FA-55711 / Astronomical coordinate conventions / Open access

Celestial tangent projection: Celestial TAN east coordinate omits perspective or admits the back hemisphere · case 01

The adapter reports an incorrect chart east while other fields remain valid.

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

ROOT CAUSE

Celestial TAN east coordinate omits perspective or admits the back hemisphere. Faulty expression: d['e'] if d['z']>0 else None

VERIFIED REPAIR

Preserve the declared model convention at this site: d['e']/d['z'] if d['z']>0 else None

Unsuccessful approach: A partial convention repair still uses d['e']/abs(d['z']) if d['z']!=0 else None

Case contract

A supplied unnormalized direction basis has dot products east e, north n, and center z. The TAN chart accepts z>0 and returns e/z,n/z. Scale s and reference pixels rx,ry map this chart to detector pixels. Behind-plane rays are explicitly returned as None. Output fields are defined by: chart_east = d['e']/d['z'] if d['z']>0 else None; chart_north = d['n']/d['z'] if d['z']>0 else None; pixel_x = d['rx']+d['e']/d['z']/d['s'] if d['z']>0 else None; pixel_y = d['ry']+d['n']/d['z']/d['s'] if d['z']>0 else None; chart_valid = d['z']>0; reciprocal_center = 1/d['z'] if d['z']>0 else None

