{"abstract":"The drive force is frozen at cos(0) and forced response is wrong.","category":"Physics integrator stability","checks":8,"contract":"solve(x0, v0, k, c, F, wf, dt, steps): unit mass x''=-k*x-c*v+F*cos(wf*t) with wf in rad/s, t starting at 0, integrated with classical RK4. Return [x, v, t] rounded to 6.","contract_signature":"x0, v0, k, c, F, wf, dt, steps","evaluation_group":"w2-physics_integrator_stability-forced-oscillator-rk4","failed_approach":"Advancing t before evaluating stage one shifts every stage by one step.","family":"w2-physics_integrator_stability-forced-oscillator-rk4-clock-advance","id":"FA-87021","implementations":{"attempt":{"sha256":"ec07809cfae632a3f432334348e28846296d9f3b57cf23a7b09fca1449e7e19c","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x0, v0, k, c, F, wf, dt, steps):\n    def f(t, x, v):\n        return v, -k * x - c * v + F * math.cos(wf * t)\n    t = 0.0\n    x, v = x0, v0\n    for _ in range(steps):\n        t = t + dt\n        k1x, k1v = f(t, x, v)\n        k2x, k2v = f(t + dt / 2, x + dt / 2 * k1x, v + dt / 2 * k1v)\n        k3x, k3v = f(t + dt / 2, x + dt / 2 * k2x, v + dt / 2 * k2v)\n        k4x, k4v = f(t + dt, x + dt * k3x, v + dt * k3v)\n        x = x + dt / 6 * (k1x + 2 * k2x + 2 * k3x + k4x)\n        v = v + dt / 6 * (k1v + 2 * k2v + 2 * k3v + k4v)\n    return [round(x, 6), round(v, 6), round(t, 6)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[[[0.844, 0.886, 19.018, 1.354, 1.974, 2.862, 0.2, 4], [-0.48866, -0.348254, 0.8]], [[-0.109, -0.682, 16.643, 0.151, 1.208, 3.199, 0.05, 3], [-0.171504, -0.13078, 0.15]], [[0.488, -0.59, 18.046, 0.065, 1.27, 1.284, 0.2, 3], [-0.348659, -0.553321, 0.6]], [[0.477, 0.804, 9.463, 0.795, 0.343, 4.866, 0.2, 1], [0.539279, -0.178827, 0.2]], [[0.594, 0.724, 5.574, 1.414, 0.54, 2.544, 0.2, 5], [0.050911, -1.000788, 1.0]], [[0.873, 0.152, 12.557, 0.098, 1.074, 1.939, 0.1, 6], [-0.290594, -2.488439, 0.6]], [[-0.015, 0.798, 18.348, 1.42, 1.862, 3.955, 0.05, 2], [0.067066, 0.815353, 0.1]], [[0.206, 0.096, 17.287, 0.284, 1.767, 2.847, 0.2, 1], [0.188435, -0.265686, 0.2]]], [[[-0.492, -0.144, 14.57, 1.424, 1.521, 1.605, 0.05, 3], [-0.421761, 1.012157, 0.15]], [[0.003, 0.395, 12.77, 0.296, 0.352, 4.733, 0.1, 2], [0.078731, 0.325617, 0.2]], [[-0.926, 0.952, 5.429, 0.55, 1.365, 4.948, 0.2, 1], [-0.633361, 1.884933, 0.2]], [[-0.534, 0.495, 13.551, 1.071, 1.879, 2.403, 0.1, 7], [0.467684, 0.332973, 0.7]], [[-0.435, -0.421, 0.535, 1.01, 1.434, 4.069, 0.2, 1], [-0.481308, -0.068347, 0.2]], [[-0.017, 0.68, 3.032, 0.837, 0.432, 2.962, 0.05, 8], [0.225745, 0.477143, 0.4]], [[0.35, 0.024, 2.459, 0.489, 1.678, 3.184, 0.2, 2], [0.401172, 0.137673, 0.4]], [[-0.032, 0.808, 18.227, 0.749, 0.437, 3.703, 0.1, 1], [0.04836, 0.775101, 