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FA-55271 / Astronomical coordinate conventions / Open access

Catalog propagated covariance: Acceleration variance is propagated with the position acceleration coefficient unsquared · case 01

The adapter reports an incorrect acceleration position variance while other fields remain valid.

Verified by executionVariant 1 · 6 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Acceleration variance is propagated with the position acceleration coefficient unsquared. Faulty expression: d['t']**2*d['a']

THE FAILURE

Acceleration variance is propagated with the position acceleration coefficient unsquared. Faulty expression: d['t']**2*d['a']

Unsuccessful approach: A partial convention repair still uses d['t']**4*d['a']/2

Case contract

A catalog supplies position variance p, proper-motion variance m, covariance pm, elapsed interval t, acceleration variance a, and angular scale s. Under the stipulated independent acceleration model position covariance is p+2*t*pm+t*t*m+t**4*a/4. Motion output excludes acceleration unless explicitly requested. Output fields are defined by: position_variance = d['p']+2*d['t']*d['pm']+d['t']**2*d['m']+d['t']**4*d['a']/4; position_motion_covariance = d['pm']+d['t']*d['m']; acceleration_position_variance = d['t']**4*d['a']/4; motion_variance = d['m']+d['t']**2*d['a']; scaled_motion_covariance = (d['pm']+d['t']*d['m'])*d['s']**2; backward_cross_covariance = d['pm']-d['t']*d['m']

