FAILURE MAP
← Case archive

FA-55626 / Astronomical coordinate conventions / Open access

Air vacuum line coordinate: Inverse air-wavelength conversion repeats the vacuum mapping · case 01

The adapter reports an incorrect air wavelength while other fields remain valid.

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

ROOT CAUSE

Inverse air-wavelength conversion repeats the vacuum mapping. Faulty expression: d['L']*d['a']/d['b']

THE FAILURE

Inverse air-wavelength conversion repeats the vacuum mapping. Faulty expression: d['L']*d['a']/d['b']

Unsuccessful approach: A partial convention repair still uses d['L']-d['a']/d['b']

Case contract

The supplied index n=a/b is a positive rational greater than zero. This finite constant-index adapter maps air wavelength to vacuum by multiplication n. Frequency belongs to vacuum wavelength; flux densities change inversely with wavelength-bin Jacobian. It does not model dispersion of refractive index. Output fields are defined by: vacuum_wavelength = d['L']*d['a']/d['b']; air_wavelength = d['L']*d['b']/d['a']; vacuum_width = d['width']*d['a']/d['b']; vacuum_density = d['F']*d['b']/d['a']; vacuum_frequency = d['c']*d['b']/(d['L']*d['a']); line_displacement = d['L']*(d['a']-d['b'])/d['b']

