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FA-55916 / Astronomical coordinate conventions / Open access

Nested sky cell address: All-sky nested pixel count omits the base-face multiplicity · case 01

The adapter reports an incorrect face count while other fields remain valid.

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

ROOT CAUSE

All-sky nested pixel count omits the base-face multiplicity. Faulty expression: 12*2**d['o']

VERIFIED REPAIR

Preserve the declared model convention at this site: 12*4**d['o']

Unsuccessful approach: A partial convention repair still uses 4**d['o']

Case contract

A stipulated hierarchical sky tessellation has 12 base faces and four nested children per cell. At order o a face has 4**o pixels. p is the local pixel index, f the face, k the child digit. Parent and descendant ranges are nested indexing operations; no geometric HEALPix projection is implemented. Output fields are defined by: global_pixel = d['f']*4**d['o']+d['p']; parent_local = d['p']//4; child_local = 4*d['p']+d['k']; descendant_first = d['p']*4**d['depth']; descendant_stop = (d['p']+1)*4**d['depth']; face_count = 12*4**d['o']

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 {'global_pixel': d['f']*4**d['o']+d['p'], 'parent_local': d['p']//4, 'child_local': 4*d['p']+d['k'], 'descendant_first': d['p']*4**d['depth'], 'descendant_stop': (d['p']+1)*4**d['depth'], 'face_count': 12*2**d['o']}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = {1: [({'o': 2, 'p': 5, 'f': 3, 'k': 2, 'depth': 2}, {'global_pixel': 53, 'parent_local': 1, 'child_local': 22, 'descendant_first': 80, 'descendant_stop': 96, 'face_count': 192}), ({'o': 2, 'p': 0, 'f': 0, 'k': 0, 'depth': 2}, {'global_pixel': 0, 'parent_local': 0, 'child_local': 0, 'descendant_first': 0, 'descendant_stop': 16, 'face_count': 192}), ({'o': 2, 'p': 5, 'f': 11, 'k': 3, 'depth': 2}, {'global_pixel': 181, 'parent_local': 1, 'child_local': 23, 'descendant_first': 80, 'descendant_stop': 96, 'face_count': 192}), ({'o': 2, 'p': 5, 'f': 3, 'k': 2, 'depth': 0}, {'global_pixel': 53, 'parent_local': 1, 'child_local': 22, 'descendant_first': 5, 'descendant_stop': 6, 'face_count': 192}), ({'o': 2, 'p': 2, 'f': 1, 'k': 2, 'depth': 2}, {'global_pixel': 18, 'parent_local': 0, 'child_local': 10, 'descendant_first': 32, 'descendant_stop': 48, 'face_count': 192}), ({'o': 3, 'p': 20, 'f': 3, 'k': 2, 'depth': 1}, {'global_pixel': 212, 'parent_local': 5, 'child_local': 82, 'descendant_first': 80, 'descendant_stop': 84, 'face_count': 768})], 2: [({'o': 2, 'p': 6, 'f': 3, 'k': 2, 'depth': 2}, {'global_pixel': 54, 'parent_local': 1, 'child_local': 26, 'descendant_first': 96, 'descendant_stop': 112, 'face_count': 192}), ({'o': 2, 'p': 1, 'f': 0, 'k': 0, 'depth': 2}, {'global_pixel': 1, 'parent_local': 0, 'child_local': 