0.1]]], [[[0.156, -0.808, 12.089, 0.635, 0.926, 3.013, 0.05, 7], [-0.092465, -0.474045, 0.35]], [[-0.743, 0.606, 18.791, 0.354, 1.009, 2.833, 0.1, 3], [-0.053531, 3.257429, 0.3]], [[-0.226, -0.701, 16.947, 0.853, 0.897, 1.169, 0.1, 3], [-0.195897, 0.805228, 0.3]], [[-0.571, 0.019, 10.668, 1.333, 0.813, 4.88, 0.1, 10], [0.238859, -0.217571, 1.0]], [[-0.262, -0.939, 2.411, 0.717, 1.809, 4.573, 0.2, 3], [-0.441532, -0.085208, 0.6]], [[0.395, -0.904, 16.019, 1.336, 1.807, 0.641, 0.1, 9], [-0.000556, 0.633994, 0.9]], [[-0.394, 0.849, 18.783, 1.27, 1.837, 1.788, 0.1, 10], [0.047492, -1.406422, 1.0]], [[-0.722, -0.414, 11.067, 1.242, 1.818, 2.28, 0.2, 2], [-0.248164, 2.157098, 0.4]]], [[[0.008, 0.621, 19.737, 0.731, 0.589, 2.671, 0.2, 10], [0.072111, -0.089781, 2.0]], [[-0.772, 0.752, 2.823, 0.497, 1.621, 2.92, 0.1, 6], [0.065151, 1.550767, 0.6]], [[-0.442, 0.797, 6.557, 1.401, 1.795, 3.756, 0.1, 9], [0.25065, -0.396817, 0.9]], [[-0.198, -0.028, 4.048, 0.079, 1.642, 1.588, 0.2, 8], [0.361524, -1.100738, 1.6]], [[-0.262, 0.32, 14.578, 0.644, 0.243, 3.924, 0.1, 3], [-0.039877, 0.966063, 0.3]], [[0.906, -0.658, 3.163, 1.453, 1.529, 3.675, 0.2, 7], [-0.365644, -0.533183, 1.4]], [[-0.83, 0.207, 3.417, 1.347, 0.61, 3.166, 0.1, 6], [-0.347709, 1.031334, 0.6]], [[-0.484, -0.908, 18.372, 0.481, 1.964, 2.315, 0.2, 2], [-0.051507, 2.343495, 0.4]]], [[[-0.341, 0.921, 14.484, 0.78, 0.993, 4.954, 0.1, 11], [-0.092121, -0.961694, 1.1]], [[-0.279, -0.59, 18.348, 0.337, 0.803, 4.86, 0.05, 13], [0.195004, 0.648818, 0.65]], [[0.163, 0.02, 4.507, 0.115, 0.982, 3.557, 0.1, 3], [0.175188, 0.032334, 0.3]], [[0.96, 0.368, 6.136, 0.868, 0.713, 4.277, 0.1, 13], [-0.632372, -0.226167, 1.3]], [[0.48, 0.991, 13.504, 0.938, 1.754, 1.99, 0.2, 8], [-0.112907, 0.598276, 1.6]], [[-0.235, 0.94, 18.166, 1.391, 0.342, 1.087, 0.1, 3], [0.096306, 0.958657, 0.3]], [[0.613, 0.575, 19.459, 1.488, 0.738, 4.191, 0.1, 1], [0.612276, -0.562497, 0.1]], [[-0.25, -0.588, 8.961, 0.399, 0.698, 2.615, 0.1, 5], [-0.152947, 0.804646, 0.5]]]]\nfor i, (args, expected) in enumerate(fixtures[N-1]):\n    check(\"case %d\" % i, 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":"72de12110af1ec5a71705f5103c526641be1e7dd78ff147cf0339aaa4ce81bb5","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x0, v0, k, c, F, wf, dt, steps):\n    def f(t, x, v):\n        return v, -k * x - c * v + F * math.cos(wf * t)\n    t = 0.0\n    x, v = x0, v0\n    for _ in range(steps):\n        k1x, k1v = f(t, x, v)\n        k2x, k2v = f(t + dt / 2, x + dt / 2 * k1x, v + dt / 2 * k1v)\n        k3x, k3v = f(t + dt / 2, x + dt / 2 * k2x, v + dt / 2 * k2v)\n        k4x, k4v = f(t + dt, x + dt * k3x, v + dt * k3v)\n        x = x + dt / 6 * (k1x + 2 * k2x + 2 * k3x + k4x)\n        v = v + dt / 6 * (k1v + 2 * k2v + 