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 {'chart_east': d['e'] if d['z']>0 else None, 'chart_north': d['n']/d['z'] if d['z']>0 else None, 'pixel_x': d['rx']+d['e']/d['z']/d['s'] if d['z']>0 else None, 'pixel_y': d['ry']+d['n']/d['z']/d['s'] if d['z']>0 else None, 'chart_valid': d['z']>0, 'reciprocal_center': 1/d['z'] if d['z']>0 else None}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = {1: [({'e': 2, 'n': 3, 'z': 4, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': 0.5, 'chart_north': 0.75, 'pixel_x': 10.25, 'pixel_y': 20.375, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 2, 'n': 3, 'z': 0, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': None, 'chart_north': None, 'pixel_x': None, 'pixel_y': None, 'chart_valid': False, 'reciprocal_center': None}), ({'e': 2, 'n': 3, 'z': -2, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': None, 'chart_north': None, 'pixel_x': None, 'pixel_y': None, 'chart_valid': False, 'reciprocal_center': None}), ({'e': 0, 'n': 0, 'z': 4, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': 0.0, 'chart_north': 0.0, 'pixel_x': 10.0, 'pixel_y': 20.0, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 2, 'n': 3, 'z': 4, 's': -2, 'rx': 10, 'ry': 20}, {'chart_east': 0.5, 'chart_north': 0.75, 'pixel_x': 9.75, 'pixel_y': 19.625, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 2, 'n': 3, 'z': 1, 's': 2, 'rx': 0, 'ry': 0}, {'chart_east': 2.0, 'chart_north': 3.0, 'pixel_x': 1.0, 'pixel_y': 1.5, 'chart_valid': True, 'reciprocal_center': 1.0})], 2: [({'e': 3, 'n': 3, 'z': 4, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': 0.75, 'chart_north': 0.75, 'pixel_x': 10.375, 'pixel_y': 20.375, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 3, 'n': 3, 'z': 0, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': None, 'chart_north': None, 'pixel_x': None, 'pixel_y': None, 'chart_valid': False, 'reciprocal_center': None}), ({'e': 3, 'n': 3, 'z': -2, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': None, 'chart_north': None, 'pixel_x': None, 'pixel_y': None, 'chart_valid': False, 'reciprocal_center': None}), ({'e': 1, 'n': 0, 'z': 4, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': 0.25, 'chart_north': 0.0, 'pixel_x': 10.125, 'pixel_y': 20.0, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 3, 'n': 3, 'z': 4, 's': -2, 'rx': 10, 'ry': 20}, {'chart_east': 0.75, 'chart_north': 0.75, 'pixel_x': 9.625, 'pixel_y': 19.625, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 3, 'n': 3, 'z': 1, 's': 2, 'rx': 0, 'ry': 0}, {'chart_east': 3.0, 'chart_north': 3.0, 'pixel_x': 1.5, 'pixel_y': 1.5, 'chart_valid': True, 'reciprocal_center': 1.0})], 3: [({'e': 4, 'n': 3, 'z': 4, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': 1.0, 'chart_north': 0.75, 'pixel_x': 10.5, 'pixel_y': 20.375, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 4, 'n': 3, 'z': 0, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': None, 'chart_north': None, 'pixel_x': None, 'pixel_y': None, 'chart_valid': False, 'reciprocal_center': None}), ({'e': 4, 'n': 3, 'z': -2, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': None, 'chart_north': None, 'pixel_x': None, 'pixel_y': None, 'chart_valid': False, 'reciprocal_center': None}), ({'e': 2, 'n': 0, 'z': 4, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': 0.5, 'chart_north': 0.0, 'pixel_x': 10.25, 'pixel_y': 20.0, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 4, 'n': 3, 'z': 4, 's': -2, 'rx': 10, 'ry': 20}, {'chart_east': 1.0, 'chart_north': 0.75, 'pixel_x': 9.5, 'pixel_y': 19.625, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 4, 'n': 3, 'z': 1, 's': 2, 'rx': 0, 'ry': 0}, {'chart_east': 4.0, 'chart_north': 3.0, 'pixel_x': 2.0, 'pixel_y': 1.5, 'chart_valid': True, 'reciprocal_center': 1.0})], 4: [({'e': 5, 'n': 3, 'z': 4, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': 1.25, 'chart_north': 0.75, 'pixel_x': 