FA-70316 / Map projection transforms / Open access

Seven-parameter Helmert datum shift: convention selector · case 01

Published parameters apply the rotation in the opposite sense, leaving metre-level residuals.

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

ROOT CAUSE

The rotation angles are negated for the position-vector convention instead of the coordinate-frame convention.

THE FAILURE

The rotation angles are negated for the position-vector convention instead of the coordinate-frame convention.

Unsuccessful approach: Negating for both conventions breaks position-vector parameter sets.

Case contract

Input [X, Y, Z, tx, ty, tz, rx, ry, rz, s, convention] with metres, rotations in arc-seconds and scale in ppm. Rotations are converted to radians; for "coordinate_frame" they are negated, for "position_vector" used as is. m = 1 + s*1e-6. X' = tx + m(X - rz Y + ry Z); Y' = ty + m(rz X + Y - rx Z); Z' = tz + m(-ry X + rx Y + Z). Return [X', Y', Z'] rounded to 3 decimals.

Why this case matters

Datum transformations between national and global frames use these seven parameters; convention and unit slips cause metre-level offsets that pass casual inspection.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    X, Y, Z, tx, ty, tz, rx, ry, rz, s, conv = x
    k = math.pi / (180 * 3600)
    rx, ry, rz = rx * k, ry * k, rz * k
    if conv == 'position_vector':
        rx, ry, rz = -rx, -ry, -rz
    m = 1 + s * 1e-6
    Xo = tx + m * (X - rz * Y + ry * Z)
    Yo = ty + m * (rz * X + Y - rx * Z)
    Zo = tz + m * (-ry * X + rx * Y + Z)
    return [round(Xo, 3), round(Yo, 3), round(Zo, 3)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', [-5541091.088, -2232325.705, -6352955.267, -217.202, 252.693, 193.877, -0.3013, 2.5369, -0.4898, 7.2933, 'coordinate_frame'], [-5541265.265, -2232093.171, -6352879.137]), ('control #1', [-4612717.254, 854010.104, -297229.761, 35.767, -284.925, 195.294, -3.1116, -2.0049, -2.6038, -4.6626, 'position_vector'], [-4612646.31, 853774.942, -297090.8]), ('control #2', [1975468.993, -227743.085, 2770505.24, 403.916, 391.722, 260.454, 2.194, 0.0057, 3.3578, 9.7343, 'coordinate_frame'], [1975888.355, -227356.269, 2770795.14]), ('control #3', [-189321.127, 3352090.605, -2404357.859, -152.685, 61.282, -123.245, -4.7005, -0.5925, -4.5929, 7.6062, 'coordinate_frame'], [-189556.8, 3352227.961, -2404422.458]), ('control #4', [-6228293.209, -1104665.934, 4388800.498, 448.343, 5.84, -248.246, 0.9162, -1.8119, 1.9656, -3.1531, 'position_vector'], [-6227853.253, -1104735.458, 4388478.796]), ('control #5', [-2535544.339, -5957215.045, -4097405.578, -66.0, -207.215, 331.819, 3.4107, -4.2707, 0.0925, 8.1975, 'position_vector'], [-2535543.615, -5957404.478, -4097258.353]), ('boundary #22', [4027894.006, 307045.6, 4919474.91, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 'coordinate_frame'], [4027894.006, 307045.6, 4919474.91]), ('boundary #25', [1000.0, 2000.0, 3000.0, 1.0, 2.0, 3.0, 0.0, 0.0, 0.0, 0.0, 'position_vector'], [1001.0, 2002.0, 3003.0])], [('control #1', [-4612717.254, 854010.104, -297229.761, 35.767, -284.925, 195.294, -3.1116, -2.0049, -2.6038, -4.6626, 