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FA-55766 / Astronomical coordinate conventions / Open access

Celestial sin projection: SIN center displacement is confused with the center direction cosine · case 01

The adapter reports an incorrect center offset while other fields remain valid.

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

ROOT CAUSE

SIN center displacement is confused with the center direction cosine. Faulty expression: d['z']

VERIFIED REPAIR

Preserve the declared model convention at this site: 1-d['z']

Unsuccessful approach: A partial convention repair still uses abs(d['z'])

Case contract

A reduced SIN sky projection supplies direction east e,north n,center z and obliqueness coefficients a,b. Its plane coordinates are e+a*(1-z),n+b*(1-z). Orthographic mode a=b=0 still has front/back hemisphere ambiguity; forward metadata preserves z for inverse branch selection. Output fields are defined by: plane_east = d['e']+d['a']*(1-d['z']); plane_north = d['n']+d['b']*(1-d['z']); hemisphere = 'front' if d['z']>=0 else 'back'; undo_obliqueness_east = d['e']-d['a']*(1-d['z']); undo_obliqueness_north = d['n']-d['b']*(1-d['z']); center_offset = 1-d['z']

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 {'plane_east': d['e']+d['a']*(1-d['z']), 'plane_north': d['n']+d['b']*(1-d['z']), 'hemisphere': 'front' if d['z']>=0 else 'back', 'undo_obliqueness_east': d['e']-d['a']*(1-d['z']), 'undo_obliqueness_north': d['n']-d['b']*(1-d['z']), 'center_offset': d['z']}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = {1: [({'e': 2, 'n': 3, 'z': 0.5, 'a': 2, 'b': -3}, {'plane_east': 3.0, 'plane_north': 1.5, 'hemisphere': 'front', 'undo_obliqueness_east': 1.0, 'undo_obliqueness_north': 4.5, 'center_offset': 0.5}), ({'e': 2, 'n': 3, 'z': 0.5, 'a': 0, 'b': 0}, {'plane_east': 2.0, 'plane_north': 3.0, 'hemisphere': 'front', 'undo_obliqueness_east': 2.0, 'undo_obliqueness_north': 3.0, 'center_offset': 0.5}), ({'e': 2, 'n': 3, 'z': 1, 'a': 2, 'b': -3}, {'plane_east': 2, 'plane_north': 3, 'hemisphere': 'front', 'undo_obliqueness_east': 2, 'undo_obliqueness_north': 3, 'center_offset': 0}), ({'e': 2, 'n': 3, 'z': -0.5, 'a': 2, 'b': -3}, {'plane_east': 5.0, 'plane_north': -1.5, 'hemisphere': 'back', 'undo_obliqueness_east': -1.0, 'undo_obliqueness_north': 7.5, 'center_offset': 1.5}), ({'e': 2, 'n': 3, 'z': 0, 'a': 2, 'b': -3}, {'plane_east': 4, 'plane_north': 0, 'hemisphere': 'front', 'undo_obliqueness_east': 0, 'undo_obliqueness_north': 6, 'center_offset': 1}), ({'e': 2, 'n': 3, 'z': 0.5, 'a': -2, 'b': 4}, {'plane_east': 1.0, 'plane_north': 5.0, 'hemisphere': 'front', 'undo_obliqueness_east': 3.0, 'undo_obliqueness_north': 1.0, 'center_offset': 0.5})], 2: [({'e': 3, 'n': 3, 'z': 0.5, 'a': 2, 'b': -3}, {'plane_east': 4.0, 'plane_north': 1.5, 'hemisphere': 'front', 'undo_obliqueness_east': 2.0, 'undo_obliqueness_north': 4.5, 'center_offset': 0.5}), ({'e': 3, 'n': 3, 'z': 0.5, 'a': 0, 'b': 0}, {'plane_east': 3.0, 'plane_north': 3.0, 'hemisphere': 'front', 'undo_obliqueness_east': 3.0, 'undo_obliqueness_north': 