{"abstract":"Near-parabolic orbits get a slightly wrong C.","category":"Orbital propagation","checks":7,"contract":"Input z. For z>1e-6: C=(1-cos s)/z, S=(s-sin s)/s^3 with s=sqrt z; for z<-1e-6: C=(cosh s-1)/(-z), S=(sinh s-s)/s^3 with s=sqrt(-z); otherwise series C=1/2-z/24+z^2/720, S=1/6-z/120+z^2/5040. Return [C,S] rounded to 10.","evaluation_group":"w2-orbital_propagation-stumpff","failed_approach":"Using z/12 changes the curvature coefficient.","family":"w2-orbital_propagation-stumpff-series-sign","id":"FA-69631","implementations":{"attempt":{"sha256":"1b7258ac888de2553ff0406cab9e07251c6e3d1c549ef717c9ab3a0deda3af88","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    z=x\n    if z>1e-6:\n        s=math.sqrt(z)\n        c=(1-math.cos(s))/z; S=(s-math.sin(s))/s**3\n    elif z<-1e-6:\n        s=math.sqrt(-z)\n        c=(math.cosh(s)-1)/(-z); S=(math.sinh(s)-s)/s**3\n    else:\n        c=1/2-z/12+z*z/720; S=1/6-z/120+z*z/5040\n    return [round(c,10),round(S,10)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('stumpff functions for universal variables 1e-07', 1e-07, [0.4999999958, 0.1666666658]), ('stumpff functions for universal variables 4.0', 4.0, [0.3540367091, 0.1363378216]), ('stumpff functions for universal variables 0.5', 0.5, [0.4795108058, 0.1625492603]), ('stumpff functions for universal variables 30.0', 30.0, [0.0102526963, 0.0377242152]), ('stumpff functions for universal variables 0.0', 0.0, [0.5, 0.1666666667]), ('stumpff functions for universal variables -1e-07', -1e-07, [0.5000000042, 0.1666666675]), ('stumpff functions for universal variables -0.5', -0.5, [0.521183673, 0.1708832825])], [('stumpff functions for universal variables -1e-07', -1e-07, [0.5000000042, 0.1666666675]), ('stumpff functions for universal variables 1e-07', 1e-07, [0.4999999958, 0.1666666658]), ('stumpff functions for universal variables 0.0', 0.0, [0.5, 0.1666666667]), ('stumpff functions for universal variables -0.5', -0.5, [0.521183673, 0.1708832825]), ('stumpff functions for universal variables -4.0', -4.0, [0.6905489228, 0.203357551]), ('stumpff functions for universal variables -25.0', -25.0, [2.928397941, 0.5536256846]), ('stumpff functions for universal variables 9.8696', 9.8696, [0.2026424576, 0.1013212062])], [('stumpff functions for universal variables 1e-07', 1e-07, [0.4999999958, 0.1666666658]), ('stumpff functions for universal variables -0.5', -0.5, [0.521183673, 0.1708832825]), ('stumpff functions for universal variables -4.0', -4.0, [0.6905489228, 0.203357551]), ('stumpff functions for universal variables -25.0', -25.0, [2.928397941, 0.5536256846]), ('stumpff functions for universal variables 9.8696', 9.8696, [0.2026424576, 0.1013212062]), ('stumpff functions for universal variables 0.05', 0.05, [0.4979201358, 0.1662504957]), ('stumpff functions for universal variables -0.05', -0.05, [0.5020868087, 0.1670838297])], [('stumpff functions for universal variables -1e-07', -1e-07, [0.5000000042, 0.1666666675]), ('stumpff functions for universal variables 9.8696', 9.8696, [0.2026424576, 0.1013212062]), ('stumpff functions for universal variables 0.05', 0.05, [0.4979201358, 0.1662504957]), ('stumpff functions for universal variables -0.05', -0.05, [0.5020868087, 0.1670838297]), ('stumpff functions for universal variables 2e-06', 2e-06, [0.4999999167, 0.16666665]), ('stumpff functions for universal variables -3e-06', -3e-06, [0.500000125, 0.1666666917]), ('stumpff functions for universal variables 4.0', 4.0, [0.3540367091, 0.1363378216])], [('stumpff functions for universal variables 1e-07', 1e-07, [0.4999999958, 0.1666666658]), ('stumpff functions for universal variables 2e-06', 2e-06, [0.4999999167, 0.16666665]), ('stumpff functions for universal variables -3e-06', -3e-06, [0.500000125, 0.1666666917]), ('stumpff functions for universal variables 4.0', 4.0, [0.3540367091, 0.1363378216]), ('stumpff functions for universal variables 0.5', 0.5, [0.4795108058, 0.1625492603]), ('stumpff functions for universal variables 30.0', 30.0, [0.0102526963, 0.0377242152]), ('stumpff functions for universal variables 0.0', 0.0, [0.5, 0.1666666667])]]\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":"fb4c97fd11191003d3727f380a6067cc6245a186265faf4c0ba3ad0942e7e901","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    z=x\n    if z>1e-6:\n        s=math.sqrt(z)\n        c=(1-math.cos(s))/z; S=(s-math.sin(s))/s**3\n    elif z<-1e-6:\n        s=math.sqrt(-z)\n        c=(math.cosh(s)-1)/(-z); S=(math.sinh(s)-s)/s**3\n    else:\n        c=1/2+z/24+z*z/720; S=1/6-z/120+z*z/5040\n    return [round(c,10),round(S,10)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('stumpff functions for universal variables 1e-07', 1e-07, [0.4999999958, 0.1666666658]), ('stumpff functions for universal variables 4.0', 4.0, [0.3540367091, 0.1363378216]), ('stumpff functions for universal variables 0.5', 0.5, [0.4795108058, 0.1625492603]), ('stumpff functions for universal variables 30.0', 30.0, [0.0102526963, 0.0377242152]), ('stumpff functions for universal variables 0.0', 0.0, [0.5, 0.1666666667]), ('stumpff functions for universal variables -1e-07', -1e-07, [0.5000000042, 0.1666666675]), ('stumpff functions for universal variables -0.5', -0.5, [0.521183673, 0.1708832825])], [('stumpff functions for universal variables -1e-07', -1e-07, [0.5000000042, 0.1666666675]), ('stumpff functions for universal variables 1e-07', 1e-07, [0.4999999958, 0.1666666658]), ('stumpff functions for universal variables 0.0', 0.0, [0.5, 0.1666666667]), ('stumpff functions for universal variables -0.5', -0.5, [0.521183673, 0.1708832825]), ('stumpff functions for universal variables -4.0', -4.0, [0.6905489228, 0.203357551]), ('stumpff functions for universal variables -25.0', -25.0, [2.928397941, 0.5536256846]), ('stumpff functions for universal variables 9.8696', 9.8696, [0.2026424576, 0.1013212062])], [('stumpff functions for universal variables 1e-07', 1e-07, [0.4999999958, 0.1666666658]), ('stumpff functions for universal variables -0.5', -0.5, [0.521183673, 0.1708832825]), ('stumpff functions for universal variables -4.0', -4.0, [0.6905489228, 0.203357551]), ('stumpff functions for universal variables -25.0', -25.0, [2.928397941, 0.5536256846]), ('stumpff functions for universal variables 9.8696', 9.8696, [0.2026424576, 0.1013212062]), ('stumpff functions for universal variables 0.05', 0.05, [0.4979201358, 0.1662504957]), ('stumpff functions for universal variables -0.05', -0.05, [0.5020868087, 0.1670838297])], [('stumpff functions for universal variables -1e-07', -1e-07, [0.5000000042, 0.1666666675]), ('stumpff functions for universal variables 9.8696', 9.8696, [0.2026424576, 0.1013212062]), ('stumpff functions for universal variables 0.05', 0.05, [0.4979201358, 0.1662504957]), ('stumpff functions for universal variables -0.05', -0.05, [0.5020868087, 0.1670838297]), ('stumpff functions for universal variables 2e-06', 2e-06, [0.4999999167, 0.16666665]), ('stumpff functions for universal variables -3e-06', -3e-06, [0.500000125, 0.1666666917]), ('stumpff functions for universal variables 4.0', 4.0, [0.3540367091, 0.1363378216])], [('stumpff functions for universal variables 1e-07', 1e-07, [0.4999999958, 0.1666666658]), ('stumpff functions for universal variables 2e-06', 2e-06, [0.4999999167, 0.16666665]), ('stumpff functions for universal variables -3e-06', -3e-06, [0.500000125, 0.1666666917]), ('stumpff functions for universal variables 4.0', 4.0, [0.3540367091, 