'position_vector'], [-4612646.31, 853774.942, -297090.8]), ('control #4', [-6228293.209, -1104665.934, 4388800.498, 448.343, 5.84, -248.246, 0.9162, -1.8119, 1.9656, -3.1531, 'position_vector'], [-6227853.253, -1104735.458, 4388478.796]), ('control #5', [-2535544.339, -5957215.045, -4097405.578, -66.0, -207.215, 331.819, 3.4107, -4.2707, 0.0925, 8.1975, 'position_vector'], [-2535543.615, -5957404.478, -4097258.353]), ('control #6', [3627823.551, 5819563.217, -5921733.519, 228.087, -10.934, -497.542, -2.8114, -0.0659, -0.388, 7.4115, 'coordinate_frame'], [3628065.687, 5819682.953, -5922196.787]), ('control #7', [-1973240.205, 3874957.505, 5178356.07, -328.689, -442.829, -41.798, -4.7714, -2.8648, -4.9782, -2.8322, 'position_vector'], [-1973541.705, 3874671.113, 5178182.563]), ('control #8', [3575522.137, 5452586.84, 1656910.978, 298.786, 393.9, -294.606, 0.0728, 4.841, -0.7608, 8.8812, 'position_vector'], [3575911.678, 5453015.392, 1656549.094]), ('boundary #22', [4027894.006, 307045.6, 4919474.91, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 'coordinate_frame'], [4027894.006, 307045.6, 4919474.91]), ('boundary #25', [1000.0, 2000.0, 3000.0, 1.0, 2.0, 3.0, 0.0, 0.0, 0.0, 0.0, 'position_vector'], [1001.0, 2002.0, 3003.0])], [('control #2', [1975468.993, -227743.085, 2770505.24, 403.916, 391.722, 260.454, 2.194, 0.0057, 3.3578, 9.7343, 'coordinate_frame'], [1975888.355, -227356.269, 2770795.14]), ('control #5', [-2535544.339, -5957215.045, -4097405.578, -66.0, -207.215, 331.819, 3.4107, -4.2707, 0.0925, 8.1975, 'position_vector'], [-2535543.615, -5957404.478, -4097258.353]), ('control #8', [3575522.137, 5452586.84, 1656910.978, 298.786, 393.9, -294.606, 0.0728, 4.841, -0.7608, 8.8812, 'position_vector'], [3575911.678, 5453015.392, 1656549.094]), ('control #9', [-1240296.101, -552884.937, -952528.764, -360.154, 285.951, 384.058, -2.5191, -3.2475, 0.9833, 0.1835, 'position_vector'], [-1240638.85, -552616.633, -952157.656]), ('control #10', [1307969.679, 563540.708, -1431729.813, -333.759, -148.113, 140.284, -1.8868, 2.9579, 1.9314, -9.4043, 'position_vector'], [1307597.811, 563386.446, -1431599.976]), ('control #11', [-3904352.966, -2722509.047, -2822388.255, 181.432, 495.341, 160.587, -1.285, -3.3165, -0.7058, 5.5208, 'position_vector'], [-3904157.024, -2722032.96, -2822289.067]), ('boundary #22', [4027894.006, 307045.6, 4919474.91, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 'coordinate_frame'], [4027894.006, 307045.6, 4919474.91]), ('boundary #25', [1000.0, 2000.0, 3000.0, 1.0, 2.0, 3.0, 0.0, 0.0, 0.0, 0.0, 'position_vector'], [1001.0, 2002.0, 3003.0])], [('control #3', [-189321.127, 3352090.605, -2404357.859, -152.685, 61.282, -123.245, -4.7005, -0.5925, -4.5929, 7.6062, 'coordinate_frame'], [-189556.8, 3352227.961, -2404422.458]), ('control #7', [-1973240.205, 3874957.505, 5178356.07, -328.689, -442.829, -41.798, -4.7714, -2.8648, -4.9782, -2.8322, 'position_vector'], [-1973541.705, 3874671.113, 5178182.563]), ('control #11', [-3904352.966, -2722509.047, -2822388.255, 181.432, 495.341, 160.587, -1.285, -3.3165, -0.7058, 5.5208, 