{"abstract":"The reported departure asymptote lies on the wrong side of the latus rectum.","category":"Orbital propagation","checks":7,"contract":"Input [M, e] with e>1 (else None). Solve e sinh H - H = M by Newton from H=asinh(M/e) (60 iterations max, stop when step<1e-13). Return [H, nu, nu_inf] rounded to 9 with nu=2 atan(sqrt((e+1)/(e-1)) tanh(H/2)) and asymptote nu_inf=acos(-1/e).","evaluation_group":"w2-orbital_propagation-kepler_hyperbolic","failed_approach":"atan(sqrt(e^2-1)) is the same supplementary angle as acos(1/e).","family":"w2-orbital_propagation-kepler_hyperbolic-asymptote-angle","id":"FA-69611","implementations":{"attempt":{"sha256":"e076de9358c8ea05ae06131de74a614634920d33b3f258dd2f4c8791de6da584","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    M,e=x\n    if e<=1: return None\n    H=math.asinh(M/e)\n    for _ in range(60):\n        d=(e*math.sinh(H)-H-M)/(e*math.cosh(H)-1)\n        H-=d\n        if abs(d)<1e-13: break\n    nu=2*math.atan(math.sqrt((e+1)/(e-1))*math.tanh(H/2))\n    return [round(H,9),round(nu,9),round(math.atan(math.sqrt(e*e-1)),9)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('hyperbolic kepler solver [0.5, 1.2]', [0.5, 1.2], [1.097223034, 2.055391897, 2.55590711]), ('hyperbolic kepler solver [2.0, 1.5]', [2.0, 1.5], [1.61268581, 1.961096791, 2.300523983]), ('hyperbolic kepler solver [10.0, 2.5]', [10.0, 2.5], [2.296335107, 1.790713502, 1.982313173]), ('hyperbolic kepler solver [-3.0, 1.1]', [-3.0, 1.1], [-2.270719072, -2.617037695, 2.711892987]), ('hyperbolic kepler solver [0.0, 3.0]', [0.0, 3.0], [0.0, 0.0, 1.910633236]), ('hyperbolic kepler solver [50.0, 1.05]', [50.0, 1.05], [4.645312748, 2.825835675, 2.831748014]), ('hyperbolic kepler solver [-0.2, 4.0]', [-0.2, 4.0], [-0.066601003, -0.085896903, 1.823476582])], [('hyperbolic kepler solver [2.0, 1.5]', [2.0, 1.5], [1.61268581, 1.961096791, 2.300523983]), ('hyperbolic kepler solver [-3.0, 1.1]', [-3.0, 1.1], [-2.270719072, -2.617037695, 2.711892987]), ('hyperbolic kepler solver [0.0, 3.0]', [0.0, 3.0], [0.0, 0.0, 1.910633236]), ('hyperbolic kepler solver [50.0, 1.05]', [50.0, 1.05], [4.645312748, 2.825835675, 2.831748014]), ('hyperbolic kepler solver [-0.2, 4.0]', [-0.2, 4.0], [-0.066601003, -0.085896903, 1.823476582]), ('hyperbolic kepler solver [1.0, 1.0]', [1.0, 1.0], None), ('hyperbolic kepler solver [5.0, 1.8]', [5.0, 1.8], [2.078164038, 1.937063662, 2.159827297])], [('hyperbolic kepler solver [10.0, 2.5]', [10.0, 2.5], [2.296335107, 1.790713502, 1.982313173]), ('hyperbolic kepler solver [-0.2, 4.0]', [-0.2, 4.0], [-0.066601003, -0.085896903, 1.823476582]), ('hyperbolic kepler solver [1.0, 1.0]', [1.0, 1.0], None), ('hyperbolic kepler solver [5.0, 1.8]', [5.0, 1.8], [2.078164038, 1.937063662, 2.159827297]), ('hyperbolic kepler solver [0.8, 10.0]', [0.8, 10.0], [0.088759344, 0.097984305, 1.670963748]), ('hyperbolic kepler solver [0.5, 1.2]', [0.5, 1.2], [1.097223034, 2.055391897, 2.55590711]), ('hyperbolic kepler solver [2.0, 1.5]', [2.0, 1.5], [1.61268581, 1.961096791, 2.300523983])], [('hyperbolic kepler solver [-3.0, 1.1]', [-3.0, 1.1], [-2.270719072, -2.617037695, 2.711892987]), ('hyperbolic kepler solver [0.8, 10.0]', [0.8, 10.0], [0.088759344, 0.097984305, 1.670963748]), ('hyperbolic