Why this case matters

Catalog, detector, sky-coordinate, and spectroscopy adapters must preserve the association between numeric coordinates and their declared reference conventions.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(d):
    return {'position_variance': d['p']+2*d['t']*d['pm']+d['t']**2*d['m']+d['t']**4*d['a']/4, 'position_motion_covariance': d['pm']+d['t']*d['m'], 'acceleration_position_variance': d['t']**2*d['a'], 'motion_variance': d['m']+d['t']**2*d['a'], 'scaled_motion_covariance': (d['pm']+d['t']*d['m'])*d['s']**2, 'backward_cross_covariance': d['pm']-d['t']*d['m']}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = {1: [({'p': 4, 'm': 2, 'pm': 1, 't': 3, 'a': 2, 's': 2}, {'position_variance': 68.5, 'position_motion_covariance': 7, 'acceleration_position_variance': 40.5, 'motion_variance': 20, 'scaled_motion_covariance': 28, 'backward_cross_covariance': -5}), ({'p': 4, 'm': 2, 'pm': 1, 't': 0, 'a': 2, 's': 2}, {'position_variance': 4.0, 'position_motion_covariance': 1, 'acceleration_position_variance': 0.0, 'motion_variance': 2, 'scaled_motion_covariance': 4, 'backward_cross_covariance': 1}), ({'p': 4, 'm': 2, 'pm': 1, 't': -2, 'a': 2, 's': 2}, {'position_variance': 16.0, 'position_motion_covariance': -3, 'acceleration_position_variance': 8.0, 'motion_variance': 10, 'scaled_motion_covariance': -12, 'backward_cross_covariance': 5}), ({'p': 4, 'm': 2, 'pm': 0, 't': 3, 'a': 0, 's': 2}, {'position_variance': 22.0, 'position_motion_covariance': 6, 'acceleration_position_variance': 0.0, 'motion_variance': 2, 'scaled_motion_covariance': 24, 'backward_cross_covariance': -6}), ({'p': 4, 'm': 2, 'pm': -1, 't': 3, 'a': 2, 's': -3}, {'position_variance': 56.5, 'position_motion_covariance': 5, 'acceleration_position_variance': 40.5, 'motion_variance': 20, 'scaled_motion_covariance': 45, 'backward_cross_covariance': -7}), ({'p': 4, 'm': 0, 'pm': 1, 't': 3, 'a': 4, 's': 2}, {'position_variance': 91.0, 'position_motion_covariance': 1, 'acceleration_position_variance': 81.0, 'motion_variance': 36, 'scaled_motion_covariance': 4, 'backward_cross_covariance': 1})], 2: [({'p': 5, 'm': 2, 'pm': 1, 't': 3, 'a': 2, 's': 2}, {'position_variance': 69.5, 'position_motion_covariance': 7, 'acceleration_position_variance': 40.5, 'motion_variance': 20, 'scaled_motion_covariance': 28, 'backward_cross_covariance': -5}), ({'p': 5, 'm': 2, 'pm': 1, 't': 0, 'a': 2, 's': 2}, {'position_variance': 5.0, 'position_motion_covariance': 1, 'acceleration_position_variance': 0.0, 'motion_variance': 2, 'scaled_motion_covariance': 4, 'backward_cross_covariance': 1}), ({'p': 5, 'm': 2, 'pm': 1, 't': -2, 'a': 2, 's': 2}, {'position_variance': 17.0, 'position_motion_covariance': -3, 'acceleration_position_variance': 8.0, 'motion_variance': 10, 'scaled_motion_covariance': -12, 'backward_cross_covariance': 5}), ({'p': 5, 'm': 2, 'pm': 0, 't': 3, 'a': 0, 's': 2}, {'position_variance': 23.0, 'position_motion_covariance': 6, 'acceleration_position_variance': 0.0, 'motion_variance': 2, 'scaled_motion_covariance': 24, 'backward_cross_covariance': -6}), ({'p': 5, 'm': 2, 'pm': -1, 't': 3, 'a': 2, 's': -3}, {'position_variance': 57.5, 'position_motion_covariance': 5, 'acceleration_position_variance': 40.5, 'motion_variance': 20, 'scaled_motion_covariance': 45, 'backward_cross_covariance': -7}), ({'p': 5, 'm': 0, 'pm': 1, 't': 3, 'a': 4, 's': 2}, {'position_variance': 92.0, 'position_motion_covariance': 1, 'acceleration_position_variance': 81.0, 'motion_variance': 36, 