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FA-56316 / Astronomical coordinate conventions / Open access

Wcs header card semantics: Case-folding spectral CUNIT conflates milli- and mega-frequency prefixes · case 01

The adapter reports an incorrect frequency hz while other fields remain valid.

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

ROOT CAUSE

Case-folding spectral CUNIT conflates milli- and mega-frequency prefixes. Faulty expression: d['frequency']*{'hz':1,'khz':1000,'mhz':1000000}[d['unit'].lower()]

THE FAILURE

Case-folding spectral CUNIT conflates milli- and mega-frequency prefixes. Faulty expression: d['frequency']*{'hz':1,'khz':1000,'mhz':1000000}[d['unit'].lower()]

Unsuccessful approach: A partial convention repair still uses d['frequency']

Case contract

A bounded FITS-like header adapter parses the projection code at CTYPE characters 5:8, supports exact case-sensitive frequency units Hz,kHz,MHz,mHz, defaults absent CRPIX to one but preserves explicit zero, resolves WCSNAME to its suffix, and binds PV parameters to world-axis number. Effective dimensionality is max(NAXIS,WCSAXES). Output fields are defined by: projection = d['ctype'][5:8]; frequency_hz = d['frequency']*{'Hz':1,'kHz':1000,'MHz':1000000,'mHz':0.001}[d['unit']]; reference_pixel = 1 if d['crpix'] is None else d['crpix']; dimension = max(d['naxis'],d['wcsaxes']); selected_suffix = next(k for k,v in d['names'].items() if v==d['name']); projection_parameter = d['pv'][d['world']]