kepler solver [0.5, 1.2]', [0.5, 1.2], [1.097223034, 2.055391897, 2.55590711]), ('hyperbolic kepler solver [2.0, 1.5]', [2.0, 1.5], [1.61268581, 1.961096791, 2.300523983]), ('hyperbolic kepler solver [10.0, 2.5]', [10.0, 2.5], [2.296335107, 1.790713502, 1.982313173]), ('hyperbolic kepler solver [0.0, 3.0]', [0.0, 3.0], [0.0, 0.0, 1.910633236]), ('hyperbolic kepler solver [50.0, 1.05]', [50.0, 1.05], [4.645312748, 2.825835675, 2.831748014])], [('hyperbolic kepler solver [0.0, 3.0]', [0.0, 3.0], [0.0, 0.0, 1.910633236]), ('hyperbolic kepler solver [10.0, 2.5]', [10.0, 2.5], [2.296335107, 1.790713502, 1.982313173]), ('hyperbolic kepler solver [-3.0, 1.1]', [-3.0, 1.1], [-2.270719072, -2.617037695, 2.711892987]), ('hyperbolic kepler solver [50.0, 1.05]', [50.0, 1.05], [4.645312748, 2.825835675, 2.831748014]), ('hyperbolic kepler solver [-0.2, 4.0]', [-0.2, 4.0], [-0.066601003, -0.085896903, 1.823476582]), ('hyperbolic kepler solver [1.0, 1.0]', [1.0, 1.0], None), ('hyperbolic kepler solver [5.0, 1.8]', [5.0, 1.8], [2.078164038, 1.937063662, 2.159827297])]]\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":"a8357803b1b87bfe65c837c2a0bafcf26bcc9f4e055ce049ad34e7648fd414e9","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    M,e=x\n    if e<=1: return None\n    H=math.asinh(M/e)\n    for _ in range(60):\n        d=(e*math.sinh(H)-H-M)/(e*math.cosh(H)-1)\n        H-=d\n        if abs(d)<1e-13: break\n    nu=2*math.atan(math.sqrt((e+1)/(e-1))*math.tanh(H/2))\n    return [round(H,9),round(nu,9),round(math.acos(1/e),9)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('hyperbolic kepler solver [0.5, 1.2]', [0.5, 1.2], [1.097223034, 2.055391897, 2.55590711]), ('hyperbolic kepler solver [2.0, 1.5]', [2.0, 1.5], [1.61268581, 1.961096791, 2.300523983]), ('hyperbolic kepler solver [10.0, 2.5]', [10.0, 2.5], [2.296335107, 1.790713502, 1.982313173]), ('hyperbolic kepler solver [-3.0, 1.1]', [-3.0, 1.1], [-2.270719072, -2.617037695, 2.711892987]), ('hyperbolic kepler solver [0.0, 3.0]', [0.0, 3.0], [0.0, 0.0, 1.910633236]), ('hyperbolic kepler solver [50.0, 1.05]', [50.0, 1.05], [4.645312748, 2.825835675, 2.831748014]), ('hyperbolic kepler solver [-0.2, 4.0]', [-0.2, 4.0], [-0.066601003, -0.085896903, 1.823476582])], [('hyperbolic kepler solver [2.0, 1.5]', [2.0, 1.5], [1.61268581, 1.961096791, 2.300523983]), ('hyperbolic kepler solver [-3.0, 1.1]', [-3.0, 1.1], [-2.270719072, -2.617037695, 2.711892987]), ('hyperbolic kepler solver [0.0, 3.0]', [0.0, 3.0], [0.0, 0.0, 1.910633236]), ('hyperbolic kepler solver [50.0, 1.05]', [50.0, 1.05], [4.645312748, 2.825835675, 2.831748014]), ('hyperbolic kepler solver [-0.2, 4.0]', [-0.2, 4.0], [-0.066601003, -0.085896903, 1.823476582]), ('hyperbolic kepler solver [1.0, 1.0]', [1.0, 1.0], None), ('hyperbolic kepler solver [5.0, 1.8]', [5.0, 1.8], [2.078164038, 1.937063662, 2.159827297])], [('hyperbolic kepler solver [10.0, 2.5]', [10.0, 2.5], [2.296335107, 1.790713502, 1.982313173]), ('hyperbolic kepler solver [-0.2, 4.0]', [-0.2, 4.0], [-0.066601003, -0.085896903, 1.823476582]), ('hyperbolic kepler solver [1.0, 1.0]', [1.0, 1.0], None), ('hyperbolic kepler solver [5.0, 1.8]', [5.0, 1.8], [2.078164038, 1.937063662, 2.159827297]), ('hyperbolic kepler solver [0.8, 