3.0, 'center_offset': 0.5}), ({'e': 3, 'n': 3, 'z': 1, 'a': 2, 'b': -3}, {'plane_east': 3, 'plane_north': 3, 'hemisphere': 'front', 'undo_obliqueness_east': 3, 'undo_obliqueness_north': 3, 'center_offset': 0}), ({'e': 3, 'n': 3, 'z': -0.5, 'a': 2, 'b': -3}, {'plane_east': 6.0, 'plane_north': -1.5, 'hemisphere': 'back', 'undo_obliqueness_east': 0.0, 'undo_obliqueness_north': 7.5, 'center_offset': 1.5}), ({'e': 3, 'n': 3, 'z': 0, 'a': 2, 'b': -3}, {'plane_east': 5, 'plane_north': 0, 'hemisphere': 'front', 'undo_obliqueness_east': 1, 'undo_obliqueness_north': 6, 'center_offset': 1}), ({'e': 3, 'n': 3, 'z': 0.5, 'a': -2, 'b': 4}, {'plane_east': 2.0, 'plane_north': 5.0, 'hemisphere': 'front', 'undo_obliqueness_east': 4.0, 'undo_obliqueness_north': 1.0, 'center_offset': 0.5})], 3: [({'e': 4, 'n': 3, 'z': 0.5, 'a': 2, 'b': -3}, {'plane_east': 5.0, 'plane_north': 1.5, 'hemisphere': 'front', 'undo_obliqueness_east': 3.0, 'undo_obliqueness_north': 4.5, 'center_offset': 0.5}), ({'e': 4, 'n': 3, 'z': 0.5, 'a': 0, 'b': 0}, {'plane_east': 4.0, 'plane_north': 3.0, 'hemisphere': 'front', 'undo_obliqueness_east': 4.0, 'undo_obliqueness_north': 3.0, 'center_offset': 0.5}), ({'e': 4, 'n': 3, 'z': 1, 'a': 2, 'b': -3}, {'plane_east': 4, 'plane_north': 3, 'hemisphere': 'front', 'undo_obliqueness_east': 4, 'undo_obliqueness_north': 3, 'center_offset': 0}), ({'e': 4, 'n': 3, 'z': -0.5, 'a': 2, 'b': -3}, {'plane_east': 7.0, 'plane_north': -1.5, 'hemisphere': 'back', 'undo_obliqueness_east': 1.0, 'undo_obliqueness_north': 7.5, 'center_offset': 1.5}), ({'e': 4, 'n': 3, 'z': 0, 'a': 2, 'b': -3}, {'plane_east': 6, 'plane_north': 0, 'hemisphere': 'front', 'undo_obliqueness_east': 2, 'undo_obliqueness_north': 6, 'center_offset': 1}), ({'e': 4, 'n': 3, 'z': 0.5, 'a': -2, 'b': 4}, {'plane_east': 3.0, 'plane_north': 5.0, 'hemisphere': 'front', 'undo_obliqueness_east': 5.0, 'undo_obliqueness_north': 1.0, 'center_offset': 0.5})], 4: [({'e': 5, 'n': 3, 'z': 0.5, 'a': 2, 'b': -3}, {'plane_east': 6.0, 'plane_north': 1.5, 'hemisphere': 'front', 'undo_obliqueness_east': 4.0, 'undo_obliqueness_north': 4.5, 'center_offset': 0.5}), ({'e': 5, 'n': 3, 'z': 0.5, 'a': 0, 'b': 0}, {'plane_east': 5.0, 'plane_north': 3.0, 'hemisphere': 'front', 'undo_obliqueness_east': 5.0, 'undo_obliqueness_north': 3.0, 'center_offset': 0.5}), ({'e': 5, 'n': 3, 'z': 1, 'a': 2, 'b': -3}, {'plane_east': 5, 'plane_north': 3, 'hemisphere': 'front', 'undo_obliqueness_east': 5, 'undo_obliqueness_north': 3, 'center_offset': 0}), ({'e': 5, 'n': 3, 'z': -0.5, 'a': 2, 'b': -3}, {'plane_east': 8.0, 'plane_north': -1.5, 'hemisphere': 'back', 'undo_obliqueness_east': 2.0, 'undo_obliqueness_north': 7.5, 'center_offset': 1.5}), ({'e': 5, 'n': 3, 'z': 0, 'a': 2, 'b': -3}, {'plane_east': 7, 'plane_north': 0, 'hemisphere': 'front', 'undo_obliqueness_east': 3, 'undo_obliqueness_north': 6, 'center_offset': 1}), ({'e': 5, 'n': 3, 'z': 0.5, 'a': -2, 'b': 4}, {'plane_east': 4.0, 'plane_north': 5.0, 'hemisphere': 'front', 'undo_obliqueness_east': 6.0, 'undo_obliqueness_north': 1.0, 'center_offset': 