FAILURE MAP
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FA-69906 / Map projection transforms / Open access

Slippy map tile index from coordinates: row lower clamp · case 01

Latitudes beyond the mercator limit produce negative row numbers.

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

ROOT CAUSE

The row is clamped only at the south edge; latitudes north of 85.0511 give negative rows.

THE FAILURE

The row is clamped only at the south edge; latitudes north of 85.0511 give negative rows.

Unsuccessful approach: The lower bound is 1 instead of 0, so genuine top-row tiles move down one row.

Case contract

Input [lon, lat, z] with lon in [-180, 180], any latitude, z >= 0. With n = 2**z tiles per axis, column = floor((lon+180)/360*n) and row = floor((1 - asinh(tan(lat))/pi)/2*n) (row 0 at the north edge); both are clamped to [0, n-1] so lon=180 falls in the last column and latitudes beyond the mercator limit fall in the edge rows. Return [z, column, row].

Why this case matters

Tile servers and caches key storage by these indices; an off-by-one or flipped axis fetches the wrong image.

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, z = x
    n = 2 ** z
    phi = math.radians(max(-89.9, min(89.9, lat)))
    xf = (lon + 180.0) / 360.0 * n
    yf = (1.0 - math.asinh(math.tan(phi)) / math.pi) / 2.0 * n
    xt = min(max(math.floor(xf), 0), n - 1)
    yt = min(math.floor(yf), n - 1)
    return [z, xt, yt]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('boundary #0', [180.0, 0.0, 3], [3, 7, 4]), ('boundary #1', [-180.0, 10.0, 4], [4, 0, 7]), ('boundary #2', [10.0, 89.0, 5], [5, 16, 0]), ('boundary #3', [10.0, -89.0, 5], [5, 16, 31]), ('control #4', [13.4, 52.5, 10], [10, 550, 335]), ('control #5', [-74.0, 40.7, 12], [12, 1206, 1540]), ('control #6', [151.2, -33.9, 7], [7, 117, 76]), ('boundary #20', [-30.0, 87.0, 4], [4, 6, 0])], [('boundary #3', [10.0, -89.0, 5], [5, 16, 31]), ('control #4', [13.4, 52.5, 10], [10, 550, 335]), ('control #5', [-74.0, 40.7, 12], [12, 1206, 1540]), ('control #6', [151.2, -33.9, 7], [7, 117, 76]), ('control #7', [0.0, 0.0, 1], [1, 1, 1]), ('control #8', [2.35, 48.85, 15], [15, 16597, 11274]), ('boundary #20', [-30.0, 87.0, 4], [4, 6, 0]), ('boundary #21', [120.0, 86.0, 9], [9, 426, 0])], [('control #6', [151.2, -33.9, 7], [7, 117, 76]), ('control #7', [0.0, 0.0, 1], [1, 1, 1]), ('control #8', [2.35, 48.85, 15], [15, 16597, 11274]), ('control #9', [-122.4, 37.8, 9], [9, 81, 197]), ('control #10', [100.5, 13.7, 6], [6, 49, 29]), ('control #11', [-58.4, -34.6, 11], [11, 691, 1234]), ('boundary #21', [120.0, 86.0, 9], [9, 426, 0]), ('boundary #22', [180.0, 86.0, 1], [1, 1, 0])], [('boundary #2', [10.0, 89.0, 5], [5, 16, 0]), ('control #10', [100.5, 13.7, 6], [6, 49, 29]), ('control #11', [-58.4, -34.6, 11], [11, 691, 1234]), ('boundary #12', [179.99, -85.0, 2], [2, 3, 3]), ('control #13', [37.6, 55.75, 8], [8, 154, 80]), ('control #14', [-0.12, 51.5, 16], [16, 32746, 21794]), ('control #15', [18.4, -33.9, 13], [13, 4514, 4916]), ('boundary #22', [180.0, 86.0, 1], [1, 1, 0])], [('boundary #2', [10.0, 89.0, 5], [5, 16, 0]), ('control #13', [37.6, 55.75, 8], [8, 154, 80]), ('control #14', [-0.12, 51.5, 16], [16, 32746, 21794]), ('control #15', [18.4, -33.9, 13], [13, 4514, 4916]), ('boundary #16', [0.0, 0.0, 0], [0, 0, 0]), ('control #17', [139.7, 35.7, 14], [14, 14549, 6450]), ('boundary #18', [180.0, 45.0, 6], [6, 63, 23]), ('boundary #21', [120.0, 86.0, 9], [9, 426, 0])]]
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
boundary #0[3, 7, 4][3, 7, 4]Passed
boundary #1[4, 0, 7][4, 0, 7]Passed
boundary #2[5, 16, -9][5, 16, 0]Failed
boundary #3[5, 16, 31][5, 16, 31]Passed
control #4[10, 550, 335][10, 550, 335]Passed
control #5[12, 1206, 1540][12, 1206, 1540]Passed
control #6[7, 117, 76][7, 117, 76]Passed
boundary #20[4, 6, -2][4, 6, 0]Failed