10.0]', [0.8, 10.0], [0.088759344, 0.097984305, 1.670963748]), ('hyperbolic kepler solver [0.5, 1.2]', [0.5, 1.2], [1.097223034, 2.055391897, 2.55590711]), ('hyperbolic kepler solver [2.0, 1.5]', [2.0, 1.5], [1.61268581, 1.961096791, 2.300523983])], [('hyperbolic kepler solver [-3.0, 1.1]', [-3.0, 1.1], [-2.270719072, -2.617037695, 2.711892987]), ('hyperbolic kepler solver [0.8, 10.0]', [0.8, 10.0], [0.088759344, 0.097984305, 1.670963748]), ('hyperbolic kepler solver [0.5, 1.2]', [0.5, 1.2], [1.097223034, 2.055391897, 2.55590711]), ('hyperbolic kepler solver [2.0, 1.5]', [2.0, 1.5], [1.61268581, 1.961096791, 2.300523983]), ('hyperbolic kepler solver [10.0, 2.5]', [10.0, 2.5], [2.296335107, 1.790713502, 1.982313173]), ('hyperbolic kepler solver [0.0, 3.0]', [0.0, 3.0], [0.0, 0.0, 1.910633236]), ('hyperbolic kepler solver [50.0, 1.05]', [50.0, 1.05], [4.645312748, 2.825835675, 2.831748014])], [('hyperbolic kepler solver [0.0, 3.0]', [0.0, 3.0], [0.0, 0.0, 1.910633236]), ('hyperbolic kepler solver [10.0, 2.5]', [10.0, 2.5], [2.296335107, 1.790713502, 1.982313173]), ('hyperbolic kepler solver [-3.0, 1.1]', [-3.0, 1.1], [-2.270719072, -2.617037695, 2.711892987]), ('hyperbolic kepler solver [50.0, 1.05]', [50.0, 1.05], [4.645312748, 2.825835675, 2.831748014]), ('hyperbolic kepler solver [-0.2, 4.0]', [-0.2, 4.0], [-0.066601003, -0.085896903, 1.823476582]), ('hyperbolic kepler solver [1.0, 1.0]', [1.0, 1.0], None), ('hyperbolic kepler solver [5.0, 1.8]', [5.0, 1.8], [2.078164038, 1.937063662, 2.159827297])]]\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":"3882ba5d23cea8394af7ce18307113e24e9a467019cc7d905b486c8ecb4b9d5e","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    M,e=x\n    if e<=1: return None\n    H=math.asinh(M/e)\n    for _ in range(60):\n        d=(e*math.sinh(H)-H-M)/(e*math.cosh(H)-1)\n        H-=d\n        if abs(d)<1e-13: break\n    nu=2*math.atan(math.sqrt((e+1)/(e-1))*math.tanh(H/2))\n    return [round(H,9),round(nu,9),round(math.acos(-1/e),9)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('hyperbolic kepler solver [0.5, 1.2]', [0.5, 1.2], [1.097223034, 2.055391897, 2.55590711]), ('hyperbolic kepler solver [2.0, 1.5]', [2.0, 1.5], [1.61268581, 1.961096791, 2.300523983]), ('hyperbolic kepler solver [10.0, 2.5]', [10.0, 2.5], [2.296335107, 1.790713502, 1.982313173]), ('hyperbolic kepler solver [-3.0, 1.1]', [-3.0, 1.1], [-2.270719072, -2.617037695, 2.711892987]), ('hyperbolic kepler solver [0.0, 3.0]', [0.0, 3.0], [0.0, 0.0, 1.910633236]), ('hyperbolic kepler solver [50.0, 1.05]', [50.0, 1.05], [4.645312748, 2.825835675, 2.831748014]), ('hyperbolic kepler solver [-0.2, 4.0]', [-0.2, 4.0], [-0.066601003, -0.085896903, 1.823476582])], [('hyperbolic kepler solver [2.0, 1.5]', [2.0, 1.5], [1.61268581, 1.961096791, 2.300523983]), ('hyperbolic kepler solver [-3.0, 1.1]', [-3.0, 1.1], [-2.270719072, -2.617037695, 2.711892987]), ('hyperbolic kepler solver [0.0, 3.0]', [0.0, 3.0], [0.0, 0.0, 1.910633236]), ('hyperbolic kepler solver [50.0, 1.05]', [50.0, 1.05], [4.645312748, 2.825835675, 2.831748014]), ('hyperbolic kepler solver [-0.2, 4.0]', [-0.2, 4.0], [-0.066601003, -0.085896903, 1.823476582]), ('hyperbolic kepler solver [1.0, 1.0]', [1.0, 1.0], None), ('hyperbolic kepler solver [5.0, 1.8]', [5.0, 1.8], [2.078164038, 1.937063662, 2.159827297])], [('hyperbolic kepler solver [10.0, 2.5]', [10.0, 2.5], [2.296335107, 1.790713502, 1.982313173]), ('hyperbolic kepler solver [-0.2, 4.0]', [-0.2, 4.0], [-0.066601003, -0.085896903, 1.823476582]), ('hyperbolic kepler solver [1.0, 1.0]', [1.0, 1.0], None), ('hyperbolic kepler solver [5.0, 1.8]', [5.0, 1.8], [2.078164038, 1.937063662, 2.159827297]), ('hyperbolic kepler solver [0.8, 10.0]', [0.8, 10.0], [0.088759344, 0.097984305, 1.670963748]), ('hyperbolic kepler solver [0.5, 1.2]', [0.5, 1.2], [1.097223034, 2.055391897, 2.55590711]), ('hyperbolic kepler solver [2.0, 1.5]', [2.0, 1.5], [1.61268581, 1.961096791, 2.300523983])], [('hyperbolic kepler solver [-3.0, 1.1]', [-3.0, 1.1], [-2.270719072, -2.617037695, 2.711892987]), ('hyperbolic kepler solver [0.8, 10.0]', [0.8, 10.0], [0.088759344, 0.097984305, 1.670963748]), ('hyperbolic kepler solver [0.5, 1.2]', [0.5, 1.2], [1.097223034, 2.055391897, 2.55590711]), ('hyperbolic kepler solver [2.0, 1.5]', [2.0, 1.5], [1.61268581, 1.961096791, 2.300523983]), ('hyperbolic kepler solver [10.0, 2.5]', [10.0, 2.5], [2.296335107, 1.790713502, 1.982313173]), ('hyperbolic kepler solver [0.0, 3.0]', [0.0, 3.0], [0.0, 0.0, 1.910633236]), ('hyperbolic kepler solver [50.0, 1.05]', [50.0, 1.05], [4.645312748, 2.825835675, 2.831748014])], [('hyperbolic kepler solver [0.0, 3.0]', [0.0, 3.0], [0.0, 0.0, 1.910633236]), ('hyperbolic kepler solver [10.0, 2.5]', [10.0, 2.5], [2.296335107, 1.790713502, 1.982313173]), ('hyperbolic kepler solver [-3.0, 1.1]', [-3.0, 1.1], [-2.270719072, -2.617037695, 2.711892987]), ('hyperbolic kepler solver [50.0, 1.05]', [50.0, 1.05], [4.645312748, 2.825835675, 2.831748014]), ('hyperbolic kepler solver [-0.2, 4.0]', [-0.2, 4.0], [-0.066601003, -0.085896903, 1.823476582]), ('hyperbolic kepler solver [1.0, 1.0]', [1.0, 1.0], None), ('hyperbolic kepler solver [5.0, 1.8]', [5.0, 1.8], [2.078164038, 1.937063662, 2.159827297])]]\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":"A deterministic toy two-body model with stipulated constants and conventions; not flight dynamics software or a validated SGP4 implementation. 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-orbital_propagation-kepler_hyperbolic-asymptote-angle","generated_at":"2026-09-29T14:48:13.111757+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Orbit determination and mission planning chain many small conversions; one wrong branch or unit silently moves a spacecraft by kilometres.","repair":"Use acos(-1/e).","root_cause":"nu_inf is computed as acos(1/e).","sha256":"86667ef2276b505351cf239a1858a7121e5df2520590dfffed15250c82b23466","title":"Hyperbolic Kepler solver: Asymptote angle uses +1/e · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":39.46,"exit_code":1,"observations":[{"actual":[1.097223034,2.055391897,0.585685543],"check":"hyperbolic kepler solver [0.5, 1.2]","expected":[1.097223034,2.055391897,2.55590711],"passed":false},{"actual":[1.61268581,1.961096791,0.841068671],"check":"hyperbolic kepler solver [2.0, 1.5]","expected":[1.61268581,1.961096791,2.300523983],"passed":false},{"actual":[2.296335107,1.790713502,1.159279481],"check":"hyperbolic kepler solver [10.0, 