'scaled_motion_covariance': 4, 'backward_cross_covariance': 1})], 3: [({'p': 6, 'm': 2, 'pm': 1, 't': 3, 'a': 2, 's': 2}, {'position_variance': 70.5, 'position_motion_covariance': 7, 'acceleration_position_variance': 40.5, 'motion_variance': 20, 'scaled_motion_covariance': 28, 'backward_cross_covariance': -5}), ({'p': 6, 'm': 2, 'pm': 1, 't': 0, 'a': 2, 's': 2}, {'position_variance': 6.0, 'position_motion_covariance': 1, 'acceleration_position_variance': 0.0, 'motion_variance': 2, 'scaled_motion_covariance': 4, 'backward_cross_covariance': 1}), ({'p': 6, 'm': 2, 'pm': 1, 't': -2, 'a': 2, 's': 2}, {'position_variance': 18.0, 'position_motion_covariance': -3, 'acceleration_position_variance': 8.0, 'motion_variance': 10, 'scaled_motion_covariance': -12, 'backward_cross_covariance': 5}), ({'p': 6, 'm': 2, 'pm': 0, 't': 3, 'a': 0, 's': 2}, {'position_variance': 24.0, 'position_motion_covariance': 6, 'acceleration_position_variance': 0.0, 'motion_variance': 2, 'scaled_motion_covariance': 24, 'backward_cross_covariance': -6}), ({'p': 6, 'm': 2, 'pm': -1, 't': 3, 'a': 2, 's': -3}, {'position_variance': 58.5, 'position_motion_covariance': 5, 'acceleration_position_variance': 40.5, 'motion_variance': 20, 'scaled_motion_covariance': 45, 'backward_cross_covariance': -7}), ({'p': 6, 'm': 0, 'pm': 1, 't': 3, 'a': 4, 's': 2}, {'position_variance': 93.0, 'position_motion_covariance': 1, 'acceleration_position_variance': 81.0, 'motion_variance': 36, 'scaled_motion_covariance': 4, 'backward_cross_covariance': 1})], 4: [({'p': 7, 'm': 2, 'pm': 1, 't': 3, 'a': 2, 's': 2}, {'position_variance': 71.5, 'position_motion_covariance': 7, 'acceleration_position_variance': 40.5, 'motion_variance': 20, 'scaled_motion_covariance': 28, 'backward_cross_covariance': -5}), ({'p': 7, 'm': 2, 'pm': 1, 't': 0, 'a': 2, 's': 2}, {'position_variance': 7.0, 'position_motion_covariance': 1, 'acceleration_position_variance': 0.0, 'motion_variance': 2, 'scaled_motion_covariance': 4, 'backward_cross_covariance': 1}), ({'p': 7, 'm': 2, 'pm': 1, 't': -2, 'a': 2, 's': 2}, {'position_variance': 19.0, 'position_motion_covariance': -3, 'acceleration_position_variance': 8.0, 'motion_variance': 10, 'scaled_motion_covariance': -12, 'backward_cross_covariance': 5}), ({'p': 7, 'm': 2, 'pm': 0, 't': 3, 'a': 0, 's': 2}, {'position_variance': 25.0, 'position_motion_covariance': 6, 'acceleration_position_variance': 0.0, 'motion_variance': 2, 'scaled_motion_covariance': 24, 'backward_cross_covariance': -6}), ({'p': 7, 'm': 2, 'pm': -1, 't': 3, 'a': 2, 's': -3}, {'position_variance': 59.5, 'position_motion_covariance': 5, 'acceleration_position_variance': 40.5, 'motion_variance': 20, 'scaled_motion_covariance': 45, 'backward_cross_covariance': -7}), ({'p': 7, 'm': 0, 'pm': 1, 't': 3, 'a': 4, 's': 2}, {'position_variance': 94.0, 'position_motion_covariance': 1, 'acceleration_position_variance': 81.0, 'motion_variance': 36, 'scaled_motion_covariance': 4, 'backward_cross_covariance': 1})], 5: [({'p': 8, 'm': 2, 'pm': 1, 't': 3, 'a': 2, 's': 2}, {'position_variance': 72.5, 'position_motion_covariance': 7, 'acceleration_position_variance': 40.5, 'motion_variance': 20, 'scaled_motion_covariance': 28, 'backward_cross_covariance': -5}), ({'p': 8, 'm': 2, 'pm': 1, 't': 0, 'a': 2, 's': 2}, {'position_variance': 8.0, 'position_motion_covariance': 1, 'acceleration_position_variance': 0.0, 'motion_variance': 2, 'scaled_motion_covariance': 4, 'backward_cross_covariance': 1}), ({'p': 8, 'm': 2, 'pm': 1, 't': -2, 