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FA-69991 / Map projection transforms / Open access

UTM zone and latitude band lookup: antimeridian zone cap · case 01

Points exactly on +180 get a non-existent zone 61.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The cap only triggers above 61, so lon=180 yields zone 61.

VERIFIED REPAIR

At the antimeridian zone cap step restore `if zone > 60: zone = 60`, leaving the rest of the model unchanged.

Unsuccessful approach: Wrapping the overflow to zone 1 moves lon=180 to the far side of the grid instead of the last zone.

Case contract

Input [lon, lat]. zone = floor((lon+180)/6)+1, with lon=180 mapped to zone 60. Exceptions: lat in [56, 64) and lon in [3, 12) is zone 32; lat in [72, 84] uses zone 31 for lon in [0, 9), 33 for [9, 21), 35 for [21, 33) and 37 for [33, 42). Band letters "CDEFGHJKLMNPQRSTUVWX" (no I or O) cover 8 degrees each from -80; band X also covers up to 84 inclusive. Outside [-80, 84] the band is None. Return [zone, band].

Why this case matters

Grid references, MGRS labels and CRS selection rely on the zone and band, including the Norway and Svalbard exceptions.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    lon, lat = x
    zone = int(math.floor((lon + 180.0) / 6.0)) + 1
    if zone > 61:
        zone = 60
    if 56.0 <= lat < 64.0 and 3.0 <= lon < 12.0:
        zone = 32
    if 72.0 <= lat <= 84.0 and 0.0 <= lon < 42.0:
        if lon < 9.0:
            zone = 31
        elif lon < 21.0:
            zone = 33
        elif lon < 33.0:
            zone = 35
        else:
            zone = 37
    letters = 'CDEFGHJKLMNPQRSTUVWX'
    if lat < -80.0 or lat > 84.0:
        band = None
    else:
        band = letters[min(int((lat + 80.0) // 8), 19)]
    return [zone, band]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', [-63.1, 21.44], [20, 'Q']), ('control #1', [-175.96, 80.22], [1, 'X']), ('control #2', [115.33, 82.84], [50, 'X']), ('control #3', [-84.72, -46.68], [16, 'G']), ('control #4', [-159.4, -47.6], [4, 'G']), ('control #5', [-170.34, 33.06], [2, 'S']), ('boundary #12', [180.0, 10.0], [60, 'P']), ('boundary #38', [180.0, -45.0], [60, 'G'])], [('control #3', [-84.72, -46.68], [16, 'G']), ('control #4', [-159.4, -47.6], [4, 'G']), ('control #5', [-170.34, 33.06], [2, 'S']), ('control #6', [-48.09, 53.12], [22, 'U']), ('control #7', [93.32, -22.41], [46, 'K']), ('control #8', [-119.29, -22.68], [11, 'K']), ('boundary #12', [180.0, 10.0], [60, 'P']), ('boundary #38', [180.0, -45.0], [60, 'G'])], [('control #6', [-48.09, 53.12], [22, 'U']), ('control #7', [93.32, -22.41], [46, 'K']), ('control #8', [-119.29, -22.68], [11, 'K']), ('control #9', [-168.15, 26.03], [2, 'R']), ('control #10', [-111.05, -54.91], [12, 'F']), ('control #11', [139.05, -8.2], [54, 'L']), ('boundary #12', [180.0, 10.0], [60, 'P']), ('boundary #38', [180.0, -45.0], [60, 'G'])], [('control #9', [-168.15, 26.03], [2, 'R']), ('control #10', [-111.05, -54.91], [12, 'F']), ('control #11', [139.05, -8.2], [54, 'L']), ('boundary #12', [180.0, 10.0], [60, 'P']), ('boundary #13', [-180.0, -10.0], [1, 'L']), ('regression #14', [5.0, 60.0], [32, 'V']), ('boundary #15', [3.0, 56.0], [32, 'V']), ('boundary #38', [180.0, -45.0], [60, 'G'])], [('boundary #12', [180.0, 10.0], [60, 'P']), ('boundary #13', [-180.0, -10.0], [1, 'L']), ('regression #14', [5.0, 60.0], [32, 'V']), ('boundary #15', [3.0, 56.0], [32, 'V']), ('boundary #16', [2.99, 60.0], [31, 'V']), ('boundary #17', [11.99, 63.99], [32, 'V']), ('boundary #18', [8.0, 64.0], [32, 'W']), ('boundary #38', [180.0, -45.0], [60, 'G'])]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(args), 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
control #0[20, 'Q'][20, 'Q']Passed
control #1[1, 'X'][1, 'X']Passed
control #2[50, 'X'][50, 'X']Passed
control #3[16, 'G'][16, 'G']Passed
control #4[4, 'G'][4, 'G']Passed
control #5[2, 'S'][2, 'S']Passed
boundary #12[61, 'P'][60, 'P']Failed
boundary #38[61, 'G'][60, 'G']Failed

