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FA-12066 / Sensor fusion consistency / Open access

Measurement channel permutation leaves covariance behind · case 01

An uncertainty belongs to the wrong sensor channel.

Verified by executionVariant 1 · 6 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Only the measurement vector is reordered.

VERIFIED REPAIR

Apply the same channel permutation to both covariance dimensions.

Unsuccessful approach: Permuting rows alone breaks diagonal association and symmetry.

Case contract

Given a 2x2 measurement covariance in source order and a permutation of [0,1], return covariance in requested channel order.

Why this case matters

Deterministic sensor-fusion model isolating one consistency contract; no hardware or production estimator is simulated.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(covariance, order):
    return covariance
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('unequal uncertainties', solve([[N,0],[0,4*N]],[1,0]), [[4*N,0],[0,N]])
check('cross covariance', solve([[2*N,N],[N,3*N]],[1,0]), [[3*N,N],[N,2*N]])
check('negative cross covariance', solve([[2*N,-N],[-N,3*N]],[1,0]), [[3*N,-N],[-N,2*N]])
check('identity channel order', solve([[N,0],[0,2*N]],[0,1]), [[N,0],[0,2*N]])
check('equal variances', solve([[2*N,N],[N,2*N]],[1,0]), [[2*N,N],[N,2*N]])
check('zero covariance boundary', solve([[0,0],[0,N]],[1,0]), [[N,0],[0,0]])
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
unequal uncertainties[[1, 0], [0, 4]][[4, 0], [0, 1]]Failed
cross covariance[[2, 1], [1, 3]][[3, 1], [1, 2]]Failed
negative cross covariance[[2, -1], [-1, 3]][[3, -1], [-1, 2]]Failed
identity channel order[[1, 0], [0, 2]][[1, 0], [0, 2]]Passed
equal variances[[2, 1], [1, 2]][[2, 1], [1, 2]]Passed
zero covariance boundary[[0, 0], [0, 1]][[1, 0], [0, 0]]Failed

SHA-256 / 8d1d79a22b6bda7331864f2bf33381a1b1ff1766f72b14398a1cb089c1eda5dc

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(covariance, order):
    return [covariance[i] for i in order]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('unequal uncertainties', solve([[N,0],[0,4*N]],[1,0]), [[4*N,0],[0,N]])
check('cross covariance', solve([[2*N,N],[N,3*N]],[1,0]), [[3*N,N],[N,2*N]])
check('negative cross covariance', solve([[2*N,-N],[-N,3*N]],[1,0]), [[3*N,-N],[-N,2*N]])
check('identity channel order', solve([[N,0],[0,2*N]],[0,1]), [[N,0],[0,2*N]])
check('equal variances', solve([[2*N,N],[N,2*N]],[1,0]), [[2*N,N],[N,2*N]])
check('zero covariance boundary', solve([[0,0],[0,N]],[1,0]), [[N,0],[0,0]])
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
unequal uncertainties[[0, 4], [1, 0]][[4, 0], [0, 1]]Failed
cross covariance[[1, 3], [2, 1]][[3, 1], [1, 2]]Failed
negative cross covariance[[-1, 3], [2, -1]][[3, -1], [-1, 2]]Failed
identity channel order[[1, 0], [0, 2]][[1, 0], [0, 2]]Passed
equal variances[[1, 2], [2, 1]][[2, 1], [1, 2]]Failed
zero covariance boundary[[0, 1], [0, 0]][[1, 0], [0, 0]]Failed

SHA-256 / a86a64fdfd6c7b018070bbe54f5337903b19e17d109a168f7a0e4912d17d7c05

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(covariance, order):
    return [[covariance[i][j] for j in order] for i in order]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('unequal uncertainties', solve([[N,0],[0,4*N]],[1,0]), [[4*N,0],[0,N]])
check('cross covariance', solve([[2*N,N],[N,3*N]],[1,0]), [[3*N,N],[N,2*N]])
check('negative cross covariance', solve([[2*N,-N],[-N,3*N]],[1,0]), [[3*N,-N],[-N,2*N]])
check('identity channel order', solve([[N,0],[0,2*N]],[0,1]), [[N,0],[0,2*N]])
check('equal variances', solve([[2*N,N],[N,2*N]],[1,0]), [[2*N,N],[N,2*N]])
check('zero covariance boundary', solve([[0,0],[0,N]],[1,0]), [[N,0],[0,0]])
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
unequal uncertainties[[4, 0], [0, 1]][[4, 0], [0, 1]]Passed
cross covariance[[3, 1], [1, 2]][[3, 1], [1, 2]]Passed
negative cross covariance[[3, -1], [-1, 2]][[3, -1], [-1, 2]]Passed
identity channel order[[1, 0], [0, 2]][[1, 0], [0, 2]]Passed
equal variances[[2, 1], [1, 2]][[2, 1], [1, 2]]Passed
zero covariance boundary[[1, 0], [0, 0]][[1, 0], [0, 0]]Passed

SHA-256 / b26e20cf6a9bd3ad0e98fdb5836905ce1613c14532a4d930e037301ef2a0aa63

Verification & scope

Exact small scalar or two-axis models; no nonlinear dynamics, numerical conditioning, or real sensor noise simulation. 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 2026-09-29T14:38:53.573488+00:00.

Case digest / c165ef0038674d119cbc1aac812f8b4a0664c51ba08864f43855ed28a0142c59