4, 'descendant_first': 16, 'descendant_stop': 32, 'face_count': 192}), ({'o': 2, 'p': 6, 'f': 11, 'k': 3, 'depth': 2}, {'global_pixel': 182, 'parent_local': 1, 'child_local': 27, 'descendant_first': 96, 'descendant_stop': 112, 'face_count': 192}), ({'o': 2, 'p': 6, 'f': 3, 'k': 2, 'depth': 0}, {'global_pixel': 54, 'parent_local': 1, 'child_local': 26, 'descendant_first': 6, 'descendant_stop': 7, 'face_count': 192}), ({'o': 2, 'p': 3, 'f': 1, 'k': 2, 'depth': 2}, {'global_pixel': 19, 'parent_local': 0, 'child_local': 14, 'descendant_first': 48, 'descendant_stop': 64, 'face_count': 192}), ({'o': 3, 'p': 21, 'f': 3, 'k': 2, 'depth': 1}, {'global_pixel': 213, 'parent_local': 5, 'child_local': 86, 'descendant_first': 84, 'descendant_stop': 88, 'face_count': 768})], 3: [({'o': 2, 'p': 7, 'f': 3, 'k': 2, 'depth': 2}, {'global_pixel': 55, 'parent_local': 1, 'child_local': 30, 'descendant_first': 112, 'descendant_stop': 128, 'face_count': 192}), ({'o': 2, 'p': 2, 'f': 0, 'k': 0, 'depth': 2}, {'global_pixel': 2, 'parent_local': 0, 'child_local': 8, 'descendant_first': 32, 'descendant_stop': 48, 'face_count': 192}), ({'o': 2, 'p': 7, 'f': 11, 'k': 3, 'depth': 2}, {'global_pixel': 183, 'parent_local': 1, 'child_local': 31, 'descendant_first': 112, 'descendant_stop': 128, 'face_count': 192}), ({'o': 2, 'p': 7, 'f': 3, 'k': 2, 'depth': 0}, {'global_pixel': 55, 'parent_local': 1, 'child_local': 30, 'descendant_first': 7, 'descendant_stop': 8, 'face_count': 192}), ({'o': 2, 'p': 4, 'f': 1, 'k': 2, 'depth': 2}, {'global_pixel': 20, 'parent_local': 1, 'child_local': 18, 'descendant_first': 64, 'descendant_stop': 80, 'face_count': 192}), ({'o': 3, 'p': 22, 'f': 3, 'k': 2, 'depth': 1}, {'global_pixel': 214, 'parent_local': 5, 'child_local': 90, 'descendant_first': 88, 'descendant_stop': 92, 'face_count': 768})], 4: [({'o': 2, 'p': 8, 'f': 3, 'k': 2, 'depth': 2}, {'global_pixel': 56, 'parent_local': 2, 'child_local': 34, 'descendant_first': 128, 'descendant_stop': 144, 'face_count': 192}), ({'o': 2, 'p': 3, 'f': 0, 'k': 0, 'depth': 2}, {'global_pixel': 3, 'parent_local': 0, 'child_local': 12, 'descendant_first': 48, 'descendant_stop': 64, 'face_count': 192}), ({'o': 2, 'p': 8, 'f': 11, 'k': 3, 'depth': 2}, {'global_pixel': 184, 'parent_local': 2, 'child_local': 35, 'descendant_first': 128, 'descendant_stop': 144, 'face_count': 192}), ({'o': 2, 'p': 8, 'f': 3, 'k': 2, 'depth': 0}, {'global_pixel': 56, 'parent_local': 2, 'child_local': 34, 'descendant_first': 8, 'descendant_stop': 9, 'face_count': 192}), ({'o': 2, 'p': 5, 'f': 1, 'k': 2, 'depth': 2}, {'global_pixel': 21, 'parent_local': 1, 'child_local': 22, 'descendant_first': 80, 'descendant_stop': 96, 'face_count': 192}), ({'o': 3, 'p': 23, 'f': 3, 'k': 2, 'depth': 1}, {'global_pixel': 215, 'parent_local': 5, 'child_local': 