6, \"determinant\": 135}, \"passed\": false}, {\"check\": \"astronomical fixture 1\", \"actual\": {\"scaled_variance_x\": 9, \"scaled_covariance\": 3, \"rotated_covariance\": -3, \"projected_variance\": 18, \"projected_cross_term\": 6, \"determinant\": 135}, \"expected\": {\"scaled_variance_x\": 9, \"scaled_covariance\": 3, \"rotated_covariance\": -3, \"projected_variance\": 36, \"projected_cross_term\": 6, \"determinant\": 135}, \"passed\": false}, {\"check\": \"astronomical fixture 2\", \"actual\": {\"scaled_variance_x\": 36, \"scaled_covariance\": 0, \"rotated_covariance\": 0, \"projected_variance\": 18, \"projected_cross_term\": 0, \"determinant\": 144}, \"expected\": {\"scaled_variance_x\": 36, \"scaled_covariance\": 0, \"rotated_covariance\": 0, \"projected_variance\": 36, \"projected_cross_term\": 0, \"determinant\": 144}, \"passed\": false}, {\"check\": \"astronomical fixture 3\", \"actual\": {\"scaled_variance_x\": 36, \"scaled_covariance\": -18, \"rotated_covariance\": -3, \"projected_variance\": 18, \"projected_cross_term\": 6, \"determinant\": 135}, \"expected\": {\"scaled_variance_x\": 36, \"scaled_covariance\": -18, \"rotated_covariance\": -3, \"projected_variance\": 36, \"projected_cross_term\": 6, \"determinant\": 135}, \"passed\": false}, {\"check\": \"astronomical fixture 4\", \"actual\": {\"scaled_variance_x\": 36, \"scaled_covariance\": -18, \"rotated_covariance\": -3, \"projected_variance\": 9, \"projected_cross_term\": 3, \"determinant\": 135}, \"expected\": {\"scaled_variance_x\": 36, \"scaled_covariance\": -18, \"rotated_covariance\": -3, \"projected_variance\": 9, \"projected_cross_term\": 3, \"determinant\": 135}, \"passed\": true}, {\"check\": \"astronomical fixture 5\", \"actual\": {\"scaled_variance_x\": 16, \"scaled_covariance\": 12, \"rotated_covariance\": 2, \"projected_variance\": 8, \"projected_cross_term\": -4, \"determinant\": 96}, \"expected\": {\"scaled_variance_x\": 16, \"scaled_covariance\": 12, \"rotated_covariance\": 2, \"projected_variance\": 16, \"projected_cross_term\": -4, \"determinant\": 96}, \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":45.316,"exit_code":0,"observations":[{"actual":{"determinant":135,"projected_cross_term":6,"projected_variance":36,"rotated_covariance":-3,"scaled_covariance":-18,"scaled_variance_x":36},"check":"astronomical fixture 0","expected":{"determinant":135,"projected_cross_term":6,"projected_variance":36,"rotated_covariance":-3,"scaled_covariance":-18,"scaled_variance_x":36},"passed":true},{"actual":{"determinant":135,"projected_cross_term":6,"projected_variance":36,"rotated_covariance":-3,"scaled_covariance":3,"scaled_variance_x":9},"check":"astronomical fixture 1","expected":{"determinant":135,"projected_cross_term":6,"projected_variance":36,"rotated_covariance":-3,"scaled_covariance":3,"scaled_variance_x":9},"passed":true},{"actual":{"determinant":144,"projected_cross_term":0,"projected_variance":36,"rotated_covariance":0,"scaled_covariance":0,"scaled_variance_x":36},"check":"astronomical fixture 2","expected":{"determinant":144,"projected_cross_term":0,"projected_variance":36,"rotated_covariance":0,"scaled_covariance":0,"scaled_variance_x":36},"passed":true},{"actual":{"determinant":135,"projected_cross_term":6,"projected_variance":36,"rotated_covariance":-3,"scaled_covariance":-18,"scaled_variance_x":36},"check":"astronomical fixture 