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 {'vacuum_wavelength': d['L']*d['a']/d['b'], 'air_wavelength': d['L']*d['a']/d['b'], 'vacuum_width': d['width']*d['a']/d['b'], 'vacuum_density': d['F']*d['b']/d['a'], 'vacuum_frequency': d['c']*d['b']/(d['L']*d['a']), 'line_displacement': d['L']*(d['a']-d['b'])/d['b']}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = {1: [({'L': 10, 'a': 3, 'b': 2, 'width': 4, 'F': 6, 'c': 120}, {'vacuum_wavelength': 15.0, 'air_wavelength': 6.666666666666667, 'vacuum_width': 6.0, 'vacuum_density': 4.0, 'vacuum_frequency': 8.0, 'line_displacement': 5.0}), ({'L': 10, 'a': 1, 'b': 1, 'width': 4, 'F': 6, 'c': 120}, {'vacuum_wavelength': 10.0, 'air_wavelength': 10.0, 'vacuum_width': 4.0, 'vacuum_density': 6.0, 'vacuum_frequency': 12.0, 'line_displacement': 0.0}), ({'L': 10, 'a': 3, 'b': 2, 'width': 0, 'F': 6, 'c': 120}, {'vacuum_wavelength': 15.0, 'air_wavelength': 6.666666666666667, 'vacuum_width': 0.0, 'vacuum_density': 4.0, 'vacuum_frequency': 8.0, 'line_displacement': 5.0}), ({'L': 10, 'a': 3, 'b': 2, 'width': 4, 'F': 0, 'c': 120}, {'vacuum_wavelength': 15.0, 'air_wavelength': 6.666666666666667, 'vacuum_width': 6.0, 'vacuum_density': 0.0, 'vacuum_frequency': 8.0, 'line_displacement': 5.0}), ({'L': 10, 'a': 4, 'b': 3, 'width': 4, 'F': 6, 'c': 120}, {'vacuum_wavelength': 13.333333333333334, 'air_wavelength': 7.5, 'vacuum_width': 5.333333333333333, 'vacuum_density': 4.5, 'vacuum_frequency': 9.0, 'line_displacement': 3.3333333333333335}), ({'L': 10, 'a': 3, 'b': 2, 'width': 4, 'F': -2, 'c': 120}, {'vacuum_wavelength': 15.0, 'air_wavelength': 6.666666666666667, 'vacuum_width': 6.0, 'vacuum_density': -1.3333333333333333, 'vacuum_frequency': 8.0, 'line_displacement': 5.0})], 2: [({'L': 11, 'a': 3, 'b': 2, 'width': 4, 'F': 6, 'c': 120}, {'vacuum_wavelength': 16.5, 'air_wavelength': 7.333333333333333, 'vacuum_width': 6.0, 'vacuum_density': 4.0, 'vacuum_frequency': 7.2727272727272725, 'line_displacement': 5.5}), ({'L': 11, 'a': 1, 'b': 1, 'width': 4, 'F': 6, 'c': 120}, {'vacuum_wavelength': 11.0, 'air_wavelength': 11.0, 'vacuum_width': 4.0, 'vacuum_density': 6.0, 'vacuum_frequency': 10.909090909090908, 'line_displacement': 0.0}), ({'L': 11, 'a': 3, 'b': 2, 'width': 0, 'F': 6, 'c': 120}, {'vacuum_wavelength': 16.5, 'air_wavelength': 7.333333333333333, 'vacuum_width': 0.0, 'vacuum_density': 4.0, 'vacuum_frequency': 7.2727272727272725, 'line_displacement': 5.5}), ({'L': 11, 'a': 3, 'b': 2, 'width': 4, 'F': 0, 'c': 120}, {'vacuum_wavelength': 16.5, 'air_wavelength': 7.333333333333333, 'vacuum_width': 6.0, 'vacuum_density': 0.0, 'vacuum_frequency': 7.2727272727272725, 'line_displacement': 5.5}), ({'L': 11, 'a': 4, 'b': 3, 'width': 4, 'F': 6, 'c': 120}, {'vacuum_wavelength': 14.666666666666666, 'air_wavelength': 8.25, 'vacuum_width': 5.333333333333333, 'vacuum_density': 4.5, 'vacuum_frequency': 8.181818181818182, 'line_displacement': 3.6666666666666665}), ({'L': 11, 'a': 3, 'b': 2, 'width': 4, 'F': -2, 'c': 120}, {'vacuum_wavelength': 16.5, 'air_wavelength': 7.333333333333333, 'vacuum_width': 6.0, 'vacuum_density': -1.3333333333333333, 'vacuum_frequency': 7.2727272727272725, 'line_displacement': 