94, 'descendant_first': 92, 'descendant_stop': 96, 'face_count': 768})], 5: [({'o': 2, 'p': 9, 'f': 3, 'k': 2, 'depth': 2}, {'global_pixel': 57, 'parent_local': 2, 'child_local': 38, 'descendant_first': 144, 'descendant_stop': 160, 'face_count': 192}), ({'o': 2, 'p': 4, 'f': 0, 'k': 0, 'depth': 2}, {'global_pixel': 4, 'parent_local': 1, 'child_local': 16, 'descendant_first': 64, 'descendant_stop': 80, 'face_count': 192}), ({'o': 2, 'p': 9, 'f': 11, 'k': 3, 'depth': 2}, {'global_pixel': 185, 'parent_local': 2, 'child_local': 39, 'descendant_first': 144, 'descendant_stop': 160, 'face_count': 192}), ({'o': 2, 'p': 9, 'f': 3, 'k': 2, 'depth': 0}, {'global_pixel': 57, 'parent_local': 2, 'child_local': 38, 'descendant_first': 9, 'descendant_stop': 10, 'face_count': 192}), ({'o': 2, 'p': 6, 'f': 1, 'k': 2, 'depth': 2}, {'global_pixel': 22, 'parent_local': 1, 'child_local': 26, 'descendant_first': 96, 'descendant_stop': 112, 'face_count': 192}), ({'o': 3, 'p': 24, 'f': 3, 'k': 2, 'depth': 1}, {'global_pixel': 216, 'parent_local': 6, 'child_local': 98, 'descendant_first': 96, 'descendant_stop': 100, 'face_count': 768})]}
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{'child_local': 22, 'descendant_first': 80, 'descendant_stop': 96, 'face_count': 48, 'global_pixel': 53, 'parent_local': 1}{'child_local': 22, 'descendant_first': 80, 'descendant_stop': 96, 'face_count': 192, 'global_pixel': 53, 'parent_local': 1}Failed
astronomical fixture 1{'child_local': 0, 'descendant_first': 0, 'descendant_stop': 16, 'face_count': 48, 'global_pixel': 0, 'parent_local': 0}{'child_local': 0, 'descendant_first': 0, 'descendant_stop': 16, 'face_count': 192, 'global_pixel': 0, 'parent_local': 0}Failed
astronomical fixture 2{'child_local': 23, 'descendant_first': 80, 'descendant_stop': 96, 'face_count': 48, 'global_pixel': 181, 'parent_local': 1}{'child_local': 23, 'descendant_first': 80, 'descendant_stop': 96, 'face_count': 192, 'global_pixel': 181, 'parent_local': 1}Failed
astronomical fixture 3{'child_local': 22, 'descendant_first': 5, 'descendant_stop': 6, 'face_count': 48, 'global_pixel': 53, 'parent_local': 1}{'child_local': 22, 'descendant_first': 5, 'descendant_stop': 6, 'face_count': 192, 'global_pixel': 53, 'parent_local': 1}Failed
astronomical fixture 4{'child_local': 10, 'descendant_first': 32, 'descendant_stop': 48, 'face_count': 48, 'global_pixel': 18, 'parent_local': 0}{'child_local': 10, 'descendant_first': 32, 'descendant_stop': 48, 'face_count': 192, 'global_pixel': 18, 'parent_local': 0}Failed
astronomical fixture 5{'child_local': 82, 'descendant_first': 80, 'descendant_stop': 84, 'face_count': 96, 'global_pixel': 212, 'parent_local': 5}{'child_local': 82, 'descendant_first': 80, 'descendant_stop': 84, 'face_count': 768, 'global_pixel': 212, 'parent_local': 5}Failed

