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FA-55051 / Astronomical coordinate conventions / Open access

Echelle order coordinate: Order extraction evaluates a tilted trace on the cross-dispersion axis · case 01

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

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

ROOT CAUSE

Order extraction evaluates a tilted trace on the cross-dispersion axis. Faulty expression: d['y']-d['t0']

THE FAILURE

Order extraction evaluates a tilted trace on the cross-dispersion axis. Faulty expression: d['y']-d['t0']

Unsuccessful approach: A partial convention repair still uses d['y']-d['t0']-d['t1']*d['y']

Case contract

A reduced echelle extractor uses detector x along dispersion and y across orders. The blaze coordinate is centered on bx, trace is t0+t1*x, order-normalized wavelength is k/m, and rectangular extraction bounds use half-height h about that trace. Orders m are positive. Output fields are defined by: trace_offset = d['y']-d['t0']-d['t1']*d['x']; blaze_coordinate = d['x']-d['bx']; order_wavelength = d['k']/d['m']; lower_aperture = d['t0']+d['t1']*d['x']-d['h']; upper_aperture = d['t0']+d['t1']*d['x']+d['h']; neighbor_trace = d['t0']+d['t1']*d['x']+d['pitch']

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 {'trace_offset': d['y']-d['t0'], 'blaze_coordinate': d['x']-d['bx'], 'order_wavelength': d['k']/d['m'], 'lower_aperture': d['t0']+d['t1']*d['x']-d['h'], 'upper_aperture': d['t0']+d['t1']*d['x']+d['h'], 'neighbor_trace': d['t0']+d['t1']*d['x']+d['pitch']}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = {1: [({'x': 4, 'y': 8, 'bx': 2, 't0': 3, 't1': 2, 'k': 120, 'm': 3, 'h': 2, 'pitch': 5}, {'trace_offset': -3, 'blaze_coordinate': 2, 'order_wavelength': 40.0, 'lower_aperture': 9, 'upper_aperture': 13, 'neighbor_trace': 16}), ({'x': 4, 'y': 8, 'bx': 2, 't0': 3, 't1': 0, 'k': 120, 'm': 3, 'h': 2, 'pitch': 5}, {'trace_offset': 5, 'blaze_coordinate': 2, 'order_wavelength': 40.0, 'lower_aperture': 1, 'upper_aperture': 5, 'neighbor_trace': 8}), ({'x': 4, 'y': 8, 'bx': 2, 't0': 3, 't1': 2, 'k': 120, 'm': 3, 'h': 0, 'pitch': 5}, {'trace_offset': -3, 'blaze_coordinate': 2, 'order_wavelength': 40.0, 'lower_aperture': 11, 'upper_aperture': 11, 'neighbor_trace': 16}), ({'x': 4, 'y': 8, 'bx': 2, 't0': 3, 't1': 2, 'k': 120, 'm': 1, 'h': 2, 'pitch': 5}, {'trace_offset': -3, 'blaze_coordinate': 2, 'order_wavelength': 120.0, 'lower_aperture': 9, 'upper_aperture': 13, 'neighbor_trace': 16}), ({'x': 4, 'y': -2, 'bx': 2, 