5.5})], 3: [({'L': 12, 'a': 3, 'b': 2, 'width': 4, 'F': 6, 'c': 120}, {'vacuum_wavelength': 18.0, 'air_wavelength': 8.0, 'vacuum_width': 6.0, 'vacuum_density': 4.0, 'vacuum_frequency': 6.666666666666667, 'line_displacement': 6.0}), ({'L': 12, 'a': 1, 'b': 1, 'width': 4, 'F': 6, 'c': 120}, {'vacuum_wavelength': 12.0, 'air_wavelength': 12.0, 'vacuum_width': 4.0, 'vacuum_density': 6.0, 'vacuum_frequency': 10.0, 'line_displacement': 0.0}), ({'L': 12, 'a': 3, 'b': 2, 'width': 0, 'F': 6, 'c': 120}, {'vacuum_wavelength': 18.0, 'air_wavelength': 8.0, 'vacuum_width': 0.0, 'vacuum_density': 4.0, 'vacuum_frequency': 6.666666666666667, 'line_displacement': 6.0}), ({'L': 12, 'a': 3, 'b': 2, 'width': 4, 'F': 0, 'c': 120}, {'vacuum_wavelength': 18.0, 'air_wavelength': 8.0, 'vacuum_width': 6.0, 'vacuum_density': 0.0, 'vacuum_frequency': 6.666666666666667, 'line_displacement': 6.0}), ({'L': 12, 'a': 4, 'b': 3, 'width': 4, 'F': 6, 'c': 120}, {'vacuum_wavelength': 16.0, 'air_wavelength': 9.0, 'vacuum_width': 5.333333333333333, 'vacuum_density': 4.5, 'vacuum_frequency': 7.5, 'line_displacement': 4.0}), ({'L': 12, 'a': 3, 'b': 2, 'width': 4, 'F': -2, 'c': 120}, {'vacuum_wavelength': 18.0, 'air_wavelength': 8.0, 'vacuum_width': 6.0, 'vacuum_density': -1.3333333333333333, 'vacuum_frequency': 6.666666666666667, 'line_displacement': 6.0})], 4: [({'L': 13, 'a': 3, 'b': 2, 'width': 4, 'F': 6, 'c': 120}, {'vacuum_wavelength': 19.5, 'air_wavelength': 8.666666666666666, 'vacuum_width': 6.0, 'vacuum_density': 4.0, 'vacuum_frequency': 6.153846153846154, 'line_displacement': 6.5}), ({'L': 13, 'a': 1, 'b': 1, 'width': 4, 'F': 6, 'c': 120}, {'vacuum_wavelength': 13.0, 'air_wavelength': 13.0, 'vacuum_width': 4.0, 'vacuum_density': 6.0, 'vacuum_frequency': 9.23076923076923, 'line_displacement': 0.0}), ({'L': 13, 'a': 3, 'b': 2, 'width': 0, 'F': 6, 'c': 120}, {'vacuum_wavelength': 19.5, 'air_wavelength': 8.666666666666666, 'vacuum_width': 0.0, 'vacuum_density': 4.0, 'vacuum_frequency': 6.153846153846154, 'line_displacement': 6.5}), ({'L': 13, 'a': 3, 'b': 2, 'width': 4, 'F': 0, 'c': 120}, {'vacuum_wavelength': 19.5, 'air_wavelength': 8.666666666666666, 'vacuum_width': 6.0, 'vacuum_density': 0.0, 'vacuum_frequency': 6.153846153846154, 'line_displacement': 6.5}), ({'L': 13, 'a': 4, 'b': 3, 'width': 4, 'F': 6, 'c': 120}, {'vacuum_wavelength': 17.333333333333332, 'air_wavelength': 9.75, 'vacuum_width': 5.333333333333333, 'vacuum_density': 4.5, 'vacuum_frequency': 6.923076923076923, 'line_displacement': 4.333333333333333}), ({'L': 13, 'a': 3, 'b': 2, 'width': 4, 'F': -2, 'c': 120}, {'vacuum_wavelength': 19.5, 'air_wavelength': 8.666666666666666, 'vacuum_width': 6.0, 'vacuum_density': -1.3333333333333333, 'vacuum_frequency': 6.153846153846154, 'line_displacement': 6.5})], 5: [({'L': 14, 'a': 3, 'b': 2, 'width': 4, 'F': 6, 'c': 120}, {'vacuum_wavelength': 21.0, 'air_wavelength': 9.333333333333334, 'vacuum_width': 6.0, 'vacuum_density': 4.0, 'vacuum_frequency': 5.714285714285714, 'line_displacement': 7.0}), ({'L': 14, 'a': 1, 'b': 1, 'width': 4, 'F': 6, 'c': 120}, {'vacuum_wavelength': 14.0, 'air_wavelength': 14.0, 'vacuum_width': 4.0, 'vacuum_density': 6.0, 'vacuum_frequency': 