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 {'projection': d['ctype'][5:8], 'frequency_hz': d['frequency']*{'hz':1,'khz':1000,'mhz':1000000}[d['unit'].lower()], 'reference_pixel': 1 if d['crpix'] is None else d['crpix'], 'dimension': max(d['naxis'],d['wcsaxes']), 'selected_suffix': next(k for k,v in d['names'].items() if v==d['name']), 'projection_parameter': d['pv'][d['world']]}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = {1: [({'ctype': 'RA---TAN-SIP', 'unit': 'mHz', 'frequency': 8, 'crpix': 0, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'TAN', 'frequency_hz': 0.008, 'reference_pixel': 0, 'dimension': 3, 'selected_suffix': 'A', 'projection_parameter': 7}), ({'ctype': 'DEC--SIN', 'unit': 'Hz', 'frequency': 8, 'crpix': None, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'SIN', 'frequency_hz': 8, 'reference_pixel': 1, 'dimension': 3, 'selected_suffix': 'A', 'projection_parameter': 7}), ({'ctype': 'GLON-CAR', 'unit': 'kHz', 'frequency': 8, 'crpix': 0, 'naxis': 4, 'wcsaxes': 2, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'CAR', 'frequency_hz': 8000, 'reference_pixel': 0, 'dimension': 4, 'selected_suffix': 'A', 'projection_parameter': 7}), ({'ctype': 'FREQ-LOG', 'unit': 'MHz', 'frequency': 8, 'crpix': 0, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'A'}, 'name': 'A', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 1, 'pixel': 2}, {'projection': 'LOG', 'frequency_hz': 8000000, 'reference_pixel': 0, 'dimension': 3, 'selected_suffix': 'A', 'projection_parameter': 5}), ({'ctype': 'RA---TAN', 'unit': 'mHz', 'frequency': 8, 'crpix': 3, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'other'}, 'name': 'primary', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'TAN', 'frequency_hz': 0.008, 'reference_pixel': 3, 'dimension': 3, 'selected_suffix': '', 'projection_parameter': 7}), ({'ctype': 'DEC--TAN-SIP', 'unit': 'Hz', 'frequency': 8, 'crpix': 0, 'naxis': 1, 'wcsaxes': 1, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 0, 'pixel': 1}, {'projection': 'TAN', 'frequency_hz': 8, 'reference_pixel': 0, 'dimension': 1, 'selected_suffix': 'A', 'projection_parameter': 2})], 2: [({'ctype': 'RA---TAN-SIP', 'unit': 'mHz', 'frequency': 9, 'crpix': 0, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'TAN', 'frequency_hz': 0.009000000000000001, 'reference_pixel': 0, 'dimension': 3, 'selected_suffix': 'A', 'projection_parameter': 7}), ({'ctype': 'DEC--SIN', 'unit': 'Hz', 'frequency': 9, 'crpix': None, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'SIN', 'frequency_hz': 9, 'reference_pixel': 1, 'dimension': 3, 'selected_suffix': 'A', 'projection_parameter': 7}), ({'ctype': 'GLON-CAR', 'unit': 'kHz', 'frequency': 9, 'crpix': 0, 'naxis': 4, 'wcsaxes': 2, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'CAR', 'frequency_hz': 9000, 'reference_pixel': 0, 'dimension': 4, 'selected_suffix': 'A', 'projection_parameter': 7}), ({'ctype': 'FREQ-LOG', 'unit': 'MHz', 'frequency': 9, 'crpix': 0, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'A'}, 'name': 'A', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 1, 'pixel': 2}, {'projection': 'LOG', 'frequency_hz': 9000000, 'reference_pixel': 0, 'dimension': 3, 'selected_suffix': 'A', 'projection_parameter': 5}), ({'ctype': 'RA---TAN', 'unit': 'mHz', 'frequency': 9, 'crpix': 3, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'other'}, 'name': 'primary', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'TAN', 'frequency_hz': 0.009000000000000001, 'reference_pixel': 3, 'dimension': 3, 'selected_suffix': '', 'projection_parameter': 7}), ({'ctype': 