FAILURE MAP
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FA-56211 / Astronomical coordinate conventions / Open access

Spectrograph grating coordinate: Inverse grating coordinate fails to remove the incident-angle contribution · case 01

The adapter reports an incorrect inferred diffraction sine while other fields remain valid.

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

ROOT CAUSE

Inverse grating coordinate fails to remove the incident-angle contribution. Faulty expression: d['m']*d['line']/d['g']+d['a']

THE FAILURE

Inverse grating coordinate fails to remove the incident-angle contribution. Faulty expression: d['m']*d['line']/d['g']+d['a']

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

Case contract

A stipulated grating adapter supplies spacing g, signed sine of incidence a, signed sine of diffraction b, positive order m, focal length F, and separate calibration line wavelength line. Wavelength is g*(a+b)/m. A Littrow reference has b=a; supplied diffraction cosine c permits a local angular dispersion derivative. Output fields are defined by: wavelength = d['g']*(d['a']+d['b'])/d['m']; littrow_wavelength = 2*d['g']*d['a']/d['m']; angular_dispersion = d['g']*d['c']/d['m']; linear_dispersion = d['g']*d['c']/(d['m']*d['F']); inferred_diffraction_sine = d['m']*d['line']/d['g']-d['a']; next_order_wavelength = d['g']*(d['a']+d['b'])/(d['m']+1)