10.625, 'pixel_y': 20.375, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 5, 'n': 3, 'z': 0, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': None, 'chart_north': None, 'pixel_x': None, 'pixel_y': None, 'chart_valid': False, 'reciprocal_center': None}), ({'e': 5, 'n': 3, 'z': -2, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': None, 'chart_north': None, 'pixel_x': None, 'pixel_y': None, 'chart_valid': False, 'reciprocal_center': None}), ({'e': 3, 'n': 0, 'z': 4, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': 0.75, 'chart_north': 0.0, 'pixel_x': 10.375, 'pixel_y': 20.0, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 5, 'n': 3, 'z': 4, 's': -2, 'rx': 10, 'ry': 20}, {'chart_east': 1.25, 'chart_north': 0.75, 'pixel_x': 9.375, 'pixel_y': 19.625, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 5, 'n': 3, 'z': 1, 's': 2, 'rx': 0, 'ry': 0}, {'chart_east': 5.0, 'chart_north': 3.0, 'pixel_x': 2.5, 'pixel_y': 1.5, 'chart_valid': True, 'reciprocal_center': 1.0})], 5: [({'e': 6, 'n': 3, 'z': 4, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': 1.5, 'chart_north': 0.75, 'pixel_x': 10.75, 'pixel_y': 20.375, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 6, 'n': 3, 'z': 0, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': None, 'chart_north': None, 'pixel_x': None, 'pixel_y': None, 'chart_valid': False, 'reciprocal_center': None}), ({'e': 6, 'n': 3, 'z': -2, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': None, 'chart_north': None, 'pixel_x': None, 'pixel_y': None, 'chart_valid': False, 'reciprocal_center': None}), ({'e': 4, 'n': 0, 'z': 4, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': 1.0, 'chart_north': 0.0, 'pixel_x': 10.5, 'pixel_y': 20.0, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 6, 'n': 3, 'z': 4, 's': -2, 'rx': 10, 'ry': 20}, {'chart_east': 1.5, 'chart_north': 0.75, 'pixel_x': 9.25, 'pixel_y': 19.625, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 6, 'n': 3, 'z': 1, 's': 2, 'rx': 0, 'ry': 0}, {'chart_east': 6.0, 'chart_north': 3.0, 'pixel_x': 3.0, 'pixel_y': 1.5, 'chart_valid': True, 'reciprocal_center': 1.0})]}
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 fixture	Actual	Expected	Outcome
astronomical fixture 0	`{'chart_east': 2, 'chart_north': 0.75, 'chart_valid': True, 'pixel_x': 10.25, 'pixel_y': 20.375, 'reciprocal_center': 0.25}`	`{'chart_east': 0.5, 'chart_north': 0.75, 'chart_valid': True, 'pixel_x': 10.25, 'pixel_y': 20.375, 'reciprocal_center': 0.25}`	Failed
astronomical fixture 1	`{'chart_east': None, 'chart_north': None, 'chart_valid': False, 'pixel_x': None, 'pixel_y': None, 'reciprocal_center': None}`	`{'chart_east': None, 'chart_north': None, 'chart_valid': False, 'pixel_x': None, 'pixel_y': None, 'reciprocal_center': None}`	Passed
astronomical fixture 2	`{'chart_east': None, 'chart_north': None, 'chart_valid': False, 'pixel_x': None, 'pixel_y': None, 'reciprocal_center': None}`	`{'chart_east': None, 'chart_north': None, 'chart_valid': False, 'pixel_x': None, 'pixel_y': None, 'reciprocal_center': None}`	Passed
astronomical fixture 3	`{'chart_east': 0, 'chart_north': 0.0, 'chart_valid': True, 'pixel_x': 10.0, 'pixel_y': 20.0, 'reciprocal_center': 0.25}`	`{'chart_east': 0.0, 'chart_north': 0.0, 'chart_valid': True, 'pixel_x': 10.0, 'pixel_y': 20.0, 'reciprocal_center': 0.25}`	Passed
astronomical fixture 4	`{'chart_east': 2, 'chart_north': 0.75, 'chart_valid': True, 'pixel_x': 9.75, 'pixel_y': 19.625, 'reciprocal_center': 0.25}`	`{'chart_east': 0.5, 'chart_north': 0.75, 'chart_valid': True, 'pixel_x': 9.75, 'pixel_y': 19.625, 'reciprocal_center': 0.25}`	Failed
astronomical fixture 5	`{'chart_east': 2, 'chart_north': 3.0, 'chart_valid': True, 'pixel_x': 1.0, 'pixel_y': 1.5, 'reciprocal_center': 1.0}`	`{'chart_east': 2.0, 'chart_north': 3.0, 'chart_valid': True, 'pixel_x': 1.0, 'pixel_y': 1.5, 'reciprocal_center': 1.0}`	Passed

