{"abstract":"Reported fused uncertainty is smaller than the shared sensor noise.","category":"Sensor fusion consistency","checks":6,"contract":"Given positive p,r and cross covariance c with c*c<p*r and p+r-2*c>0, return exact variance of the minimum-variance unbiased linear combination as a fraction string.","evaluation_group":"model-f8bfcabb14fb8343","failed_approach":"Adding covariance to the numerator without correcting the denominator remains inconsistent.","family":"z-sensor_fusion-correlated-estimates","id":"FA-12056","implementations":{"attempt":{"sha256":"97ed123f15a802e7430ba362b2bd6c31bd3530c9fb7033ce1116efcf137233ee","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(p, r, c):\n    return str(Fraction(p*r-c*c,p+r))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('positive shared noise', solve(2*N,2*N,N), str(Fraction(3*N,2)))\ncheck('negative correlation', solve(2*N,2*N,-N), str(Fraction(N,2)))\ncheck('independent equal sensors', solve(N,N,0), str(Fraction(N,2)))\ncheck('unequal independent sensors', solve(N,3*N,0), str(Fraction(3*N,4)))\ncheck('unequal shared noise', solve(2*N,5*N,N), str(Fraction(9*N,5)))\ncheck('unequal opposing noise', solve(2*N,5*N,-N), str(N))\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":"8834dc9a809f4e101cea58fb75700e103d9be2e3fcd21252af5547a6f3f1d861","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(p, r, c):\n    return str(Fraction(p*r,p+r))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('positive shared noise', solve(2*N,2*N,N), str(Fraction(3*N,2)))\ncheck('negative correlation', solve(2*N,2*N,-N), str(Fraction(N,2)))\ncheck('independent equal sensors', solve(N,N,0), str(Fraction(N,2)))\ncheck('unequal independent sensors', solve(N,3*N,0), str(Fraction(3*N,4)))\ncheck('unequal shared noise', solve(2*N,5*N,N), str(Fraction(9*N,5)))\ncheck('unequal opposing noise', solve(2*N,5*N,-N), str(N))\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":"62943b5a6e4848148906cd095f245bf1ae88d3851ce05a3a196bb2e830c32a11","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(p, r, c):\n    return str(Fraction(p*r-c*c,p+r-2*c))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('positive shared noise', solve(2*N,2*N,N), str(Fraction(3*N,2)))\ncheck('negative correlation', solve(2*N,2*N,-N), str(Fraction(N,2)))\ncheck('independent equal sensors', solve(N,N,0), str(Fraction(N,2)))\ncheck('unequal independent sensors', solve(N,3*N,0), str(Fraction(3*N,4)))\ncheck('unequal shared noise', solve(2*N,5*N,N), str(Fraction(9*N,5)))\ncheck('unequal opposing noise', solve(2*N,5*N,-N), str(N))\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":"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.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"z-sensor_fusion-correlated-estimates","generated_at":"2026-09-29T14:38:53.466020+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Deterministic sensor-fusion model isolating one consistency contract; no hardware or production estimator is simulated.","repair":"Use (p*r-c*c)/(p+r-2*c) for the declared two-estimate covariance.","root_cause":"Cross covariance is omitted from the best linear unbiased variance.","sha256":"ae546bad65da3f7c9d20aca3e0e70b788f079ed97eb90612241a896b8b8df54d","title":"Correlated estimates lose shared uncertainty during fusion · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":42.155,"exit_code":1,"observations":[{"actual":"3/4","check":"positive shared noise","expected":"3/2","passed":false},{"actual":"3/4","check":"negative correlation","expected":"1/2","passed":false},{"actual":"1/2","check":"independent equal sensors","expected":"1/2","passed":true},{"actual":"3/4","check":"unequal independent sensors","expected":"3/4","passed":true},{"actual":"9/7","check":"unequal shared noise","expected":"9/5","passed":false},{"actual":"9/7","check":"unequal opposing noise","expected":"1","passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"positive shared noise\", \"actual\": \"3/4\", \"expected\": \"3/2\", \"passed\": false}, {\"check\": \"negative correlation\", \"actual\": \"3/4\", \"expected\": \"1/2\", \"passed\": false}, {\"check\": \"independent equal sensors\", \"actual\": \"1/2\", \"expected\": \"1/2\", \"passed\": true}, {\"check\": \"unequal independent sensors\", \"actual\": \"3/4\", \"expected\": \"3/4\", \"passed\": true}, {\"check\": \"unequal shared noise\", \"actual\": \"9/7\", \"expected\": \"9/5\", \"passed\": false}, {\"check\": \"unequal opposing noise\", \"actual\": \"9/7\", \"expected\": \"1\", \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":42.623,"exit_code":1,"observations":[{"actual":"1","check":"positive shared noise","expected":"3/2","passed":false},{"actual":"1","check":"negative correlation","expected":"1/2","passed":false},{"actual":"1/2","check":"independent equal sensors","expected":"1/2","passed":true},{"actual":"3/4","check":"unequal independent sensors","expected":"3/4","passed":true},{"actual":"10/7","check":"unequal shared noise","expected":"9/5","passed":false},{"actual":"10/7","check":"unequal opposing noise","expected":"1","passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"positive shared noise\", \"actual\": \"1\", \"expected\": \"3/2\", \"passed\": false}, {\"check\": \"negative correlation\", \"actual\": \"1\", \"expected\": \"1/2\", \"passed\": false}, {\"check\": \"independent equal sensors\", \"actual\": \"1/2\", \"expected\": \"1/2\", \"passed\": true}, {\"check\": \"unequal independent sensors\", \"actual\": \"3/4\", \"expected\": \"3/4\", \"passed\": true}, {\"check\": \"unequal shared noise\", \"actual\": \"10/7\", \"expected\": \"9/5\", \"passed\": false}, {\"check\": \"unequal opposing noise\", \"actual\": \"10/7\", \"expected\": \"1\", \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":43.497,"exit_code":0,"observations":[{"actual":"3/2","check":"positive shared noise","expected":"3/2","passed":true},{"actual":"1/2","check":"negative correlation","expected":"1/2","passed":true},{"actual":"1/2","check":"independent equal sensors","expected":"1/2","passed":true},{"actual":"3/4","check":"unequal independent sensors","expected":"3/4","passed":true},{"actual":"9/5","check":"unequal shared noise","expected":"9/5","passed":true},{"actual":"1","check":"unequal opposing noise","expected":"1","passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"positive shared noise\", \"actual\": \"3/2\", \"expected\": \"3/2\", \"passed\": true}, {\"check\": \"negative correlation\", \"actual\": \"1/2\", \"expected\": \"1/2\", \"passed\": true}, {\"check\": \"independent equal sensors\", \"actual\": \"1/2\", \"expected\": \"1/2\", \"passed\": true}, {\"check\": \"unequal independent sensors\", \"actual\": \"3/4\", \"expected\": \"3/4\", \"passed\": true}, {\"check\": \"unequal shared noise\", \"actual\": \"9/5\", \"expected\": \"9/5\", \"passed\": true}, {\"check\": \"unequal opposing noise\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}