0.5})], 5: [({'e': 6, 'n': 3, 'z': 0.5, 'a': 2, 'b': -3}, {'plane_east': 7.0, 'plane_north': 1.5, 'hemisphere': 'front', 'undo_obliqueness_east': 5.0, 'undo_obliqueness_north': 4.5, 'center_offset': 0.5}), ({'e': 6, 'n': 3, 'z': 0.5, 'a': 0, 'b': 0}, {'plane_east': 6.0, 'plane_north': 3.0, 'hemisphere': 'front', 'undo_obliqueness_east': 6.0, 'undo_obliqueness_north': 3.0, 'center_offset': 0.5}), ({'e': 6, 'n': 3, 'z': 1, 'a': 2, 'b': -3}, {'plane_east': 6, 'plane_north': 3, 'hemisphere': 'front', 'undo_obliqueness_east': 6, 'undo_obliqueness_north': 3, 'center_offset': 0}), ({'e': 6, 'n': 3, 'z': -0.5, 'a': 2, 'b': -3}, {'plane_east': 9.0, 'plane_north': -1.5, 'hemisphere': 'back', 'undo_obliqueness_east': 3.0, 'undo_obliqueness_north': 7.5, 'center_offset': 1.5}), ({'e': 6, 'n': 3, 'z': 0, 'a': 2, 'b': -3}, {'plane_east': 8, 'plane_north': 0, 'hemisphere': 'front', 'undo_obliqueness_east': 4, 'undo_obliqueness_north': 6, 'center_offset': 1}), ({'e': 6, 'n': 3, 'z': 0.5, 'a': -2, 'b': 4}, {'plane_east': 5.0, 'plane_north': 5.0, 'hemisphere': 'front', 'undo_obliqueness_east': 7.0, 'undo_obliqueness_north': 1.0, 'center_offset': 0.5})]}
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{'center_offset': 0.5, 'hemisphere': 'front', 'plane_east': 3.0, 'plane_north': 1.5, 'undo_obliqueness_east': 1.0, 'undo_obliqueness_north': 4.5}{'center_offset': 0.5, 'hemisphere': 'front', 'plane_east': 3.0, 'plane_north': 1.5, 'undo_obliqueness_east': 1.0, 'undo_obliqueness_north': 4.5}Passed
astronomical fixture 1{'center_offset': 0.5, 'hemisphere': 'front', 'plane_east': 2.0, 'plane_north': 3.0, 'undo_obliqueness_east': 2.0, 'undo_obliqueness_north': 3.0}{'center_offset': 0.5, 'hemisphere': 'front', 'plane_east': 2.0, 'plane_north': 3.0, 'undo_obliqueness_east': 2.0, 'undo_obliqueness_north': 3.0}Passed
astronomical fixture 2{'center_offset': 1, 'hemisphere': 'front', 'plane_east': 2, 'plane_north': 3, 'undo_obliqueness_east': 2, 'undo_obliqueness_north': 3}{'center_offset': 0, 'hemisphere': 'front', 'plane_east': 2, 'plane_north': 3, 'undo_obliqueness_east': 2, 'undo_obliqueness_north': 3}Failed
astronomical fixture 3{'center_offset': -0.5, 'hemisphere': 'back', 'plane_east': 5.0, 'plane_north': -1.5, 'undo_obliqueness_east': -1.0, 'undo_obliqueness_north': 7.5}{'center_offset': 1.5, 'hemisphere': 'back', 'plane_east': 5.0, 'plane_north': -1.5, 'undo_obliqueness_east': -1.0, 'undo_obliqueness_north': 7.5}Failed
astronomical fixture 4{'center_offset': 0, 'hemisphere': 'front', 'plane_east': 4, 'plane_north': 0, 'undo_obliqueness_east': 0, 'undo_obliqueness_north': 6}{'center_offset': 1, 'hemisphere': 'front', 'plane_east': 4, 'plane_north': 0, 'undo_obliqueness_east': 0, 'undo_obliqueness_north': 6}Failed
astronomical fixture 5{'center_offset': 0.5, 'hemisphere': 'front', 'plane_east': 1.0, 'plane_north': 5.0, 'undo_obliqueness_east': 3.0, 'undo_obliqueness_north': 1.0}{'center_offset': 0.5, 'hemisphere': 'front', 'plane_east': 1.0, 'plane_north': 5.0, 'undo_obliqueness_east': 3.0, 'undo_obliqueness_north': 1.0}Passed

