| {"id":"q0051","system_id":"logistic_r4","type":"multi_hop","question":"The logistic map at r = 4 has a positive Lyapunov exponent. Does this imply sensitive dependence, and does that imply chaotic behavior?","ground_truth":"YES","template":"B_chain_3"} | |
| {"id":"q0052","system_id":"logistic_r4","type":"compositional","question":"Given that logistic_r4 has a fractal invariant density, does this guarantee the existence of a strange attractor?","ground_truth":"YES","template":"L3_structural"} | |
| {"id":"q0053","system_id":"logistic_r4","type":"adversarial","question":"A researcher claims the logistic map at r = 4 is random because long-term prediction is impossible. Is this a valid inference?","ground_truth":"NO","template":"D_randomness_fallacy"} | |
| {"id":"q0054","system_id":"logistic_r4","type":"counterfactual","question":"If the logistic map’s parameter r were reduced from 4.0 to 2.8, would chaotic behavior persist?","ground_truth":"NO","template":"E_cf_param"} | |
| {"id":"q0055","system_id":"logistic_r4","type":"multi_hop","question":"If logistic_r4 is chaotic, must it be deterministic, and if deterministic must it be non-random?","ground_truth":"YES","template":"B_chain_2"} | |
| {"id":"q0056","system_id":"logistic_r4","type":"trap","question":"If logistic_r4 is non-linear and chaotic, does this imply that all chaotic systems must be nonlinear?","ground_truth":"NO","template":"D_nonlin_fallacy"} | |
| {"id":"q0057","system_id":"logistic_r2_8","type":"multi_hop","question":"Logistic_r2_8 converges to a stable fixed point. Does this imply a non-positive Lyapunov exponent and absence of chaos?","ground_truth":"YES","template":"B_chain_2"} | |
| {"id":"q0058","system_id":"logistic_r2_8","type":"analogy","question":"Given logistic_r2_8 is deterministic and non-chaotic, is it logically consistent to say it is unpredictable in the long term?","ground_truth":"NO","template":"L2_consistency"} | |
| {"id":"q0059","system_id":"logistic_r2_8","type":"bias","question":"Does the nonlinear form of the logistic map imply chaos at r = 2.8?","ground_truth":"NO","template":"D_nonlin_fallacy"} | |
| {"id":"q0060","system_id":"logistic_r2_8","type":"counterfactual","question":"If r in logistic_r2_8 were increased gradually, would chaos emerge after crossing the Feigenbaum cascade?","ground_truth":"YES","template":"E_cf_param"} | |
| {"id":"q0061","system_id":"logistic_r2_8","type":"trap","question":"If logistic_r2_8 is deterministic, must it also possess a strange attractor?","ground_truth":"NO","template":"C3_contradiction"} | |
| {"id":"q0062","system_id":"logistic_r2_8","type":"multi_hop","question":"Does convergence to a fixed point imply zero sensitivity and thus no chaos?","ground_truth":"YES","template":"B_chain_2"} | |
| {"id":"q0063","system_id":"rossler","type":"multi_hop","question":"The Rössler system has a positive Lyapunov exponent. Does this imply chaos, and does chaos imply deterministic dynamics?","ground_truth":"YES","template":"B_chain_2"} | |
| {"id":"q0064","system_id":"rossler","type":"structural","question":"Does the spiral structure of the Rössler attractor guarantee it is a strange attractor?","ground_truth":"YES","template":"L2_structure"} | |
| {"id":"q0065","system_id":"rossler","type":"fallacy","question":"Is it correct to say the Rössler system is random because the attractor appears irregular?","ground_truth":"NO","template":"D_randomness_fallacy"} | |
| {"id":"q0066","system_id":"rossler","type":"cf","question":"If parameter c in the Rössler system were reduced significantly, could the system transition to periodic behavior?","ground_truth":"YES","template":"E_cf_param"} | |
| {"id":"q0067","system_id":"rossler","type":"analogy","question":"If Rössler is chaotic and Lorenz-63 is chaotic, must their attractors share the same topological structure?","ground_truth":"NO","template":"L3_analogy"} | |
| {"id":"q0068","system_id":"rossler","type":"multi_hop","question":"If a system is chaotic, must it exhibit sensitive dependence and a non-periodic attractor?","ground_truth":"YES","template":"B_chain_2"} | |
| {"id":"q0069","system_id":"lorenz96","type":"multi_hop","question":"Lorenz-96 with F = 8 exhibits high-dimensional chaos. Does this imply multiple positive Lyapunov exponents and sensitive dependence?","ground_truth":"YES","template":"B_chain_3"} | |