SHA-256 / 9209df9ff6724ee307b4bb4ef614530a386d5b8c161647b6597db27200e4aac7

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(d):
    return {'global_pixel': d['f']*4**d['o']+d['p'], 'parent_local': d['p']//4, 'child_local': 4*d['p']+d['k'], 'descendant_first': d['p']*4**d['depth'], 'descendant_stop': (d['p']+1)*4**d['depth'], 'face_count': 4**d['o']}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = {1: [({'o': 2, 'p': 5, 'f': 3, 'k': 2, 'depth': 2}, {'global_pixel': 53, 'parent_local': 1, 'child_local': 22, 'descendant_first': 80, 'descendant_stop': 96, 'face_count': 192}), ({'o': 2, 'p': 0, 'f': 0, 'k': 0, 'depth': 2}, {'global_pixel': 0, 'parent_local': 0, 'child_local': 0, 'descendant_first': 0, 'descendant_stop': 16, 'face_count': 192}), ({'o': 2, 'p': 5, 'f': 11, 'k': 3, 'depth': 2}, {'global_pixel': 181, 'parent_local': 1, 'child_local': 23, 'descendant_first': 80, 'descendant_stop': 96, 'face_count': 192}), ({'o': 2, 'p': 5, 'f': 3, 'k': 2, 'depth': 0}, {'global_pixel': 53, 'parent_local': 1, 'child_local': 22, 'descendant_first': 5, 'descendant_stop': 6, 'face_count': 192}), ({'o': 2, 'p': 2, 'f': 1, 'k': 2, 'depth': 2}, {'global_pixel': 18, 'parent_local': 0, 'child_local': 10, 'descendant_first': 32, 'descendant_stop': 48, 'face_count': 192}), ({'o': 3, 'p': 20, 'f': 3, 'k': 2, 'depth': 1}, {'global_pixel': 212, 'parent_local': 5, 'child_local': 82, 'descendant_first': 80, 'descendant_stop': 84, 'face_count': 768})], 2: [({'o': 2, 'p': 6, 'f': 3, 'k': 2, 'depth': 2}, {'global_pixel': 54, 'parent_local': 1, 'child_local': 26, 'descendant_first': 96, 'descendant_stop': 112, 'face_count': 192}), ({'o': 2, 'p': 1, 'f': 0, 'k': 0, 'depth': 2}, {'global_pixel': 1, 'parent_local': 0, 'child_local': 4, 'descendant_first': 16, 'descendant_stop': 32, 'face_count': 192}), ({'o': 2, 'p': 6, 'f': 11, 'k': 3, 'depth': 2}, {'global_pixel': 182, 'parent_local': 1, 'child_local': 27, 'descendant_first': 96, 'descendant_stop': 112, 'face_count': 192}), ({'o': 2, 'p': 6, 'f': 3, 'k': 2, 'depth': 0}, {'global_pixel': 54, 'parent_local': 1, 'child_local': 26, 'descendant_first': 6, 'descendant_stop': 7, 'face_count': 192}), ({'o': 2, 'p': 3, 'f': 1, 'k': 2, 'depth': 2}, {'global_pixel': 19, 'parent_local': 0, 'child_local': 14, 'descendant_first': 48, 'descendant_stop': 64, 'face_count': 192}), ({'o': 3, 'p': 21, 'f': 3, 'k': 2, 'depth': 1}, {'global_pixel': 213, 'parent_local': 5, 'child_local': 86, 'descendant_first': 84, 'descendant_stop': 88, 'face_count': 768})], 3: [({'o': 2, 'p': 7, 'f': 3, 'k': 2, 'depth': 2}, {'global_pixel': 55, 'parent_local': 1, 'child_local': 30, 'descendant_first': 112, 'descendant_stop': 128, 'face_count': 192}), ({'o': 2, 'p': 2, 'f': 0, 'k': 0, 'depth': 2}, {'global_pixel': 2, 'parent_local': 0, 'child_local': 8, 'descendant_first': 32, 'descendant_stop': 48, 'face_count': 192}), ({'o': 2, 'p': 7, 'f': 11, 'k': 3, 'depth': 2}, {'global_pixel': 183, 'parent_local': 1, 'child_local': 31, 'descendant_first': 112, 'descendant_stop': 128, 'face_count': 192}), ({'o': 2, 'p': 7, 'f': 3, 'k': 2, 'depth': 0}, {'global_pixel': 55, 'parent_local': 1, 'child_local': 30, 'descendant_first': 7, 'descendant_stop': 8, 'face_count': 192}), ({'o': 2, 'p': 4, 'f': 1, 'k': 2, 'depth': 2}, {'global_pixel': 20, 'parent_local': 1, 'child_local': 18, 'descendant_first': 64, 'descendant_stop': 80, 'face_count': 192}), ({'o': 3, 'p': 22, 'f': 3, 'k': 2, 'depth': 1}, {'global_pixel': 214, 'parent_local': 5, 'child_local': 90, 'descendant_first': 88, 'descendant_stop': 92, 'face_count': 768})], 4: [({'o': 2, 'p': 8, 'f': 3, 'k': 2, 'depth': 2}, {'global_pixel': 56, 'parent_local': 2, 'child_local': 34, 