8.571428571428571, 'line_displacement': 0.0}), ({'L': 14, 'a': 3, 'b': 2, 'width': 0, 'F': 6, 'c': 120}, {'vacuum_wavelength': 21.0, 'air_wavelength': 9.333333333333334, 'vacuum_width': 0.0, 'vacuum_density': 4.0, 'vacuum_frequency': 5.714285714285714, 'line_displacement': 7.0}), ({'L': 14, 'a': 3, 'b': 2, 'width': 4, 'F': 0, 'c': 120}, {'vacuum_wavelength': 21.0, 'air_wavelength': 9.333333333333334, 'vacuum_width': 6.0, 'vacuum_density': 0.0, 'vacuum_frequency': 5.714285714285714, 'line_displacement': 7.0}), ({'L': 14, 'a': 4, 'b': 3, 'width': 4, 'F': 6, 'c': 120}, {'vacuum_wavelength': 18.666666666666668, 'air_wavelength': 10.5, 'vacuum_width': 5.333333333333333, 'vacuum_density': 4.5, 'vacuum_frequency': 6.428571428571429, 'line_displacement': 4.666666666666667}), ({'L': 14, 'a': 3, 'b': 2, 'width': 4, 'F': -2, 'c': 120}, {'vacuum_wavelength': 21.0, 'air_wavelength': 9.333333333333334, 'vacuum_width': 6.0, 'vacuum_density': -1.3333333333333333, 'vacuum_frequency': 5.714285714285714, 'line_displacement': 7.0})]}
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{'air_wavelength': 15.0, 'line_displacement': 5.0, 'vacuum_density': 4.0, 'vacuum_frequency': 8.0, 'vacuum_wavelength': 15.0, 'vacuum_width': 6.0}{'air_wavelength': 6.666666666666667, 'line_displacement': 5.0, 'vacuum_density': 4.0, 'vacuum_frequency': 8.0, 'vacuum_wavelength': 15.0, 'vacuum_width': 6.0}Failed
astronomical fixture 1{'air_wavelength': 10.0, 'line_displacement': 0.0, 'vacuum_density': 6.0, 'vacuum_frequency': 12.0, 'vacuum_wavelength': 10.0, 'vacuum_width': 4.0}{'air_wavelength': 10.0, 'line_displacement': 0.0, 'vacuum_density': 6.0, 'vacuum_frequency': 12.0, 'vacuum_wavelength': 10.0, 'vacuum_width': 4.0}Passed
astronomical fixture 2{'air_wavelength': 15.0, 'line_displacement': 5.0, 'vacuum_density': 4.0, 'vacuum_frequency': 8.0, 'vacuum_wavelength': 15.0, 'vacuum_width': 0.0}{'air_wavelength': 6.666666666666667, 'line_displacement': 5.0, 'vacuum_density': 4.0, 'vacuum_frequency': 8.0, 'vacuum_wavelength': 15.0, 'vacuum_width': 0.0}Failed
astronomical fixture 3{'air_wavelength': 15.0, 'line_displacement': 5.0, 'vacuum_density': 0.0, 'vacuum_frequency': 8.0, 'vacuum_wavelength': 15.0, 'vacuum_width': 6.0}{'air_wavelength': 6.666666666666667, 'line_displacement': 5.0, 'vacuum_density': 0.0, 'vacuum_frequency': 8.0, 'vacuum_wavelength': 15.0, 'vacuum_width': 6.0}Failed
astronomical fixture 4{'air_wavelength': 13.333333333333334, 'line_displacement': 3.3333333333333335, 'vacuum_density': 4.5, 'vacuum_frequency': 9.0, 'vacuum_wavelength': 13.333333333333334, 'vacuum_width': 5.333333333333333}{'air_wavelength': 7.5, 'line_displacement': 3.3333333333333335, 'vacuum_density': 4.5, 'vacuum_frequency': 9.0, 'vacuum_wavelength': 13.333333333333334, 'vacuum_width': 5.333333333333333}Failed
astronomical fixture 5{'air_wavelength': 15.0, 'line_displacement': 5.0, 'vacuum_density': -1.3333333333333333, 'vacuum_frequency': 8.0, 'vacuum_wavelength': 15.0, 'vacuum_width': 6.0}{'air_wavelength': 6.666666666666667, 'line_displacement': 5.0, 'vacuum_density': -1.3333333333333333, 'vacuum_frequency': 8.0, 'vacuum_wavelength': 15.0, 'vacuum_width': 6.0}Failed