't0': 3, 't1': -1, 'k': 120, 'm': 3, 'h': 2, 'pitch': 5}, {'trace_offset': -1, 'blaze_coordinate': 2, 'order_wavelength': 40.0, 'lower_aperture': -3, 'upper_aperture': 1, 'neighbor_trace': 4}), ({'x': 4, 'y': 8, 'bx': -2, 't0': 3, 't1': 2, 'k': 120, 'm': 3, 'h': 2, 'pitch': 7}, {'trace_offset': -3, 'blaze_coordinate': 6, 'order_wavelength': 40.0, 'lower_aperture': 9, 'upper_aperture': 13, 'neighbor_trace': 18})], 2: [({'x': 5, 'y': 8, 'bx': 2, 't0': 3, 't1': 2, 'k': 120, 'm': 3, 'h': 2, 'pitch': 5}, {'trace_offset': -5, 'blaze_coordinate': 3, 'order_wavelength': 40.0, 'lower_aperture': 11, 'upper_aperture': 15, 'neighbor_trace': 18}), ({'x': 5, 'y': 8, 'bx': 2, 't0': 3, 't1': 0, 'k': 120, 'm': 3, 'h': 2, 'pitch': 5}, {'trace_offset': 5, 'blaze_coordinate': 3, 'order_wavelength': 40.0, 'lower_aperture': 1, 'upper_aperture': 5, 'neighbor_trace': 8}), ({'x': 5, 'y': 8, 'bx': 2, 't0': 3, 't1': 2, 'k': 120, 'm': 3, 'h': 0, 'pitch': 5}, {'trace_offset': -5, 'blaze_coordinate': 3, 'order_wavelength': 40.0, 'lower_aperture': 13, 'upper_aperture': 13, 'neighbor_trace': 18}), ({'x': 5, 'y': 8, 'bx': 2, 't0': 3, 't1': 2, 'k': 120, 'm': 1, 'h': 2, 'pitch': 5}, {'trace_offset': -5, 'blaze_coordinate': 3, 'order_wavelength': 120.0, 'lower_aperture': 11, 'upper_aperture': 15, 'neighbor_trace': 18}), ({'x': 5, 'y': -2, 'bx': 2, 't0': 3, 't1': -1, 'k': 120, 'm': 3, 'h': 2, 'pitch': 5}, {'trace_offset': 0, 'blaze_coordinate': 3, 'order_wavelength': 40.0, 'lower_aperture': -4, 'upper_aperture': 0, 'neighbor_trace': 3}), ({'x': 5, 'y': 8, 'bx': -2, 't0': 3, 't1': 2, 'k': 120, 'm': 3, 'h': 2, 'pitch': 7}, {'trace_offset': -5, 'blaze_coordinate': 7, 'order_wavelength': 40.0, 'lower_aperture': 11, 'upper_aperture': 15, 'neighbor_trace': 20})], 3: [({'x': 6, 'y': 8, 'bx': 2, 't0': 3, 't1': 2, 'k': 120, 'm': 3, 'h': 2, 'pitch': 5}, {'trace_offset': -7, 'blaze_coordinate': 4, 'order_wavelength': 40.0, 'lower_aperture': 13, 'upper_aperture': 17, 'neighbor_trace': 20}), ({'x': 6, 'y': 8, 'bx': 2, 't0': 3, 't1': 0, 'k': 120, 'm': 3, 'h': 2, 'pitch': 5}, {'trace_offset': 5, 'blaze_coordinate': 4, 'order_wavelength': 40.0, 'lower_aperture': 1, 'upper_aperture': 5, 'neighbor_trace': 8}), ({'x': 6, 'y': 8, 'bx': 2, 't0': 3, 't1': 2, 'k': 120, 'm': 3, 'h': 0, 'pitch': 5}, {'trace_offset': -7, 'blaze_coordinate': 4, 'order_wavelength': 40.0, 'lower_aperture': 15, 'upper_aperture': 15, 'neighbor_trace': 20}), ({'x': 6, 'y': 8, 'bx': 2, 't0': 3, 't1': 2, 'k': 120, 'm': 1, 'h': 2, 'pitch': 5}, {'trace_offset': -7, 