'descendant_first': 128, 'descendant_stop': 144, 'face_count': 192}), ({'o': 2, 'p': 3, 'f': 0, 'k': 0, 'depth': 2}, {'global_pixel': 3, 'parent_local': 0, 'child_local': 12, 'descendant_first': 48, 'descendant_stop': 64, 'face_count': 192}), ({'o': 2, 'p': 8, 'f': 11, 'k': 3, 'depth': 2}, {'global_pixel': 184, 'parent_local': 2, 'child_local': 35, 'descendant_first': 128, 'descendant_stop': 144, 'face_count': 192}), ({'o': 2, 'p': 8, 'f': 3, 'k': 2, 'depth': 0}, {'global_pixel': 56, 'parent_local': 2, 'child_local': 34, 'descendant_first': 8, 'descendant_stop': 9, 'face_count': 192}), ({'o': 2, 'p': 5, 'f': 1, 'k': 2, 'depth': 2}, {'global_pixel': 21, 'parent_local': 1, 'child_local': 22, 'descendant_first': 80, 'descendant_stop': 96, 'face_count': 192}), ({'o': 3, 'p': 23, 'f': 3, 'k': 2, 'depth': 1}, {'global_pixel': 215, 'parent_local': 5, 'child_local': 94, 'descendant_first': 92, 'descendant_stop': 96, 'face_count': 768})], 5: [({'o': 2, 'p': 9, 'f': 3, 'k': 2, 'depth': 2}, {'global_pixel': 57, 'parent_local': 2, 'child_local': 38, 'descendant_first': 144, 'descendant_stop': 160, 'face_count': 192}), ({'o': 2, 'p': 4, 'f': 0, 'k': 0, 'depth': 2}, {'global_pixel': 4, 'parent_local': 1, 'child_local': 16, 'descendant_first': 64, 'descendant_stop': 80, 'face_count': 192}), ({'o': 2, 'p': 9, 'f': 11, 'k': 3, 'depth': 2}, {'global_pixel': 185, 'parent_local': 2, 'child_local': 39, 'descendant_first': 144, 'descendant_stop': 160, 'face_count': 192}), ({'o': 2, 'p': 9, 'f': 3, 'k': 2, 'depth': 0}, {'global_pixel': 57, 'parent_local': 2, 'child_local': 38, 'descendant_first': 9, 'descendant_stop': 10, 'face_count': 192}), ({'o': 2, 'p': 6, 'f': 1, 'k': 2, 'depth': 2}, {'global_pixel': 22, 'parent_local': 1, 'child_local': 26, 'descendant_first': 96, 'descendant_stop': 112, 'face_count': 192}), ({'o': 3, 'p': 24, 'f': 3, 'k': 2, 'depth': 1}, {'global_pixel': 216, 'parent_local': 6, 'child_local': 98, 'descendant_first': 96, 'descendant_stop': 100, 'face_count': 768})]}
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{'child_local': 22, 'descendant_first': 80, 'descendant_stop': 96, 'face_count': 16, 'global_pixel': 53, 'parent_local': 1}{'child_local': 22, 'descendant_first': 80, 'descendant_stop': 96, 'face_count': 192, 'global_pixel': 53, 'parent_local': 1}Failed
astronomical fixture 1{'child_local': 0, 'descendant_first': 0, 'descendant_stop': 16, 'face_count': 16, 'global_pixel': 0, 'parent_local': 0}{'child_local': 0, 'descendant_first': 0, 'descendant_stop': 16, 'face_count': 192, 'global_pixel': 0, 'parent_local': 0}Failed
astronomical fixture 2{'child_local': 23, 'descendant_first': 80, 'descendant_stop': 96, 'face_count': 16, 'global_pixel': 181, 'parent_local': 1}{'child_local': 23, 'descendant_first': 80, 'descendant_stop': 96, 'face_count': 192, 'global_pixel': 181, 'parent_local': 1}Failed
astronomical fixture 3{'child_local': 22, 'descendant_first': 5, 'descendant_stop': 6, 'face_count': 16, 'global_pixel': 53, 'parent_local': 1}{'child_local': 22, 'descendant_first': 5, 'descendant_stop': 6, 'face_count': 192, 'global_pixel': 53, 'parent_local': 1}Failed
astronomical fixture 4{'child_local': 10, 'descendant_first': 32, 'descendant_stop': 48, 'face_count': 16, 'global_pixel': 18, 'parent_local': 0}{'child_local': 10, 'descendant_first': 32, 'descendant_stop': 48, 'face_count': 192, 'global_pixel': 18, 'parent_local': 0}Failed
astronomical fixture 5{'child_local': 82, 'descendant_first': 80, 'descendant_stop': 84, 'face_count': 64, 'global_pixel': 212, 'parent_local': 5}{'child_local': 82, 'descendant_first': 80, 'descendant_stop': 84, 'face_count': 768, 'global_pixel': 212, 'parent_local': 5}Failed