'a': 2, 's': 2}, {'position_variance': 20.0, 'position_motion_covariance': -3, 'acceleration_position_variance': 8.0, 'motion_variance': 10, 'scaled_motion_covariance': -12, 'backward_cross_covariance': 5}), ({'p': 8, 'm': 2, 'pm': 0, 't': 3, 'a': 0, 's': 2}, {'position_variance': 26.0, 'position_motion_covariance': 6, 'acceleration_position_variance': 0.0, 'motion_variance': 2, 'scaled_motion_covariance': 24, 'backward_cross_covariance': -6}), ({'p': 8, 'm': 2, 'pm': -1, 't': 3, 'a': 2, 's': -3}, {'position_variance': 60.5, 'position_motion_covariance': 5, 'acceleration_position_variance': 40.5, 'motion_variance': 20, 'scaled_motion_covariance': 45, 'backward_cross_covariance': -7}), ({'p': 8, 'm': 0, 'pm': 1, 't': 3, 'a': 4, 's': 2}, {'position_variance': 95.0, 'position_motion_covariance': 1, 'acceleration_position_variance': 81.0, 'motion_variance': 36, 'scaled_motion_covariance': 4, 'backward_cross_covariance': 1})]}
for i, (record, expected) in enumerate(fixtures[N]):
    check('astronomical fixture %s' % i, solve(record), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
astronomical fixture 0{'acceleration_position_variance': 18, 'backward_cross_covariance': -5, 'motion_variance': 20, 'position_motion_covariance': 7, 'position_variance': 68.5, 'scaled_motion_covariance': 28}{'acceleration_position_variance': 40.5, 'backward_cross_covariance': -5, 'motion_variance': 20, 'position_motion_covariance': 7, 'position_variance': 68.5, 'scaled_motion_covariance': 28}Failed
astronomical fixture 1{'acceleration_position_variance': 0, 'backward_cross_covariance': 1, 'motion_variance': 2, 'position_motion_covariance': 1, 'position_variance': 4.0, 'scaled_motion_covariance': 4}{'acceleration_position_variance': 0.0, 'backward_cross_covariance': 1, 'motion_variance': 2, 'position_motion_covariance': 1, 'position_variance': 4.0, 'scaled_motion_covariance': 4}Passed
astronomical fixture 2{'acceleration_position_variance': 8, 'backward_cross_covariance': 5, 'motion_variance': 10, 'position_motion_covariance': -3, 'position_variance': 16.0, 'scaled_motion_covariance': -12}{'acceleration_position_variance': 8.0, 'backward_cross_covariance': 5, 'motion_variance': 10, 'position_motion_covariance': -3, 'position_variance': 16.0, 'scaled_motion_covariance': -12}Passed
astronomical fixture 3{'acceleration_position_variance': 0, 'backward_cross_covariance': -6, 'motion_variance': 2, 'position_motion_covariance': 6, 'position_variance': 22.0, 'scaled_motion_covariance': 24}{'acceleration_position_variance': 0.0, 'backward_cross_covariance': -6, 'motion_variance': 2, 'position_motion_covariance': 6, 'position_variance': 22.0, 'scaled_motion_covariance': 24}Passed
astronomical fixture 4{'acceleration_position_variance': 18, 'backward_cross_covariance': -7, 'motion_variance': 20, 'position_motion_covariance': 5, 'position_variance': 56.5, 'scaled_motion_covariance': 45}{'acceleration_position_variance': 40.5, 'backward_cross_covariance': -7, 'motion_variance': 20, 'position_motion_covariance': 5, 'position_variance': 56.5, 'scaled_motion_covariance': 45}Failed
astronomical fixture 5{'acceleration_position_variance': 36, 'backward_cross_covariance': 1, 'motion_variance': 36, 'position_motion_covariance': 1, 'position_variance': 91.0, 'scaled_motion_covariance': 4}{'acceleration_position_variance': 81.0, 'backward_cross_covariance': 1, 'motion_variance': 36, 'position_motion_covariance': 1, 'position_variance': 91.0, 'scaled_motion_covariance': 4}Failed