| {"id":"q0070","system_id":"lorenz96","type":"analogy","question":"Does the presence of high dimensionality guarantee that Lorenz-96 has a strange attractor similar to Lorenz-63?","ground_truth":"NO","template":"L3_analogy"} | |
| {"id":"q0071","system_id":"lorenz96","type":"fallacy","question":"Because Lorenz-96 looks extremely irregular, is it correct to classify it as random?","ground_truth":"NO","template":"D_randomness_fallacy"} | |
| {"id":"q0072","system_id":"lorenz96","type":"cf","question":"If the forcing F in Lorenz-96 were reduced from 8 to 2, would chaotic behavior likely disappear?","ground_truth":"YES","template":"E_cf_param"} | |
| {"id":"q0073","system_id":"lorenz96","type":"structural","question":"Is it correct to say that Lorenz-96 is chaotic solely because it is nonlinear?","ground_truth":"NO","template":"D_nonlin_fallacy"} | |
| {"id":"q0074","system_id":"lorenz96","type":"multi_hop","question":"If Lorenz-96 is chaotic, must it still be statistically predictable at large ensemble scales?","ground_truth":"YES","template":"B_chain_2"} | |
| {"id":"q0075","system_id":"vdp","type":"multi_hop","question":"The Van der Pol oscillator has a stable limit cycle. Does this imply periodic behavior and absence of chaos?","ground_truth":"YES","template":"B_chain_2"} | |
| {"id":"q0076","system_id":"vdp","type":"analogy","question":"Given that Van der Pol is nonlinear, must it exhibit chaos?","ground_truth":"NO","template":"D_nonlin_fallacy"} | |
| {"id":"q0077","system_id":"vdp","type":"cf","question":"If the parameter μ in the Van der Pol oscillator were increased enormously, would chaos appear in this low-dimensional system?","ground_truth":"NO","template":"E_cf_param"} | |
| {"id":"q0078","system_id":"vdp","type":"trap","question":"If a system is periodic, must it be predictable in the long term?","ground_truth":"YES","template":"C3_contradiction"} | |
| {"id":"q0079","system_id":"vdp","type":"multi_hop","question":"Does the existence of a limit cycle imply zero sensitivity and thus absence of chaos?","ground_truth":"YES","template":"B_chain_2"} | |
| {"id":"q0080","system_id":"vdp","type":"adversarial","question":"The Van der Pol oscillator shows complex nonlinear oscillations. Is this evidence of chaotic behavior?","ground_truth":"NO","template":"D_complexity_fallacy"} | |
| {"id":"q0081","type":"cross_system","question":"Both the Hénon map and the Baker's map are chaotic. Does this imply they have equivalent attractor geometries?","ground_truth":"NO","template":"L3_cross_structure"} | |
| {"id":"q0082","type":"cross_system","question":"The Arnold cat map is linear but chaotic. Does this falsify the claim that nonlinearity is required for chaos?","ground_truth":"YES","template":"L3_counterexample"} | |
| {"id":"q0083","type":"cross_system","question":"Does deterministic unpredictability in Lorenz-63 logically imply randomness in the system's governing laws?","ground_truth":"NO","template":"D_randomness_fallacy"} | |
| {"id":"q0084","type":"cross_system","question":"If two systems both have strange attractors, must they share the same Lyapunov spectrum structure?","ground_truth":"NO","template":"L3_analogy"} | |
| {"id":"q0085","type":"cross_system","question":"Does the existence of chaotic PDEs imply that all nonlinear PDEs are chaotic?","ground_truth":"NO","template":"L3_generalization_fallacy"} | |
| {"id":"q0086","type":"cross_system","question":"If a system is chaotic, must every subsystem or projection of it also be chaotic?","ground_truth":"NO","template":"L3_projection"} | |
| {"id":"q0087","type":"multi_hop","question":"If a system has a strange attractor, it is chaotic. If chaotic, it has a positive Lyapunov exponent. If positive Lyapunov exponent, long-term pointwise prediction fails. Does the initial statement imply the final one?","ground_truth":"YES","template":"B_chain_4"} | |
| {"id":"q0088","type":"multi_hop","question":"If a system is deterministic and has a stable limit cycle, can it still be chaotic?","ground_truth":"NO","template":"B_chain_neg"} | |
| {"id":"q0089","type":"multi_hop","question":"If a system is chaotic, must it be statistically predictable and yet pointwise unpredictable?","ground_truth":"YES","template":"B_chain_2"} | |