SHA-256 / 006c2d84dc5daadcf2f9d306e76e5dd5b17beaae4807fee06125e0ec0d55b674

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(d):
    return {'vacuum_wavelength': d['L']*d['a']/d['b'], 'air_wavelength': d['L']-d['a']/d['b'], 'vacuum_width': d['width']*d['a']/d['b'], 'vacuum_density': d['F']*d['b']/d['a'], 'vacuum_frequency': d['c']*d['b']/(d['L']*d['a']), 'line_displacement': d['L']*(d['a']-d['b'])/d['b']}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = {1: [({'L': 10, 'a': 3, 'b': 2, 'width': 4, 'F': 6, 'c': 120}, {'vacuum_wavelength': 15.0, 'air_wavelength': 6.666666666666667, 'vacuum_width': 6.0, 'vacuum_density': 4.0, 'vacuum_frequency': 8.0, 'line_displacement': 5.0}), ({'L': 10, 'a': 1, 'b': 1, 'width': 4, 'F': 6, 'c': 120}, {'vacuum_wavelength': 10.0, 'air_wavelength': 10.0, 'vacuum_width': 4.0, 'vacuum_density': 6.0, 'vacuum_frequency': 12.0, 'line_displacement': 0.0}), ({'L': 10, 'a': 3, 'b': 2, 'width': 0, 'F': 6, 'c': 120}, {'vacuum_wavelength': 15.0, 'air_wavelength': 6.666666666666667, 'vacuum_width': 0.0, 'vacuum_density': 4.0, 'vacuum_frequency': 8.0, 'line_displacement': 5.0}), ({'L': 10, 'a': 3, 'b': 2, 'width': 4, 'F': 0, 'c': 120}, {'vacuum_wavelength': 15.0, 'air_wavelength': 6.666666666666667, 'vacuum_width': 6.0, 'vacuum_density': 0.0, 'vacuum_frequency': 8.0, 'line_displacement': 5.0}), ({'L': 10, 'a': 4, 'b': 3, 'width': 4, 'F': 6, 'c': 120}, {'vacuum_wavelength': 13.333333333333334, 'air_wavelength': 7.5, 'vacuum_width': 5.333333333333333, 'vacuum_density': 4.5, 'vacuum_frequency': 9.0, 'line_displacement': 3.3333333333333335}), ({'L': 10, 'a': 3, 'b': 2, 'width': 4, 'F': -2, 'c': 120}, {'vacuum_wavelength': 15.0, 'air_wavelength': 6.666666666666667, 'vacuum_width': 6.0, 'vacuum_density': -1.3333333333333333, 'vacuum_frequency': 8.0, 'line_displacement': 5.0})], 2: [({'L': 11, 'a': 3, 'b': 2, 'width': 4, 'F': 6, 'c': 120}, {'vacuum_wavelength': 16.5, 'air_wavelength': 7.333333333333333, 'vacuum_width': 6.0, 'vacuum_density': 4.0, 'vacuum_frequency': 7.2727272727272725, 'line_displacement': 5.5}), ({'L': 11, 'a': 1, 'b': 1, 'width': 4, 'F': 6, 'c': 120}, {'vacuum_wavelength': 11.0, 'air_wavelength': 11.0, 'vacuum_width': 4.0, 'vacuum_density': 6.0, 'vacuum_frequency': 10.909090909090908, 'line_displacement': 0.0}), ({'L': 11, 'a': 3, 'b': 2, 'width': 0, 'F': 6, 'c': 120}, {'vacuum_wavelength': 16.5, 'air_wavelength': 7.333333333333333, 'vacuum_width': 0.0, 'vacuum_density': 4.0, 'vacuum_frequency': 7.2727272727272725, 'line_displacement': 5.5}), ({'L': 11, 'a': 3, 'b': 2, 'width': 4, 'F': 0, 'c': 120}, {'vacuum_wavelength': 16.5, 'air_wavelength': 7.333333333333333, 'vacuum_width': 6.0, 'vacuum_density': 0.0, 'vacuum_frequency': 7.2727272727272725, 'line_displacement': 5.5}), ({'L': 11, 'a': 4, 'b': 3, 'width': 4, 'F': 6, 'c': 120}, {'vacuum_wavelength': 14.666666666666666, 'air_wavelength': 8.25, 'vacuum_width': 5.333333333333333, 'vacuum_density': 4.5, 'vacuum_frequency': 8.181818181818182, 'line_displacement': 3.6666666666666665}), ({'L': 11, 'a': 3, 'b': 2, 'width': 4, 'F': -2, 'c': 120}, {'vacuum_wavelength': 16.5, 'air_wavelength': 7.333333333333333, 'vacuum_width': 6.0, 'vacuum_density': -1.3333333333333333, 'vacuum_frequency': 7.2727272727272725, 'line_displacement': 5.5})], 3: [({'L': 12, 'a': 3, 'b': 2, 'width': 4, 'F': 6, 'c': 