SHA-256 / ebe8baaa3f9db3a608c5fd202da56da5595299f3b5c1091c065439f50f9ea3b5

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(d):
    return {'chart_east': d['e']/abs(d['z']) if d['z']!=0 else None, 'chart_north': d['n']/d['z'] if d['z']>0 else None, 'pixel_x': d['rx']+d['e']/d['z']/d['s'] if d['z']>0 else None, 'pixel_y': d['ry']+d['n']/d['z']/d['s'] if d['z']>0 else None, 'chart_valid': d['z']>0, 'reciprocal_center': 1/d['z'] if d['z']>0 else None}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = {1: [({'e': 2, 'n': 3, 'z': 4, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': 0.5, 'chart_north': 0.75, 'pixel_x': 10.25, 'pixel_y': 20.375, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 2, 'n': 3, 'z': 0, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': None, 'chart_north': None, 'pixel_x': None, 'pixel_y': None, 'chart_valid': False, 'reciprocal_center': None}), ({'e': 2, 'n': 3, 'z': -2, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': None, 'chart_north': None, 'pixel_x': None, 'pixel_y': None, 'chart_valid': False, 'reciprocal_center': None}), ({'e': 0, 'n': 0, 'z': 4, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': 0.0, 'chart_north': 0.0, 'pixel_x': 10.0, 'pixel_y': 20.0, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 2, 'n': 3, 'z': 4, 's': -2, 'rx': 10, 'ry': 20}, {'chart_east': 0.5, 'chart_north': 0.75, 'pixel_x': 9.75, 'pixel_y': 19.625, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 2, 'n': 3, 'z': 1, 's': 2, 'rx': 0, 'ry': 0}, {'chart_east': 2.0, 'chart_north': 3.0, 'pixel_x': 1.0, 'pixel_y': 1.5, 'chart_valid': True, 'reciprocal_center': 1.0})], 2: [({'e': 3, 'n': 3, 'z': 4, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': 0.75, 'chart_north': 0.75, 'pixel_x': 10.375, 'pixel_y': 20.375, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 3, 'n': 3, 'z': 0, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': None, 'chart_north': None, 'pixel_x': None, 'pixel_y': None, 'chart_valid': False, 'reciprocal_center': None}), ({'e': 3, 'n': 3, 'z': -2, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': None, 'chart_north': None, 'pixel_x': None, 'pixel_y': None, 'chart_valid': False, 'reciprocal_center': None}), ({'e': 1, 'n': 0, 'z': 4, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': 0.25, 'chart_north': 0.0, 'pixel_x': 10.125, 'pixel_y': 20.0, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 3, 'n': 3, 'z': 4, 's': -2, 'rx': 10, 'ry': 20}, {'chart_east': 0.75, 'chart_north': 0.75, 'pixel_x': 9.625, 'pixel_y': 19.625, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 3, 'n': 3, 'z': 1, 's': 2, 'rx': 0, 'ry': 0}, {'chart_east': 3.0, 'chart_north': 3.0, 'pixel_x': 1.5, 'pixel_y': 1.5, 'chart_valid': True, 'reciprocal_center': 1.0})], 3: [({'e': 4, 'n': 3, 'z': 4, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': 1.0, 'chart_north': 0.75, 'pixel_x': 10.5, 'pixel_y': 20.375, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 4, 'n': 3, 'z': 0, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': None, 'chart_north': None, 'pixel_x': None, 'pixel_y': None, 'chart_valid': False, 'reciprocal_center': None}), ({'e': 4, 'n': 3, 'z': -2, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': None, 'chart_north': None, 'pixel_x': None, 'pixel_y': None, 'chart_valid': False, 'reciprocal_center': None}), ({'e': 2, 'n': 0, 'z': 4, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': 0.5, 'chart_north': 0.0, 'pixel_x': 10.25, 'pixel_y': 20.0, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 4, 'n': 3, 'z': 4, 's': -2, 'rx': 10, 'ry': 20}, {'chart_east': 1.0, 'chart_north': 0.75, 'pixel_x': 9.5, 'pixel_y': 19.625, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 4, 'n': 3, 'z': 1, 's': 2, 'rx': 0, 'ry': 0}, {'chart_east': 4.0, 'chart_north': 3.0, 'pixel_x': 2.0, 'pixel_y': 1.5, 'chart_valid': True, 'reciprocal_center': 1.0})], 4: [({'e': 5, 'n': 3, 'z': 4, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': 