'DEC--TAN-SIP', 'unit': 'Hz', 'frequency': 9, 'crpix': 0, 'naxis': 1, 'wcsaxes': 1, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 0, 'pixel': 1}, {'projection': 'TAN', 'frequency_hz': 9, 'reference_pixel': 0, 'dimension': 1, 'selected_suffix': 'A', 'projection_parameter': 2})], 3: [({'ctype': 'RA---TAN-SIP', 'unit': 'mHz', 'frequency': 10, 'crpix': 0, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'TAN', 'frequency_hz': 0.01, 'reference_pixel': 0, 'dimension': 3, 'selected_suffix': 'A', 'projection_parameter': 7}), ({'ctype': 'DEC--SIN', 'unit': 'Hz', 'frequency': 10, 'crpix': None, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'SIN', 'frequency_hz': 10, 'reference_pixel': 1, 'dimension': 3, 'selected_suffix': 'A', 'projection_parameter': 7}), ({'ctype': 'GLON-CAR', 'unit': 'kHz', 'frequency': 10, 'crpix': 0, 'naxis': 4, 'wcsaxes': 2, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'CAR', 'frequency_hz': 10000, 'reference_pixel': 0, 'dimension': 4, 'selected_suffix': 'A', 'projection_parameter': 7}), ({'ctype': 'FREQ-LOG', 'unit': 'MHz', 'frequency': 10, 'crpix': 0, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'A'}, 'name': 'A', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 1, 'pixel': 2}, {'projection': 'LOG', 'frequency_hz': 10000000, 'reference_pixel': 0, 'dimension': 3, 'selected_suffix': 'A', 'projection_parameter': 5}), ({'ctype': 'RA---TAN', 'unit': 'mHz', 'frequency': 10, 'crpix': 3, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'other'}, 'name': 'primary', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'TAN', 'frequency_hz': 0.01, 'reference_pixel': 3, 'dimension': 3, 'selected_suffix': '', 'projection_parameter': 7}), ({'ctype': 'DEC--TAN-SIP', 'unit': 'Hz', 'frequency': 10, 'crpix': 0, 'naxis': 1, 'wcsaxes': 1, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 0, 'pixel': 1}, {'projection': 'TAN', 'frequency_hz': 10, 'reference_pixel': 0, 'dimension': 1, 'selected_suffix': 'A', 'projection_parameter': 2})], 4: [({'ctype': 'RA---TAN-SIP', 'unit': 'mHz', 'frequency': 11, 'crpix': 0, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'TAN', 'frequency_hz': 0.011, 'reference_pixel': 0, 'dimension': 3, 'selected_suffix': 'A', 'projection_parameter': 7}), ({'ctype': 'DEC--SIN', 'unit': 'Hz', 'frequency': 11, 'crpix': None, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'SIN', 'frequency_hz': 11, 'reference_pixel': 1, 'dimension': 3, 'selected_suffix': 'A', 'projection_parameter': 7}), ({'ctype': 'GLON-CAR', 'unit': 'kHz', 'frequency': 11, 'crpix': 0, 'naxis': 4, 'wcsaxes': 2, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'CAR', 'frequency_hz': 11000, 'reference_pixel': 0, 'dimension': 4, 'selected_suffix': 'A', 'projection_parameter': 7}), ({'ctype': 'FREQ-LOG', 'unit': 'MHz', 'frequency': 11, 'crpix': 0, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'A'}, 'name': 'A', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 1, 'pixel': 2}, {'projection': 'LOG', 'frequency_hz': 11000000, 'reference_pixel': 0, 'dimension': 3, 'selected_suffix': 'A', 'projection_parameter': 5}), ({'ctype': 'RA---TAN', 'unit': 'mHz', 'frequency': 11, 'crpix': 3, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'other'}, 'name': 'primary', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'TAN', 'frequency_hz': 0.011, 'reference_pixel': 3, 'dimension': 3, 'selected_suffix': '', 'projection_parameter': 7}), ({'ctype': 'DEC--TAN-SIP', 'unit': 'Hz', 'frequency': 11, 'crpix': 0, 'naxis': 1, 'wcsaxes': 1, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 0, 'pixel': 1}, {'projection': 'TAN', 