120}, {'vacuum_wavelength': 18.0, 'air_wavelength': 8.0, 'vacuum_width': 6.0, 'vacuum_density': 4.0, 'vacuum_frequency': 6.666666666666667, 'line_displacement': 6.0}), ({'L': 12, 'a': 1, 'b': 1, 'width': 4, 'F': 6, 'c': 120}, {'vacuum_wavelength': 12.0, 'air_wavelength': 12.0, 'vacuum_width': 4.0, 'vacuum_density': 6.0, 'vacuum_frequency': 10.0, 'line_displacement': 0.0}), ({'L': 12, 'a': 3, 'b': 2, 'width': 0, 'F': 6, 'c': 120}, {'vacuum_wavelength': 18.0, 'air_wavelength': 8.0, 'vacuum_width': 0.0, 'vacuum_density': 4.0, 'vacuum_frequency': 6.666666666666667, 'line_displacement': 6.0}), ({'L': 12, 'a': 3, 'b': 2, 'width': 4, 'F': 0, 'c': 120}, {'vacuum_wavelength': 18.0, 'air_wavelength': 8.0, 'vacuum_width': 6.0, 'vacuum_density': 0.0, 'vacuum_frequency': 6.666666666666667, 'line_displacement': 6.0}), ({'L': 12, 'a': 4, 'b': 3, 'width': 4, 'F': 6, 'c': 120}, {'vacuum_wavelength': 16.0, 'air_wavelength': 9.0, 'vacuum_width': 5.333333333333333, 'vacuum_density': 4.5, 'vacuum_frequency': 7.5, 'line_displacement': 4.0}), ({'L': 12, 'a': 3, 'b': 2, 'width': 4, 'F': -2, 'c': 120}, {'vacuum_wavelength': 18.0, 'air_wavelength': 8.0, 'vacuum_width': 6.0, 'vacuum_density': -1.3333333333333333, 'vacuum_frequency': 6.666666666666667, 'line_displacement': 6.0})], 4: [({'L': 13, 'a': 3, 'b': 2, 'width': 4, 'F': 6, 'c': 120}, {'vacuum_wavelength': 19.5, 'air_wavelength': 8.666666666666666, 'vacuum_width': 6.0, 'vacuum_density': 4.0, 'vacuum_frequency': 6.153846153846154, 'line_displacement': 6.5}), ({'L': 13, 'a': 1, 'b': 1, 'width': 4, 'F': 6, 'c': 120}, {'vacuum_wavelength': 13.0, 'air_wavelength': 13.0, 'vacuum_width': 4.0, 'vacuum_density': 6.0, 'vacuum_frequency': 9.23076923076923, 'line_displacement': 0.0}), ({'L': 13, 'a': 3, 'b': 2, 'width': 0, 'F': 6, 'c': 120}, {'vacuum_wavelength': 19.5, 'air_wavelength': 8.666666666666666, 'vacuum_width': 0.0, 'vacuum_density': 4.0, 'vacuum_frequency': 6.153846153846154, 'line_displacement': 6.5}), ({'L': 13, 'a': 3, 'b': 2, 'width': 4, 'F': 0, 'c': 120}, {'vacuum_wavelength': 19.5, 'air_wavelength': 8.666666666666666, 'vacuum_width': 6.0, 'vacuum_density': 0.0, 'vacuum_frequency': 6.153846153846154, 'line_displacement': 6.5}), ({'L': 13, 'a': 4, 'b': 3, 'width': 4, 'F': 6, 'c': 120}, {'vacuum_wavelength': 17.333333333333332, 'air_wavelength': 9.75, 'vacuum_width': 5.333333333333333, 'vacuum_density': 4.5, 'vacuum_frequency': 6.923076923076923, 'line_displacement': 4.333333333333333}), ({'L': 13, 'a': 3, 'b': 2, 'width': 4, 'F': -2, 'c': 120}, {'vacuum_wavelength': 19.5, 'air_wavelength': 8.666666666666666, 'vacuum_width': 6.0, 'vacuum_density': -1.3333333333333333, 'vacuum_frequency': 6.153846153846154, 'line_displacement': 6.5})], 5: [({'L': 14, 'a': 3, 'b': 2, 'width': 4, 'F': 6, 'c': 120}, {'vacuum_wavelength': 21.0, 'air_wavelength': 9.333333333333334, 'vacuum_width': 6.0, 'vacuum_density': 4.0, 'vacuum_frequency': 5.714285714285714, 'line_displacement': 7.0}), ({'L': 14, 'a': 1, 'b': 1, 'width': 4, 'F': 6, 'c': 120}, {'vacuum_wavelength': 14.0, 'air_wavelength': 14.0, 'vacuum_width': 4.0, 'vacuum_density': 6.0, 'vacuum_frequency': 8.571428571428571, 'line_displacement': 0.0}), ({'L': 14, 'a': 3, 'b': 2, 'width': 0, 'F': 6, 'c': 120}, {'vacuum_wavelength': 21.0, 'air_wavelength': 9.333333333333334, 'vacuum_width': 0.0, 'vacuum_density': 