SHA-256 / 4f316863b06c46ed0ed54b1ed5812a4714b09cbf8a63563d4a5ade72a5e8e1ab

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(d):
    return {'position_variance': d['p']+2*d['t']*d['pm']+d['t']**2*d['m']+d['t']**4*d['a']/4, 'position_motion_covariance': d['pm']+d['t']*d['m'], 'acceleration_position_variance': d['t']**4*d['a']/2, 'motion_variance': d['m']+d['t']**2*d['a'], 'scaled_motion_covariance': (d['pm']+d['t']*d['m'])*d['s']**2, 'backward_cross_covariance': d['pm']-d['t']*d['m']}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = {1: [({'p': 4, 'm': 2, 'pm': 1, 't': 3, 'a': 2, 's': 2}, {'position_variance': 68.5, 'position_motion_covariance': 7, 'acceleration_position_variance': 40.5, 'motion_variance': 20, 'scaled_motion_covariance': 28, 'backward_cross_covariance': -5}), ({'p': 4, 'm': 2, 'pm': 1, 't': 0, 'a': 2, 's': 2}, {'position_variance': 4.0, 'position_motion_covariance': 1, 'acceleration_position_variance': 0.0, 'motion_variance': 2, 'scaled_motion_covariance': 4, 'backward_cross_covariance': 1}), ({'p': 4, 'm': 2, 'pm': 1, 't': -2, 'a': 2, 's': 2}, {'position_variance': 16.0, 'position_motion_covariance': -3, 'acceleration_position_variance': 8.0, 'motion_variance': 10, 'scaled_motion_covariance': -12, 'backward_cross_covariance': 5}), ({'p': 4, 'm': 2, 'pm': 0, 't': 3, 'a': 0, 's': 2}, {'position_variance': 22.0, 'position_motion_covariance': 6, 'acceleration_position_variance': 0.0, 'motion_variance': 2, 'scaled_motion_covariance': 24, 'backward_cross_covariance': -6}), ({'p': 4, 'm': 2, 'pm': -1, 't': 3, 'a': 2, 's': -3}, {'position_variance': 56.5, 'position_motion_covariance': 5, 'acceleration_position_variance': 40.5, 'motion_variance': 20, 'scaled_motion_covariance': 45, 'backward_cross_covariance': -7}), ({'p': 4, 'm': 0, 'pm': 1, 't': 3, 'a': 4, 's': 2}, {'position_variance': 91.0, 'position_motion_covariance': 1, 'acceleration_position_variance': 81.0, 'motion_variance': 36, 'scaled_motion_covariance': 4, 'backward_cross_covariance': 1})], 2: [({'p': 5, 'm': 2, 'pm': 1, 't': 3, 'a': 2, 's': 2}, {'position_variance': 69.5, 'position_motion_covariance': 7, 'acceleration_position_variance': 40.5, 'motion_variance': 20, 'scaled_motion_covariance': 28, 'backward_cross_covariance': -5}), ({'p': 5, 'm': 2, 'pm': 1, 't': 0, 'a': 2, 's': 2}, {'position_variance': 5.0, 'position_motion_covariance': 1, 'acceleration_position_variance': 0.0, 'motion_variance': 2, 'scaled_motion_covariance': 4, 'backward_cross_covariance': 1}), ({'p': 5, 'm': 2, 'pm': 1, 't': -2, 'a': 2, 's': 2}, {'position_variance': 17.0, 'position_motion_covariance': -3, 'acceleration_position_variance': 8.0, 'motion_variance': 10, 'scaled_motion_covariance': -12, 'backward_cross_covariance': 5}), ({'p': 5, 'm': 2, 'pm': 0, 't': 3, 'a': 0, 's': 2}, {'position_variance': 23.0, 'position_motion_covariance': 6, 'acceleration_position_variance': 0.0, 'motion_variance': 2, 'scaled_motion_covariance': 24, 'backward_cross_covariance': -6}), ({'p': 5, 'm': 2, 'pm': -1, 't': 3, 'a': 2, 's': -3}, {'position_variance': 57.5, 'position_motion_covariance': 5, 'acceleration_position_variance': 40.5, 'motion_variance': 20, 'scaled_motion_covariance': 45, 'backward_cross_covariance': -7}), ({'p': 5, 'm': 0, 'pm': 1, 't': 3, 'a': 4, 's': 2}, {'position_variance': 92.0, 'position_motion_covariance': 1, 'acceleration_position_variance': 81.0, 'motion_variance': 36, 'scaled_motion_covariance': 4, 'backward_cross_covariance': 1})], 3: [({'p': 6, 'm': 2, 'pm': 1, 't': 3, 'a': 2, 's': 2}, {'position_variance': 70.5, 'position_motion_covariance': 7, 'acceleration_position_variance': 40.5, 