0.1363378216]), ('stumpff functions for universal variables 0.5', 0.5, [0.4795108058, 0.1625492603]), ('stumpff functions for universal variables 30.0', 30.0, [0.0102526963, 0.0377242152]), ('stumpff functions for universal variables 0.0', 0.0, [0.5, 0.1666666667])]]\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":"df2e6e846f1f133e3dcaf4ac9abb41d686782a2c0fbbda1863fe6f4c1f23e437","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    z=x\n    if z>1e-6:\n        s=math.sqrt(z)\n        c=(1-math.cos(s))/z; S=(s-math.sin(s))/s**3\n    elif z<-1e-6:\n        s=math.sqrt(-z)\n        c=(math.cosh(s)-1)/(-z); S=(math.sinh(s)-s)/s**3\n    else:\n        c=1/2-z/24+z*z/720; S=1/6-z/120+z*z/5040\n    return [round(c,10),round(S,10)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('stumpff functions for universal variables 1e-07', 1e-07, [0.4999999958, 0.1666666658]), ('stumpff functions for universal variables 4.0', 4.0, [0.3540367091, 0.1363378216]), ('stumpff functions for universal variables 0.5', 0.5, [0.4795108058, 0.1625492603]), ('stumpff functions for universal variables 30.0', 30.0, [0.0102526963, 0.0377242152]), ('stumpff functions for universal variables 0.0', 0.0, [0.5, 0.1666666667]), ('stumpff functions for universal variables -1e-07', -1e-07, [0.5000000042, 0.1666666675]), ('stumpff functions for universal variables -0.5', -0.5, [0.521183673, 0.1708832825])], [('stumpff functions for universal variables -1e-07', -1e-07, [0.5000000042, 0.1666666675]), ('stumpff functions for universal variables 1e-07', 1e-07, [0.4999999958, 0.1666666658]), ('stumpff functions for universal variables 0.0', 0.0, [0.5, 0.1666666667]), ('stumpff functions for universal variables -0.5', -0.5, [0.521183673, 0.1708832825]), ('stumpff functions for universal variables -4.0', -4.0, [0.6905489228, 0.203357551]), ('stumpff functions for universal variables -25.0', -25.0, [2.928397941, 0.5536256846]), ('stumpff functions for universal variables 9.8696', 9.8696, [0.2026424576, 0.1013212062])], [('stumpff functions for universal variables 1e-07', 1e-07, [0.4999999958, 0.1666666658]), ('stumpff functions for universal variables -0.5', -0.5, [0.521183673, 0.1708832825]), ('stumpff functions for universal variables -4.0', -4.0, [0.6905489228, 0.203357551]), ('stumpff functions for universal variables -25.0', -25.0, [2.928397941, 0.5536256846]), ('stumpff functions for universal variables 9.8696', 9.8696, [0.2026424576, 0.1013212062]), ('stumpff functions for universal variables 0.05', 0.05, [0.4979201358, 0.1662504957]), ('stumpff functions for universal variables -0.05', -0.05, [0.5020868087, 0.1670838297])], [('stumpff functions for universal variables -1e-07', -1e-07, [0.5000000042, 0.1666666675]), ('stumpff functions for universal variables 9.8696', 9.8696, [0.2026424576, 0.1013212062]), ('stumpff functions for universal variables 0.05', 0.05, [0.4979201358, 0.1662504957]), ('stumpff functions for universal variables -0.05', -0.05, [0.5020868087, 0.1670838297]), ('stumpff functions for universal variables 2e-06', 2e-06, [0.4999999167, 0.16666665]), ('stumpff functions for universal variables -3e-06', -3e-06, [0.500000125, 0.1666666917]), ('stumpff functions for universal variables 4.0', 4.0, [0.3540367091, 0.1363378216])], [('stumpff functions for universal variables 1e-07', 1e-07, [0.4999999958, 0.1666666658]), ('stumpff functions for universal variables 2e-06', 2e-06, [0.4999999167, 0.16666665]), ('stumpff functions for universal variables -3e-06', -3e-06, [0.500000125, 0.1666666917]), ('stumpff functions for universal variables 4.0', 4.0, [0.3540367091, 0.1363378216]), ('stumpff functions for universal variables 0.5', 0.5, [0.4795108058, 0.1625492603]), ('stumpff functions