{"abstract":"All tile edges crowd toward the north, the south half of the world disappears.","category":"Map projection transforms","checks":8,"contract":"Input [z, col, row, scheme] where scheme is \"xyz\" (row 0 at north) or \"tms\" (row 0 at south). Return [west, south, east, north] in degrees rounded to 6 decimals, using lon = col/n*360-180 and lat = degrees(atan(sinh(pi*(1-2*r/n)))) for an xyz row edge r, n = 2**z. A tms row t is the xyz row n-1-t.","evaluation_group":"w2-map-projection-transforms-xyz-tile-bounds","failed_approach":"Dividing by n+1 instead of n shrinks the grid so no row reaches the southern limit exactly.","family":"w2-map-projection-transforms-xyz-tile-bounds-edge-latitude-factor","id":"FA-69926","implementations":{"attempt":{"sha256":"4c7d4c6cfefa2c02bcf75884b7d7d91390f107da678112bb703c3328ea8ce02e","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    z, col, row, scheme = x\n    n = 2 ** z\n    if scheme == 'tms':\n        row = n - 1 - row\n    def edge_lat(r):\n        return math.degrees(math.atan(math.sinh(math.pi * (1 - 2 * r / (n + 1)))))\n    west = col / n * 360.0 - 180.0\n    east = (col + 1) / n * 360.0 - 180.0\n    north = edge_lat(row)\n    south = edge_lat(row + 1)\n    return [round(west, 6), round(south, 6), round(east, 6), round(north, 6)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('control #0', [0, 0, 0, 'xyz'], [-180.0, -85.051129, 180.0, 85.051129]), ('control #1', [1, 1, 0, 'xyz'], [0.0, 0.0, 180.0, 85.051129]), ('control #2', [2, 3, 3, 'tms'], [90.0, 66.51326, 180.0, 85.051129]), ('control #3', [3, 5, 2, 'xyz'], [45.0, 40.979898, 90.0, 66.51326]), ('control #4', [4, 7, 9, 'tms'], [-22.5, 21.943046, 0.0, 40.979898]), ('control #5', [5, 16, 10, 'xyz'], [0.0, 48.922499, 11.25, 55.776573]), ('control #6', [6, 33, 21, 'tms'], [5.625, -52.48278, 11.25, -48.922499]), ('control #7', [7, 100, 40, 'xyz'], [101.25, 54.162434, 104.0625, 55.776573])], [('control #1', [1, 1, 0, 'xyz'], [0.0, 0.0, 180.0, 85.051129]), ('control #2', [2, 3, 3, 'tms'], [90.0, 66.51326, 180.0, 85.051129]), ('control #5', [5, 16, 10, 'xyz'], [0.0, 48.922499, 11.25, 55.776573]), ('control #6', [6, 33, 21, 'tms'], [5.625, -52.48278, 11.25, -48.922499]), ('control #7', [7, 100, 40, 'xyz'], [101.25, 54.162434, 104.0625, 55.776573]), ('control #8', [8, 0, 255, 'xyz'], [-180.0, -85.051129, -178.59375, -84.928321]), ('control #9', [8, 255, 0, 'tms'], [178.59375, -85.051129, 180.0, -84.928321]), ('control #10', [10, 550, 335, 'xyz'], [13.359375, 52.48278, 13.710938, 52.696361])], [('control #2', [2, 3, 3, 'tms'], [90.0, 66.51326, 180.0, 85.051129]), ('control #3', [3, 5, 2, 'xyz'], [45.0, 40.979898, 90.0, 66.51326]), ('control #8', [8, 0, 255, 'xyz'], [-180.0, -85.051129, -178.59375, -84.928321]), ('control #9', [8, 255, 0, 'tms'], [178.59375, -85.051129, 180.0, -84.928321]), ('control #10', [10, 550, 335, 'xyz'], [13.359375, 52.48278, 13.710938, 52.696361]), ('control #11', [10, 550, 688, 'tms'], [13.359375, 52.48278, 13.710938, 52.696361]), ('control #12', [12, 1206, 1540, 'xyz'], [-74.003906, 40.647304, -73.916016, 40.713956]), ('control #13', [3, 0, 7, 'tms'], [-180.0, 79.171335, -135.0, 85.051129])], [('control #0', [0, 0, 0, 'xyz'], [-180.0, -85.051129, 180.0, 85.051129]), ('control #3', [3, 5, 2, 'xyz'], [45.0, 40.979898, 90.0, 66.51326]), ('control #4', [4, 7, 9, 'tms'], [-22.5, 21.943046, 0.0, 40.979898]), ('control #11', [10, 550, 688, 'tms'], [13.359375, 52.48278, 13.710938, 52.696361]), ('control #12', [12, 1206, 1540, 'xyz'], [-74.003906, 40.647304, -73.916016, 40.713956]), ('control #13', [3, 0, 7, 'tms'], [-180.0, 79.171335, -135.0, 85.051129]), ('control #14', [1, 0, 1, 'tms'], [-180.0, 0.0, 0.0, 85.051129]), ('control #15', [9, 300, 200, 'xyz'], [30.9375, 36.031332, 31.640625, 36.597889])], [('control #0', [0, 0, 0, 'xyz'], [-180.0, -85.051129, 180.0, 85.051129]), ('control #1', [1, 1, 0, 'xyz'], [0.0, 0.0, 180.0, 85.051129]), ('control #2', [2, 3, 3, 'tms'], [90.0, 66.51326, 180.0, 85.051129]), ('control #3', [3, 5, 2, 'xyz'], [45.0, 40.979898, 90.0, 66.51326]), ('control #4', [4, 7, 9, 'tms'], [-22.5, 21.943046, 0.0, 40.979898]), ('control #5', [5, 16, 10, 'xyz'], [0.0, 48.922499, 11.25, 55.776573]), ('control #14', [1, 0, 1, 'tms'], [-180.0, 0.0, 0.0, 85.051129]), ('control #15', [9, 300, 200, 'xyz'], [30.9375, 36.031332, 31.640625, 36.597889])]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"c6a6ff87c9bcbea9d4b68a1448618be4233075cb98d04c122caab8136348c196","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    z, col, row, scheme = x\n    n = 2 ** z\n    if scheme == 'tms':\n        row = n - 1 - row\n    def edge_lat(r):\n        return math.degrees(math.atan(math.sinh(math.pi * (1 - r / n))))\n    west = col / n * 360.0 - 180.0\n    east = (col + 1) / n * 360.0 - 180.0\n    north = edge_lat(row)\n    south = edge_lat(row + 1)\n    return [round(west, 6), round(south, 6), round(east, 6), round(north, 6)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('control #0', [0, 0, 0, 'xyz'], [-180.0, -85.051129, 180.0, 85.051129]), ('control #1', [1, 1, 0, 'xyz'], [0.0, 0.0, 180.0, 85.051129]), ('control #2', [2, 3, 3, 'tms'], [90.0, 66.51326, 180.0, 85.051129]), ('control #3', [3, 5, 2, 'xyz'], [45.0, 40.979898, 90.0, 66.51326]), ('control #4', [4, 7, 9, 'tms'], [-22.5, 21.943046, 0.0, 40.979898]), ('control #5', [5, 16, 10, 'xyz'], [0.0, 48.922499, 11.25, 55.776573]), ('control #6', [6, 33, 21, 'tms'], [5.625, -52.48278, 11.25, -48.922499]), ('control #7', [7, 100, 40, 'xyz'], [101.25, 54.162434, 104.0625, 55.776573])], [('control #1', [1, 1, 0, 'xyz'], [0.0, 0.0, 180.0, 85.051129]), ('control #2', [2, 3, 3, 'tms'], [90.0, 66.51326, 180.0, 85.051129]), ('control #5', [5, 16, 10, 'xyz'], [0.0, 48.922499, 11.25, 55.776573]), ('control #6', [6, 33, 21, 'tms'], [5.625, -52.48278, 11.25, -48.922499]), ('control #7', [7, 100, 40, 'xyz'], [101.25, 54.162434, 104.0625, 55.776573]), ('control #8', [8, 0, 255, 'xyz'], [-180.0, -85.051129, -178.59375, -84.928321]), ('control #9', [8, 255, 0, 'tms'], [178.59375, -85.051129, 180.0, -84.928321]), ('control #10', [10, 550, 335, 'xyz'], [13.359375, 52.48278, 13.710938, 52.696361])], [('control #2', [2, 3, 3, 'tms'], [90.0, 66.51326, 180.0, 85.051129]), ('control #3', [3, 5, 2, 'xyz'], [45.0, 40.979898, 90.0, 66.51326]), ('control #8', [8, 0, 255, 'xyz'], [-180.0, -85.051129, -178.59375, -84.928321]), ('control #9', [8, 255, 0, 'tms'], [178.59375, -85.051129, 180.0, -84.928321]), ('control #10', [10, 550, 