1.25, 'chart_north': 0.75, 'pixel_x': 10.625, 'pixel_y': 20.375, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 5, 'n': 3, 'z': 0, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': None, 'chart_north': None, 'pixel_x': None, 'pixel_y': None, 'chart_valid': False, 'reciprocal_center': None}), ({'e': 5, 'n': 3, 'z': -2, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': None, 'chart_north': None, 'pixel_x': None, 'pixel_y': None, 'chart_valid': False, 'reciprocal_center': None}), ({'e': 3, 'n': 0, 'z': 4, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': 0.75, 'chart_north': 0.0, 'pixel_x': 10.375, 'pixel_y': 20.0, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 5, 'n': 3, 'z': 4, 's': -2, 'rx': 10, 'ry': 20}, {'chart_east': 1.25, 'chart_north': 0.75, 'pixel_x': 9.375, 'pixel_y': 19.625, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 5, 'n': 3, 'z': 1, 's': 2, 'rx': 0, 'ry': 0}, {'chart_east': 5.0, 'chart_north': 3.0, 'pixel_x': 2.5, 'pixel_y': 1.5, 'chart_valid': True, 'reciprocal_center': 1.0})], 5: [({'e': 6, 'n': 3, 'z': 4, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': 1.5, 'chart_north': 0.75, 'pixel_x': 10.75, 'pixel_y': 20.375, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 6, 'n': 3, 'z': 0, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': None, 'chart_north': None, 'pixel_x': None, 'pixel_y': None, 'chart_valid': False, 'reciprocal_center': None}), ({'e': 6, 'n': 3, 'z': -2, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': None, 'chart_north': None, 'pixel_x': None, 'pixel_y': None, 'chart_valid': False, 'reciprocal_center': None}), ({'e': 4, 'n': 0, 'z': 4, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': 1.0, 'chart_north': 0.0, 'pixel_x': 10.5, 'pixel_y': 20.0, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 6, 'n': 3, 'z': 4, 's': -2, 'rx': 10, 'ry': 20}, {'chart_east': 1.5, 'chart_north': 0.75, 'pixel_x': 9.25, 'pixel_y': 19.625, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 6, 'n': 3, 'z': 1, 's': 2, 'rx': 0, 'ry': 0}, {'chart_east': 6.0, 'chart_north': 3.0, 'pixel_x': 3.0, 'pixel_y': 1.5, 'chart_valid': True, 'reciprocal_center': 1.0})]}
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 fixture	Actual	Expected	Outcome
astronomical fixture 0	`{'chart_east': 0.5, 'chart_north': 0.75, 'chart_valid': True, 'pixel_x': 10.25, 'pixel_y': 20.375, 'reciprocal_center': 0.25}`	`{'chart_east': 0.5, 'chart_north': 0.75, 'chart_valid': True, 'pixel_x': 10.25, 'pixel_y': 20.375, 'reciprocal_center': 0.25}`	Passed
astronomical fixture 1	`{'chart_east': None, 'chart_north': None, 'chart_valid': False, 'pixel_x': None, 'pixel_y': None, 'reciprocal_center': None}`	`{'chart_east': None, 'chart_north': None, 'chart_valid': False, 'pixel_x': None, 'pixel_y': None, 'reciprocal_center': None}`	Passed
astronomical fixture 2	`{'chart_east': 1.0, 'chart_north': None, 'chart_valid': False, 'pixel_x': None, 'pixel_y': None, 'reciprocal_center': None}`	`{'chart_east': None, 'chart_north': None, 'chart_valid': False, 'pixel_x': None, 'pixel_y': None, 'reciprocal_center': None}`	Failed
astronomical fixture 3	`{'chart_east': 0.0, 'chart_north': 0.0, 'chart_valid': True, 'pixel_x': 10.0, 'pixel_y': 20.0, 'reciprocal_center': 0.25}`	`{'chart_east': 0.0, 'chart_north': 0.0, 'chart_valid': True, 'pixel_x': 10.0, 'pixel_y': 20.0, 'reciprocal_center': 0.25}`	Passed
astronomical fixture 4	`{'chart_east': 0.5, 'chart_north': 0.75, 'chart_valid': True, 'pixel_x': 9.75, 'pixel_y': 19.625, 'reciprocal_center': 0.25}`	`{'chart_east': 0.5, 'chart_north': 0.75, 'chart_valid': True, 'pixel_x': 9.75, 'pixel_y': 19.625, 'reciprocal_center': 0.25}`	Passed
astronomical fixture 5	`{'chart_east': 2.0, 'chart_north': 3.0, 'chart_valid': True, 'pixel_x': 1.0, 'pixel_y': 1.5, 'reciprocal_center': 1.0}`	`{'chart_east': 2.0, 'chart_north': 3.0, 'chart_valid': True, 'pixel_x': 1.0, 'pixel_y': 1.5, 'reciprocal_center': 1.0}`	Passed