2 * k3v + k4v)\n    return [round(x, 6), round(v, 6), round(t, 6)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[[[0.844, 0.886, 19.018, 1.354, 1.974, 2.862, 0.2, 4], [-0.48866, -0.348254, 0.8]], [[-0.109, -0.682, 16.643, 0.151, 1.208, 3.199, 0.05, 3], [-0.171504, -0.13078, 0.15]], [[0.488, -0.59, 18.046, 0.065, 1.27, 1.284, 0.2, 3], [-0.348659, -0.553321, 0.6]], [[0.477, 0.804, 9.463, 0.795, 0.343, 4.866, 0.2, 1], [0.539279, -0.178827, 0.2]], [[0.594, 0.724, 5.574, 1.414, 0.54, 2.544, 0.2, 5], [0.050911, -1.000788, 1.0]], [[0.873, 0.152, 12.557, 0.098, 1.074, 1.939, 0.1, 6], [-0.290594, -2.488439, 0.6]], [[-0.015, 0.798, 18.348, 1.42, 1.862, 3.955, 0.05, 2], [0.067066, 0.815353, 0.1]], [[0.206, 0.096, 17.287, 0.284, 1.767, 2.847, 0.2, 1], [0.188435, -0.265686, 0.2]]], [[[-0.492, -0.144, 14.57, 1.424, 1.521, 1.605, 0.05, 3], [-0.421761, 1.012157, 0.15]], [[0.003, 0.395, 12.77, 0.296, 0.352, 4.733, 0.1, 2], [0.078731, 0.325617, 0.2]], [[-0.926, 0.952, 5.429, 0.55, 1.365, 4.948, 0.2, 1], [-0.633361, 1.884933, 0.2]], [[-0.534, 0.495, 13.551, 1.071, 1.879, 2.403, 0.1, 7], [0.467684, 0.332973, 0.7]], [[-0.435, -0.421, 0.535, 1.01, 1.434, 4.069, 0.2, 1], [-0.481308, -0.068347, 0.2]], [[-0.017, 0.68, 3.032, 0.837, 0.432, 2.962, 0.05, 8], [0.225745, 0.477143, 0.4]], [[0.35, 0.024, 2.459, 0.489, 1.678, 3.184, 0.2, 2], [0.401172, 0.137673, 0.4]], [[-0.032, 0.808, 18.227, 0.749, 0.437, 3.703, 0.1, 1], [0.04836, 0.775101, 0.1]]], [[[0.156, -0.808, 12.089, 0.635, 0.926, 3.013, 0.05, 7], [-0.092465, -0.474045, 0.35]], [[-0.743, 0.606, 18.791, 0.354, 1.009, 2.833, 0.1, 3], [-0.053531, 3.257429, 0.3]], [[-0.226, -0.701, 16.947, 0.853, 0.897, 1.169, 0.1, 3], [-0.195897, 0.805228, 0.3]], [[-0.571, 0.019, 10.668, 1.333, 0.813, 4.88, 0.1, 10], [0.238859, -0.217571, 1.0]], [[-0.262, -0.939, 2.411, 0.717, 1.809, 4.573, 0.2, 3], [-0.441532, -0.085208, 0.6]], [[0.395, -0.904, 16.019, 1.336, 1.807, 0.641, 0.1, 9], [-0.000556, 0.633994, 0.9]], [[-0.394, 0.849, 18.783, 1.27, 1.837, 1.788, 0.1, 10], [0.047492, -1.406422, 1.0]], [[-0.722, -0.414, 11.067, 1.242, 1.818, 2.28, 0.2, 2], [-0.248164, 2.157098, 0.4]]], [[[0.008, 0.621, 19.737, 0.731, 0.589, 2.671, 0.2, 10], [0.072111, -0.089781, 2.0]], [[-0.772, 0.752, 2.823, 0.497, 1.621, 2.92, 0.1, 6], [0.065151, 1.550767, 0.6]], [[-0.442, 0.797, 6.557, 1.401, 1.795, 3.756, 0.1, 9], [0.25065, -0.396817, 0.9]], [[-0.198, -0.028, 4.048, 0.079, 1.642, 1.588, 0.2, 8], [0.361524, -1.100738, 1.6]], [[-0.262, 0.32, 14.578, 0.644, 0.243, 3.924, 0.1, 3], [-0.039877, 0.966063, 0.3]], [[0.906, -0.658, 3.163, 1.453, 1.529, 3.675, 0.2, 7], [-0.365644, -0.533183, 1.4]], [[-0.83, 0.207, 3.417, 1.347, 0.61, 3.166, 0.1, 6], [-0.347709, 1.031334, 0.6]], [[-0.484, -0.908, 18.372, 0.481, 1.964, 2.315, 0.2, 