FA-12131 / Robotics frame conventions / Open access

Frame conversion drops the sign of cross-axis covariance · case 01

Frame conversion drops the sign of cross-axis covariance.

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

ROOT CAUSE

A covariance matrix is relabeled without applying the frame basis transform.

THE FAILURE

A covariance matrix is relabeled without applying the frame basis transform.

Unsuccessful approach: Swapping diagonal variances but leaving covariance positive omits the axis sign change.

Case contract

A symmetric 2D covariance [[a,c],[c,b]] in x,y is converted to coordinates [-y,x]. Return [[b,-c],[-c,a]]. Inputs are positive semidefinite.

Why this case matters

Robot adapters must preserve the declared frame, reference point, and representation conventions across interfaces.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

def rot(v, q):
    x,y = v
    return [(x,y),(-y,x),(-x,-y),(y,-x)][q%4]

N = 1
observations = []
def solve(a,b,c):
    return [[a,c],[c,b]]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('correlated', solve(4*N,9*N,2*N), [[9*N,-2*N],[-2*N,4*N]])
check('negative correlation', solve(4*N,9*N,-2*N), [[9*N,2*N],[2*N,4*N]])
check('diagonal', solve(N,2*N,0), [[2*N,0],[0,N]])
check('isotropic', solve(N,N,0), [[N,0],[0,N]])
check('zero uncertainty', solve(0,0,0), [[0,0],[0,0]])
check('rank one', solve(N,N,N), [[N,-N],[-N,N]])
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
correlated	`[[4, 2], [2, 9]]`	`[[9, -2], [-2, 4]]`	Failed
negative correlation	`[[4, -2], [-2, 9]]`	`[[9, 2], [2, 4]]`	Failed
diagonal	`[[1, 0], [0, 2]]`	`[[2, 0], [0, 1]]`	Failed
isotropic	`[[1, 0], [0, 1]]`	`[[1, 0], [0, 1]]`	Passed
zero uncertainty	`[[0, 0], [0, 0]]`	`[[0, 0], [0, 0]]`	Passed
rank one	`[[1, 1], [1, 1]]`	`[[1, -1], [-1, 1]]`	Failed

SHA-256 / 006cf59fdf4dc8ec16f997e2ac55ed288a8aec47076ba1e55a53da32eae511b9

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

def rot(v, q):
    x,y = v
    return [(x,y),(-y,x),(-x,-y),(y,-x)][q%4]

N = 1
observations = []
def solve(a,b,c):
    return [[b,c],[c,a]]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('correlated', solve(4*N,9*N,2*N), [[9*N,-2*N],[-2*N,4*N]])
check('negative correlation', solve(4*N,9*N,-2*N), [[9*N,2*N],[2*N,4*N]])
check('diagonal', solve(N,2*N,0), [[2*N,0],[0,N]])
check('isotropic', solve(N,N,0), [[N,0],[0,N]])
check('zero uncertainty', solve(0,0,0), [[0,0],[0,0]])
check('rank one', solve(N,N,N), [[N,-N],[-N,N]])
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
correlated	`[[9, 2], [2, 4]]`	`[[9, -2], [-2, 4]]`	Failed
negative correlation	`[[9, -2], [-2, 4]]`	`[[9, 2], [2, 4]]`	Failed
diagonal	`[[2, 0], [0, 1]]`	`[[2, 0], [0, 1]]`	Passed
isotropic	`[[1, 0], [0, 1]]`	`[[1, 0], [0, 1]]`	Passed
zero uncertainty	`[[0, 0], [0, 0]]`	`[[0, 0], [0, 0]]`	Passed
rank one	`[[1, 1], [1, 1]]`	`[[1, -1], [-1, 1]]`	Failed

SHA-256 / 955698f5f5a51dd5c1ac0c18ecd29752e5ec467f5900db069d6121884398151d

HELD IN THE MEMBER ARCHIVE

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

This mechanism has 6 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.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

Verification & scope

Small exact offline frame model; not a robot middleware implementation or continuous pose estimator. 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 2026-09-29T14:38:54.159465+00:00.

Case digest / cb5c4356f16e87b6dca1b8135e7b6a1d267accd6d2205a0f128721135bbf7254