SHA-256 / 61ccd555c6f44fd88ac8d0956209dcc043a98d98fef7d1c9ed1279d46fdd0e25

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, z = x
    n = 2 ** z
    phi = math.radians(max(-89.9, min(89.9, lat)))
    xf = (lon + 180.0) / 360.0 * n
    yf = (1.0 - math.asinh(math.tan(phi)) / math.pi) / 2.0 * n
    xt = min(max(math.floor(xf), 0), n - 1)
    yt = min(max(math.floor(yf), 1), n - 1)
    return [z, xt, yt]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('boundary #0', [180.0, 0.0, 3], [3, 7, 4]), ('boundary #1', [-180.0, 10.0, 4], [4, 0, 7]), ('boundary #2', [10.0, 89.0, 5], [5, 16, 0]), ('boundary #3', [10.0, -89.0, 5], [5, 16, 31]), ('control #4', [13.4, 52.5, 10], [10, 550, 335]), ('control #5', [-74.0, 40.7, 12], [12, 1206, 1540]), ('control #6', [151.2, -33.9, 7], [7, 117, 76]), ('boundary #20', [-30.0, 87.0, 4], [4, 6, 0])], [('boundary #3', [10.0, -89.0, 5], [5, 16, 31]), ('control #4', [13.4, 52.5, 10], [10, 550, 335]), ('control #5', [-74.0, 40.7, 12], [12, 1206, 1540]), ('control #6', [151.2, -33.9, 7], [7, 117, 76]), ('control #7', [0.0, 0.0, 1], [1, 1, 1]), ('control #8', [2.35, 48.85, 15], [15, 16597, 11274]), ('boundary #20', [-30.0, 87.0, 4], [4, 6, 0]), ('boundary #21', [120.0, 86.0, 9], [9, 426, 0])], [('control #6', [151.2, -33.9, 7], [7, 117, 76]), ('control #7', [0.0, 0.0, 1], [1, 1, 1]), ('control #8', [2.35, 48.85, 15], [15, 16597, 11274]), ('control #9', [-122.4, 37.8, 9], [9, 81, 197]), ('control #10', [100.5, 13.7, 6], [6, 49, 29]), ('control #11', [-58.4, -34.6, 11], [11, 691, 1234]), ('boundary #21', [120.0, 86.0, 9], [9, 426, 0]), ('boundary #22', [180.0, 86.0, 1], [1, 1, 0])], [('boundary #2', [10.0, 89.0, 5], [5, 16, 0]), ('control #10', [100.5, 13.7, 6], [6, 49, 29]), ('control #11', [-58.4, -34.6, 11], [11, 691, 1234]), ('boundary #12', [179.99, -85.0, 2], [2, 3, 3]), ('control #13', [37.6, 55.75, 8], [8, 154, 80]), ('control #14', [-0.12, 51.5, 16], [16, 32746, 21794]), ('control #15', [18.4, -33.9, 13], [13, 4514, 4916]), ('boundary #22', [180.0, 86.0, 1], [1, 1, 0])], [('boundary #2', [10.0, 89.0, 5], [5, 16, 0]), ('control #13', [37.6, 55.75, 8], [8, 154, 80]), ('control #14', [-0.12, 51.5, 16], [16, 32746, 21794]), ('control #15', [18.4, -33.9, 13], [13, 4514, 4916]), ('boundary #16', [0.0, 0.0, 0], [0, 0, 0]), ('control #17', [139.7, 35.7, 14], [14, 14549, 6450]), ('boundary #18', [180.0, 45.0, 6], [6, 63, 23]), ('boundary #21', [120.0, 86.0, 9], [9, 426, 0])]]
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
boundary #0[3, 7, 4][3, 7, 4]Passed
boundary #1[4, 0, 7][4, 0, 7]Passed
boundary #2[5, 16, 1][5, 16, 0]Failed
boundary #3[5, 16, 31][5, 16, 31]Passed
control #4[10, 550, 335][10, 550, 335]Passed
control #5[12, 1206, 1540][12, 1206, 1540]Passed
control #6[7, 117, 76][7, 117, 76]Passed
boundary #20[4, 6, 1][4, 6, 0]Failed

SHA-256 / fa89dfc215ff393118bf1e25355ac30493b1b36215d75e80d12c54fd6fadfe6d

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 8 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.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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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 2026-09-29T14:48:15.788832+00:00.

Case digest / 17accd0251cc0c74be640a541aa9f015f48738c0274443099b3ed7dae25b8a1b