'frequency_hz': 11, 'reference_pixel': 0, 'dimension': 1, 'selected_suffix': 'A', 'projection_parameter': 2})], 5: [({'ctype': 'RA---TAN-SIP', 'unit': 'mHz', 'frequency': 12, 'crpix': 0, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'TAN', 'frequency_hz': 0.012, 'reference_pixel': 0, 'dimension': 3, 'selected_suffix': 'A', 'projection_parameter': 7}), ({'ctype': 'DEC--SIN', 'unit': 'Hz', 'frequency': 12, 'crpix': None, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'SIN', 'frequency_hz': 12, 'reference_pixel': 1, 'dimension': 3, 'selected_suffix': 'A', 'projection_parameter': 7}), ({'ctype': 'GLON-CAR', 'unit': 'kHz', 'frequency': 12, 'crpix': 0, 'naxis': 4, 'wcsaxes': 2, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'CAR', 'frequency_hz': 12000, 'reference_pixel': 0, 'dimension': 4, 'selected_suffix': 'A', 'projection_parameter': 7}), ({'ctype': 'FREQ-LOG', 'unit': 'MHz', 'frequency': 12, 'crpix': 0, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'A'}, 'name': 'A', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 1, 'pixel': 2}, {'projection': 'LOG', 'frequency_hz': 12000000, 'reference_pixel': 0, 'dimension': 3, 'selected_suffix': 'A', 'projection_parameter': 5}), ({'ctype': 'RA---TAN', 'unit': 'mHz', 'frequency': 12, 'crpix': 3, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'other'}, 'name': 'primary', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'TAN', 'frequency_hz': 0.012, 'reference_pixel': 3, 'dimension': 3, 'selected_suffix': '', 'projection_parameter': 7}), ({'ctype': 'DEC--TAN-SIP', 'unit': 'Hz', 'frequency': 12, 'crpix': 0, 'naxis': 1, 'wcsaxes': 1, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 0, 'pixel': 1}, {'projection': 'TAN', 'frequency_hz': 12, 'reference_pixel': 0, 'dimension': 1, 'selected_suffix': 'A', 'projection_parameter': 2})]}
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{'dimension': 3, 'frequency_hz': 8000000, 'projection': 'TAN', 'projection_parameter': 7, 'reference_pixel': 0, 'selected_suffix': 'A'}{'dimension': 3, 'frequency_hz': 0.008, 'projection': 'TAN', 'projection_parameter': 7, 'reference_pixel': 0, 'selected_suffix': 'A'}Failed
astronomical fixture 1{'dimension': 3, 'frequency_hz': 8, 'projection': 'SIN', 'projection_parameter': 7, 'reference_pixel': 1, 'selected_suffix': 'A'}{'dimension': 3, 'frequency_hz': 8, 'projection': 'SIN', 'projection_parameter': 7, 'reference_pixel': 1, 'selected_suffix': 'A'}Passed
astronomical fixture 2{'dimension': 4, 'frequency_hz': 8000, 'projection': 'CAR', 'projection_parameter': 7, 'reference_pixel': 0, 'selected_suffix': 'A'}{'dimension': 4, 'frequency_hz': 8000, 'projection': 'CAR', 'projection_parameter': 7, 'reference_pixel': 0, 'selected_suffix': 'A'}Passed
astronomical fixture 3{'dimension': 3, 'frequency_hz': 8000000, 'projection': 'LOG', 'projection_parameter': 5, 'reference_pixel': 0, 'selected_suffix': 'A'}{'dimension': 3, 'frequency_hz': 8000000, 'projection': 'LOG', 'projection_parameter': 5, 'reference_pixel': 0, 'selected_suffix': 'A'}Passed
astronomical fixture 4{'dimension': 3, 'frequency_hz': 8000000, 'projection': 'TAN', 'projection_parameter': 7, 'reference_pixel': 3, 'selected_suffix': ''}{'dimension': 3, 'frequency_hz': 0.008, 'projection': 'TAN', 'projection_parameter': 7, 'reference_pixel': 3, 'selected_suffix': ''}Failed
astronomical fixture 5{'dimension': 1, 'frequency_hz': 8, 'projection': 'TAN', 'projection_parameter': 2, 'reference_pixel': 0, 'selected_suffix': 'A'}{'dimension': 1, 'frequency_hz': 8, 'projection': 'TAN', 'projection_parameter': 2, 'reference_pixel': 0, 'selected_suffix': 'A'}Passed