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 {'wavelength': d['g']*(d['a']+d['b'])/d['m'], 'littrow_wavelength': 2*d['g']*d['a']/d['m'], 'angular_dispersion': d['g']*d['c']/d['m'], 'linear_dispersion': d['g']*d['c']/(d['m']*d['F']), 'inferred_diffraction_sine': d['m']*d['line']/d['g']+d['a'], 'next_order_wavelength': d['g']*(d['a']+d['b'])/(d['m']+1)}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = {1: [({'g': 120, 'a': 0.5, 'b': 0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 30.0, 'littrow_wavelength': 40.0, 'angular_dispersion': 20.0, 'linear_dispersion': 2.0, 'inferred_diffraction_sine': -0.25, 'next_order_wavelength': 22.5}), ({'g': 120, 'a': 0, 'b': 0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 10.0, 'littrow_wavelength': 0.0, 'angular_dispersion': 20.0, 'linear_dispersion': 2.0, 'inferred_diffraction_sine': 0.25, 'next_order_wavelength': 7.5}), ({'g': 120, 'a': 0.5, 'b': -0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 10.0, 'littrow_wavelength': 40.0, 'angular_dispersion': 20.0, 'linear_dispersion': 2.0, 'inferred_diffraction_sine': -0.25, 'next_order_wavelength': 7.5}), ({'g': 120, 'a': 0.5, 'b': 0.25, 'm': 1, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 90.0, 'littrow_wavelength': 120.0, 'angular_dispersion': 60.0, 'linear_dispersion': 6.0, 'inferred_diffraction_sine': -0.4166666666666667, 'next_order_wavelength': 45.0}), ({'g': 120, 'a': 0.25, 'b': 0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 20.0, 'littrow_wavelength': 20.0, 'angular_dispersion': 20.0, 'linear_dispersion': 2.0, 'inferred_diffraction_sine': 0.0, 'next_order_wavelength': 15.0}), ({'g': 120, 'a': 0.5, 'b': 0.25, 'm': 3, 'F': 20, 'c': 1, 'line': 10}, {'wavelength': 30.0, 'littrow_wavelength': 40.0, 'angular_dispersion': 40.0, 'linear_dispersion': 2.0, 'inferred_diffraction_sine': -0.25, 'next_order_wavelength': 22.5})], 2: [({'g': 121, 'a': 0.5, 'b': 0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 30.25, 'littrow_wavelength': 40.333333333333336, 'angular_dispersion': 20.166666666666668, 'linear_dispersion': 2.0166666666666666, 'inferred_diffraction_sine': -0.25206611570247933, 'next_order_wavelength': 22.6875}), ({'g': 121, 'a': 0, 'b': 0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 10.083333333333334, 'littrow_wavelength': 0.0, 'angular_dispersion': 20.166666666666668, 'linear_dispersion': 2.0166666666666666, 'inferred_diffraction_sine': 0.24793388429752067, 'next_order_wavelength': 7.5625}), ({'g': 121, 'a': 0.5, 'b': -0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 10.083333333333334, 'littrow_wavelength': 40.333333333333336, 'angular_dispersion': 20.166666666666668, 'linear_dispersion': 2.0166666666666666, 'inferred_diffraction_sine': -0.25206611570247933, 'next_order_wavelength': 7.5625}), ({'g': 121, 'a': 0.5, 'b': 0.25, 'm': 1, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 90.75, 'littrow_wavelength': 121.0, 'angular_dispersion': 60.5, 'linear_dispersion': 6.05, 'inferred_diffraction_sine': -0.41735537190082644, 'next_order_wavelength': 45.375}), ({'g': 121, 'a': 0.25, 'b': 0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 20.166666666666668, 'littrow_wavelength': 20.166666666666668, 'angular_dispersion': 20.166666666666668, 'linear_dispersion': 2.0166666666666666, 'inferred_diffraction_sine': -0.002066115702479332, 'next_order_wavelength': 15.125}), ({'g': 121, 'a': 0.5, 'b': 0.25, 'm': 3, 'F': 20, 'c': 1, 'line': 10}, {'wavelength': 30.25, 'littrow_wavelength': 40.333333333333336, 'angular_dispersion': 40.333333333333336, 'linear_dispersion': 2.0166666666666666, 'inferred_diffraction_sine': -0.25206611570247933, 'next_order_wavelength': 22.6875})], 3: [({'g': 122, 'a': 0.5, 'b': 0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 30.5, 'littrow_wavelength': 40.666666666666664, 'angular_dispersion': 20.333333333333332, 'linear_dispersion': 2.033333333333333, 'inferred_diffraction_sine': -0.2540983606557377, 'next_order_wavelength': 22.875}), ({'g': 122, 'a': 0, 'b': 0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 10.166666666666666, 'littrow_wavelength': 0.0, 'angular_dispersion': 20.333333333333332, 'linear_dispersion': 2.033333333333333, 'inferred_diffraction_sine': 0.2459016393442623, 'next_order_wavelength': 7.625}), ({'g': 122, 'a': 0.5, 'b': -0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 10.166666666666666, 'littrow_wavelength': 40.666666666666664, 'angular_dispersion': 20.333333333333332, 'linear_dispersion': 2.033333333333333, 'inferred_diffraction_sine': -0.2540983606557377, 'next_order_wavelength': 7.625}), ({'g': 122, 'a': 0.5, 'b': 0.25, 'm': 1, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 91.5, 'littrow_wavelength': 122.0, 'angular_dispersion': 61.0, 'linear_dispersion': 6.1, 'inferred_diffraction_sine': -0.4180327868852459, 'next_order_wavelength': 45.75}), ({'g': 122, 'a': 0.25, 'b': 0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 20.333333333333332, 'littrow_wavelength': 20.333333333333332, 'angular_dispersion': 20.333333333333332, 'linear_dispersion': 2.033333333333333, 'inferred_diffraction_sine': -0.0040983606557377095, 'next_order_wavelength': 15.25}), ({'g': 122, 'a': 0.5, 'b': 0.25, 'm': 3, 'F': 20, 'c': 1, 'line': 10}, {'wavelength': 30.5, 'littrow_wavelength': 40.666666666666664, 'angular_dispersion': 40.666666666666664, 'linear_dispersion': 2.033333333333333, 'inferred_diffraction_sine': -0.2540983606557377, 'next_order_wavelength': 22.875})], 4: [({'g': 123, 'a': 0.5, 'b': 0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 30.75, 'littrow_wavelength': 41.0, 'angular_dispersion': 20.5, 'linear_dispersion': 2.05, 'inferred_diffraction_sine': -0.25609756097560976, 'next_order_wavelength': 23.0625}), ({'g': 123, 'a': 0, 'b': 0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 10.25, 'littrow_wavelength': 0.0, 'angular_dispersion': 20.5, 'linear_dispersion': 2.05, 'inferred_diffraction_sine': 0.24390243902439024, 'next_order_wavelength': 7.6875}), ({'g': 123, 'a': 0.5, 'b': -0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 10.25, 'littrow_wavelength': 41.0, 'angular_dispersion': 20.5, 'linear_dispersion': 2.05, 'inferred_diffraction_sine': -0.25609756097560976, 'next_order_wavelength': 7.6875}), ({'g': 123, 'a': 0.5, 'b': 0.25, 'm': 1, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 92.25, 'littrow_wavelength': 123.0, 'angular_dispersion': 61.5, 'linear_dispersion': 6.15, 'inferred_diffraction_sine': -0.4186991869918699, 'next_order_wavelength': 46.125}), ({'g': 123, 'a': 0.25, 'b': 0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 20.5, 'littrow_wavelength': 20.5, 'angular_dispersion': 20.5, 'linear_dispersion': 2.05, 'inferred_diffraction_sine': -0.0060975609756097615, 'next_order_wavelength': 15.375}), ({'g': 123, 'a': 0.5, 'b': 0.25, 'm': 3, 'F': 20, 'c': 1, 'line': 10}, {'wavelength': 30.75, 'littrow_wavelength': 41.0, 'angular_dispersion': 41.0, 'linear_dispersion': 2.05, 'inferred_diffraction_sine': -0.25609756097560976, 'next_order_wavelength': 23.0625})], 5: [({'g': 124, 'a': 0.5, 'b': 0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 31.0, 'littrow_wavelength': 41.333333333333336, 'angular_dispersion': 20.666666666666668, 'linear_dispersion': 2.066666666666667, 'inferred_diffraction_sine': -0.25806451612903225, 'next_order_wavelength': 23.25}), ({'g': 124, 'a': 0, 'b': 