for universal variables 30.0', 30.0, [0.0102526963, 0.0377242152]), ('stumpff functions for universal variables 0.0', 0.0, [0.5, 0.1666666667])]]\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-stumpff-series-sign","generated_at":"2026-09-29T14:48:13.222339+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 1/2 - z/24 + z^2/720.","root_cause":"The series is 1/2+z/24.","sha256":"64cb1266b11846be51557f884ae6ece6b183aa8cabfe357fa6ac270bd427a095","title":"Stumpff functions for universal variables: Near-zero C series has the wrong linear sign · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":43.87,"exit_code":1,"observations":[{"actual":[0.4999999917,0.1666666658],"check":"stumpff functions for universal variables 1e-07","expected":[0.4999999958,0.1666666658],"passed":false},{"actual":[0.3540367091,0.1363378216],"check":"stumpff functions for universal variables 4.0","expected":[0.3540367091,0.1363378216],"passed":true},{"actual":[0.4795108058,0.1625492603],"check":"stumpff functions for universal variables 0.5","expected":[0.4795108058,0.1625492603],"passed":true},{"actual":[0.0102526963,0.0377242152],"check":"stumpff functions for universal variables 30.0","expected":[0.0102526963,0.0377242152],"passed":true},{"actual":[0.5,0.1666666667],"check":"stumpff functions for universal variables 0.0","expected":[0.5,0.1666666667],"passed":true},{"actual":[0.5000000083,0.1666666675],"check":"stumpff functions for universal variables -1e-07","expected":[0.5000000042,0.1666666675],"passed":false},{"actual":[0.521183673,0.1708832825],"check":"stumpff functions for universal variables -0.5","expected":[0.521183673,0.1708832825],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"stumpff functions for universal variables 1e-07\", \"actual\": [0.4999999917, 0.1666666658], \"expected\": [0.4999999958, 0.1666666658], \"passed\": false}, {\"check\": \"stumpff functions for universal variables 4.0\", \"actual\": [0.3540367091, 0.1363378216], \"expected\": [0.3540367091, 0.1363378216], \"passed\": true}, {\"check\": \"stumpff functions for universal variables 0.5\", \"actual\": [0.4795108058, 0.1625492603], \"expected\": [0.4795108058, 0.1625492603], \"passed\": true}, {\"check\": \"stumpff functions for universal variables 30.0\", \"actual\": [0.0102526963, 0.0377242152], \"expected\": [0.0102526963, 0.0377242152], \"passed\": true}, {\"check\": \"stumpff functions for universal variables 0.0\", \"actual\": [0.5, 0.1666666667], \"expected\": [0.5, 0.1666666667], \"passed\": true}, {\"check\": \"stumpff functions for universal variables -1e-07\", \"actual\": [0.5000000083, 0.1666666675], \"expected\": [0.5000000042, 0.1666666675], \"passed\": false}, {\"check\": \"stumpff functions for universal variables -0.5\", \"actual\": [0.521183673, 0.1708832825], \"expected\": [0.521183673, 0.1708832825], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":37.907,"exit_code":1,"observations":[{"actual":[0.5000000042,0.1666666658],"check":"stumpff functions for universal variables 1e-07","expected":[0.4999999958,0.1666666658],"passed":false},{"actual":[0.3540367091,0.1363378216],"check":"stumpff functions for universal variables 4.0","expected":[0.3540367091,0.1363378216],"passed":true},{"actual":[0.4795108058,0.1625492603],"check":"stumpff functions for universal variables 0.5","expected":[0.4795108058,0.1625492603],"passed":true},{"actual":[0.0102526963,0.0377242152],"check":"stumpff functions for universal variables 30.0","expected":[0.0102526963,0.0377242152],"passed":true},{"actual":[0.5,0.1666666667],"check":"stumpff functions for universal variables 0.0","expected":[0.5,0.1666666667],"passed":true},{"actual":[0.4999999958,0.1666666675],"check":"stumpff functions for