SHA-256 / f2439f24f730e3aca8de6ef840fff99cbc8623b02e10669ef7d25f8088c6316d

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(d):
    return {'projection': d['ctype'][5:8], 'frequency_hz': d['frequency'], 'reference_pixel': 1 if d['crpix'] is None else d['crpix'], 'dimension': max(d['naxis'],d['wcsaxes']), 'selected_suffix': next(k for k,v in d['names'].items() if v==d['name']), 'projection_parameter': d['pv'][d['world']]}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = {1: [({'ctype': 'RA---TAN-SIP', 'unit': 'mHz', 'frequency': 8, 'crpix': 0, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'TAN', 'frequency_hz': 0.008, 'reference_pixel': 0, 'dimension': 3, 'selected_suffix': 'A', 'projection_parameter': 7}), ({'ctype': 'DEC--SIN', 'unit': 'Hz', 'frequency': 8, 'crpix': None, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'SIN', 'frequency_hz': 8, 'reference_pixel': 1, 'dimension': 3, 'selected_suffix': 'A', 'projection_parameter': 7}), ({'ctype': 'GLON-CAR', 'unit': 'kHz', 'frequency': 8, 'crpix': 0, 'naxis': 4, 'wcsaxes': 2, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'CAR', 'frequency_hz': 8000, 'reference_pixel': 0, 'dimension': 4, 'selected_suffix': 'A', 'projection_parameter': 7}), ({'ctype': 'FREQ-LOG', 'unit': 'MHz', 'frequency': 8, 'crpix': 0, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'A'}, 'name': 'A', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 1, 'pixel': 2}, {'projection': 'LOG', 'frequency_hz': 8000000, 'reference_pixel': 0, 'dimension': 3, 'selected_suffix': 'A', 'projection_parameter': 5}), ({'ctype': 'RA---TAN', 'unit': 'mHz', 'frequency': 8, 'crpix': 3, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'other'}, 'name': 'primary', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'TAN', 'frequency_hz': 0.008, 'reference_pixel': 3, 'dimension': 3, 'selected_suffix': '', 'projection_parameter': 7}), ({'ctype': 'DEC--TAN-SIP', 'unit': 'Hz', 'frequency': 8, 'crpix': 0, 'naxis': 1, 'wcsaxes': 1, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 0, 'pixel': 1}, {'projection': 'TAN', 'frequency_hz': 8, 'reference_pixel': 0, 'dimension': 1, 'selected_suffix': 'A', 'projection_parameter': 2})], 2: [({'ctype': 'RA---TAN-SIP', 'unit': 'mHz', 'frequency': 9, 'crpix': 0, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'TAN', 'frequency_hz': 0.009000000000000001, 'reference_pixel': 0, 'dimension': 3, 'selected_suffix': 'A', 'projection_parameter': 7}), ({'ctype': 'DEC--SIN', 'unit': 'Hz', 'frequency': 9, 'crpix': None, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'SIN', 'frequency_hz': 9, 'reference_pixel': 1, 'dimension': 3, 'selected_suffix': 'A', 'projection_parameter': 7}), ({'ctype': 'GLON-CAR', 'unit': 'kHz', 'frequency': 9, 'crpix': 0, 'naxis': 4, 'wcsaxes': 2, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'CAR', 'frequency_hz': 9000, 'reference_pixel': 0, 'dimension': 4, 'selected_suffix': 'A', 'projection_parameter': 7}), ({'ctype': 'FREQ-LOG', 'unit': 'MHz', 'frequency': 9, 'crpix': 0, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'A'}, 'name': 'A', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 1, 'pixel': 2}, {'projection': 'LOG', 'frequency_hz': 9000000, 'reference_pixel': 0, 'dimension': 3, 'selected_suffix': 'A', 'projection_parameter': 5}), ({'ctype': 'RA---TAN', 'unit': 'mHz', 'frequency': 9, 'crpix': 3, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'other'}, 'name': 'primary', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'TAN', 'frequency_hz': 0.009000000000000001, 'reference_pixel': 3, 'dimension': 3, 'selected_suffix': '', 'projection_parameter': 7}), ({'ctype': 'DEC--TAN-SIP', 'unit': 'Hz', 'frequency': 9, 'crpix': 0, 'naxis': 1, 'wcsaxes': 1, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 