SHA-256 / 7bc0e21649ee5073374349907f50dc3912779feeff8c19ea02beaf141b60a6b6

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(d):
    return {'plane_east': d['e']+d['a']*(1-d['z']), 'plane_north': d['n']+d['b']*(1-d['z']), 'hemisphere': 'front' if d['z']>=0 else 'back', 'undo_obliqueness_east': d['e']-d['a']*(1-d['z']), 'undo_obliqueness_north': d['n']-d['b']*(1-d['z']), 'center_offset': abs(d['z'])}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = {1: [({'e': 2, 'n': 3, 'z': 0.5, 'a': 2, 'b': -3}, {'plane_east': 3.0, 'plane_north': 1.5, 'hemisphere': 'front', 'undo_obliqueness_east': 1.0, 'undo_obliqueness_north': 4.5, 'center_offset': 0.5}), ({'e': 2, 'n': 3, 'z': 0.5, 'a': 0, 'b': 0}, {'plane_east': 2.0, 'plane_north': 3.0, 'hemisphere': 'front', 'undo_obliqueness_east': 2.0, 'undo_obliqueness_north': 3.0, 'center_offset': 0.5}), ({'e': 2, 'n': 3, 'z': 1, 'a': 2, 'b': -3}, {'plane_east': 2, 'plane_north': 3, 'hemisphere': 'front', 'undo_obliqueness_east': 2, 'undo_obliqueness_north': 3, 'center_offset': 0}), ({'e': 2, 'n': 3, 'z': -0.5, 'a': 2, 'b': -3}, {'plane_east': 5.0, 'plane_north': -1.5, 'hemisphere': 'back', 'undo_obliqueness_east': -1.0, 'undo_obliqueness_north': 7.5, 'center_offset': 1.5}), ({'e': 2, 'n': 3, 'z': 0, 'a': 2, 'b': -3}, {'plane_east': 4, 'plane_north': 0, 'hemisphere': 'front', 'undo_obliqueness_east': 0, 'undo_obliqueness_north': 6, 'center_offset': 1}), ({'e': 2, 'n': 3, 'z': 0.5, 'a': -2, 'b': 4}, {'plane_east': 1.0, 'plane_north': 5.0, 'hemisphere': 'front', 'undo_obliqueness_east': 3.0, 'undo_obliqueness_north': 1.0, 'center_offset': 0.5})], 2: [({'e': 3, 'n': 3, 'z': 0.5, 'a': 2, 'b': -3}, {'plane_east': 4.0, 'plane_north': 1.5, 'hemisphere': 'front', 'undo_obliqueness_east': 2.0, 'undo_obliqueness_north': 4.5, 'center_offset': 0.5}), ({'e': 3, 'n': 3, 'z': 0.5, 'a': 0, 'b': 0}, {'plane_east': 3.0, 'plane_north': 3.0, 'hemisphere': 'front', 'undo_obliqueness_east': 3.0, 'undo_obliqueness_north': 3.0, 'center_offset': 0.5}), ({'e': 3, 'n': 3, 'z': 1, 'a': 2, 'b': -3}, {'plane_east': 3, 'plane_north': 3, 'hemisphere': 'front', 'undo_obliqueness_east': 3, 'undo_obliqueness_north': 3, 'center_offset': 0}), ({'e': 3, 'n': 3, 'z': -0.5, 'a': 2, 'b': -3}, {'plane_east': 6.0, 'plane_north': -1.5, 'hemisphere': 'back', 'undo_obliqueness_east': 0.0, 'undo_obliqueness_north': 7.5, 'center_offset': 1.5}), ({'e': 3, 'n': 3, 'z': 0, 'a': 2, 'b': -3}, {'plane_east': 5, 'plane_north': 0, 'hemisphere': 'front', 'undo_obliqueness_east': 1, 'undo_obliqueness_north': 6, 'center_offset': 1}), ({'e': 3, 'n': 3, 'z': 0.5, 'a': -2, 'b': 4}, {'plane_east': 2.0, 'plane_north': 5.0, 'hemisphere': 'front', 'undo_obliqueness_east': 4.0, 'undo_obliqueness_north': 1.0, 'center_offset': 0.5})], 3: [({'e': 4, 'n': 3, 'z': 0.5, 'a': 2, 'b': -3}, {'plane_east': 5.0, 'plane_north': 1.5, 'hemisphere': 'front', 'undo_obliqueness_east': 3.0, 'undo_obliqueness_north': 4.5, 'center_offset': 0.5}), ({'e': 4, 'n': 3, 'z': 0.5, 'a': 0, 'b': 0}, {'plane_east': 4.0, 'plane_north': 3.0, 'hemisphere': 'front', 'undo_obliqueness_east': 4.0, 'undo_obliqueness_north': 3.0, 'center_offset': 0.5}), ({'e': 4, 'n': 3, 'z': 1, 'a': 2, 'b': -3}, {'plane_east': 4, 'plane_north': 3, 'hemisphere': 'front', 'undo_obliqueness_east': 4, 'undo_obliqueness_north': 3, 'center_offset': 0}), ({'e': 4, 'n': 3, 'z': -0.5, 'a': 2, 'b': -3}, {'plane_east': 7.0, 'plane_north': -1.5, 'hemisphere': 'back', 'undo_obliqueness_east': 1.0, 'undo_obliqueness_north': 7.5, 'center_offset': 1.5}), ({'e': 4, 'n': 3, 'z': 0, 'a': 2, 'b': -3}, {'plane_east': 6, 'plane_north': 0, 'hemisphere': 'front', 'undo_obliqueness_east': 2, 'undo_obliqueness_north': 6, 'center_offset': 1}), ({'e': 4, 'n': 3, 'z': 0.5, 'a': -2, 'b': 4}, {'plane_east': 3.0, 'plane_north': 5.0, 'hemisphere': 'front', 'undo_obliqueness_east': 5.0, 'undo_obliqueness_north': 1.0, 'center_offset': 0.5})], 4: [({'e': 5, 'n': 3, 'z': 0.5, 'a': 2, 'b': -3}, {'plane_east': 6.0, 'plane_north': 1.5, 'hemisphere': 'front', 'undo_obliqueness_east': 4.0, 