'position_vector'], [-3904157.024, -2722032.96, -2822289.067]), ('control #12', [2647634.641, -1578921.141, -5093066.149, -355.392, 203.405, 165.947, 0.2987, -4.1705, -3.9905, -0.2744, 'position_vector'], [2647350.953, -1578761.15, -5092847.558]), ('control #13', [-3520096.56, -3120177.457, -123254.85, 462.196, 402.077, 308.458, 1.3023, 3.5694, 0.8414, 8.6398, 'position_vector'], [-3519654.182, -3119815.919, -122906.241]), ('control #14', [-6389654.874, -3984093.2, -3011962.836, 356.165, -201.583, 189.984, 2.6426, 1.938, -0.6636, -3.7122, 'coordinate_frame'], [-6389233.872, -3984339.138, -3011770.663]), ('boundary #22', [4027894.006, 307045.6, 4919474.91, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 'coordinate_frame'], [4027894.006, 307045.6, 4919474.91]), ('boundary #25', [1000.0, 2000.0, 3000.0, 1.0, 2.0, 3.0, 0.0, 0.0, 0.0, 0.0, 'position_vector'], [1001.0, 2002.0, 3003.0])], [('control #4', [-6228293.209, -1104665.934, 4388800.498, 448.343, 5.84, -248.246, 0.9162, -1.8119, 1.9656, -3.1531, 'position_vector'], [-6227853.253, -1104735.458, 4388478.796]), ('control #9', [-1240296.101, -552884.937, -952528.764, -360.154, 285.951, 384.058, -2.5191, -3.2475, 0.9833, 0.1835, 'position_vector'], [-1240638.85, -552616.633, -952157.656]), ('control #14', [-6389654.874, -3984093.2, -3011962.836, 356.165, -201.583, 189.984, 2.6426, 1.938, -0.6636, -3.7122, 'coordinate_frame'], [-6389233.872, -3984339.138, -3011770.663]), ('control #15', [4550537.139, 2792317.331, 1441981.13, 76.583, -265.303, -460.556, -0.538, -4.9358, -3.9263, 0.893, 'coordinate_frame'], [4550599.139, 2792137.381, 1441420.253]), ('control #16', [6034311.204, -4464484.503, 922428.188, 291.409, -257.511, -47.177, 0.8272, -3.8801, -0.5275, 8.0745, 'position_vector'], [6034622.567, -4464797.194, 922484.069]), ('control #17', [5230974.683, -6230904.331, 2167328.689, 237.623, -185.552, -261.576, 1.7677, -1.5195, 4.1454, -3.6432, 'coordinate_frame'], [5231083.99, -6231153.737, 2167074.081]), ('boundary #22', [4027894.006, 307045.6, 4919474.91, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 'coordinate_frame'], [4027894.006, 307045.6, 4919474.91]), ('boundary #25', [1000.0, 2000.0, 3000.0, 1.0, 2.0, 3.0, 0.0, 0.0, 0.0, 0.0, 'position_vector'], [1001.0, 2002.0, 3003.0])]]
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 fixture	Actual	Expected	Outcome
control #0	`[-5541432.141, -2232085.415, -6352736.311]`	`[-5541265.265, -2232093.171, -6352879.137]`	Failed
control #1	`[-4612673.649, 853667.452, -296975.363]`	`[-4612646.31, 853774.942, -297090.8]`	Failed
control #2	`[1975895.923, -227350.89, 2770790.186]`	`[1975888.355, -227356.269, 2770795.14]`	Failed
control #3	`[-189393.704, 3352126.807, -2404576.326]`	`[-189556.8, 3352227.961, -2404422.458]`	Failed
control #4	`[-6227797.202, -1104577.764, 4388598.032]`	`[-6227853.253, -1104735.458, 4388478.796]`	Failed
control #5	`[-2535718.633, -5957537.711, -4096956.342]`	`[-2535543.615, -5957404.478, -4097258.353]`	Failed
boundary #22	`[4027894.006, 307045.6, 4919474.91]`	`[4027894.006, 307045.6, 4919474.91]`	Passed
boundary #25	`[1001.0, 2002.0, 3003.0]`	`[1001.0, 2002.0, 3003.0]`	Passed