SHA-256 / 084516ff155e67835e43ccac2b9482906bd0a1d4c40ed91a754b7a564da94fb9

3 / The verified repair

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

N = 1
observations = []
def solve(d):
    return {'global_pixel': d['f']*4**d['o']+d['p'], 'parent_local': d['p']//4, 'child_local': 4*d['p']+d['k'], 'descendant_first': d['p']*4**d['depth'], 'descendant_stop': (d['p']+1)*4**d['depth'], 'face_count': 12*4**d['o']}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = {1: [({'o': 2, 'p': 5, 'f': 3, 'k': 2, 'depth': 2}, {'global_pixel': 53, 'parent_local': 1, 'child_local': 22, 'descendant_first': 80, 'descendant_stop': 96, 'face_count': 192}), ({'o': 2, 'p': 0, 'f': 0, 'k': 0, 'depth': 2}, {'global_pixel': 0, 'parent_local': 0, 'child_local': 0, 'descendant_first': 0, 'descendant_stop': 16, 'face_count': 192}), ({'o': 2, 'p': 5, 'f': 11, 'k': 3, 'depth': 2}, {'global_pixel': 181, 'parent_local': 1, 'child_local': 23, 'descendant_first': 80, 'descendant_stop': 96, 'face_count': 192}), ({'o': 2, 'p': 5, 'f': 3, 'k': 2, 'depth': 0}, {'global_pixel': 53, 'parent_local': 1, 'child_local': 22, 'descendant_first': 5, 'descendant_stop': 6, 'face_count': 192}), ({'o': 2, 'p': 2, 'f': 1, 'k': 2, 'depth': 2}, {'global_pixel': 18, 'parent_local': 0, 'child_local': 10, 'descendant_first': 32, 'descendant_stop': 48, 'face_count': 192}), ({'o': 3, 'p': 20, 'f': 3, 'k': 2, 'depth': 1}, {'global_pixel': 212, 'parent_local': 5, 'child_local': 82, 'descendant_first': 80, 'descendant_stop': 84, 'face_count': 768})], 2: [({'o': 2, 'p': 6, 'f': 3, 'k': 2, 'depth': 2}, {'global_pixel': 54, 'parent_local': 1, 'child_local': 26, 'descendant_first': 96, 'descendant_stop': 112, 'face_count': 192}), ({'o': 2, 'p': 1, 'f': 0, 'k': 0, 'depth': 2}, {'global_pixel': 1, 'parent_local': 0, 'child_local': 4, 'descendant_first': 16, 'descendant_stop': 32, 'face_count': 192}), ({'o': 2, 'p': 6, 'f': 11, 'k': 3, 'depth': 2}, {'global_pixel': 182, 'parent_local': 1, 'child_local': 27, 'descendant_first': 96, 'descendant_stop': 112, 'face_count': 192}), ({'o': 2, 'p': 6, 'f': 3, 'k': 2, 'depth': 0}, {'global_pixel': 54, 'parent_local': 1, 'child_local': 26, 'descendant_first': 6, 'descendant_stop': 7, 'face_count': 192}), ({'o': 2, 'p': 3, 'f': 1, 'k': 2, 'depth': 2}, {'global_pixel': 19, 'parent_local': 0, 'child_local': 14, 'descendant_first': 48, 'descendant_stop': 64, 'face_count': 192}), ({'o': 3, 'p': 21, 'f': 3, 'k': 2, 'depth': 1}, {'global_pixel': 213, 'parent_local': 5, 'child_local': 86, 'descendant_first': 84, 'descendant_stop': 88, 