'undo_obliqueness_north': 4.5, 'center_offset': 0.5}), ({'e': 5, 'n': 3, 'z': 0.5, 'a': 0, 'b': 0}, {'plane_east': 5.0, 'plane_north': 3.0, 'hemisphere': 'front', 'undo_obliqueness_east': 5.0, 'undo_obliqueness_north': 3.0, 'center_offset': 0.5}), ({'e': 5, 'n': 3, 'z': 1, 'a': 2, 'b': -3}, {'plane_east': 5, 'plane_north': 3, 'hemisphere': 'front', 'undo_obliqueness_east': 5, 'undo_obliqueness_north': 3, 'center_offset': 0}), ({'e': 5, 'n': 3, 'z': -0.5, 'a': 2, 'b': -3}, {'plane_east': 8.0, 'plane_north': -1.5, 'hemisphere': 'back', 'undo_obliqueness_east': 2.0, 'undo_obliqueness_north': 7.5, 'center_offset': 1.5}), ({'e': 5, 'n': 3, 'z': 0, 'a': 2, 'b': -3}, {'plane_east': 7, 'plane_north': 0, 'hemisphere': 'front', 'undo_obliqueness_east': 3, 'undo_obliqueness_north': 6, 'center_offset': 1}), ({'e': 5, 'n': 3, 'z': 0.5, 'a': -2, 'b': 4}, {'plane_east': 4.0, 'plane_north': 5.0, 'hemisphere': 'front', 'undo_obliqueness_east': 6.0, 'undo_obliqueness_north': 1.0, 'center_offset': 0.5})], 5: [({'e': 6, 'n': 3, 'z': 0.5, 'a': 2, 'b': -3}, {'plane_east': 7.0, 'plane_north': 1.5, 'hemisphere': 'front', 'undo_obliqueness_east': 5.0, 'undo_obliqueness_north': 4.5, 'center_offset': 0.5}), ({'e': 6, 'n': 3, 'z': 0.5, 'a': 0, 'b': 0}, {'plane_east': 6.0, 'plane_north': 3.0, 'hemisphere': 'front', 'undo_obliqueness_east': 6.0, 'undo_obliqueness_north': 3.0, 'center_offset': 0.5}), ({'e': 6, 'n': 3, 'z': 1, 'a': 2, 'b': -3}, {'plane_east': 6, 'plane_north': 3, 'hemisphere': 'front', 'undo_obliqueness_east': 6, 'undo_obliqueness_north': 3, 'center_offset': 0}), ({'e': 6, 'n': 3, 'z': -0.5, 'a': 2, 'b': -3}, {'plane_east': 9.0, 'plane_north': -1.5, 'hemisphere': 'back', 'undo_obliqueness_east': 3.0, 'undo_obliqueness_north': 7.5, 'center_offset': 1.5}), ({'e': 6, 'n': 3, 'z': 0, 'a': 2, 'b': -3}, {'plane_east': 8, 'plane_north': 0, 'hemisphere': 'front', 'undo_obliqueness_east': 4, 'undo_obliqueness_north': 6, 'center_offset': 1}), ({'e': 6, 'n': 3, 'z': 0.5, 'a': -2, 'b': 4}, {'plane_east': 5.0, 'plane_north': 5.0, 'hemisphere': 'front', 'undo_obliqueness_east': 7.0, 'undo_obliqueness_north': 1.0, 'center_offset': 0.5})]}
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{'center_offset': 0.5, 'hemisphere': 'front', 'plane_east': 3.0, 'plane_north': 1.5, 'undo_obliqueness_east': 1.0, 'undo_obliqueness_north': 4.5}{'center_offset': 0.5, 'hemisphere': 'front', 'plane_east': 3.0, 'plane_north': 1.5, 'undo_obliqueness_east': 1.0, 'undo_obliqueness_north': 4.5}Passed
astronomical fixture 1{'center_offset': 0.5, 'hemisphere': 'front', 'plane_east': 2.0, 'plane_north': 3.0, 'undo_obliqueness_east': 2.0, 'undo_obliqueness_north': 3.0}{'center_offset': 0.5, 'hemisphere': 'front', 'plane_east': 2.0, 'plane_north': 3.0, 'undo_obliqueness_east': 2.0, 'undo_obliqueness_north': 3.0}Passed
astronomical fixture 2{'center_offset': 1, 'hemisphere': 'front', 'plane_east': 2, 'plane_north': 3, 'undo_obliqueness_east': 2, 'undo_obliqueness_north': 3}{'center_offset': 0, 'hemisphere': 'front', 'plane_east': 2, 'plane_north': 3, 'undo_obliqueness_east': 2, 'undo_obliqueness_north': 3}Failed
astronomical fixture 3{'center_offset': 0.5, 'hemisphere': 'back', 'plane_east': 5.0, 'plane_north': -1.5, 'undo_obliqueness_east': -1.0, 'undo_obliqueness_north': 7.5}{'center_offset': 1.5, 'hemisphere': 'back', 'plane_east': 5.0, 'plane_north': -1.5, 'undo_obliqueness_east': -1.0, 'undo_obliqueness_north': 7.5}Failed
astronomical fixture 4{'center_offset': 0, 'hemisphere': 'front', 'plane_east': 4, 'plane_north': 0, 'undo_obliqueness_east': 0, 'undo_obliqueness_north': 6}{'center_offset': 1, 'hemisphere': 'front', 'plane_east': 4, 'plane_north': 0, 'undo_obliqueness_east': 0, 'undo_obliqueness_north': 6}Failed
astronomical fixture 5{'center_offset': 0.5, 'hemisphere': 'front', 'plane_east': 1.0, 'plane_north': 5.0, 'undo_obliqueness_east': 3.0, 'undo_obliqueness_north': 1.0}{'center_offset': 0.5, 'hemisphere': 'front', 'plane_east': 1.0, 'plane_north': 5.0, 'undo_obliqueness_east': 3.0, 'undo_obliqueness_north': 1.0}Passed