2.5]","expected":[2.296335107,1.790713502,1.982313173],"passed":false},{"actual":[-2.270719072,-2.617037695,0.429699666],"check":"hyperbolic kepler solver [-3.0, 1.1]","expected":[-2.270719072,-2.617037695,2.711892987],"passed":false},{"actual":[0.0,0.0,1.230959417],"check":"hyperbolic kepler solver [0.0, 3.0]","expected":[0.0,0.0,1.910633236],"passed":false},{"actual":[4.645312748,2.825835675,0.30984464],"check":"hyperbolic kepler solver [50.0, 1.05]","expected":[4.645312748,2.825835675,2.831748014],"passed":false},{"actual":[-0.066601003,-0.085896903,1.318116072],"check":"hyperbolic kepler solver [-0.2, 4.0]","expected":[-0.066601003,-0.085896903,1.823476582],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"hyperbolic kepler solver [0.5, 1.2]\", \"actual\": [1.097223034, 2.055391897, 0.585685543], \"expected\": [1.097223034, 2.055391897, 2.55590711], \"passed\": false}, {\"check\": \"hyperbolic kepler solver [2.0, 1.5]\", \"actual\": [1.61268581, 1.961096791, 0.841068671], \"expected\": [1.61268581, 1.961096791, 2.300523983], \"passed\": false}, {\"check\": \"hyperbolic kepler solver [10.0, 2.5]\", \"actual\": [2.296335107, 1.790713502, 1.159279481], \"expected\": [2.296335107, 1.790713502, 1.982313173], \"passed\": false}, {\"check\": \"hyperbolic kepler solver [-3.0, 1.1]\", \"actual\": [-2.270719072, -2.617037695, 0.429699666], \"expected\": [-2.270719072, -2.617037695, 2.711892987], \"passed\": false}, {\"check\": \"hyperbolic kepler solver [0.0, 3.0]\", \"actual\": [0.0, 0.0, 1.230959417], \"expected\": [0.0, 0.0, 1.910633236], \"passed\": false}, {\"check\": \"hyperbolic kepler solver [50.0, 1.05]\", \"actual\": [4.645312748, 2.825835675, 0.30984464], \"expected\": [4.645312748, 2.825835675, 2.831748014], \"passed\": false}, {\"check\": \"hyperbolic kepler solver [-0.2, 4.0]\", \"actual\": [-0.066601003, -0.085896903, 1.318116072], \"expected\": [-0.066601003, -0.085896903, 1.823476582], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":39.642,"exit_code":1,"observations":[{"actual":[1.097223034,2.055391897,0.585685543],"check":"hyperbolic kepler solver [0.5, 1.2]","expected":[1.097223034,2.055391897,2.55590711],"passed":false},{"actual":[1.61268581,1.961096791,0.841068671],"check":"hyperbolic kepler solver [2.0, 1.5]","expected":[1.61268581,1.961096791,2.300523983],"passed":false},{"actual":[2.296335107,1.790713502,1.159279481],"check":"hyperbolic kepler solver [10.0, 2.5]","expected":[2.296335107,1.790713502,1.982313173],"passed":false},{"actual":[-2.270719072,-2.617037695,0.429699666],"check":"hyperbolic kepler solver [-3.0, 1.1]","expected":[-2.270719072,-2.617037695,2.711892987],"passed":false},{"actual":[0.0,0.0,1.230959417],"check":"hyperbolic kepler solver [0.0, 3.0]","expected":[0.0,0.0,1.910633236],"passed":false},{"actual":[4.645312748,2.825835675,0.30984464],"check":"hyperbolic kepler solver [50.0, 1.05]","expected":[4.645312748,2.825835675,2.831748014],"passed":false},{"actual":[-0.066601003,-0.085896903,1.318116072],"check":"hyperbolic kepler solver [-0.2, 4.0]","expected":[-0.066601003,-0.085896903,1.823476582],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"hyperbolic kepler solver [0.5, 1.2]\", \"actual\": [1.097223034, 2.055391897, 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