SHA-256 / e359e39217c053aa1108afccd7e452be82b43557efb3d045d0765e775c99ada1

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(d):
    return {'chart_east': d['e']/d['z'] if d['z']>0 else None, 'chart_north': d['n']/d['z'] if d['z']>0 else None, 'pixel_x': d['rx']+d['e']/d['z']/d['s'] if d['z']>0 else None, 'pixel_y': d['ry']+d['n']/d['z']/d['s'] if d['z']>0 else None, 'chart_valid': d['z']>0, 'reciprocal_center': 1/d['z'] if d['z']>0 else None}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = {1: [({'e': 2, 'n': 3, 'z': 4, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': 0.5, 'chart_north': 0.75, 'pixel_x': 10.25, 'pixel_y': 20.375, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 2, 'n': 3, 'z': 0, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': None, 'chart_north': None, 'pixel_x': None, 'pixel_y': None, 'chart_valid': False, 'reciprocal_center': None}), ({'e': 2, 'n': 3, 'z': -2, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': None, 'chart_north': None, 'pixel_x': None, 'pixel_y': None, 'chart_valid': False, 'reciprocal_center': None}), ({'e': 0, 'n': 0, 'z': 4, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': 0.0, 'chart_north': 0.0, 'pixel_x': 10.0, 'pixel_y': 20.0, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 2, 'n': 3, 'z': 4, 's': -2, 'rx': 10, 'ry': 20}, {'chart_east': 0.5, 'chart_north': 0.75, 'pixel_x': 9.75, 'pixel_y': 19.625, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 2, 'n': 3, 'z': 1, 's': 2, 'rx': 0, 'ry': 0}, {'chart_east': 2.0, 'chart_north': 3.0, 'pixel_x': 1.0, 'pixel_y': 1.5, 'chart_valid': True, 'reciprocal_center': 1.0})], 2: [({'e': 3, 'n': 3, 'z': 4, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': 0.75, 'chart_north': 0.75, 'pixel_x': 10.375, 'pixel_y': 20.375, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 3, 'n': 3, 'z': 0, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': None, 'chart_north': None, 'pixel_x': None, 'pixel_y': None, 'chart_valid': False, 'reciprocal_center': None}), ({'e': 3, 'n': 3, 'z': -2, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': None, 'chart_north': None, 'pixel_x': None, 'pixel_y': None, 'chart_valid': False, 'reciprocal_center': None}), ({'e': 1, 'n': 0, 'z': 4, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': 0.25, 'chart_north': 0.0, 'pixel_x': 10.125, 'pixel_y': 20.0, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 3, 'n': 3, 'z': 4, 's': -2, 'rx': 10, 'ry': 20}, {'chart_east': 0.75, 'chart_north': 0.75, 'pixel_x': 9.625, 'pixel_y': 19.625, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 3, 'n': 3, 'z': 1, 's': 2, 'rx': 0, 'ry': 0}, {'chart_east': 3.0, 'chart_north': 3.0, 'pixel_x': 1.5, 'pixel_y': 1.5, 'chart_valid': True, 'reciprocal_center': 1.0})], 3: [({'e': 4, 'n': 3, 'z': 4, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': 1.0, 'chart_north': 0.75, 'pixel_x': 10.5, 'pixel_y': 20.375, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 4, 'n': 3, 'z': 0, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': None, 'chart_north': None, 'pixel_x': None, 'pixel_y': None, 'chart_valid': False, 'reciprocal_center': None}), ({'e': 4, 'n': 3, 'z': -2, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': None, 'chart_north': None, 'pixel_x': None, 'pixel_y': None, 'chart_valid': False, 'reciprocal_center': None}), ({'e': 2, 'n': 0, 'z': 4, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': 0.5, 'chart_north': 0.0, 'pixel_x': 10.25, 'pixel_y': 20.0, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 4, 'n': 3, 'z': 4, 's': -2, 'rx': 10, 'ry': 20}, {'chart_east': 1.0, 'chart_north': 0.75, 'pixel_x': 9.5, 'pixel_y': 19.625, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 4, 'n': 3, 'z': 1, 's': 2, 'rx': 0, 'ry': 0}, {'chart_east': 4.0, 'chart_north': 3.0, 'pixel_x': 2.0, 'pixel_y': 1.5, 'chart_valid': True, 'reciprocal_center': 1.0})], 4: [({'e': 5, 'n': 3, 'z': 4, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': 1.25, 'chart_north': 0.75, 'pixel_x': 10.625, 'pixel_y': 20.375, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 