SHA-256 / cf3864b125a8a0e3cedce2040d973cd907b291d17a782e79c8d3481c7f519d2c

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    lon, lat = x
    zone = int(math.floor((lon + 180.0) / 6.0)) + 1
    if zone > 60:
        zone = 1
    if 56.0 <= lat < 64.0 and 3.0 <= lon < 12.0:
        zone = 32
    if 72.0 <= lat <= 84.0 and 0.0 <= lon < 42.0:
        if lon < 9.0:
            zone = 31
        elif lon < 21.0:
            zone = 33
        elif lon < 33.0:
            zone = 35
        else:
            zone = 37
    letters = 'CDEFGHJKLMNPQRSTUVWX'
    if lat < -80.0 or lat > 84.0:
        band = None
    else:
        band = letters[min(int((lat + 80.0) // 8), 19)]
    return [zone, band]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', [-63.1, 21.44], [20, 'Q']), ('control #1', [-175.96, 80.22], [1, 'X']), ('control #2', [115.33, 82.84], [50, 'X']), ('control #3', [-84.72, -46.68], [16, 'G']), ('control #4', [-159.4, -47.6], [4, 'G']), ('control #5', [-170.34, 33.06], [2, 'S']), ('boundary #12', [180.0, 10.0], [60, 'P']), ('boundary #38', [180.0, -45.0], [60, 'G'])], [('control #3', [-84.72, -46.68], [16, 'G']), ('control #4', [-159.4, -47.6], [4, 'G']), ('control #5', [-170.34, 33.06], [2, 'S']), ('control #6', [-48.09, 53.12], [22, 'U']), ('control #7', [93.32, -22.41], [46, 'K']), ('control #8', [-119.29, -22.68], [11, 'K']), ('boundary #12', [180.0, 10.0], [60, 'P']), ('boundary #38', [180.0, -45.0], [60, 'G'])], [('control #6', [-48.09, 53.12], [22, 'U']), ('control #7', [93.32, -22.41], [46, 'K']), ('control #8', [-119.29, -22.68], [11, 'K']), ('control #9', [-168.15, 26.03], [2, 'R']), ('control #10', [-111.05, -54.91], [12, 'F']), ('control #11', [139.05, -8.2], [54, 'L']), ('boundary #12', [180.0, 10.0], [60, 'P']), ('boundary #38', [180.0, -45.0], [60, 'G'])], [('control #9', [-168.15, 26.03], [2, 'R']), ('control #10', [-111.05, -54.91], [12, 'F']), ('control #11', [139.05, -8.2], [54, 'L']), ('boundary #12', [180.0, 10.0], [60, 'P']), ('boundary #13', [-180.0, -10.0], [1, 'L']), ('regression #14', [5.0, 60.0], [32, 'V']), ('boundary #15', [3.0, 56.0], [32, 'V']), ('boundary #38', [180.0, -45.0], [60, 'G'])], [('boundary #12', [180.0, 10.0], [60, 'P']), ('boundary #13', [-180.0, -10.0], [1, 'L']), ('regression #14', [5.0, 60.0], [32, 'V']), ('boundary #15', [3.0, 56.0], [32, 'V']), ('boundary #16', [2.99, 60.0], [31, 'V']), ('boundary #17', [11.99, 63.99], [32, 'V']), ('boundary #18', [8.0, 64.0], [32, 'W']), ('boundary #38', [180.0, -45.0], [60, 'G'])]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(args), 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
control #0[20, 'Q'][20, 'Q']Passed
control #1[1, 'X'][1, 'X']Passed
control #2[50, 'X'][50, 'X']Passed
control #3[16, 'G'][16, 'G']Passed
control #4[4, 'G'][4, 'G']Passed
control #5[2, 'S'][2, 'S']Passed
boundary #12[1, 'P'][60, 'P']Failed
boundary #38[1, 'G'][60, 'G']Failed

