{"abstract":"Universal-variable propagation diverges on hyperbolic arcs.","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.","contract_signature":"x","evaluation_group":"w2-orbital_propagation-stumpff","failed_approach":"Dividing by z instead of -z flips it back negative.","family":"w2-orbital_propagation-stumpff-hyperbolic-c-sign","id":"FA-69616","implementations":{"attempt":{"sha256":"6d3728ad391830f0747fb86f1eed742e952fbc49a726cedbfeef88d44fd255af","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 -0.5', -0.5, [0.521183673, 0.1708832825]), ('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 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 -1e-07', -1e-07, [0.5000000042, 0.1666666675])], [('stumpff functions for universal variables -4.0', -4.0, [0.6905489228, 0.203357551]), ('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 -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 -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 -25.0', -25.0, [2.928397941, 0.5536256846]), ('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 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 -0.05', -0.05, [0.5020868087, 0.1670838297]), ('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 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 -3e-06', -3e-06, [0.500000125, 0.1666666917]), ('stumpff functions for universal variables 2e-06', 2e-06, [0.4999999167, 0.16666665]), ('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 1e-07', 1e-07, [0.4999999958, 0.1666666658]), ('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":"b0009c6c6cc9c5bc00eeb4c4689a3a766d586bf45fab765ef22e862074c1d5fc","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=(1-math.cosh(s))/(-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 -0.5', -0.5, [0.521183673, 0.1708832825]), ('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 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 -1e-07', -1e-07, [0.5000000042, 0.1666666675])], [('stumpff functions for universal variables -4.0', -4.0, [0.6905489228, 0.203357551]), ('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 -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 -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 -25.0', -25.0, [2.928397941, 0.5536256846]), ('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 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 -0.05', -0.05, [0.5020868087, 0.1670838297]), ('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 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 -3e-06', -3e-06, [0.500000125, 0.1666666917]), ('stumpff functions for universal variables 2e-06', 2e-06, [0.4999999167, 0.16666665]), ('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 1e-07', 1e-07, [0.4999999958, 0.1666666658]), ('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-hyperbolic-c-sign","generated_at":"2026-09-29T14:48:13.198188+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.","root_cause":"The hyperbolic branch computes (1-cosh s)/(-z).","sha256":"26340e80b282364dbcf0e787fb53c0fbb8c00a9e778264e6b135d18206ddf285","title":"Stumpff functions for universal variables: Hyperbolic C is negative · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":39.175,"exit_code":1,"observations":[{"actual":[-0.521183673,0.1708832825],"check":"stumpff functions for universal variables -0.5","expected":[0.521183673,0.1708832825],"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":[0.4999999958,0.1666666658],"check":"stumpff functions for universal variables 1e-07","expected":[0.4999999958,0.1666666658],"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}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"stumpff functions for universal variables -0.5\", \"actual\": [-0.521183673, 0.1708832825], \"expected\": [0.521183673, 0.1708832825], \"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 1e-07\", \"actual\": [0.4999999958, 0.1666666658], \"expected\": [0.4999999958, 0.1666666658], \"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}], \"passed\": false}\n"},"broken":{"elapsed_ms":38.428,"exit_code":1,"observations":[{"actual":[-0.521183673,0.1708832825],"check":"stumpff functions for universal variables -0.5","expected":[0.521183673,0.1708832825],"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":[0.4999999958,0.1666666658],"check":"stumpff functions for universal variables 1e-07","expected":[0.4999999958,0.1666666658],"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}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"stumpff functions for universal variables -0.5\", \"actual\": [-0.521183673, 0.1708832825], \"expected\": [0.521183673, 0.1708832825], \"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 1e-07\", \"actual\": [0.4999999958, 0.1666666658], \"expected\": [0.4999999958, 0.1666666658], \"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}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}