0, 'pixel': 1}, {'projection': 'TAN', 'frequency_hz': 9, 'reference_pixel': 0, 'dimension': 1, 'selected_suffix': 'A', 'projection_parameter': 2})], 3: [({'ctype': 'RA---TAN-SIP', 'unit': 'mHz', 'frequency': 10, 'crpix': 0, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'TAN', 'frequency_hz': 0.01, 'reference_pixel': 0, 'dimension': 3, 'selected_suffix': 'A', 'projection_parameter': 7}), ({'ctype': 'DEC--SIN', 'unit': 'Hz', 'frequency': 10, 'crpix': None, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'SIN', 'frequency_hz': 10, 'reference_pixel': 1, 'dimension': 3, 'selected_suffix': 'A', 'projection_parameter': 7}), ({'ctype': 'GLON-CAR', 'unit': 'kHz', 'frequency': 10, 'crpix': 0, 'naxis': 4, 'wcsaxes': 2, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'CAR', 'frequency_hz': 10000, 'reference_pixel': 0, 'dimension': 4, 'selected_suffix': 'A', 'projection_parameter': 7}), ({'ctype': 'FREQ-LOG', 'unit': 'MHz', 'frequency': 10, 'crpix': 0, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'A'}, 'name': 'A', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 1, 'pixel': 2}, {'projection': 'LOG', 'frequency_hz': 10000000, 'reference_pixel': 0, 'dimension': 3, 'selected_suffix': 'A', 'projection_parameter': 5}), ({'ctype': 'RA---TAN', 'unit': 'mHz', 'frequency': 10, 'crpix': 3, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'other'}, 'name': 'primary', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'TAN', 'frequency_hz': 0.01, 'reference_pixel': 3, 'dimension': 3, 'selected_suffix': '', 'projection_parameter': 7}), ({'ctype': 'DEC--TAN-SIP', 'unit': 'Hz', 'frequency': 10, 'crpix': 0, 'naxis': 1, 'wcsaxes': 1, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 0, 'pixel': 1}, {'projection': 'TAN', 'frequency_hz': 10, 'reference_pixel': 0, 'dimension': 1, 'selected_suffix': 'A', 'projection_parameter': 2})], 4: [({'ctype': 'RA---TAN-SIP', 'unit': 'mHz', 'frequency': 11, 'crpix': 0, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'TAN', 'frequency_hz': 0.011, 'reference_pixel': 0, 'dimension': 3, 'selected_suffix': 'A', 'projection_parameter': 7}), ({'ctype': 'DEC--SIN', 'unit': 'Hz', 'frequency': 11, 'crpix': None, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'SIN', 'frequency_hz': 11, 'reference_pixel': 1, 'dimension': 3, 'selected_suffix': 'A', 'projection_parameter': 7}), ({'ctype': 'GLON-CAR', 'unit': 'kHz', 'frequency': 11, 'crpix': 0, 'naxis': 4, 'wcsaxes': 2, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'CAR', 'frequency_hz': 11000, 'reference_pixel': 0, 'dimension': 4, 'selected_suffix': 'A', 'projection_parameter': 7}), ({'ctype': 'FREQ-LOG', 'unit': 'MHz', 'frequency': 11, 'crpix': 0, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'A'}, 'name': 'A', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 1, 'pixel': 2}, {'projection': 'LOG', 'frequency_hz': 11000000, 'reference_pixel': 0, 'dimension': 3, 'selected_suffix': 'A', 'projection_parameter': 5}), ({'ctype': 'RA---TAN', 'unit': 'mHz', 'frequency': 11, 'crpix': 3, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'other'}, 'name': 'primary', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'TAN', 'frequency_hz': 0.011, 'reference_pixel': 3, 'dimension': 3, 'selected_suffix': '', 'projection_parameter': 7}), ({'ctype': 'DEC--TAN-SIP', 'unit': 'Hz', 'frequency': 11, 'crpix': 0, 'naxis': 1, 'wcsaxes': 1, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 0, 'pixel': 1}, {'projection': 'TAN', 'frequency_hz': 11, 'reference_pixel': 0, 'dimension': 1, 'selected_suffix': 'A', 'projection_parameter': 2})], 5: [({'ctype': 'RA---TAN-SIP', 'unit': 'mHz', 'frequency': 12, 'crpix': 0, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'TAN', 'frequency_hz': 0.012, 