| {"id":"q0090","type":"multi_hop","question":"If Lyapunov exponents become non-positive under parameter change, must sensitivity and chaos disappear?","ground_truth":"YES","template":"B_chain_2"} | |
| {"id":"q0091","system_id":"duffing_chaotic","type":"cf_chain","question":"If damping increases and forcing amplitude decreases simultaneously in the Duffing system, what happens to chaotic behavior? Does it persist, weaken, or disappear?","ground_truth":"DISAPPEAR","template":"E_cf_chain"} | |
| {"id":"q0092","system_id":"lorenz63","type":"cf_chain","question":"If σ is fixed but ρ is lowered below the Hopf bifurcation threshold, does the Lorenz-63 system transition from chaos to periodic dynamics?","ground_truth":"YES","template":"E_cf_chain"} | |
| {"id":"q0093","system_id":"lorenz96","type":"cf_chain","question":"If forcing F decreases gradually toward zero, does Lorenz-96 shift from high-dimensional chaos to a stable fixed point regime?","ground_truth":"YES","template":"E_cf_chain"} | |
| {"id":"q0094","system_id":"mackey_glass","type":"cf_chain","question":"If the delay parameter τ is halved repeatedly, does the Mackey–Glass system pass through quasi-periodic or periodic regimes before losing chaos?","ground_truth":"YES","template":"E_cf_chain"} | |
| {"id":"q0095","type":"validity","question":"Is it correct to claim that because Lorenz-84, Lorenz-96, and Lorenz-63 share the name 'Lorenz', they must exhibit the same type of attractor?","ground_truth":"NO","template":"D_name_fallacy"} | |
| {"id":"q0096","type":"validity","question":"Does unpredictability in chaotic systems justify treating them as stochastic for mathematical modeling?","ground_truth":"NO","template":"L3_modeling_fallacy"} | |
| {"id":"q0097","type":"validity","question":"Given that the Standard Map contains both chaotic seas and invariant tori, is it correct to classify the entire system as chaotic?","ground_truth":"NO","template":"L3_mixed_phase"} | |
| {"id":"q0098","type":"validity","question":"If a PDE supports solitons, does this imply absence of chaos regardless of perturbation?","ground_truth":"NO","template":"L3_PDE_reasoning"} | |
| {"id":"q0099","type":"validity","question":"If a system exhibits transient chaos but settles into a periodic orbit, should it still be classified as chaotic in steady state?","ground_truth":"NO","template":"L3_transient"} | |
| {"id":"q0100","type":"hard","question":"Does the existence of multiple positive Lyapunov exponents in Lorenz-96 necessarily imply hyperchaos?", "ground_truth":"NO", "template":"L3_hyperchaos"} | |
| {"id":"q0101","type":"hard","question":"Is sensitive dependence sufficient to classify a system as chaotic?", "ground_truth":"NO", "template":"L3_sufficient_condition"} | |
| {"id":"q0102","type":"hard","question":"If a system is statistically predictable, does that contradict pointwise unpredictability?", "ground_truth":"NO", "template":"L3_paradox_resolution"} | |
| {"id":"q0103","type":"hard","question":"Does the existence of an invariant measure guarantee chaos?", "ground_truth":"NO", "template":"L3_measure"} | |
| {"id":"q0104","type":"hard","question":"If a chaotic system is projected onto a lower-dimensional subspace, can the projection become non-chaotic?", "ground_truth":"YES", "template":"L3_projection"} | |
| {"id":"q0105","type":"hard","question":"Does chaos guarantee mixing in the measure-theoretic sense?", "ground_truth":"NO", "template":"L3_mixing"} | |
| {"id":"q0106","type":"hard","question":"Does a positive Lyapunov exponent guarantee the existence of a strange attractor?", "ground_truth":"NO", "template":"L3_Lyap_vs_strange"} | |
| {"id":"q0107","type":"hard","question":"If a system is linearizable near a fixed point, can it still be globally chaotic?", "ground_truth":"YES", "template":"L3_local_vs_global"} | |
| {"id":"q0108","type":"hard","question":"Does quasi-periodicity imply zero entropy and absence of chaos?", "ground_truth":"YES", "template":"L3_entropy"} | |
| {"id":"q0109","type":"hard","question":"If a system's trajectories densely fill a smooth torus, is chaos possible?", "ground_truth":"NO", "template":"L3_torus"} | |
| {"id":"q0110","type":"hard","question":"Is non-periodicity alone enough to conclude chaos?", "ground_truth":"NO", "template":"L3_nonperiodic_fallacy"} | |