0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 10.333333333333334, 'littrow_wavelength': 0.0, 'angular_dispersion': 20.666666666666668, 'linear_dispersion': 2.066666666666667, 'inferred_diffraction_sine': 0.24193548387096775, 'next_order_wavelength': 7.75}), ({'g': 124, 'a': 0.5, 'b': -0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 10.333333333333334, 'littrow_wavelength': 41.333333333333336, 'angular_dispersion': 20.666666666666668, 'linear_dispersion': 2.066666666666667, 'inferred_diffraction_sine': -0.25806451612903225, 'next_order_wavelength': 7.75}), ({'g': 124, 'a': 0.5, 'b': 0.25, 'm': 1, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 93.0, 'littrow_wavelength': 124.0, 'angular_dispersion': 62.0, 'linear_dispersion': 6.2, 'inferred_diffraction_sine': -0.41935483870967744, 'next_order_wavelength': 46.5}), ({'g': 124, 'a': 0.25, 'b': 0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 20.666666666666668, 'littrow_wavelength': 20.666666666666668, 'angular_dispersion': 20.666666666666668, 'linear_dispersion': 2.066666666666667, 'inferred_diffraction_sine': -0.008064516129032251, 'next_order_wavelength': 15.5}), ({'g': 124, 'a': 0.5, 'b': 0.25, 'm': 3, 'F': 20, 'c': 1, 'line': 10}, {'wavelength': 31.0, 'littrow_wavelength': 41.333333333333336, 'angular_dispersion': 41.333333333333336, 'linear_dispersion': 2.066666666666667, 'inferred_diffraction_sine': -0.25806451612903225, 'next_order_wavelength': 23.25})]}
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{'angular_dispersion': 20.0, 'inferred_diffraction_sine': 0.75, 'linear_dispersion': 2.0, 'littrow_wavelength': 40.0, 'next_order_wavelength': 22.5, 'wavelength': 30.0}{'angular_dispersion': 20.0, 'inferred_diffraction_sine': -0.25, 'linear_dispersion': 2.0, 'littrow_wavelength': 40.0, 'next_order_wavelength': 22.5, 'wavelength': 30.0}Failed
astronomical fixture 1{'angular_dispersion': 20.0, 'inferred_diffraction_sine': 0.25, 'linear_dispersion': 2.0, 'littrow_wavelength': 0.0, 'next_order_wavelength': 7.5, 'wavelength': 10.0}{'angular_dispersion': 20.0, 'inferred_diffraction_sine': 0.25, 'linear_dispersion': 2.0, 'littrow_wavelength': 0.0, 'next_order_wavelength': 7.5, 'wavelength': 10.0}Passed
astronomical fixture 2{'angular_dispersion': 20.0, 'inferred_diffraction_sine': 0.75, 'linear_dispersion': 2.0, 'littrow_wavelength': 40.0, 'next_order_wavelength': 7.5, 'wavelength': 10.0}{'angular_dispersion': 20.0, 'inferred_diffraction_sine': -0.25, 'linear_dispersion': 2.0, 'littrow_wavelength': 40.0, 'next_order_wavelength': 7.5, 'wavelength': 10.0}Failed
astronomical fixture 3{'angular_dispersion': 60.0, 'inferred_diffraction_sine': 0.5833333333333334, 'linear_dispersion': 6.0, 'littrow_wavelength': 120.0, 'next_order_wavelength': 45.0, 'wavelength': 90.0}{'angular_dispersion': 60.0, 'inferred_diffraction_sine': -0.4166666666666667, 'linear_dispersion': 6.0, 'littrow_wavelength': 120.0, 'next_order_wavelength': 45.0, 'wavelength': 90.0}Failed
astronomical fixture 4{'angular_dispersion': 20.0, 'inferred_diffraction_sine': 0.5, 'linear_dispersion': 2.0, 'littrow_wavelength': 20.0, 'next_order_wavelength': 15.0, 'wavelength': 20.0}{'angular_dispersion': 20.0, 'inferred_diffraction_sine': 0.0, 'linear_dispersion': 2.0, 'littrow_wavelength': 20.0, 'next_order_wavelength': 15.0, 'wavelength': 20.0}Failed
astronomical fixture 5{'angular_dispersion': 40.0, 'inferred_diffraction_sine': 0.75, 'linear_dispersion': 2.0, 'littrow_wavelength': 40.0, 'next_order_wavelength': 22.5, 'wavelength': 30.0}{'angular_dispersion': 40.0, 'inferred_diffraction_sine': -0.25, 'linear_dispersion': 2.0, 'littrow_wavelength': 40.0, 'next_order_wavelength': 22.5, 'wavelength': 30.0}Failed