'blaze_coordinate': 4, 'order_wavelength': 120.0, 'lower_aperture': 13, 'upper_aperture': 17, 'neighbor_trace': 20}), ({'x': 6, 'y': -2, 'bx': 2, 't0': 3, 't1': -1, 'k': 120, 'm': 3, 'h': 2, 'pitch': 5}, {'trace_offset': 1, 'blaze_coordinate': 4, 'order_wavelength': 40.0, 'lower_aperture': -5, 'upper_aperture': -1, 'neighbor_trace': 2}), ({'x': 6, 'y': 8, 'bx': -2, 't0': 3, 't1': 2, 'k': 120, 'm': 3, 'h': 2, 'pitch': 7}, {'trace_offset': -7, 'blaze_coordinate': 8, 'order_wavelength': 40.0, 'lower_aperture': 13, 'upper_aperture': 17, 'neighbor_trace': 22})], 4: [({'x': 7, 'y': 8, 'bx': 2, 't0': 3, 't1': 2, 'k': 120, 'm': 3, 'h': 2, 'pitch': 5}, {'trace_offset': -9, 'blaze_coordinate': 5, 'order_wavelength': 40.0, 'lower_aperture': 15, 'upper_aperture': 19, 'neighbor_trace': 22}), ({'x': 7, 'y': 8, 'bx': 2, 't0': 3, 't1': 0, 'k': 120, 'm': 3, 'h': 2, 'pitch': 5}, {'trace_offset': 5, 'blaze_coordinate': 5, 'order_wavelength': 40.0, 'lower_aperture': 1, 'upper_aperture': 5, 'neighbor_trace': 8}), ({'x': 7, 'y': 8, 'bx': 2, 't0': 3, 't1': 2, 'k': 120, 'm': 3, 'h': 0, 'pitch': 5}, {'trace_offset': -9, 'blaze_coordinate': 5, 'order_wavelength': 40.0, 'lower_aperture': 17, 'upper_aperture': 17, 'neighbor_trace': 22}), ({'x': 7, 'y': 8, 'bx': 2, 't0': 3, 't1': 2, 'k': 120, 'm': 1, 'h': 2, 'pitch': 5}, {'trace_offset': -9, 'blaze_coordinate': 5, 'order_wavelength': 120.0, 'lower_aperture': 15, 'upper_aperture': 19, 'neighbor_trace': 22}), ({'x': 7, 'y': -2, 'bx': 2, 't0': 3, 't1': -1, 'k': 120, 'm': 3, 'h': 2, 'pitch': 5}, {'trace_offset': 2, 'blaze_coordinate': 5, 'order_wavelength': 40.0, 'lower_aperture': -6, 'upper_aperture': -2, 'neighbor_trace': 1}), ({'x': 7, 'y': 8, 'bx': -2, 't0': 3, 't1': 2, 'k': 120, 'm': 3, 'h': 2, 'pitch': 7}, {'trace_offset': -9, 'blaze_coordinate': 9, 'order_wavelength': 40.0, 'lower_aperture': 15, 'upper_aperture': 19, 'neighbor_trace': 24})], 5: [({'x': 8, 'y': 8, 'bx': 2, 't0': 3, 't1': 2, 'k': 120, 'm': 3, 'h': 2, 'pitch': 5}, {'trace_offset': -11, 'blaze_coordinate': 6, 'order_wavelength': 40.0, 'lower_aperture': 17, 'upper_aperture': 21, 'neighbor_trace': 24}), ({'x': 8, 'y': 8, 'bx': 2, 't0': 3, 't1': 0, 'k': 120, 'm': 3, 'h': 2, 'pitch': 5}, {'trace_offset': 5, 'blaze_coordinate': 6, 'order_wavelength': 40.0, 'lower_aperture': 1, 'upper_aperture': 5, 'neighbor_trace': 8}), ({'x': 8, 'y': 8, 'bx': 2, 't0': 3, 't1': 2, 'k': 120, 'm': 3, 'h': 0, 'pitch': 5}, {'trace_offset': -11, 'blaze_coordinate': 6, 'order_wavelength': 40.0, 'lower_aperture': 19, 