4.0, 'vacuum_frequency': 5.714285714285714, 'line_displacement': 7.0}), ({'L': 14, 'a': 3, 'b': 2, 'width': 4, 'F': 0, 'c': 120}, {'vacuum_wavelength': 21.0, 'air_wavelength': 9.333333333333334, 'vacuum_width': 6.0, 'vacuum_density': 0.0, 'vacuum_frequency': 5.714285714285714, 'line_displacement': 7.0}), ({'L': 14, 'a': 4, 'b': 3, 'width': 4, 'F': 6, 'c': 120}, {'vacuum_wavelength': 18.666666666666668, 'air_wavelength': 10.5, 'vacuum_width': 5.333333333333333, 'vacuum_density': 4.5, 'vacuum_frequency': 6.428571428571429, 'line_displacement': 4.666666666666667}), ({'L': 14, 'a': 3, 'b': 2, 'width': 4, 'F': -2, 'c': 120}, {'vacuum_wavelength': 21.0, 'air_wavelength': 9.333333333333334, 'vacuum_width': 6.0, 'vacuum_density': -1.3333333333333333, 'vacuum_frequency': 5.714285714285714, 'line_displacement': 7.0})]}
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{'air_wavelength': 8.5, 'line_displacement': 5.0, 'vacuum_density': 4.0, 'vacuum_frequency': 8.0, 'vacuum_wavelength': 15.0, 'vacuum_width': 6.0}{'air_wavelength': 6.666666666666667, 'line_displacement': 5.0, 'vacuum_density': 4.0, 'vacuum_frequency': 8.0, 'vacuum_wavelength': 15.0, 'vacuum_width': 6.0}Failed
astronomical fixture 1{'air_wavelength': 9.0, 'line_displacement': 0.0, 'vacuum_density': 6.0, 'vacuum_frequency': 12.0, 'vacuum_wavelength': 10.0, 'vacuum_width': 4.0}{'air_wavelength': 10.0, 'line_displacement': 0.0, 'vacuum_density': 6.0, 'vacuum_frequency': 12.0, 'vacuum_wavelength': 10.0, 'vacuum_width': 4.0}Failed
astronomical fixture 2{'air_wavelength': 8.5, 'line_displacement': 5.0, 'vacuum_density': 4.0, 'vacuum_frequency': 8.0, 'vacuum_wavelength': 15.0, 'vacuum_width': 0.0}{'air_wavelength': 6.666666666666667, 'line_displacement': 5.0, 'vacuum_density': 4.0, 'vacuum_frequency': 8.0, 'vacuum_wavelength': 15.0, 'vacuum_width': 0.0}Failed
astronomical fixture 3{'air_wavelength': 8.5, 'line_displacement': 5.0, 'vacuum_density': 0.0, 'vacuum_frequency': 8.0, 'vacuum_wavelength': 15.0, 'vacuum_width': 6.0}{'air_wavelength': 6.666666666666667, 'line_displacement': 5.0, 'vacuum_density': 0.0, 'vacuum_frequency': 8.0, 'vacuum_wavelength': 15.0, 'vacuum_width': 6.0}Failed
astronomical fixture 4{'air_wavelength': 8.666666666666666, 'line_displacement': 3.3333333333333335, 'vacuum_density': 4.5, 'vacuum_frequency': 9.0, 'vacuum_wavelength': 13.333333333333334, 'vacuum_width': 5.333333333333333}{'air_wavelength': 7.5, 'line_displacement': 3.3333333333333335, 'vacuum_density': 4.5, 'vacuum_frequency': 9.0, 'vacuum_wavelength': 13.333333333333334, 'vacuum_width': 5.333333333333333}Failed
astronomical fixture 5{'air_wavelength': 8.5, 'line_displacement': 5.0, 'vacuum_density': -1.3333333333333333, 'vacuum_frequency': 8.0, 'vacuum_wavelength': 15.0, 'vacuum_width': 6.0}{'air_wavelength': 6.666666666666667, 'line_displacement': 5.0, 'vacuum_density': -1.3333333333333333, 'vacuum_frequency': 8.0, 'vacuum_wavelength': 15.0, 'vacuum_width': 6.0}Failed

SHA-256 / 59a848e607517ebb378eafdd0c1342c5c3fa3f5dba091b097f83e8fae58152e1

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.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

Sign in to the archive ↗

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 2026-09-29T14:45:59.850622+00:00.

Case digest / f8eeb8d6102aedeef4b0ae327a3ea4f5ac31e4a7af68bdeb32bee8fa0ded2a57