SHA-256 / 120f2221b9cdcf8b449feb18ea2da6a8d22273fc8ebd15dd3c30e6433f2489bf

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(d):
    return {'plane_east': d['e']+d['a']*(1-d['z']), 'plane_north': d['n']+d['b']*(1-d['z']), 'hemisphere': 'front' if d['z']>=0 else 'back', 'undo_obliqueness_east': d['e']-d['a']*(1-d['z']), 'undo_obliqueness_north': d['n']-d['b']*(1-d['z']), 'center_offset': 1-d['z']}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = {1: [({'e': 2, 'n': 3, 'z': 0.5, 'a': 2, 'b': -3}, {'plane_east': 3.0, 'plane_north': 1.5, 'hemisphere': 'front', 'undo_obliqueness_east': 1.0, 'undo_obliqueness_north': 4.5, 'center_offset': 0.5}), ({'e': 2, 'n': 3, 'z': 0.5, 'a': 0, 'b': 0}, {'plane_east': 2.0, 'plane_north': 3.0, 'hemisphere': 'front', 'undo_obliqueness_east': 2.0, 'undo_obliqueness_north': 3.0, 'center_offset': 0.5}), ({'e': 2, 'n': 3, 'z': 1, 'a': 2, 'b': -3}, {'plane_east': 2, 'plane_north': 3, 'hemisphere': 'front', 'undo_obliqueness_east': 2, 'undo_obliqueness_north': 3, 'center_offset': 0}), ({'e': 2, 'n': 3, 'z': -0.5, 'a': 2, 'b': -3}, {'plane_east': 5.0, 'plane_north': -1.5, 'hemisphere': 'back', 'undo_obliqueness_east': -1.0, 'undo_obliqueness_north': 7.5, 'center_offset': 1.5}), ({'e': 2, 'n': 3, 'z': 0, 'a': 2, 'b': -3}, {'plane_east': 4, 'plane_north': 0, 'hemisphere': 'front', 'undo_obliqueness_east': 0, 'undo_obliqueness_north': 6, 'center_offset': 1}), ({'e': 2, 'n': 3, 'z': 0.5, 'a': -2, 'b': 4}, {'plane_east': 1.0, 'plane_north': 5.0, 'hemisphere': 'front', 'undo_obliqueness_east': 3.0, 'undo_obliqueness_north': 1.0, 'center_offset': 0.5})], 2: [({'e': 3, 'n': 3, 'z': 0.5, 'a': 2, 'b': -3}, {'plane_east': 4.0, 'plane_north': 1.5, 'hemisphere': 'front', 'undo_obliqueness_east': 2.0, 'undo_obliqueness_north': 4.5, 'center_offset': 0.5}), ({'e': 3, 'n': 3, 'z': 0.5, 'a': 0, 'b': 0}, {'plane_east': 3.0, 'plane_north': 3.0, 'hemisphere': 'front', 'undo_obliqueness_east': 3.0, 'undo_obliqueness_north': 3.0, 'center_offset': 0.5}), ({'e': 3, 'n': 3, 'z': 1, 'a': 2, 'b': -3}, {'plane_east': 3, 'plane_north': 3, 'hemisphere': 'front', 'undo_obliqueness_east': 3, 'undo_obliqueness_north': 3, 'center_offset': 0}), ({'e': 3, 'n': 3, 'z': -0.5, 'a': 2, 'b': -3}, {'plane_east': 6.0, 'plane_north': -1.5, 'hemisphere': 'back', 'undo_obliqueness_east': 0.0, 'undo_obliqueness_north': 7.5, 'center_offset': 1.5}), ({'e': 3, 'n': 3, 'z': 0, 'a': 2, 'b': -3}, {'plane_east': 5, 'plane_north': 0, 'hemisphere': 'front', 'undo_obliqueness_east': 1, 'undo_obliqueness_north': 6, 'center_offset': 1}), ({'e': 3, 'n': 3, 'z': 0.5, 'a': -2, 'b': 4}, {'plane_east': 2.0, 'plane_north': 5.0, 'hemisphere': 'front', 'undo_obliqueness_east': 4.0, 'undo_obliqueness_north': 1.0, 'center_offset': 0.5})], 3: [({'e': 4, 'n': 3, 'z': 