FA-70006 / Map projection transforms / Open access

UTM zone and latitude band lookup: band x extension · case 01

Points in the 12-degree band X above 80N are labelled C.

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

ROOT CAUSE

The band index wraps modulo 20 instead of saturating, so the extended band X becomes band C.

VERIFIED REPAIR

At the band x extension step restore `min(int((lat + 80.0) // 8), 19)`, leaving the rest of the model unchanged.

Unsuccessful approach: Saturating at index 18 labels every point north of 72N as band W.

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 > 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[int((lat + 80.0) // 8) % 20]
    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']), ('control #6', [-48.09, 53.12], [22, 'U']), ('control #7', [93.32, -22.41], [46, 'K'])], [('control #2', [115.33, 82.84], [50, 'X']), ('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']), ('control #9', [-168.15, 26.03], [2, 'R']), ('regression #19', [8.0, 78.0], [31, 'X'])], [('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']), ('regression #19', [8.0, 78.0], [31, 'X']), ('boundary #21', [20.9, 80.0], [33, 'X'])], [('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 #20', [9.0, 75.0], [33, 'X']), ('boundary #23', [41.9, 83.0], [37, 'X'])], [('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 #21', [20.9, 80.0], [33, 'X']), ('boundary #24', [10.0, 84.0], [33, 'X'])]]
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 fixture	Actual	Expected	Outcome
control #0	`[20, 'Q']`	`[20, 'Q']`	Passed
control #1	`[1, 'C']`	`[1, 'X']`	Failed
control #2	`[50, 'C']`	`[50, 'X']`	Failed
control #3	`[16, 'G']`	`[16, 'G']`	Passed
control #4	`[4, 'G']`	`[4, 'G']`	Passed
control #5	`[2, 'S']`	`[2, 'S']`	Passed
control #6	`[22, 'U']`	`[22, 'U']`	Passed
control #7	`[46, 'K']`	`[46, 'K']`	Passed

SHA-256 / 38217a4e41e11ff76791a4d81196ebff3bb61cb0f1d59b852deb9bb9b6fe696f

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 = 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), 18)]
    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']), ('control #6', [-48.09, 53.12], [22, 'U']), ('control #7', [93.32, -22.41], [46, 'K'])], [('control #2', [115.33, 82.84], [50, 'X']), ('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']), ('control #9', [-168.15, 26.03], [2, 'R']), ('regression #19', [8.0, 78.0], [31, 'X'])], [('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']), ('regression #19', [8.0, 78.0], [31, 'X']), ('boundary #21', [20.9, 80.0], [33, 'X'])], [('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 #20', [9.0, 75.0], [33, 'X']), ('boundary #23', [41.9, 83.0], [37, 'X'])], [('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 #21', [20.9, 80.0], [33, 'X']), ('boundary #24', [10.0, 84.0], [33, 'X'])]]
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 fixture	Actual	Expected	Outcome
control #0	`[20, 'Q']`	`[20, 'Q']`	Passed
control #1	`[1, 'W']`	`[1, 'X']`	Failed
control #2	`[50, 'W']`	`[50, 'X']`	Failed
control #3	`[16, 'G']`	`[16, 'G']`	Passed
control #4	`[4, 'G']`	`[4, 'G']`	Passed
control #5	`[2, 'S']`	`[2, 'S']`	Passed
control #6	`[22, 'U']`	`[22, 'U']`	Passed
control #7	`[46, 'K']`	`[46, 'K']`	Passed

SHA-256 / bf77b875c37500d93a5596d76d52fd8ff701c38a1e61c54abd20f4cda0a0f26d

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']), ('control #6', [-48.09, 53.12], [22, 'U']), ('control #7', [93.32, -22.41], [46, 'K'])], [('control #2', [115.33, 82.84], [50, 'X']), ('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']), ('control #9', [-168.15, 26.03], [2, 'R']), ('regression #19', [8.0, 78.0], [31, 'X'])], [('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']), ('regression #19', [8.0, 78.0], [31, 'X']), ('boundary #21', [20.9, 80.0], [33, 'X'])], [('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 #20', [9.0, 75.0], [33, 'X']), ('boundary #23', [41.9, 83.0], [37, 'X'])], [('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 #21', [20.9, 80.0], [33, 'X']), ('boundary #24', [10.0, 84.0], [33, 'X'])]]
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 fixture	Actual	Expected	Outcome
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
control #6	`[22, 'U']`	`[22, 'U']`	Passed
control #7	`[46, 'K']`	`[46, 'K']`	Passed

SHA-256 / 131dc4c0ebba6b88358392c17a845b7efebeb0cdd824706d0ffd528d70950104

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 2026-09-29T14:48:16.613935+00:00.

Case digest / d5a2906356d6af117eee11b3085281410f60f9021fe4e281292c5ca10e49cdb8