'upper_aperture': 19, 'neighbor_trace': 24}), ({'x': 8, 'y': 8, 'bx': 2, 't0': 3, 't1': 2, 'k': 120, 'm': 1, 'h': 2, 'pitch': 5}, {'trace_offset': -11, 'blaze_coordinate': 6, 'order_wavelength': 120.0, 'lower_aperture': 17, 'upper_aperture': 21, 'neighbor_trace': 24}), ({'x': 8, 'y': -2, 'bx': 2, 't0': 3, 't1': -1, 'k': 120, 'm': 3, 'h': 2, 'pitch': 5}, {'trace_offset': 3, 'blaze_coordinate': 6, 'order_wavelength': 40.0, 'lower_aperture': -7, 'upper_aperture': -3, 'neighbor_trace': 0}), ({'x': 8, 'y': 8, 'bx': -2, 't0': 3, 't1': 2, 'k': 120, 'm': 3, 'h': 2, 'pitch': 7}, {'trace_offset': -11, 'blaze_coordinate': 10, 'order_wavelength': 40.0, 'lower_aperture': 17, 'upper_aperture': 21, 'neighbor_trace': 26})]}
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{'blaze_coordinate': 2, 'lower_aperture': 9, 'neighbor_trace': 16, 'order_wavelength': 40.0, 'trace_offset': 5, 'upper_aperture': 13}{'blaze_coordinate': 2, 'lower_aperture': 9, 'neighbor_trace': 16, 'order_wavelength': 40.0, 'trace_offset': -3, 'upper_aperture': 13}Failed
astronomical fixture 1{'blaze_coordinate': 2, 'lower_aperture': 1, 'neighbor_trace': 8, 'order_wavelength': 40.0, 'trace_offset': 5, 'upper_aperture': 5}{'blaze_coordinate': 2, 'lower_aperture': 1, 'neighbor_trace': 8, 'order_wavelength': 40.0, 'trace_offset': 5, 'upper_aperture': 5}Passed
astronomical fixture 2{'blaze_coordinate': 2, 'lower_aperture': 11, 'neighbor_trace': 16, 'order_wavelength': 40.0, 'trace_offset': 5, 'upper_aperture': 11}{'blaze_coordinate': 2, 'lower_aperture': 11, 'neighbor_trace': 16, 'order_wavelength': 40.0, 'trace_offset': -3, 'upper_aperture': 11}Failed
astronomical fixture 3{'blaze_coordinate': 2, 'lower_aperture': 9, 'neighbor_trace': 16, 'order_wavelength': 120.0, 'trace_offset': 5, 'upper_aperture': 13}{'blaze_coordinate': 2, 'lower_aperture': 9, 'neighbor_trace': 16, 'order_wavelength': 120.0, 'trace_offset': -3, 'upper_aperture': 13}Failed
astronomical fixture 4{'blaze_coordinate': 2, 'lower_aperture': -3, 'neighbor_trace': 4, 'order_wavelength': 40.0, 'trace_offset': -5, 'upper_aperture': 1}{'blaze_coordinate': 2, 'lower_aperture': -3, 'neighbor_trace': 4, 'order_wavelength': 40.0, 'trace_offset': -1, 'upper_aperture': 1}Failed
astronomical fixture 5{'blaze_coordinate': 6, 'lower_aperture': 9, 'neighbor_trace': 18, 'order_wavelength': 40.0, 'trace_offset': 5, 'upper_aperture': 13}{'blaze_coordinate': 6, 'lower_aperture': 9, 'neighbor_trace': 18, 'order_wavelength': 40.0, 'trace_offset': -3, 'upper_aperture': 13}Failed