'reference_pixel': 0, 'dimension': 3, 'selected_suffix': 'A', 'projection_parameter': 7}), ({'ctype': 'DEC--SIN', 'unit': 'Hz', 'frequency': 12, 'crpix': None, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'SIN', 'frequency_hz': 12, 'reference_pixel': 1, 'dimension': 3, 'selected_suffix': 'A', 'projection_parameter': 7}), ({'ctype': 'GLON-CAR', 'unit': 'kHz', 'frequency': 12, 'crpix': 0, 'naxis': 4, 'wcsaxes': 2, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'CAR', 'frequency_hz': 12000, 'reference_pixel': 0, 'dimension': 4, 'selected_suffix': 'A', 'projection_parameter': 7}), ({'ctype': 'FREQ-LOG', 'unit': 'MHz', 'frequency': 12, 'crpix': 0, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'A'}, 'name': 'A', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 1, 'pixel': 2}, {'projection': 'LOG', 'frequency_hz': 12000000, 'reference_pixel': 0, 'dimension': 3, 'selected_suffix': 'A', 'projection_parameter': 5}), ({'ctype': 'RA---TAN', 'unit': 'mHz', 'frequency': 12, 'crpix': 3, 'naxis': 2, 'wcsaxes': 3, 'names': {'': 'primary', 'A': 'other'}, 'name': 'primary', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 2, 'pixel': 1}, {'projection': 'TAN', 'frequency_hz': 0.012, 'reference_pixel': 3, 'dimension': 3, 'selected_suffix': '', 'projection_parameter': 7}), ({'ctype': 'DEC--TAN-SIP', 'unit': 'Hz', 'frequency': 12, 'crpix': 0, 'naxis': 1, 'wcsaxes': 1, 'names': {'': 'primary', 'A': 'target'}, 'name': 'target', 'pv': {0: 2, 1: 5, 2: 7}, 'world': 0, 'pixel': 1}, {'projection': 'TAN', 'frequency_hz': 12, 'reference_pixel': 0, 'dimension': 1, 'selected_suffix': 'A', 'projection_parameter': 2})]}
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{'dimension': 3, 'frequency_hz': 8, 'projection': 'TAN', 'projection_parameter': 7, 'reference_pixel': 0, 'selected_suffix': 'A'}{'dimension': 3, 'frequency_hz': 0.008, 'projection': 'TAN', 'projection_parameter': 7, 'reference_pixel': 0, 'selected_suffix': 'A'}Failed
astronomical fixture 1{'dimension': 3, 'frequency_hz': 8, 'projection': 'SIN', 'projection_parameter': 7, 'reference_pixel': 1, 'selected_suffix': 'A'}{'dimension': 3, 'frequency_hz': 8, 'projection': 'SIN', 'projection_parameter': 7, 'reference_pixel': 1, 'selected_suffix': 'A'}Passed
astronomical fixture 2{'dimension': 4, 'frequency_hz': 8, 'projection': 'CAR', 'projection_parameter': 7, 'reference_pixel': 0, 'selected_suffix': 'A'}{'dimension': 4, 'frequency_hz': 8000, 'projection': 'CAR', 'projection_parameter': 7, 'reference_pixel': 0, 'selected_suffix': 'A'}Failed
astronomical fixture 3{'dimension': 3, 'frequency_hz': 8, 'projection': 'LOG', 'projection_parameter': 5, 'reference_pixel': 0, 'selected_suffix': 'A'}{'dimension': 3, 'frequency_hz': 8000000, 'projection': 'LOG', 'projection_parameter': 5, 'reference_pixel': 0, 'selected_suffix': 'A'}Failed
astronomical fixture 4{'dimension': 3, 'frequency_hz': 8, 'projection': 'TAN', 'projection_parameter': 7, 'reference_pixel': 3, 'selected_suffix': ''}{'dimension': 3, 'frequency_hz': 0.008, 'projection': 'TAN', 'projection_parameter': 7, 'reference_pixel': 3, 'selected_suffix': ''}Failed
astronomical fixture 5{'dimension': 1, 'frequency_hz': 8, 'projection': 'TAN', 'projection_parameter': 2, 'reference_pixel': 0, 'selected_suffix': 'A'}{'dimension': 1, 'frequency_hz': 8, 'projection': 'TAN', 'projection_parameter': 2, 'reference_pixel': 0, 'selected_suffix': 'A'}Passed

SHA-256 / 827a216b57c3defccedc00e5b42f1b999107c70dd575321335c5cded50641589

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.

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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 2026-09-29T14:46:06.217461+00:00.

Case digest / 15f09c19180e9095afe7f7809782627433fc0bbccf9007b6c561a20b1003faa3