'face_count': 768})], 3: [({'o': 2, 'p': 7, 'f': 3, 'k': 2, 'depth': 2}, {'global_pixel': 55, 'parent_local': 1, 'child_local': 30, 'descendant_first': 112, 'descendant_stop': 128, 'face_count': 192}), ({'o': 2, 'p': 2, 'f': 0, 'k': 0, 'depth': 2}, {'global_pixel': 2, 'parent_local': 0, 'child_local': 8, 'descendant_first': 32, 'descendant_stop': 48, 'face_count': 192}), ({'o': 2, 'p': 7, 'f': 11, 'k': 3, 'depth': 2}, {'global_pixel': 183, 'parent_local': 1, 'child_local': 31, 'descendant_first': 112, 'descendant_stop': 128, 'face_count': 192}), ({'o': 2, 'p': 7, 'f': 3, 'k': 2, 'depth': 0}, {'global_pixel': 55, 'parent_local': 1, 'child_local': 30, 'descendant_first': 7, 'descendant_stop': 8, 'face_count': 192}), ({'o': 2, 'p': 4, 'f': 1, 'k': 2, 'depth': 2}, {'global_pixel': 20, 'parent_local': 1, 'child_local': 18, 'descendant_first': 64, 'descendant_stop': 80, 'face_count': 192}), ({'o': 3, 'p': 22, 'f': 3, 'k': 2, 'depth': 1}, {'global_pixel': 214, 'parent_local': 5, 'child_local': 90, 'descendant_first': 88, 'descendant_stop': 92, 'face_count': 768})], 4: [({'o': 2, 'p': 8, 'f': 3, 'k': 2, 'depth': 2}, {'global_pixel': 56, 'parent_local': 2, 'child_local': 34, 'descendant_first': 128, 'descendant_stop': 144, 'face_count': 192}), ({'o': 2, 'p': 3, 'f': 0, 'k': 0, 'depth': 2}, {'global_pixel': 3, 'parent_local': 0, 'child_local': 12, 'descendant_first': 48, 'descendant_stop': 64, 'face_count': 192}), ({'o': 2, 'p': 8, 'f': 11, 'k': 3, 'depth': 2}, {'global_pixel': 184, 'parent_local': 2, 'child_local': 35, 'descendant_first': 128, 'descendant_stop': 144, 'face_count': 192}), ({'o': 2, 'p': 8, 'f': 3, 'k': 2, 'depth': 0}, {'global_pixel': 56, 'parent_local': 2, 'child_local': 34, 'descendant_first': 8, 'descendant_stop': 9, 'face_count': 192}), ({'o': 2, 'p': 5, 'f': 1, 'k': 2, 'depth': 2}, {'global_pixel': 21, 'parent_local': 1, 'child_local': 22, 'descendant_first': 80, 'descendant_stop': 96, 'face_count': 192}), ({'o': 3, 'p': 23, 'f': 3, 'k': 2, 'depth': 1}, {'global_pixel': 215, 'parent_local': 5, 'child_local': 94, 'descendant_first': 92, 'descendant_stop': 96, 'face_count': 768})], 5: [({'o': 2, 'p': 9, 'f': 3, 'k': 2, 'depth': 2}, {'global_pixel': 57, 'parent_local': 2, 'child_local': 38, 'descendant_first': 144, 'descendant_stop': 160, 'face_count': 192}), ({'o': 2, 'p': 4, 'f': 0, 'k': 0, 'depth': 2}, {'global_pixel': 4, 'parent_local': 1, 'child_local': 16, 'descendant_first': 64, 'descendant_stop': 80, 'face_count': 192}), ({'o': 2, 'p': 9, 'f': 11, 'k': 3, 'depth': 2}, {'global_pixel': 185, 'parent_local': 