335, 'xyz'], [13.359375, 52.48278, 13.710938, 52.696361]), ('control #11', [10, 550, 688, 'tms'], [13.359375, 52.48278, 13.710938, 52.696361]), ('control #12', [12, 1206, 1540, 'xyz'], [-74.003906, 40.647304, -73.916016, 40.713956]), ('control #13', [3, 0, 7, 'tms'], [-180.0, 79.171335, -135.0, 85.051129])], [('control #0', [0, 0, 0, 'xyz'], [-180.0, -85.051129, 180.0, 85.051129]), ('control #3', [3, 5, 2, 'xyz'], [45.0, 40.979898, 90.0, 66.51326]), ('control #4', [4, 7, 9, 'tms'], [-22.5, 21.943046, 0.0, 40.979898]), ('control #11', [10, 550, 688, 'tms'], [13.359375, 52.48278, 13.710938, 52.696361]), ('control #12', [12, 1206, 1540, 'xyz'], [-74.003906, 40.647304, -73.916016, 40.713956]), ('control #13', [3, 0, 7, 'tms'], [-180.0, 79.171335, -135.0, 85.051129]), ('control #14', [1, 0, 1, 'tms'], [-180.0, 0.0, 0.0, 85.051129]), ('control #15', [9, 300, 200, 'xyz'], [30.9375, 36.031332, 31.640625, 36.597889])], [('control #0', [0, 0, 0, 'xyz'], [-180.0, -85.051129, 180.0, 85.051129]), ('control #1', [1, 1, 0, 'xyz'], [0.0, 0.0, 180.0, 85.051129]), ('control #2', [2, 3, 3, 'tms'], [90.0, 66.51326, 180.0, 85.051129]), ('control #3', [3, 5, 2, 'xyz'], [45.0, 40.979898, 90.0, 66.51326]), ('control #4', [4, 7, 9, 'tms'], [-22.5, 21.943046, 0.0, 40.979898]), ('control #5', [5, 16, 10, 'xyz'], [0.0, 48.922499, 11.25, 55.776573]), ('control #14', [1, 0, 1, 'tms'], [-180.0, 0.0, 0.0, 85.051129]), ('control #15', [9, 300, 200, 'xyz'], [30.9375, 36.031332, 31.640625, 36.597889])]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"fixed":{"sha256":"ba901fc9ed43b5caaae7a7aec163a1e094fb9dbc34f30a03bf478d09b6d7bb7b","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    z, col, row, scheme = x\n    n = 2 ** z\n    if scheme == 'tms':\n        row = n - 1 - row\n    def edge_lat(r):\n        return math.degrees(math.atan(math.sinh(math.pi * (1 - 2 * r / n))))\n    west = col / n * 360.0 - 180.0\n    east = (col + 1) / n * 360.0 - 180.0\n    north = edge_lat(row)\n    south = edge_lat(row + 1)\n    return [round(west, 6), round(south, 6), round(east, 6), round(north, 6)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('control #0', [0, 0, 0, 'xyz'], [-180.0, -85.051129, 180.0, 85.051129]), ('control #1', [1, 1, 0, 'xyz'], [0.0, 0.0, 180.0, 85.051129]), ('control #2', [2, 3, 3, 'tms'], [90.0, 66.51326, 180.0, 85.051129]), ('control #3', [3, 5, 2, 'xyz'], [45.0, 40.979898, 90.0, 66.51326]), ('control #4', [4, 7, 9, 'tms'], [-22.5, 21.943046, 0.0, 40.979898]), ('control #5', [5, 16, 10, 'xyz'], [0.0, 48.922499, 11.25, 55.776573]), ('control #6', [6, 33, 21, 'tms'], [5.625, -52.48278, 11.25, -48.922499]), ('control #7', [7, 100, 40, 'xyz'], [101.25, 54.162434, 104.0625, 55.776573])], [('control #1', [1, 1, 0, 'xyz'], [0.0, 0.0, 180.0, 85.051129]), ('control #2', [2, 3, 3, 'tms'], [90.0, 66.51326, 180.0, 85.051129]), ('control #5', [5, 16, 10, 'xyz'], [0.0, 48.922499, 11.25, 55.776573]), ('control #6', [6, 33, 21, 'tms'], [5.625, -52.48278, 11.25, -48.922499]), ('control #7', [7, 100, 40, 'xyz'], [101.25, 54.162434, 104.0625, 55.776573]), ('control #8', [8, 0, 255, 'xyz'], [-180.0, -85.051129, -178.59375, -84.928321]), ('control #9', [8, 255, 0, 'tms'], [178.59375, -85.051129, 180.0, -84.928321]), ('control #10', [10, 550, 335, 'xyz'], [13.359375, 52.48278, 13.710938, 52.696361])], [('control #2', [2, 3, 3, 'tms'], [90.0, 66.51326, 180.0, 85.051129]), ('control #3', [3, 5, 2, 'xyz'], [45.0, 40.979898, 90.0, 66.51326]), ('control #8', [8, 0, 255, 'xyz'], [-180.0, -85.051129, -178.59375, -84.928321]), ('control #9', [8, 255, 0, 'tms'], [178.59375, -85.051129, 180.0, -84.928321]), ('control #10', [10, 550, 335, 'xyz'], [13.359375, 52.48278, 13.710938, 52.696361]), ('control #11', [10, 550, 688, 'tms'], [13.359375, 52.48278, 13.710938, 52.696361]), ('control #12', [12, 1206, 1540, 'xyz'], [-74.003906, 40.647304, -73.916016, 40.713956]), ('control #13', [3, 0, 7, 'tms'], [-180.0, 79.171335, -135.0, 85.051129])], [('control #0', [0, 0, 0, 'xyz'], [-180.0, -85.051129, 180.0, 85.051129]), ('control #3', [3, 5, 2, 'xyz'], [45.0, 40.979898, 90.0, 66.51326]), ('control #4', [4, 7, 9, 'tms'], [-22.5, 21.943046, 0.0, 40.979898]), ('control #11', [10, 550, 688, 'tms'], [13.359375, 52.48278, 13.710938, 52.696361]), ('control #12', [12, 1206, 1540, 'xyz'], [-74.003906, 40.647304, -73.916016, 40.713956]), ('control #13', [3, 0, 7, 'tms'], [-180.0, 79.171335, -135.0, 85.051129]), ('control #14', [1, 0, 1, 'tms'], [-180.0, 0.0, 0.0, 85.051129]), ('control #15', [9, 300, 200, 'xyz'], [30.9375, 36.031332, 31.640625, 36.597889])], [('control #0', [0, 0, 0, 'xyz'], [-180.0, -85.051129, 180.0, 85.051129]), ('control #1', [1, 1, 0, 'xyz'], [0.0, 0.0, 180.0, 85.051129]), ('control #2', [2, 3, 3, 'tms'], [90.0, 66.51326, 180.0, 85.051129]), ('control #3', [3, 5, 2, 'xyz'], [45.0, 40.979898, 90.0, 66.51326]), ('control #4', [4, 7, 9, 'tms'], [-22.5, 21.943046, 0.0, 40.979898]), ('control #5', [5, 16, 10, 'xyz'], [0.0, 48.922499, 11.25, 55.776573]), ('control #14', [1, 0, 1, 'tms'], [-180.0, 0.0, 0.0, 85.051129]), ('control #15', [9, 300, 200, 'xyz'], [30.9375, 36.031332, 31.640625, 36.597889])]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"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.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"w2-map-projection-transforms-xyz-tile-bounds-edge-latitude-factor","generated_at":"2026-09-29T14:48:15.874073+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Tile footprints drive cache invalidation, label placement and raster reprojection; wrong edges misalign tiles.","repair":"At the edge latitude factor step restore `math.pi * (1 - 2 * r / n)`, leaving the rest of the model unchanged.","root_cause":"The sinh argument uses (1 - r/n) instead of (1 - 2r/n), mapping the bottom row edge to the equator.","sha256":"eee59b96a4db35c89fdfd294abccb834569da75c3923bc0b5cae4117e23ab3b0","title":"Geographic bounds of a map tile: edge latitude factor · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":42.705,"exit_code":1,"observations":[{"actual":[-180.0,0.0,180.0,85.051129],"check":"control #0","expected":[-180.0,-85.051129,180.0,85.051129],"passed":false},{"actual":[0.0,51.326035,180.0,85.051129],"check":"control #1","expected":[0.0,0.0,180.0,85.051129],"passed":false},{"actual":[90.0,72.732786,180.0,85.051129],"check":"control #2","expected":[90.0,66.51326,180.0,85.051129],"passed":false},{"actual":[45.0,51.326035,90.0,70.193377],"check":"control #3","expected":[45.0,40.979898,90.0,66.51326],"passed":false},{"actual":[-22.5,30.252369,0.0,46.700873],"check":"control #4","expected":[-22.5,21.943046,0.0,40.979898],"passed":false},{"actual":[0.0,51.326035,11.25,57.647182],"check":"control #5","expected":[0.0,48.922499,11.25,55.776573],"passed":false},{"actual":[5.625,-50.157843,11.25,-46.47698],"check":"control #6","expected":[5.625,-52.48278,11.25,-48.922499],"passed":false},{"actual":[101.25,54.682497,104.0625,56.263977],"check":"control #7","expected":[101.25,54.162434,104.0625,55.776573],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"control #0\", \"actual\": [-180.0, 0.0, 180.0, 85.051129], \"expected\": [-180.0, -85.051129, 180.0, 85.051129], \"passed\": false}, {\"check\": \"control #1\", \"actual\": [0.0, 51.326035, 180.0, 85.051129], \"expected\": [0.0, 0.0, 180.0, 85.051129], \"passed\": false}, {\"check\": \"control #2\", \"actual\": [90.0, 72.732786, 180.0, 85.051129], \"expected\": [90.0, 66.51326, 180.0, 85.051129], \"passed\": false}, {\"check\": \"control #3\", \"actual\": [45.0, 51.326035, 90.0, 70.193377], \"expected\": [45.0, 40.979898, 90.0, 66.51326], \"passed\": false}, {\"check\": \"control #4\", \"actual\": [-22.5, 30.252369, 0.0, 46.700873], \"expected\": [-22.5, 21.943046, 0.0, 40.979898], \"passed\": false}, {\"check\": \"control #5\", \"actual\": [0.0, 51.326035, 11.25, 57.647182], \"expected\": [0.0, 48.922499, 11.25, 55.776573], \"passed\": false}, {\"check\": \"control #6\", \"actual\": [5.625, -50.157843, 11.25, -46.47698], \"expected\": [5.625, -52.48278, 11.25, -48.922499], \"passed\": false}, {\"check\": \"control #7\", \"actual\": [101.25, 54.682497, 104.0625, 56.263977], \"expected\": [101.25, 54.162434, 104.0625, 55.776573], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":39.54,"exit_code":1,"observations":[{"actual":[-180.0,0.0,180.0,85.051129],"check":"control #0","expected":[-180.0,-85.051129,180.0,85.051129],"passed":false},{"actual":[0.0,66.51326,180.0,85.051129],"check":"control #1","expected":[0.0,0.0,180.0,85.051129],"passed":false},{"actual":[90.0,79.171335,180.0,85.051129],"check":"control #2","expected":[90.0,66.51326,180.0,85.051129],"passed":false},{"actual":[45.0,74.019543,90.0,79.171335],"check":"control #3","expected":[45.0,40.979898,90.0,66.51326],"passed":false},{"actual":[-22.5,70.612614,0.0,74.019543],"check":"control #4","expected":[-22.5,21.943046,0.0,40.979898],"passed":false},{"actual":[0.0,75.497157,11.25,76.840816],"check":"control #5","expected":[0.0,48.922499,11.25,55.776573],"passed":false},{"actual":[5.625,50.736455,11.25,52.48278],"check":"control #6","expected":[5.625,-52.48278,11.25,-48.922499],"passed":false},{"actual":[101.25,76.516819,104.0625,76.840816],"check":"control #7","expected":[101.25,54.162434,104.0625,55.776573],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"control #0\", \"actual\": [-180.0, 0.0, 180.0, 85.051129], \"expected\": [-180.0, -85.051129, 180.0, 85.051129], \"passed\": false}, {\"check\": \"control #1\", \"actual\": [0.0, 66.51326, 180.0, 85.051129], \"expected\": [0.0, 0.0, 180.0, 85.051129], \"passed\": false}, {\"check\": \"control #2\", \"actual\": [90.0, 79.171335, 180.0, 85.051129], \"expected\": 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