SHA-256 / 06b1a6d82fa012b56ff8dd3e54d510b7622e815b2e3c2876522b6adfe020411e

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(d):
    return {'trace_offset': d['y']-d['t0']-d['t1']*d['y'], 'blaze_coordinate': d['x']-d['bx'], 'order_wavelength': d['k']/d['m'], 'lower_aperture': d['t0']+d['t1']*d['x']-d['h'], 'upper_aperture': d['t0']+d['t1']*d['x']+d['h'], 'neighbor_trace': d['t0']+d['t1']*d['x']+d['pitch']}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = {1: [({'x': 4, 'y': 8, 'bx': 2, 't0': 3, 't1': 2, 'k': 120, 'm': 3, 'h': 2, 'pitch': 5}, {'trace_offset': -3, 'blaze_coordinate': 2, 'order_wavelength': 40.0, 'lower_aperture': 9, 'upper_aperture': 13, 'neighbor_trace': 16}), ({'x': 4, 'y': 8, 'bx': 2, 't0': 3, 't1': 0, 'k': 120, 'm': 3, 'h': 2, 'pitch': 5}, {'trace_offset': 5, 'blaze_coordinate': 2, 'order_wavelength': 40.0, 'lower_aperture': 1, 'upper_aperture': 5, 'neighbor_trace': 8}), ({'x': 4, 'y': 8, 'bx': 2, 't0': 3, 't1': 2, 'k': 120, 'm': 3, 'h': 0, 'pitch': 5}, {'trace_offset': -3, 'blaze_coordinate': 2, 'order_wavelength': 40.0, 'lower_aperture': 11, 'upper_aperture': 11, 'neighbor_trace': 16}), ({'x': 4, 'y': 8, 'bx': 2, 't0': 3, 't1': 2, 'k': 120, 'm': 1, 'h': 2, 'pitch': 5}, {'trace_offset': -3, 'blaze_coordinate': 2, 'order_wavelength': 120.0, 'lower_aperture': 9, 'upper_aperture': 13, 'neighbor_trace': 16}), ({'x': 4, 'y': -2, 'bx': 2, 't0': 3, 't1': -1, 'k': 120, 'm': 3, 'h': 2, 'pitch': 5}, {'trace_offset': -1, 'blaze_coordinate': 2, 'order_wavelength': 40.0, 'lower_aperture': -3, 'upper_aperture': 1, 'neighbor_trace': 4}), ({'x': 4, 'y': 8, 'bx': -2, 't0': 3, 't1': 2, 'k': 120, 'm': 3, 'h': 2, 'pitch': 7}, {'trace_offset': -3, 'blaze_coordinate': 6, 'order_wavelength': 40.0, 'lower_aperture': 9, 'upper_aperture': 13, 'neighbor_trace': 18})], 2: [({'x': 5, 'y': 8, 'bx': 2, 't0': 3, 't1': 2, 'k': 120, 'm': 3, 'h': 2, 'pitch': 5}, {'trace_offset': -5, 'blaze_coordinate': 3, 'order_wavelength': 40.0, 'lower_aperture': 11, 'upper_aperture': 15, 'neighbor_trace': 18}), ({'x': 5, 'y': 8, 'bx': 2, 't0': 3, 't1': 0, 'k': 120, 'm': 3, 'h': 2, 'pitch': 5}, {'trace_offset': 5, 'blaze_coordinate': 3, 'order_wavelength': 40.0, 'lower_aperture': 1, 'upper_aperture': 5, 'neighbor_trace': 8}), ({'x': 5, 'y': 8, 'bx': 2, 't0': 3, 't1': 2, 'k': 120, 'm': 3, 'h': 0, 'pitch': 5}, {'trace_offset': -5, 'blaze_coordinate': 3, 'order_wavelength': 40.0, 'lower_aperture': 13, 'upper_aperture': 13, 'neighbor_trace': 18}), ({'x': 5, 'y': 8, 'bx': 2, 't0': 3, 't1': 2, 'k': 120, 'm': 1, 'h': 2, 'pitch': 5}, {'trace_offset': -5, 'blaze_coordinate': 3, 'order_wavelength': 120.0, 'lower_aperture': 11, 'upper_aperture': 15, 'neighbor_trace': 18}), ({'x': 5, 'y': -2, 'bx': 2, 't0': 3, 't1': -1, 'k': 120, 'm': 3, 'h': 2, 'pitch': 5}, {'trace_offset': 0, 'blaze_coordinate': 3, 'order_wavelength': 40.0, 'lower_aperture': -4, 'upper_aperture': 0, 'neighbor_trace': 3}), ({'x': 5, 'y': 8, 'bx': -2, 't0': 3, 't1': 2, 'k': 120, 'm': 3, 'h': 2, 'pitch': 7}, {'trace_offset': -5, 'blaze_coordinate': 7, 'order_wavelength': 40.0, 'lower_aperture': 11, 'upper_aperture': 15, 'neighbor_trace': 