SHA-256 / 96a16c6a6cc14916592c93e2a5c23f093cb6b5ea5d79474e4436cbe1912af944

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    lon, lat = x
    zone = int(math.floor((lon + 180.0) / 6.0)) + 1
    if zone > 60:
        zone = 60
    if 56.0 <= lat < 64.0 and 3.0 <= lon < 12.0:
        zone = 32
    if 72.0 <= lat <= 84.0 and 0.0 <= lon < 42.0:
        if lon < 9.0:
            zone = 31
        elif lon < 21.0:
            zone = 33
        elif lon < 33.0:
            zone = 35
        else:
            zone = 37
    letters = 'CDEFGHJKLMNPQRSTUVWX'
    if lat < -80.0 or lat > 84.0:
        band = None
    else:
        band = letters[min(int((lat + 80.0) // 8), 19)]
    return [zone, band]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', [-63.1, 21.44], [20, 'Q']), ('control #1', [-175.96, 80.22], [1, 'X']), ('control #2', [115.33, 82.84], [50, 'X']), ('control #3', [-84.72, -46.68], [16, 'G']), ('control #4', [-159.4, -47.6], [4, 'G']), ('control #5', [-170.34, 33.06], [2, 'S']), ('boundary #12', [180.0, 10.0], [60, 'P']), ('boundary #38', [180.0, -45.0], [60, 'G'])], [('control #3', [-84.72, -46.68], [16, 'G']), ('control #4', [-159.4, -47.6], [4, 'G']), ('control #5', [-170.34, 33.06], [2, 'S']), ('control #6', [-48.09, 53.12], [22, 'U']), ('control #7', [93.32, -22.41], [46, 'K']), ('control #8', [-119.29, -22.68], [11, 'K']), ('boundary #12', [180.0, 10.0], [60, 'P']), ('boundary #38', [180.0, -45.0], [60, 'G'])], [('control #6', [-48.09, 53.12], [22, 'U']), ('control #7', [93.32, -22.41], [46, 'K']), ('control #8', [-119.29, -22.68], [11, 'K']), ('control #9', [-168.15, 26.03], [2, 'R']), ('control #10', [-111.05, -54.91], [12, 'F']), ('control #11', [139.05, -8.2], [54, 'L']), ('boundary #12', [180.0, 10.0], [60, 'P']), ('boundary #38', [180.0, -45.0], [60, 'G'])], [('control #9', [-168.15, 26.03], [2, 'R']), ('control #10', [-111.05, -54.91], [12, 'F']), ('control #11', [139.05, -8.2], [54, 'L']), ('boundary #12', [180.0, 10.0], [60, 'P']), ('boundary #13', [-180.0, -10.0], [1, 'L']), ('regression #14', [5.0, 60.0], [32, 'V']), ('boundary #15', [3.0, 56.0], [32, 'V']), ('boundary #38', [180.0, -45.0], [60, 'G'])], [('boundary #12', [180.0, 10.0], [60, 'P']), ('boundary #13', [-180.0, -10.0], [1, 'L']), ('regression #14', [5.0, 60.0], [32, 'V']), ('boundary #15', [3.0, 56.0], [32, 'V']), ('boundary #16', [2.99, 60.0], [31, 'V']), ('boundary #17', [11.99, 63.99], [32, 'V']), ('boundary #18', [8.0, 64.0], [32, 'W']), ('boundary #38', [180.0, -45.0], [60, 'G'])]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(args), 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
control #0[20, 'Q'][20, 'Q']Passed
control #1[1, 'X'][1, 'X']Passed
control #2[50, 'X'][50, 'X']Passed
control #3[16, 'G'][16, 'G']Passed
control #4[4, 'G'][4, 'G']Passed
control #5[2, 'S'][2, 'S']Passed
boundary #12[60, 'P'][60, 'P']Passed
boundary #38[60, 'G'][60, 'G']Passed

SHA-256 / 4d5fff41ffa71b6cba1c24dd2f086ec20098773671ddbbda26f27b7ff681b7bf

Verification & scope

Stipulated deterministic toy contract on a bounded input domain; results are rounded as stated and no conformance with any published standard or library is claimed. 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 2026-09-29T14:48:16.444990+00:00.

Case digest / 0485c6ddc732865454d85f80401823dfe0eaf51e87e28606ed4abcd90bae1197