2], [-0.051507, 2.343495, 0.4]]], [[[-0.341, 0.921, 14.484, 0.78, 0.993, 4.954, 0.1, 11], [-0.092121, -0.961694, 1.1]], [[-0.279, -0.59, 18.348, 0.337, 0.803, 4.86, 0.05, 13], [0.195004, 0.648818, 0.65]], [[0.163, 0.02, 4.507, 0.115, 0.982, 3.557, 0.1, 3], [0.175188, 0.032334, 0.3]], [[0.96, 0.368, 6.136, 0.868, 0.713, 4.277, 0.1, 13], [-0.632372, -0.226167, 1.3]], [[0.48, 0.991, 13.504, 0.938, 1.754, 1.99, 0.2, 8], [-0.112907, 0.598276, 1.6]], [[-0.235, 0.94, 18.166, 1.391, 0.342, 1.087, 0.1, 3], [0.096306, 0.958657, 0.3]], [[0.613, 0.575, 19.459, 1.488, 0.738, 4.191, 0.1, 1], [0.612276, -0.562497, 0.1]], [[-0.25, -0.588, 8.961, 0.399, 0.698, 2.615, 0.1, 5], [-0.152947, 0.804646, 0.5]]]]\nfor i, (args, expected) in enumerate(fixtures[N-1]):\n    check(\"case %d\" % i, 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 bounded teaching model with stipulated toy conventions and rounded float output; not a production physics engine or a proof of numerical stability. 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-physics_integrator_stability-forced-oscillator-rk4-clock-advance","generated_at":"2026-09-29T14:50:54.980409+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Game and robotics physics loops depend on integrator update order, step control and stabilization terms; a wrong decision point turns a stable simulation into drifting or exploding motion.","root_cause":"The t += dt statement is missing.","sha256":"50c983c563216cb2d71caf736a8551becbb94e5fa8ca0279cb5b77e048b54afc","title":"RK4 loop never advances the simulation clock · 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":41.578,"exit_code":1,"observations":[{"actual":[-0.572882,-0.330509,0.8],"check":"case 0","expected":[-0.48866,-0.348254,0.8],"passed":false},{"actual":[-0.172001,-0.139372,0.15],"check":"case 1","expected":[-0.171504,-0.13078,0.15],"passed":false},{"actual":[-0.362789,-0.595435,0.6],"check":"case 2","expected":[-0.348659,-0.553321,0.6],"passed":false},{"actual":[0.535051,-0.223909,0.2],"check":"case 3","expected":[0.539279,-0.178827,0.2],"passed":false},{"actual":[0.004201,-1.035609,1.0],"check":"case 4","expected":[0.050911,-1.000788,1.0],"passed":false},{"actual":[-0.303182,-2.532475,0.6],"check":"case 5","expected":[-0.290594,-2.488439,0.6],"passed":false},{"actual":[0.066669,0.805454,0.1],"check":"case 6","expected":[0.067066,0.815353,0.1],"passed":false},{"actual":[0.179915,-0.359568,0.2],"check":"case 7","expected":[0.188435,-0.265686,0.2],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"case 0\", \"actual\": [-0.572882, -0.330509, 0.8], \"expected\": [-0.48866, -0.348254, 0.8], \"passed\": false}, {\"check\": \"case 1\", \"actual\": [-0.172001, -0.139372, 0.15], \"expected\": [-0.171504, -0.13078, 