SHA-256 / d5e4765258105ce9fce1b4378c1ecadfcfcc2e25d5f948d9ad476565eb2262e5

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(d):
    return {'wavelength': d['g']*(d['a']+d['b'])/d['m'], 'littrow_wavelength': 2*d['g']*d['a']/d['m'], 'angular_dispersion': d['g']*d['c']/d['m'], 'linear_dispersion': d['g']*d['c']/(d['m']*d['F']), 'inferred_diffraction_sine': d['line']/d['g']-d['a'], 'next_order_wavelength': d['g']*(d['a']+d['b'])/(d['m']+1)}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = {1: [({'g': 120, 'a': 0.5, 'b': 0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 30.0, 'littrow_wavelength': 40.0, 'angular_dispersion': 20.0, 'linear_dispersion': 2.0, 'inferred_diffraction_sine': -0.25, 'next_order_wavelength': 22.5}), ({'g': 120, 'a': 0, 'b': 0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 10.0, 'littrow_wavelength': 0.0, 'angular_dispersion': 20.0, 'linear_dispersion': 2.0, 'inferred_diffraction_sine': 0.25, 'next_order_wavelength': 7.5}), ({'g': 120, 'a': 0.5, 'b': -0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 10.0, 'littrow_wavelength': 40.0, 'angular_dispersion': 20.0, 'linear_dispersion': 2.0, 'inferred_diffraction_sine': -0.25, 'next_order_wavelength': 7.5}), ({'g': 120, 'a': 0.5, 'b': 0.25, 'm': 1, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 90.0, 'littrow_wavelength': 120.0, 'angular_dispersion': 60.0, 'linear_dispersion': 6.0, 'inferred_diffraction_sine': -0.4166666666666667, 'next_order_wavelength': 45.0}), ({'g': 120, 'a': 0.25, 'b': 0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 20.0, 'littrow_wavelength': 20.0, 'angular_dispersion': 20.0, 'linear_dispersion': 2.0, 'inferred_diffraction_sine': 0.0, 'next_order_wavelength': 15.0}), ({'g': 120, 'a': 0.5, 'b': 0.25, 'm': 3, 'F': 20, 'c': 1, 'line': 10}, {'wavelength': 30.0, 'littrow_wavelength': 40.0, 'angular_dispersion': 40.0, 'linear_dispersion': 2.0, 'inferred_diffraction_sine': -0.25, 'next_order_wavelength': 22.5})], 2: [({'g': 121, 'a': 0.5, 'b': 0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 30.25, 'littrow_wavelength': 40.333333333333336, 'angular_dispersion': 20.166666666666668, 'linear_dispersion': 2.0166666666666666, 'inferred_diffraction_sine': -0.25206611570247933, 'next_order_wavelength': 22.6875}), ({'g': 121, 'a': 0, 'b': 0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 10.083333333333334, 'littrow_wavelength': 0.0, 'angular_dispersion': 20.166666666666668, 'linear_dispersion': 2.0166666666666666, 'inferred_diffraction_sine': 0.24793388429752067, 'next_order_wavelength': 7.5625}), ({'g': 121, 'a': 0.5, 'b': -0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 10.083333333333334, 'littrow_wavelength': 40.333333333333336, 'angular_dispersion': 20.166666666666668, 'linear_dispersion': 2.0166666666666666, 'inferred_diffraction_sine': -0.25206611570247933, 'next_order_wavelength': 7.5625}), ({'g': 121, 'a': 0.5, 'b': 0.25, 'm': 1, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 90.75, 'littrow_wavelength': 121.0, 'angular_dispersion': 60.5, 'linear_dispersion': 6.05, 'inferred_diffraction_sine': -0.41735537190082644, 'next_order_wavelength': 45.375}), ({'g': 121, 'a': 0.25, 'b': 0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 20.166666666666668, 'littrow_wavelength': 20.166666666666668, 'angular_dispersion': 20.166666666666668, 'linear_dispersion': 2.0166666666666666, 'inferred_diffraction_sine': -0.002066115702479332, 'next_order_wavelength': 15.125}), ({'g': 121, 'a': 0.5, 'b': 0.25, 'm': 3, 'F': 20, 'c': 1, 'line': 10}, {'wavelength': 30.25, 'littrow_wavelength': 40.333333333333336, 'angular_dispersion': 40.333333333333336, 'linear_dispersion': 2.0166666666666666, 'inferred_diffraction_sine': -0.25206611570247933, 'next_order_wavelength': 22.6875})], 3: [({'g': 122, 'a': 0.5, 'b': 