20})], 3: [({'x': 6, 'y': 8, 'bx': 2, 't0': 3, 't1': 2, 'k': 120, 'm': 3, 'h': 2, 'pitch': 5}, {'trace_offset': -7, 'blaze_coordinate': 4, 'order_wavelength': 40.0, 'lower_aperture': 13, 'upper_aperture': 17, 'neighbor_trace': 20}), ({'x': 6, 'y': 8, 'bx': 2, 't0': 3, 't1': 0, 'k': 120, 'm': 3, 'h': 2, 'pitch': 5}, {'trace_offset': 5, 'blaze_coordinate': 4, 'order_wavelength': 40.0, 'lower_aperture': 1, 'upper_aperture': 5, 'neighbor_trace': 8}), ({'x': 6, 'y': 8, 'bx': 2, 't0': 3, 't1': 2, 'k': 120, 'm': 3, 'h': 0, 'pitch': 5}, {'trace_offset': -7, 'blaze_coordinate': 4, 'order_wavelength': 40.0, 'lower_aperture': 15, 'upper_aperture': 15, 'neighbor_trace': 20}), ({'x': 6, 'y': 8, 'bx': 2, 't0': 3, 't1': 2, 'k': 120, 'm': 1, 'h': 2, 'pitch': 5}, {'trace_offset': -7, 'blaze_coordinate': 4, 'order_wavelength': 120.0, 'lower_aperture': 13, 'upper_aperture': 17, 'neighbor_trace': 20}), ({'x': 6, 'y': -2, 'bx': 2, 't0': 3, 't1': -1, 'k': 120, 'm': 3, 'h': 2, 'pitch': 5}, {'trace_offset': 1, 'blaze_coordinate': 4, 'order_wavelength': 40.0, 'lower_aperture': -5, 'upper_aperture': -1, 'neighbor_trace': 2}), ({'x': 6, 'y': 8, 'bx': -2, 't0': 3, 't1': 2, 'k': 120, 'm': 3, 'h': 2, 'pitch': 7}, {'trace_offset': -7, 'blaze_coordinate': 8, 'order_wavelength': 40.0, 'lower_aperture': 13, 'upper_aperture': 17, 'neighbor_trace': 22})], 4: [({'x': 7, 'y': 8, 'bx': 2, 't0': 3, 't1': 2, 'k': 120, 'm': 3, 'h': 2, 'pitch': 5}, {'trace_offset': -9, 'blaze_coordinate': 5, 'order_wavelength': 40.0, 'lower_aperture': 15, 'upper_aperture': 19, 'neighbor_trace': 22}), ({'x': 7, 'y': 8, 'bx': 2, 't0': 3, 't1': 0, 'k': 120, 'm': 3, 'h': 2, 'pitch': 5}, {'trace_offset': 5, 'blaze_coordinate': 5, 'order_wavelength': 40.0, 'lower_aperture': 1, 'upper_aperture': 5, 'neighbor_trace': 8}), ({'x': 7, 'y': 8, 'bx': 2, 't0': 3, 't1': 2, 'k': 120, 'm': 3, 'h': 0, 'pitch': 5}, {'trace_offset': -9, 'blaze_coordinate': 5, 'order_wavelength': 40.0, 'lower_aperture': 17, 'upper_aperture': 17, 'neighbor_trace': 22}), ({'x': 7, 'y': 8, 'bx': 2, 't0': 3, 't1': 2, 'k': 120, 'm': 1, 'h': 2, 'pitch': 5}, {'trace_offset': -9, 'blaze_coordinate': 5, 'order_wavelength': 120.0, 'lower_aperture': 15, 'upper_aperture': 19, 'neighbor_trace': 22}), ({'x': 7, 'y': -2, 'bx': 2, 't0': 3, 't1': -1, 'k': 120, 'm': 3, 'h': 2, 'pitch': 5}, {'trace_offset': 2, 'blaze_coordinate': 5, 'order_wavelength': 40.0, 'lower_aperture': -6, 'upper_aperture': -2, 'neighbor_trace': 1}), ({'x': 7, 'y': 8, 'bx': -2, 't0': 3, 't1': 2, 'k': 120, 'm': 3, 'h': 2, 'pitch': 7}, {'trace_offset': -9, 'blaze_coordinate': 9, 'order_wavelength': 40.0, 'lower_aperture': 15, 'upper_aperture': 19, 'neighbor_trace': 24})], 5: [({'x': 8, 'y': 8, 'bx': 2, 't0': 3, 't1': 2, 'k': 120, 'm': 3, 'h': 2, 'pitch': 5}, {'trace_offset': -11, 'blaze_coordinate': 6, 'order_wavelength': 40.0, 'lower_aperture': 17, 'upper_aperture': 21, 'neighbor_trace': 24}), ({'x': 8, 'y': 8, 'bx': 2, 't0': 3, 't1': 0, 'k': 120, 'm': 3, 'h': 2, 'pitch': 5}, {'trace_offset': 5, 'blaze_coordinate': 6, 'order_wavelength': 40.0, 'lower_aperture': 1, 'upper_aperture': 5, 'neighbor_trace': 