0.5, 'a': 2, 'b': -3}, {'plane_east': 5.0, 'plane_north': 1.5, 'hemisphere': 'front', 'undo_obliqueness_east': 3.0, 'undo_obliqueness_north': 4.5, 'center_offset': 0.5}), ({'e': 4, 'n': 3, 'z': 0.5, 'a': 0, 'b': 0}, {'plane_east': 4.0, 'plane_north': 3.0, 'hemisphere': 'front', 'undo_obliqueness_east': 4.0, 'undo_obliqueness_north': 3.0, 'center_offset': 0.5}), ({'e': 4, 'n': 3, 'z': 1, 'a': 2, 'b': -3}, {'plane_east': 4, 'plane_north': 3, 'hemisphere': 'front', 'undo_obliqueness_east': 4, 'undo_obliqueness_north': 3, 'center_offset': 0}), ({'e': 4, 'n': 3, 'z': -0.5, 'a': 2, 'b': -3}, {'plane_east': 7.0, 'plane_north': -1.5, 'hemisphere': 'back', 'undo_obliqueness_east': 1.0, 'undo_obliqueness_north': 7.5, 'center_offset': 1.5}), ({'e': 4, 'n': 3, 'z': 0, 'a': 2, 'b': -3}, {'plane_east': 6, 'plane_north': 0, 'hemisphere': 'front', 'undo_obliqueness_east': 2, 'undo_obliqueness_north': 6, 'center_offset': 1}), ({'e': 4, 'n': 3, 'z': 0.5, 'a': -2, 'b': 4}, {'plane_east': 3.0, 'plane_north': 5.0, 'hemisphere': 'front', 'undo_obliqueness_east': 5.0, 'undo_obliqueness_north': 1.0, 'center_offset': 0.5})], 4: [({'e': 5, 'n': 3, 'z': 0.5, 'a': 2, 'b': -3}, {'plane_east': 6.0, 'plane_north': 1.5, 'hemisphere': 'front', 'undo_obliqueness_east': 4.0, 'undo_obliqueness_north': 4.5, 'center_offset': 0.5}), ({'e': 5, 'n': 3, 'z': 0.5, 'a': 0, 'b': 0}, {'plane_east': 5.0, 'plane_north': 3.0, 'hemisphere': 'front', 'undo_obliqueness_east': 5.0, 'undo_obliqueness_north': 3.0, 'center_offset': 0.5}), ({'e': 5, 'n': 3, 'z': 1, 'a': 2, 'b': -3}, {'plane_east': 5, 'plane_north': 3, 'hemisphere': 'front', 'undo_obliqueness_east': 5, 'undo_obliqueness_north': 3, 'center_offset': 0}), ({'e': 5, 'n': 3, 'z': -0.5, 'a': 2, 'b': -3}, {'plane_east': 8.0, 'plane_north': -1.5, 'hemisphere': 'back', 'undo_obliqueness_east': 2.0, 'undo_obliqueness_north': 7.5, 'center_offset': 1.5}), ({'e': 5, 'n': 3, 'z': 0, 'a': 2, 'b': -3}, {'plane_east': 7, 'plane_north': 0, 'hemisphere': 'front', 'undo_obliqueness_east': 3, 'undo_obliqueness_north': 6, 'center_offset': 1}), ({'e': 5, 'n': 3, 'z': 0.5, 'a': -2, 'b': 4}, {'plane_east': 4.0, 'plane_north': 5.0, 'hemisphere': 'front', 'undo_obliqueness_east': 6.0, 'undo_obliqueness_north': 1.0, 'center_offset': 0.5})], 5: [({'e': 6, 'n': 3, 'z': 0.5, 'a': 2, 'b': -3}, {'plane_east': 7.0, 'plane_north': 1.5, 'hemisphere': 'front', 'undo_obliqueness_east': 5.0, 'undo_obliqueness_north': 4.5, 'center_offset': 0.5}), ({'e': 6, 'n': 3, 'z': 0.5, 'a': 0, 'b': 0}, {'plane_east': 6.0, 'plane_north': 3.0, 'hemisphere': 'front', 'undo_obliqueness_east': 6.0, 'undo_obliqueness_north': 3.0, 'center_offset': 0.5}), ({'e': 6, 'n': 3, 'z': 1, 'a': 2, 'b': -3}, {'plane_east': 6, 'plane_north': 3, 'hemisphere': 'front', 'undo_obliqueness_east': 