universal variables -1e-07","expected":[0.5000000042,0.1666666675],"passed":false},{"actual":[0.521183673,0.1708832825],"check":"stumpff functions for universal variables -0.5","expected":[0.521183673,0.1708832825],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"stumpff functions for universal variables 1e-07\", \"actual\": [0.5000000042, 0.1666666658], \"expected\": [0.4999999958, 0.1666666658], \"passed\": false}, {\"check\": \"stumpff functions for universal variables 4.0\", \"actual\": [0.3540367091, 0.1363378216], \"expected\": [0.3540367091, 0.1363378216], \"passed\": true}, {\"check\": \"stumpff functions for universal variables 0.5\", \"actual\": [0.4795108058, 0.1625492603], \"expected\": [0.4795108058, 0.1625492603], \"passed\": true}, {\"check\": \"stumpff functions for universal variables 30.0\", \"actual\": [0.0102526963, 0.0377242152], \"expected\": [0.0102526963, 0.0377242152], \"passed\": true}, {\"check\": \"stumpff functions for universal variables 0.0\", \"actual\": [0.5, 0.1666666667], \"expected\": [0.5, 0.1666666667], \"passed\": true}, {\"check\": \"stumpff functions for universal variables -1e-07\", \"actual\": [0.4999999958, 0.1666666675], \"expected\": [0.5000000042, 0.1666666675], \"passed\": false}, {\"check\": \"stumpff functions for universal variables -0.5\", \"actual\": [0.521183673, 0.1708832825], \"expected\": [0.521183673, 0.1708832825], \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":39.923,"exit_code":0,"observations":[{"actual":[0.4999999958,0.1666666658],"check":"stumpff functions for universal variables 1e-07","expected":[0.4999999958,0.1666666658],"passed":true},{"actual":[0.3540367091,0.1363378216],"check":"stumpff functions for universal variables 4.0","expected":[0.3540367091,0.1363378216],"passed":true},{"actual":[0.4795108058,0.1625492603],"check":"stumpff functions for universal variables 0.5","expected":[0.4795108058,0.1625492603],"passed":true},{"actual":[0.0102526963,0.0377242152],"check":"stumpff functions for universal variables 30.0","expected":[0.0102526963,0.0377242152],"passed":true},{"actual":[0.5,0.1666666667],"check":"stumpff functions for universal variables 0.0","expected":[0.5,0.1666666667],"passed":true},{"actual":[0.5000000042,0.1666666675],"check":"stumpff functions for universal variables -1e-07","expected":[0.5000000042,0.1666666675],"passed":true},{"actual":[0.521183673,0.1708832825],"check":"stumpff functions for universal variables -0.5","expected":[0.521183673,0.1708832825],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"stumpff functions for universal variables 1e-07\", \"actual\": [0.4999999958, 0.1666666658], \"expected\": [0.4999999958, 0.1666666658], \"passed\": true}, {\"check\": \"stumpff functions for universal variables 4.0\", \"actual\": [0.3540367091, 0.1363378216], \"expected\": [0.3540367091, 0.1363378216], \"passed\": true}, {\"check\": \"stumpff functions for universal variables 0.5\", \"actual\": [0.4795108058, 0.1625492603], \"expected\": [0.4795108058, 0.1625492603], \"passed\": true}, {\"check\": \"stumpff functions for universal variables 30.0\", \"actual\": [0.0102526963, 0.0377242152], \"expected\": [0.0102526963, 0.0377242152], \"passed\": true}, {\"check\": \"stumpff functions for universal variables 0.0\", \"actual\": [0.5, 0.1666666667], \"expected\": [0.5, 0.1666666667], \"passed\": true}, {\"check\": \"stumpff functions for universal variables -1e-07\", \"actual\": [0.5000000042, 0.1666666675], \"expected\": [0.5000000042, 0.1666666675], \"passed\": true}, {\"check\": \"stumpff functions for universal variables -0.5\", \"actual\": [0.521183673, 0.1708832825], \"expected\": [0.521183673, 0.1708832825], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}