0.15], \"passed\": false}, {\"check\": \"case 2\", \"actual\": [-0.362789, -0.595435, 0.6], \"expected\": [-0.348659, -0.553321, 0.6], \"passed\": false}, {\"check\": \"case 3\", \"actual\": [0.535051, -0.223909, 0.2], \"expected\": [0.539279, -0.178827, 0.2], \"passed\": false}, {\"check\": \"case 4\", \"actual\": [0.004201, -1.035609, 1.0], \"expected\": [0.050911, -1.000788, 1.0], \"passed\": false}, {\"check\": \"case 5\", \"actual\": [-0.303182, -2.532475, 0.6], \"expected\": [-0.290594, -2.488439, 0.6], \"passed\": false}, {\"check\": \"case 6\", \"actual\": [0.066669, 0.805454, 0.1], \"expected\": [0.067066, 0.815353, 0.1], \"passed\": false}, {\"check\": \"case 7\", \"actual\": [0.179915, -0.359568, 0.2], \"expected\": [0.188435, -0.265686, 0.2], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":42.024,"exit_code":1,"observations":[{"actual":[-0.371706,0.061267,0.0],"check":"case 0","expected":[-0.48866,-0.348254,0.8],"passed":false},{"actual":[-0.171296,-0.124801,0.0],"check":"case 1","expected":[-0.171504,-0.13078,0.15],"passed":false},{"actual":[-0.341068,-0.504592,0.0],"check":"case 2","expected":[-0.348659,-0.553321,0.6],"passed":false},{"actual":[0.539279,-0.178827,0.0],"check":"case 3","expected":[0.539279,-0.178827,0.2],"passed":false},{"actual":[0.120687,-0.789393,0.0],"check":"case 4","expected":[0.050911,-1.000788,1.0],"passed":false},{"actual":[-0.273667,-2.384462,0.0],"check":"case 5","expected":[-0.290594,-2.488439,0.6],"passed":false},{"actual":[0.06714,0.818834,0.0],"check":"case 6","expected":[0.067066,0.815353,0.1],"passed":false},{"actual":[0.188435,-0.265686,0.0],"check":"case 7","expected":[0.188435,-0.265686,0.2],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"case 0\", \"actual\": [-0.371706, 0.061267, 0.0], \"expected\": [-0.48866, -0.348254, 0.8], \"passed\": false}, {\"check\": \"case 1\", \"actual\": [-0.171296, -0.124801, 0.0], \"expected\": [-0.171504, -0.13078, 0.15], \"passed\": false}, {\"check\": \"case 2\", \"actual\": [-0.341068, -0.504592, 0.0], \"expected\": [-0.348659, -0.553321, 0.6], \"passed\": false}, {\"check\": \"case 3\", \"actual\": [0.539279, -0.178827, 0.0], \"expected\": [0.539279, -0.178827, 0.2], \"passed\": false}, {\"check\": \"case 4\", \"actual\": [0.120687, -0.789393, 0.0], \"expected\": [0.050911, -1.000788, 1.0], \"passed\": false}, {\"check\": \"case 5\", \"actual\": [-0.273667, -2.384462, 0.0], \"expected\": [-0.290594, -2.488439, 0.6], \"passed\": false}, {\"check\": \"case 6\", \"actual\": [0.06714, 0.818834, 0.0], \"expected\": [0.067066, 0.815353, 0.1], \"passed\": false}, {\"check\": \"case 7\", \"actual\": [0.188435, -0.265686, 0.0], \"expected\": [0.188435, -0.265686, 0.2], \"passed\": false}], \"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."}}