0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 30.5, 'littrow_wavelength': 40.666666666666664, 'angular_dispersion': 20.333333333333332, 'linear_dispersion': 2.033333333333333, 'inferred_diffraction_sine': -0.2540983606557377, 'next_order_wavelength': 22.875}), ({'g': 122, 'a': 0, 'b': 0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 10.166666666666666, 'littrow_wavelength': 0.0, 'angular_dispersion': 20.333333333333332, 'linear_dispersion': 2.033333333333333, 'inferred_diffraction_sine': 0.2459016393442623, 'next_order_wavelength': 7.625}), ({'g': 122, 'a': 0.5, 'b': -0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 10.166666666666666, 'littrow_wavelength': 40.666666666666664, 'angular_dispersion': 20.333333333333332, 'linear_dispersion': 2.033333333333333, 'inferred_diffraction_sine': -0.2540983606557377, 'next_order_wavelength': 7.625}), ({'g': 122, 'a': 0.5, 'b': 0.25, 'm': 1, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 91.5, 'littrow_wavelength': 122.0, 'angular_dispersion': 61.0, 'linear_dispersion': 6.1, 'inferred_diffraction_sine': -0.4180327868852459, 'next_order_wavelength': 45.75}), ({'g': 122, 'a': 0.25, 'b': 0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 20.333333333333332, 'littrow_wavelength': 20.333333333333332, 'angular_dispersion': 20.333333333333332, 'linear_dispersion': 2.033333333333333, 'inferred_diffraction_sine': -0.0040983606557377095, 'next_order_wavelength': 15.25}), ({'g': 122, 'a': 0.5, 'b': 0.25, 'm': 3, 'F': 20, 'c': 1, 'line': 10}, {'wavelength': 30.5, 'littrow_wavelength': 40.666666666666664, 'angular_dispersion': 40.666666666666664, 'linear_dispersion': 2.033333333333333, 'inferred_diffraction_sine': -0.2540983606557377, 'next_order_wavelength': 22.875})], 4: [({'g': 123, 'a': 0.5, 'b': 0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 30.75, 'littrow_wavelength': 41.0, 'angular_dispersion': 20.5, 'linear_dispersion': 2.05, 'inferred_diffraction_sine': -0.25609756097560976, 'next_order_wavelength': 23.0625}), ({'g': 123, 'a': 0, 'b': 0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 10.25, 'littrow_wavelength': 0.0, 'angular_dispersion': 20.5, 'linear_dispersion': 2.05, 'inferred_diffraction_sine': 0.24390243902439024, 'next_order_wavelength': 7.6875}), ({'g': 123, 'a': 0.5, 'b': -0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 10.25, 'littrow_wavelength': 41.0, 'angular_dispersion': 20.5, 'linear_dispersion': 2.05, 'inferred_diffraction_sine': -0.25609756097560976, 'next_order_wavelength': 7.6875}), ({'g': 123, 'a': 0.5, 'b': 0.25, 'm': 1, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 92.25, 'littrow_wavelength': 123.0, 'angular_dispersion': 61.5, 'linear_dispersion': 6.15, 'inferred_diffraction_sine': -0.4186991869918699, 'next_order_wavelength': 46.125}), ({'g': 123, 'a': 0.25, 'b': 0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 20.5, 'littrow_wavelength': 20.5, 'angular_dispersion': 20.5, 'linear_dispersion': 2.05, 'inferred_diffraction_sine': -0.0060975609756097615, 'next_order_wavelength': 15.375}), ({'g': 123, 'a': 0.5, 'b': 0.25, 'm': 3, 'F': 20, 'c': 1, 'line': 10}, {'wavelength': 30.75, 'littrow_wavelength': 41.0, 'angular_dispersion': 41.0, 'linear_dispersion': 2.05, 'inferred_diffraction_sine': -0.25609756097560976, 'next_order_wavelength': 23.0625})], 5: [({'g': 124, 'a': 0.5, 'b': 0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 31.0, 'littrow_wavelength': 41.333333333333336, 'angular_dispersion': 20.666666666666668, 'linear_dispersion': 2.066666666666667, 'inferred_diffraction_sine': -0.25806451612903225, 'next_order_wavelength': 23.25}), ({'g': 124, 'a': 0, 'b': 0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 10.333333333333334, 'littrow_wavelength': 0.0, 'angular_dispersion': 20.666666666666668, 'linear_dispersion': 2.066666666666667, 'inferred_diffraction_sine': 