5, 'n': 3, 'z': 0, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': None, 'chart_north': None, 'pixel_x': None, 'pixel_y': None, 'chart_valid': False, 'reciprocal_center': None}), ({'e': 5, 'n': 3, 'z': -2, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': None, 'chart_north': None, 'pixel_x': None, 'pixel_y': None, 'chart_valid': False, 'reciprocal_center': None}), ({'e': 3, 'n': 0, 'z': 4, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': 0.75, 'chart_north': 0.0, 'pixel_x': 10.375, 'pixel_y': 20.0, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 5, 'n': 3, 'z': 4, 's': -2, 'rx': 10, 'ry': 20}, {'chart_east': 1.25, 'chart_north': 0.75, 'pixel_x': 9.375, 'pixel_y': 19.625, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 5, 'n': 3, 'z': 1, 's': 2, 'rx': 0, 'ry': 0}, {'chart_east': 5.0, 'chart_north': 3.0, 'pixel_x': 2.5, 'pixel_y': 1.5, 'chart_valid': True, 'reciprocal_center': 1.0})], 5: [({'e': 6, 'n': 3, 'z': 4, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': 1.5, 'chart_north': 0.75, 'pixel_x': 10.75, 'pixel_y': 20.375, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 6, 'n': 3, 'z': 0, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': None, 'chart_north': None, 'pixel_x': None, 'pixel_y': None, 'chart_valid': False, 'reciprocal_center': None}), ({'e': 6, 'n': 3, 'z': -2, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': None, 'chart_north': None, 'pixel_x': None, 'pixel_y': None, 'chart_valid': False, 'reciprocal_center': None}), ({'e': 4, 'n': 0, 'z': 4, 's': 2, 'rx': 10, 'ry': 20}, {'chart_east': 1.0, 'chart_north': 0.0, 'pixel_x': 10.5, 'pixel_y': 20.0, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 6, 'n': 3, 'z': 4, 's': -2, 'rx': 10, 'ry': 20}, {'chart_east': 1.5, 'chart_north': 0.75, 'pixel_x': 9.25, 'pixel_y': 19.625, 'chart_valid': True, 'reciprocal_center': 0.25}), ({'e': 6, 'n': 3, 'z': 1, 's': 2, 'rx': 0, 'ry': 0}, {'chart_east': 6.0, 'chart_north': 3.0, 'pixel_x': 3.0, 'pixel_y': 1.5, 'chart_valid': True, 'reciprocal_center': 1.0})]}
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 fixture	Actual	Expected	Outcome
astronomical fixture 0	`{'chart_east': 0.5, 'chart_north': 0.75, 'chart_valid': True, 'pixel_x': 10.25, 'pixel_y': 20.375, 'reciprocal_center': 0.25}`	`{'chart_east': 0.5, 'chart_north': 0.75, 'chart_valid': True, 'pixel_x': 10.25, 'pixel_y': 20.375, 'reciprocal_center': 0.25}`	Passed
astronomical fixture 1	`{'chart_east': None, 'chart_north': None, 'chart_valid': False, 'pixel_x': None, 'pixel_y': None, 'reciprocal_center': None}`	`{'chart_east': None, 'chart_north': None, 'chart_valid': False, 'pixel_x': None, 'pixel_y': None, 'reciprocal_center': None}`	Passed
astronomical fixture 2	`{'chart_east': None, 'chart_north': None, 'chart_valid': False, 'pixel_x': None, 'pixel_y': None, 'reciprocal_center': None}`	`{'chart_east': None, 'chart_north': None, 'chart_valid': False, 'pixel_x': None, 'pixel_y': None, 'reciprocal_center': None}`	Passed
astronomical fixture 3	`{'chart_east': 0.0, 'chart_north': 0.0, 'chart_valid': True, 'pixel_x': 10.0, 'pixel_y': 20.0, 'reciprocal_center': 0.25}`	`{'chart_east': 0.0, 'chart_north': 0.0, 'chart_valid': True, 'pixel_x': 10.0, 'pixel_y': 20.0, 'reciprocal_center': 0.25}`	Passed
astronomical fixture 4	`{'chart_east': 0.5, 'chart_north': 0.75, 'chart_valid': True, 'pixel_x': 9.75, 'pixel_y': 19.625, 'reciprocal_center': 0.25}`	`{'chart_east': 0.5, 'chart_north': 0.75, 'chart_valid': True, 'pixel_x': 9.75, 'pixel_y': 19.625, 'reciprocal_center': 0.25}`	Passed
astronomical fixture 5	`{'chart_east': 2.0, 'chart_north': 3.0, 'chart_valid': True, 'pixel_x': 1.0, 'pixel_y': 1.5, 'reciprocal_center': 1.0}`	`{'chart_east': 2.0, 'chart_north': 3.0, 'chart_valid': True, 'pixel_x': 1.0, 'pixel_y': 1.5, 'reciprocal_center': 1.0}`	Passed

SHA-256 / ff542a40b4e71eae96aac0d270505c99ec2e3539755442d90ea5389cf023b8b7

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 2026-09-29T14:46:00.473077+00:00.

Case digest / 37218959c2c9ca4055defa72cdea53128bfa3dce94600be810e0934417f6d52b