6, 'undo_obliqueness_north': 3, 'center_offset': 0}), ({'e': 6, 'n': 3, 'z': -0.5, 'a': 2, 'b': -3}, {'plane_east': 9.0, 'plane_north': -1.5, 'hemisphere': 'back', 'undo_obliqueness_east': 3.0, 'undo_obliqueness_north': 7.5, 'center_offset': 1.5}), ({'e': 6, 'n': 3, 'z': 0, 'a': 2, 'b': -3}, {'plane_east': 8, 'plane_north': 0, 'hemisphere': 'front', 'undo_obliqueness_east': 4, 'undo_obliqueness_north': 6, 'center_offset': 1}), ({'e': 6, 'n': 3, 'z': 0.5, 'a': -2, 'b': 4}, {'plane_east': 5.0, 'plane_north': 5.0, 'hemisphere': 'front', 'undo_obliqueness_east': 7.0, 'undo_obliqueness_north': 1.0, 'center_offset': 0.5})]}
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{'center_offset': 0.5, 'hemisphere': 'front', 'plane_east': 3.0, 'plane_north': 1.5, 'undo_obliqueness_east': 1.0, 'undo_obliqueness_north': 4.5}{'center_offset': 0.5, 'hemisphere': 'front', 'plane_east': 3.0, 'plane_north': 1.5, 'undo_obliqueness_east': 1.0, 'undo_obliqueness_north': 4.5}Passed
astronomical fixture 1{'center_offset': 0.5, 'hemisphere': 'front', 'plane_east': 2.0, 'plane_north': 3.0, 'undo_obliqueness_east': 2.0, 'undo_obliqueness_north': 3.0}{'center_offset': 0.5, 'hemisphere': 'front', 'plane_east': 2.0, 'plane_north': 3.0, 'undo_obliqueness_east': 2.0, 'undo_obliqueness_north': 3.0}Passed
astronomical fixture 2{'center_offset': 0, 'hemisphere': 'front', 'plane_east': 2, 'plane_north': 3, 'undo_obliqueness_east': 2, 'undo_obliqueness_north': 3}{'center_offset': 0, 'hemisphere': 'front', 'plane_east': 2, 'plane_north': 3, 'undo_obliqueness_east': 2, 'undo_obliqueness_north': 3}Passed
astronomical fixture 3{'center_offset': 1.5, 'hemisphere': 'back', 'plane_east': 5.0, 'plane_north': -1.5, 'undo_obliqueness_east': -1.0, 'undo_obliqueness_north': 7.5}{'center_offset': 1.5, 'hemisphere': 'back', 'plane_east': 5.0, 'plane_north': -1.5, 'undo_obliqueness_east': -1.0, 'undo_obliqueness_north': 7.5}Passed
astronomical fixture 4{'center_offset': 1, 'hemisphere': 'front', 'plane_east': 4, 'plane_north': 0, 'undo_obliqueness_east': 0, 'undo_obliqueness_north': 6}{'center_offset': 1, 'hemisphere': 'front', 'plane_east': 4, 'plane_north': 0, 'undo_obliqueness_east': 0, 'undo_obliqueness_north': 6}Passed
astronomical fixture 5{'center_offset': 0.5, 'hemisphere': 'front', 'plane_east': 1.0, 'plane_north': 5.0, 'undo_obliqueness_east': 3.0, 'undo_obliqueness_north': 1.0}{'center_offset': 0.5, 'hemisphere': 'front', 'plane_east': 1.0, 'plane_north': 5.0, 'undo_obliqueness_east': 3.0, 'undo_obliqueness_north': 1.0}Passed

SHA-256 / bad7b92b12b1b441dd1a7783a0a1a85bdb6a9049d5a39a5b6424ad196ba876c6

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 2026-09-29T14:46:00.954962+00:00.

Case digest / 595a87a103b56cffcb32837af780a8ce10ee9ac4c88551bf7d51d683be12becc