2, 'child_local': 39, 'descendant_first': 144, 'descendant_stop': 160, 'face_count': 192}), ({'o': 2, 'p': 9, 'f': 3, 'k': 2, 'depth': 0}, {'global_pixel': 57, 'parent_local': 2, 'child_local': 38, 'descendant_first': 9, 'descendant_stop': 10, 'face_count': 192}), ({'o': 2, 'p': 6, 'f': 1, 'k': 2, 'depth': 2}, {'global_pixel': 22, 'parent_local': 1, 'child_local': 26, 'descendant_first': 96, 'descendant_stop': 112, 'face_count': 192}), ({'o': 3, 'p': 24, 'f': 3, 'k': 2, 'depth': 1}, {'global_pixel': 216, 'parent_local': 6, 'child_local': 98, 'descendant_first': 96, 'descendant_stop': 100, 'face_count': 768})]}
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{'child_local': 22, 'descendant_first': 80, 'descendant_stop': 96, 'face_count': 192, 'global_pixel': 53, 'parent_local': 1}{'child_local': 22, 'descendant_first': 80, 'descendant_stop': 96, 'face_count': 192, 'global_pixel': 53, 'parent_local': 1}Passed
astronomical fixture 1{'child_local': 0, 'descendant_first': 0, 'descendant_stop': 16, 'face_count': 192, 'global_pixel': 0, 'parent_local': 0}{'child_local': 0, 'descendant_first': 0, 'descendant_stop': 16, 'face_count': 192, 'global_pixel': 0, 'parent_local': 0}Passed
astronomical fixture 2{'child_local': 23, 'descendant_first': 80, 'descendant_stop': 96, 'face_count': 192, 'global_pixel': 181, 'parent_local': 1}{'child_local': 23, 'descendant_first': 80, 'descendant_stop': 96, 'face_count': 192, 'global_pixel': 181, 'parent_local': 1}Passed
astronomical fixture 3{'child_local': 22, 'descendant_first': 5, 'descendant_stop': 6, 'face_count': 192, 'global_pixel': 53, 'parent_local': 1}{'child_local': 22, 'descendant_first': 5, 'descendant_stop': 6, 'face_count': 192, 'global_pixel': 53, 'parent_local': 1}Passed
astronomical fixture 4{'child_local': 10, 'descendant_first': 32, 'descendant_stop': 48, 'face_count': 192, 'global_pixel': 18, 'parent_local': 0}{'child_local': 10, 'descendant_first': 32, 'descendant_stop': 48, 'face_count': 192, 'global_pixel': 18, 'parent_local': 0}Passed
astronomical fixture 5{'child_local': 82, 'descendant_first': 80, 'descendant_stop': 84, 'face_count': 768, 'global_pixel': 212, 'parent_local': 5}{'child_local': 82, 'descendant_first': 80, 'descendant_stop': 84, 'face_count': 768, 'global_pixel': 212, 'parent_local': 5}Passed

SHA-256 / 9db4f34742138547d26b073fafb4a2b8f2fed559c2adf000c0be6a60e827b1d4

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 2026-09-29T14:46:02.324201+00:00.

Case digest / 52badabb234e554f34a45245aea620cd931c0fccf93659ce4fb8eedf0fceb037