SHA-256 / df7cbcf52b3bbdc7c8c30e6c96e8ffcad7be4719496ee7d5fda94844de2a5f3c

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    X, Y, Z, tx, ty, tz, rx, ry, rz, s, conv = x
    k = math.pi / (180 * 3600)
    rx, ry, rz = rx * k, ry * k, rz * k
    if conv in ('coordinate_frame', 'position_vector'):
        rx, ry, rz = -rx, -ry, -rz
    m = 1 + s * 1e-6
    Xo = tx + m * (X - rz * Y + ry * Z)
    Yo = ty + m * (rz * X + Y - rx * Z)
    Zo = tz + m * (-ry * X + rx * Y + Z)
    return [round(Xo, 3), round(Yo, 3), round(Zo, 3)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', [-5541091.088, -2232325.705, -6352955.267, -217.202, 252.693, 193.877, -0.3013, 2.5369, -0.4898, 7.2933, 'coordinate_frame'], [-5541265.265, -2232093.171, -6352879.137]), ('control #1', [-4612717.254, 854010.104, -297229.761, 35.767, -284.925, 195.294, -3.1116, -2.0049, -2.6038, -4.6626, 'position_vector'], [-4612646.31, 853774.942, -297090.8]), ('control #2', [1975468.993, -227743.085, 2770505.24, 403.916, 391.722, 260.454, 2.194, 0.0057, 3.3578, 9.7343, 'coordinate_frame'], [1975888.355, -227356.269, 2770795.14]), ('control #3', [-189321.127, 3352090.605, -2404357.859, -152.685, 61.282, -123.245, -4.7005, -0.5925, -4.5929, 7.6062, 'coordinate_frame'], [-189556.8, 3352227.961, -2404422.458]), ('control #4', [-6228293.209, -1104665.934, 4388800.498, 448.343, 5.84, -248.246, 0.9162, -1.8119, 1.9656, -3.1531, 'position_vector'], [-6227853.253, -1104735.458, 4388478.796]), ('control #5', [-2535544.339, -5957215.045, -4097405.578, -66.0, -207.215, 331.819, 3.4107, -4.2707, 0.0925, 8.1975, 'position_vector'], [-2535543.615, -5957404.478, -4097258.353]), ('boundary #22', [4027894.006, 307045.6, 4919474.91, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 'coordinate_frame'], [4027894.006, 307045.6, 4919474.91]), ('boundary #25', [1000.0, 2000.0, 3000.0, 1.0, 2.0, 3.0, 0.0, 0.0, 0.0, 0.0, 'position_vector'], [1001.0, 2002.0, 3003.0])], [('control #1', [-4612717.254, 854010.104, -297229.761, 35.767, -284.925, 195.294, -3.1116, -2.0049, -2.6038, -4.6626, 'position_vector'], [-4612646.31, 853774.942, -297090.8]), ('control #4', [-6228293.209, -1104665.934, 4388800.498, 448.343, 5.84, -248.246, 0.9162, -1.8119, 1.9656, -3.1531, 'position_vector'], [-6227853.253, -1104735.458, 4388478.796]), ('control #5', [-2535544.339, -5957215.045, -4097405.578, -66.0, -207.215, 331.819, 3.4107, -4.2707, 0.0925, 8.1975, 'position_vector'], [-2535543.615, -5957404.478, -4097258.353]), ('control #6', [3627823.551, 5819563.217, -5921733.519, 228.087, -10.934, -497.542, -2.8114, -0.0659, -0.388, 7.4115, 'coordinate_frame'], [3628065.687, 5819682.953, -5922196.787]), ('control #7', [-1973240.205, 3874957.505, 5178356.07, -328.689, -442.829, -41.798, -4.7714, -2.8648, -4.9782, -2.8322, 'position_vector'], [-1973541.705, 3874671.113, 5178182.563]), ('control #8', [3575522.137, 5452586.84, 1656910.978, 298.786, 393.9, -294.606, 0.0728, 4.841, -0.7608, 8.8812, 'position_vector'], [3575911.678, 5453015.392, 1656549.094]), ('boundary #22', [4027894.006, 307045.6, 4919474.91, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 'coordinate_frame'], [4027894.006, 307045.6, 4919474.91]), ('boundary #25', [1000.0, 2000.0, 3000.0, 1.0, 2.0, 3.0, 0.0, 0.0, 0.0, 0.0, 'position_vector'], [1001.0, 2002.0, 3003.0])], [('control #2', [1975468.993, -227743.085, 2770505.24, 403.916, 391.722, 260.454, 2.194, 0.0057, 3.3578, 9.7343, 'coordinate_frame'], [1975888.355, -227356.269, 2770795.14]), ('control #5', [-2535544.339, -5957215.045, -4097405.578, -66.0, -207.215, 331.819, 3.4107, -4.2707, 0.0925, 8.1975, 'position_vector'], [-2535543.615, -5957404.478, -4097258.353]), ('control #8', [3575522.137, 5452586.84, 1656910.978, 298.786, 393.9, -294.606, 0.0728, 4.841, -0.7608, 8.8812, 'position_vector'], [3575911.678, 5453015.392, 1656549.094]), ('control #9', [-1240296.101, -552884.937, -952528.764, -360.154, 285.951, 384.058, -2.5191, -3.2475, 0.9833, 0.1835, 'position_vector'], [-1240638.85, -552616.633, -952157.656]), ('control #10', [1307969.679, 563540.708, -1431729.813, -333.759, -148.113, 140.284, -1.8868, 2.9579, 1.9314, -9.4043, 'position_vector'], [1307597.811, 563386.446, -1431599.976]), ('control #11', [-3904352.966, -2722509.047, -2822388.255, 181.432, 495.341, 160.587, -1.285, -3.3165, -0.7058, 5.5208, 'position_vector'], [-3904157.024, -2722032.96, -2822289.067]), ('boundary #22', [4027894.006, 307045.6, 4919474.91, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 'coordinate_frame'], [4027894.006, 307045.6, 4919474.91]), ('boundary #25', [1000.0, 2000.0, 3000.0, 1.0, 2.0, 3.0, 0.0, 0.0, 0.0, 0.0, 'position_vector'], [1001.0, 2002.0, 3003.0])], [('control #3', [-189321.127, 3352090.605, -2404357.859, -152.685, 61.282, -123.245, -4.7005, -0.5925, -4.5929, 7.6062, 'coordinate_frame'], [-189556.8, 3352227.961, -2404422.458]), ('control #7', [-1973240.205, 3874957.505, 5178356.07, -328.689, -442.829, -41.798, -4.7714, -2.8648, -4.9782, -2.8322, 'position_vector'], [-1973541.705, 3874671.113, 5178182.563]), ('control #11', [-3904352.966, -2722509.047, -2822388.255, 181.432, 495.341, 160.587, -1.285, -3.3165, -0.7058, 5.5208, 'position_vector'], [-3904157.024, -2722032.96, -2822289.067]), ('control #12', [2647634.641, -1578921.141, -5093066.149, -355.392, 203.405, 165.947, 0.2987, -4.1705, -3.9905, -0.2744, 'position_vector'], [2647350.953, -1578761.15, -5092847.558]), ('control #13', [-3520096.56, -3120177.457, -123254.85, 462.196, 402.077, 308.458, 1.3023, 3.5694, 0.8414, 8.6398, 'position_vector'], [-3519654.182, -3119815.919, -122906.241]), ('control #14', [-6389654.874, -3984093.2, -3011962.836, 356.165, -201.583, 189.984, 2.6426, 1.938, -0.6636, -3.7122, 