8}), ({'x': 8, 'y': 8, 'bx': 2, 't0': 3, 't1': 2, 'k': 120, 'm': 3, 'h': 0, 'pitch': 5}, {'trace_offset': -11, 'blaze_coordinate': 6, 'order_wavelength': 40.0, 'lower_aperture': 19, 'upper_aperture': 19, 'neighbor_trace': 24}), ({'x': 8, 'y': 8, 'bx': 2, 't0': 3, 't1': 2, 'k': 120, 'm': 1, 'h': 2, 'pitch': 5}, {'trace_offset': -11, 'blaze_coordinate': 6, 'order_wavelength': 120.0, 'lower_aperture': 17, 'upper_aperture': 21, 'neighbor_trace': 24}), ({'x': 8, 'y': -2, 'bx': 2, 't0': 3, 't1': -1, 'k': 120, 'm': 3, 'h': 2, 'pitch': 5}, {'trace_offset': 3, 'blaze_coordinate': 6, 'order_wavelength': 40.0, 'lower_aperture': -7, 'upper_aperture': -3, 'neighbor_trace': 0}), ({'x': 8, 'y': 8, 'bx': -2, 't0': 3, 't1': 2, 'k': 120, 'm': 3, 'h': 2, 'pitch': 7}, {'trace_offset': -11, 'blaze_coordinate': 10, 'order_wavelength': 40.0, 'lower_aperture': 17, 'upper_aperture': 21, 'neighbor_trace': 26})]}
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{'blaze_coordinate': 2, 'lower_aperture': 9, 'neighbor_trace': 16, 'order_wavelength': 40.0, 'trace_offset': -11, 'upper_aperture': 13}{'blaze_coordinate': 2, 'lower_aperture': 9, 'neighbor_trace': 16, 'order_wavelength': 40.0, 'trace_offset': -3, 'upper_aperture': 13}Failed
astronomical fixture 1{'blaze_coordinate': 2, 'lower_aperture': 1, 'neighbor_trace': 8, 'order_wavelength': 40.0, 'trace_offset': 5, 'upper_aperture': 5}{'blaze_coordinate': 2, 'lower_aperture': 1, 'neighbor_trace': 8, 'order_wavelength': 40.0, 'trace_offset': 5, 'upper_aperture': 5}Passed
astronomical fixture 2{'blaze_coordinate': 2, 'lower_aperture': 11, 'neighbor_trace': 16, 'order_wavelength': 40.0, 'trace_offset': -11, 'upper_aperture': 11}{'blaze_coordinate': 2, 'lower_aperture': 11, 'neighbor_trace': 16, 'order_wavelength': 40.0, 'trace_offset': -3, 'upper_aperture': 11}Failed
astronomical fixture 3{'blaze_coordinate': 2, 'lower_aperture': 9, 'neighbor_trace': 16, 'order_wavelength': 120.0, 'trace_offset': -11, 'upper_aperture': 13}{'blaze_coordinate': 2, 'lower_aperture': 9, 'neighbor_trace': 16, 'order_wavelength': 120.0, 'trace_offset': -3, 'upper_aperture': 13}Failed
astronomical fixture 4{'blaze_coordinate': 2, 'lower_aperture': -3, 'neighbor_trace': 4, 'order_wavelength': 40.0, 'trace_offset': -7, 'upper_aperture': 1}{'blaze_coordinate': 2, 'lower_aperture': -3, 'neighbor_trace': 4, 'order_wavelength': 40.0, 'trace_offset': -1, 'upper_aperture': 1}Failed
astronomical fixture 5{'blaze_coordinate': 6, 'lower_aperture': 9, 'neighbor_trace': 18, 'order_wavelength': 40.0, 'trace_offset': -11, 'upper_aperture': 13}{'blaze_coordinate': 6, 'lower_aperture': 9, 'neighbor_trace': 18, 'order_wavelength': 40.0, 'trace_offset': -3, 'upper_aperture': 13}Failed

SHA-256 / 12eee8bb8f7bf77e64ba77ff69a765c93033c973623e04391565f0a63639ee92

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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.

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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 2026-09-29T14:45:54.369446+00:00.

Case digest / 27ff8d9ffd3443b9b749af8b672ada94ee106444c42d18fb982cdabddcfa6860