3","expected":{"determinant":135,"projected_cross_term":6,"projected_variance":36,"rotated_covariance":-3,"scaled_covariance":-18,"scaled_variance_x":36},"passed":true},{"actual":{"determinant":135,"projected_cross_term":3,"projected_variance":9,"rotated_covariance":-3,"scaled_covariance":-18,"scaled_variance_x":36},"check":"astronomical fixture 4","expected":{"determinant":135,"projected_cross_term":3,"projected_variance":9,"rotated_covariance":-3,"scaled_covariance":-18,"scaled_variance_x":36},"passed":true},{"actual":{"determinant":96,"projected_cross_term":-4,"projected_variance":16,"rotated_covariance":2,"scaled_covariance":12,"scaled_variance_x":16},"check":"astronomical fixture 5","expected":{"determinant":96,"projected_cross_term":-4,"projected_variance":16,"rotated_covariance":2,"scaled_covariance":12,"scaled_variance_x":16},"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"astronomical fixture 0\", \"actual\": {\"scaled_variance_x\": 36, \"scaled_covariance\": -18, \"rotated_covariance\": -3, \"projected_variance\": 36, \"projected_cross_term\": 6, \"determinant\": 135}, \"expected\": {\"scaled_variance_x\": 36, \"scaled_covariance\": -18, \"rotated_covariance\": -3, \"projected_variance\": 36, \"projected_cross_term\": 6, \"determinant\": 135}, \"passed\": true}, {\"check\": \"astronomical fixture 1\", \"actual\": {\"scaled_variance_x\": 9, \"scaled_covariance\": 3, \"rotated_covariance\": -3, \"projected_variance\": 36, \"projected_cross_term\": 6, \"determinant\": 135}, \"expected\": {\"scaled_variance_x\": 9, \"scaled_covariance\": 3, \"rotated_covariance\": -3, \"projected_variance\": 36, \"projected_cross_term\": 6, \"determinant\": 135}, \"passed\": true}, {\"check\": \"astronomical fixture 2\", \"actual\": {\"scaled_variance_x\": 36, \"scaled_covariance\": 0, \"rotated_covariance\": 0, \"projected_variance\": 36, \"projected_cross_term\": 0, \"determinant\": 144}, \"expected\": {\"scaled_variance_x\": 36, \"scaled_covariance\": 0, \"rotated_covariance\": 0, \"projected_variance\": 36, \"projected_cross_term\": 0, \"determinant\": 144}, \"passed\": true}, {\"check\": \"astronomical fixture 3\", \"actual\": {\"scaled_variance_x\": 36, \"scaled_covariance\": -18, \"rotated_covariance\": -3, \"projected_variance\": 36, \"projected_cross_term\": 6, \"determinant\": 135}, \"expected\": {\"scaled_variance_x\": 36, \"scaled_covariance\": -18, \"rotated_covariance\": -3, \"projected_variance\": 36, \"projected_cross_term\": 6, \"determinant\": 135}, \"passed\": true}, {\"check\": \"astronomical fixture 4\", \"actual\": {\"scaled_variance_x\": 36, \"scaled_covariance\": -18, \"rotated_covariance\": -3, \"projected_variance\": 9, \"projected_cross_term\": 3, \"determinant\": 135}, \"expected\": {\"scaled_variance_x\": 36, \"scaled_covariance\": -18, \"rotated_covariance\": -3, \"projected_variance\": 9, \"projected_cross_term\": 3, \"determinant\": 135}, \"passed\": true}, {\"check\": \"astronomical fixture 5\", \"actual\": {\"scaled_variance_x\": 16, \"scaled_covariance\": 12, \"rotated_covariance\": 2, \"projected_variance\": 16, \"projected_cross_term\": -4, \"determinant\": 96}, \"expected\": {\"scaled_variance_x\": 16, \"scaled_covariance\": 12, \"rotated_covariance\": 2, \"projected_variance\": 16, \"projected_cross_term\": -4, \"determinant\": 96}, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}