'coordinate_frame'], [-6389233.872, -3984339.138, -3011770.663]), ('boundary #22', [4027894.006, 307045.6, 4919474.91, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 'coordinate_frame'], [4027894.006, 307045.6, 4919474.91]), ('boundary #25', [1000.0, 2000.0, 3000.0, 1.0, 2.0, 3.0, 0.0, 0.0, 0.0, 0.0, 'position_vector'], [1001.0, 2002.0, 3003.0])], [('control #4', [-6228293.209, -1104665.934, 4388800.498, 448.343, 5.84, -248.246, 0.9162, -1.8119, 1.9656, -3.1531, 'position_vector'], [-6227853.253, -1104735.458, 4388478.796]), ('control #9', [-1240296.101, -552884.937, -952528.764, -360.154, 285.951, 384.058, -2.5191, -3.2475, 0.9833, 0.1835, 'position_vector'], [-1240638.85, -552616.633, -952157.656]), ('control #14', [-6389654.874, -3984093.2, -3011962.836, 356.165, -201.583, 189.984, 2.6426, 1.938, -0.6636, -3.7122, 'coordinate_frame'], [-6389233.872, -3984339.138, -3011770.663]), ('control #15', [4550537.139, 2792317.331, 1441981.13, 76.583, -265.303, -460.556, -0.538, -4.9358, -3.9263, 0.893, 'coordinate_frame'], [4550599.139, 2792137.381, 1441420.253]), ('control #16', [6034311.204, -4464484.503, 922428.188, 291.409, -257.511, -47.177, 0.8272, -3.8801, -0.5275, 8.0745, 'position_vector'], [6034622.567, -4464797.194, 922484.069]), ('control #17', [5230974.683, -6230904.331, 2167328.689, 237.623, -185.552, -261.576, 1.7677, -1.5195, 4.1454, -3.6432, 'coordinate_frame'], [5231083.99, -6231153.737, 2167074.081]), ('boundary #22', [4027894.006, 307045.6, 4919474.91, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 'coordinate_frame'], [4027894.006, 307045.6, 4919474.91]), ('boundary #25', [1000.0, 2000.0, 3000.0, 1.0, 2.0, 3.0, 0.0, 0.0, 0.0, 0.0, 'position_vector'], [1001.0, 2002.0, 3003.0])]]
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 fixture	Actual	Expected	Outcome
control #0	`[-5541265.265, -2232093.171, -6352879.137]`	`[-5541265.265, -2232093.171, -6352879.137]`	Passed
control #1	`[-4612673.649, 853667.452, -296975.363]`	`[-4612646.31, 853774.942, -297090.8]`	Failed
control #2	`[1975888.355, -227356.269, 2770795.14]`	`[1975888.355, -227356.269, 2770795.14]`	Passed
control #3	`[-189556.8, 3352227.961, -2404422.458]`	`[-189556.8, 3352227.961, -2404422.458]`	Passed
control #4	`[-6227797.202, -1104577.764, 4388598.032]`	`[-6227853.253, -1104735.458, 4388478.796]`	Failed
control #5	`[-2535718.633, -5957537.711, -4096956.342]`	`[-2535543.615, -5957404.478, -4097258.353]`	Failed
boundary #22	`[4027894.006, 307045.6, 4919474.91]`	`[4027894.006, 307045.6, 4919474.91]`	Passed
boundary #25	`[1001.0, 2002.0, 3003.0]`	`[1001.0, 2002.0, 3003.0]`	Passed

SHA-256 / 77ae5e8d44dd999e700273152ed3c078d14b4acaa75fcf452899f6b429493b75

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 2026-09-29T14:48:19.774514+00:00.

Case digest / 2fce2884b339346be1919d391023ca138b74ad214e5fafc027c72cec9611eb49