0.24193548387096775, 'next_order_wavelength': 7.75}), ({'g': 124, 'a': 0.5, 'b': -0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 10.333333333333334, 'littrow_wavelength': 41.333333333333336, 'angular_dispersion': 20.666666666666668, 'linear_dispersion': 2.066666666666667, 'inferred_diffraction_sine': -0.25806451612903225, 'next_order_wavelength': 7.75}), ({'g': 124, 'a': 0.5, 'b': 0.25, 'm': 1, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 93.0, 'littrow_wavelength': 124.0, 'angular_dispersion': 62.0, 'linear_dispersion': 6.2, 'inferred_diffraction_sine': -0.41935483870967744, 'next_order_wavelength': 46.5}), ({'g': 124, 'a': 0.25, 'b': 0.25, 'm': 3, 'F': 10, 'c': 0.5, 'line': 10}, {'wavelength': 20.666666666666668, 'littrow_wavelength': 20.666666666666668, 'angular_dispersion': 20.666666666666668, 'linear_dispersion': 2.066666666666667, 'inferred_diffraction_sine': -0.008064516129032251, 'next_order_wavelength': 15.5}), ({'g': 124, 'a': 0.5, 'b': 0.25, 'm': 3, 'F': 20, 'c': 1, 'line': 10}, {'wavelength': 31.0, 'littrow_wavelength': 41.333333333333336, 'angular_dispersion': 41.333333333333336, 'linear_dispersion': 2.066666666666667, 'inferred_diffraction_sine': -0.25806451612903225, 'next_order_wavelength': 23.25})]}
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{'angular_dispersion': 20.0, 'inferred_diffraction_sine': -0.4166666666666667, 'linear_dispersion': 2.0, 'littrow_wavelength': 40.0, 'next_order_wavelength': 22.5, 'wavelength': 30.0}{'angular_dispersion': 20.0, 'inferred_diffraction_sine': -0.25, 'linear_dispersion': 2.0, 'littrow_wavelength': 40.0, 'next_order_wavelength': 22.5, 'wavelength': 30.0}Failed
astronomical fixture 1{'angular_dispersion': 20.0, 'inferred_diffraction_sine': 0.08333333333333333, 'linear_dispersion': 2.0, 'littrow_wavelength': 0.0, 'next_order_wavelength': 7.5, 'wavelength': 10.0}{'angular_dispersion': 20.0, 'inferred_diffraction_sine': 0.25, 'linear_dispersion': 2.0, 'littrow_wavelength': 0.0, 'next_order_wavelength': 7.5, 'wavelength': 10.0}Failed
astronomical fixture 2{'angular_dispersion': 20.0, 'inferred_diffraction_sine': -0.4166666666666667, 'linear_dispersion': 2.0, 'littrow_wavelength': 40.0, 'next_order_wavelength': 7.5, 'wavelength': 10.0}{'angular_dispersion': 20.0, 'inferred_diffraction_sine': -0.25, 'linear_dispersion': 2.0, 'littrow_wavelength': 40.0, 'next_order_wavelength': 7.5, 'wavelength': 10.0}Failed
astronomical fixture 3{'angular_dispersion': 60.0, 'inferred_diffraction_sine': -0.4166666666666667, 'linear_dispersion': 6.0, 'littrow_wavelength': 120.0, 'next_order_wavelength': 45.0, 'wavelength': 90.0}{'angular_dispersion': 60.0, 'inferred_diffraction_sine': -0.4166666666666667, 'linear_dispersion': 6.0, 'littrow_wavelength': 120.0, 'next_order_wavelength': 45.0, 'wavelength': 90.0}Passed
astronomical fixture 4{'angular_dispersion': 20.0, 'inferred_diffraction_sine': -0.16666666666666669, 'linear_dispersion': 2.0, 'littrow_wavelength': 20.0, 'next_order_wavelength': 15.0, 'wavelength': 20.0}{'angular_dispersion': 20.0, 'inferred_diffraction_sine': 0.0, 'linear_dispersion': 2.0, 'littrow_wavelength': 20.0, 'next_order_wavelength': 15.0, 'wavelength': 20.0}Failed
astronomical fixture 5{'angular_dispersion': 40.0, 'inferred_diffraction_sine': -0.4166666666666667, 'linear_dispersion': 2.0, 'littrow_wavelength': 40.0, 'next_order_wavelength': 22.5, 'wavelength': 30.0}{'angular_dispersion': 40.0, 'inferred_diffraction_sine': -0.25, 'linear_dispersion': 2.0, 'littrow_wavelength': 40.0, 'next_order_wavelength': 22.5, 'wavelength': 30.0}Failed

SHA-256 / 252e9c064ae133c0cf658887807cc56ede26a3fe94da54026acf20a89bcafa72

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 2026-09-29T14:46:05.017654+00:00.

Case digest / 96b130af45027c8803cd8ccf874ce307a04e33e87ef6f4b1b0d751adec077f8e