'motion_variance': 20, 'scaled_motion_covariance': 28, 'backward_cross_covariance': -5}), ({'p': 6, 'm': 2, 'pm': 1, 't': 0, 'a': 2, 's': 2}, {'position_variance': 6.0, 'position_motion_covariance': 1, 'acceleration_position_variance': 0.0, 'motion_variance': 2, 'scaled_motion_covariance': 4, 'backward_cross_covariance': 1}), ({'p': 6, 'm': 2, 'pm': 1, 't': -2, 'a': 2, 's': 2}, {'position_variance': 18.0, 'position_motion_covariance': -3, 'acceleration_position_variance': 8.0, 'motion_variance': 10, 'scaled_motion_covariance': -12, 'backward_cross_covariance': 5}), ({'p': 6, 'm': 2, 'pm': 0, 't': 3, 'a': 0, 's': 2}, {'position_variance': 24.0, 'position_motion_covariance': 6, 'acceleration_position_variance': 0.0, 'motion_variance': 2, 'scaled_motion_covariance': 24, 'backward_cross_covariance': -6}), ({'p': 6, 'm': 2, 'pm': -1, 't': 3, 'a': 2, 's': -3}, {'position_variance': 58.5, 'position_motion_covariance': 5, 'acceleration_position_variance': 40.5, 'motion_variance': 20, 'scaled_motion_covariance': 45, 'backward_cross_covariance': -7}), ({'p': 6, 'm': 0, 'pm': 1, 't': 3, 'a': 4, 's': 2}, {'position_variance': 93.0, 'position_motion_covariance': 1, 'acceleration_position_variance': 81.0, 'motion_variance': 36, 'scaled_motion_covariance': 4, 'backward_cross_covariance': 1})], 4: [({'p': 7, 'm': 2, 'pm': 1, 't': 3, 'a': 2, 's': 2}, {'position_variance': 71.5, 'position_motion_covariance': 7, 'acceleration_position_variance': 40.5, 'motion_variance': 20, 'scaled_motion_covariance': 28, 'backward_cross_covariance': -5}), ({'p': 7, 'm': 2, 'pm': 1, 't': 0, 'a': 2, 's': 2}, {'position_variance': 7.0, 'position_motion_covariance': 1, 'acceleration_position_variance': 0.0, 'motion_variance': 2, 'scaled_motion_covariance': 4, 'backward_cross_covariance': 1}), ({'p': 7, 'm': 2, 'pm': 1, 't': -2, 'a': 2, 's': 2}, {'position_variance': 19.0, 'position_motion_covariance': -3, 'acceleration_position_variance': 8.0, 'motion_variance': 10, 'scaled_motion_covariance': -12, 'backward_cross_covariance': 5}), ({'p': 7, 'm': 2, 'pm': 0, 't': 3, 'a': 0, 's': 2}, {'position_variance': 25.0, 'position_motion_covariance': 6, 'acceleration_position_variance': 0.0, 'motion_variance': 2, 'scaled_motion_covariance': 24, 'backward_cross_covariance': -6}), ({'p': 7, 'm': 2, 'pm': -1, 't': 3, 'a': 2, 's': -3}, {'position_variance': 59.5, 'position_motion_covariance': 5, 'acceleration_position_variance': 40.5, 'motion_variance': 20, 'scaled_motion_covariance': 45, 'backward_cross_covariance': -7}), ({'p': 7, 'm': 0, 'pm': 1, 't': 3, 'a': 4, 's': 2}, {'position_variance': 94.0, 'position_motion_covariance': 1, 'acceleration_position_variance': 81.0, 'motion_variance': 36, 'scaled_motion_covariance': 4, 'backward_cross_covariance': 1})], 5: [({'p': 8, 'm': 2, 'pm': 1, 't': 3, 'a': 2, 's': 2}, {'position_variance': 72.5, 'position_motion_covariance': 7, 'acceleration_position_variance': 40.5, 'motion_variance': 20, 'scaled_motion_covariance': 28, 'backward_cross_covariance': -5}), ({'p': 8, 'm': 2, 'pm': 1, 't': 0, 'a': 2, 's': 2}, {'position_variance': 8.0, 'position_motion_covariance': 1, 'acceleration_position_variance': 0.0, 'motion_variance': 2, 'scaled_motion_covariance': 4, 'backward_cross_covariance': 1}), ({'p': 8, 'm': 2, 'pm': 1, 't': -2, 'a': 2, 's': 2}, {'position_variance': 20.0, 'position_motion_covariance': -3, 'acceleration_position_variance': 8.0, 'motion_variance': 10, 'scaled_motion_covariance': -12, 'backward_cross_covariance': 5}), ({'p': 8, 'm': 2, 'pm': 0, 't': 3, 'a': 0, 's': 2}, {'position_variance': 26.0, 'position_motion_covariance': 6, 'acceleration_position_variance': 0.0, 'motion_variance': 2, 'scaled_motion_covariance': 24, 'backward_cross_covariance': -6}), ({'p': 8, 'm': 2, 'pm': -1, 't': 3, 'a': 2, 's': -3}, {'position_variance': 60.5, 'position_motion_covariance': 5, 'acceleration_position_variance': 40.5, 'motion_variance': 20, 'scaled_motion_covariance': 45, 'backward_cross_covariance': -7}), ({'p': 8, 'm': 0, 'pm': 1, 't': 3, 'a': 4, 's': 2}, {'position_variance': 95.0, 'position_motion_covariance': 1, 'acceleration_position_variance': 81.0, 'motion_variance': 36, 'scaled_motion_covariance': 4, 'backward_cross_covariance': 1})]}
for i, (record, expected) in enumerate(fixtures[N]):
    check('astronomical fixture %s' % i, solve(record), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
astronomical fixture 0{'acceleration_position_variance': 81.0, 'backward_cross_covariance': -5, 'motion_variance': 20, 'position_motion_covariance': 7, 'position_variance': 68.5, 'scaled_motion_covariance': 28}{'acceleration_position_variance': 40.5, 'backward_cross_covariance': -5, 'motion_variance': 20, 'position_motion_covariance': 7, 'position_variance': 68.5, 'scaled_motion_covariance': 28}Failed
astronomical fixture 1{'acceleration_position_variance': 0.0, 'backward_cross_covariance': 1, 'motion_variance': 2, 'position_motion_covariance': 1, 'position_variance': 4.0, 'scaled_motion_covariance': 4}{'acceleration_position_variance': 0.0, 'backward_cross_covariance': 1, 'motion_variance': 2, 'position_motion_covariance': 1, 'position_variance': 4.0, 'scaled_motion_covariance': 4}Passed
astronomical fixture 2{'acceleration_position_variance': 16.0, 'backward_cross_covariance': 5, 'motion_variance': 10, 'position_motion_covariance': -3, 'position_variance': 16.0, 'scaled_motion_covariance': -12}{'acceleration_position_variance': 8.0, 'backward_cross_covariance': 5, 'motion_variance': 10, 'position_motion_covariance': -3, 'position_variance': 16.0, 'scaled_motion_covariance': -12}Failed
astronomical fixture 3{'acceleration_position_variance': 0.0, 'backward_cross_covariance': -6, 'motion_variance': 2, 'position_motion_covariance': 6, 'position_variance': 22.0, 'scaled_motion_covariance': 24}{'acceleration_position_variance': 0.0, 'backward_cross_covariance': -6, 'motion_variance': 2, 'position_motion_covariance': 6, 'position_variance': 22.0, 'scaled_motion_covariance': 24}Passed
astronomical fixture 4{'acceleration_position_variance': 81.0, 'backward_cross_covariance': -7, 'motion_variance': 20, 'position_motion_covariance': 5, 'position_variance': 56.5, 'scaled_motion_covariance': 45}{'acceleration_position_variance': 40.5, 'backward_cross_covariance': -7, 'motion_variance': 20, 'position_motion_covariance': 5, 'position_variance': 56.5, 'scaled_motion_covariance': 45}Failed
astronomical fixture 5{'acceleration_position_variance': 162.0, 'backward_cross_covariance': 1, 'motion_variance': 36, 'position_motion_covariance': 1, 'position_variance': 91.0, 'scaled_motion_covariance': 4}{'acceleration_position_variance': 81.0, 'backward_cross_covariance': 1, 'motion_variance': 36, 'position_motion_covariance': 1, 'position_variance': 91.0, 'scaled_motion_covariance': 4}Failed

SHA-256 / 1640ffc72c9a9bc7fb49cb3b0cd90061d39c1a213b9720d366a249d6491cefd2

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 6 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

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Verification & scope

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.

Observations recorded using Python 3.12.14 at 2026-09-29T14:45:56.410104+00:00.

Case digest / f28297fc90cd40caa5d721e24f345f8d831f7e7b211c767034244a5e40ef6349