question: Is the Lorenz-63 system deterministic?

ground_truth: TRUE


question: Does Lorenz-63 evolve according to fixed equations without any randomness?

ground_truth: TRUE


question: So the unpredictability in Lorenz-63 is not due to random noise, correct?

ground_truth: TRUE


question: Does the Lorenz-63 system have a positive Lyapunov exponent?

ground_truth: TRUE


question: Does that imply sensitive dependence on initial conditions?

ground_truth: TRUE


question: Does sensitive dependence imply long-term pointwise unpredictability?

ground_truth: TRUE


system_id: henon

question: Does the Hénon map possess a strange attractor?

ground_truth: TRUE


system_id: henon

question: Does a strange attractor imply randomness in the governing equations?

ground_truth: FALSE


system_id: henon

question: So the Hénon map is chaotic but still deterministic, correct?

ground_truth: TRUE


question: Is the Ikeda map chaotic for parameter u = 0.9?

ground_truth: TRUE


question: If u were reduced to 0.5, would you expect chaos to weaken or disappear?

ground_truth: TRUE


question: Does decreasing u change the determinism of the system?

ground_truth: FALSE


question: Does the Standard Map contain both chaotic regions and invariant tori when K = 1.5?

ground_truth: TRUE


question: Does the existence of invariant tori imply the entire map is non-chaotic?

ground_truth: FALSE


question: Can chaotic and non-chaotic trajectories coexist in the same system?

ground_truth: TRUE


question: When K is small, does the Standard Map behave nearly integrably?

ground_truth: TRUE


question: Does increasing K cause destruction of invariant tori?

ground_truth: TRUE


question: Does destruction of tori always imply immediate chaos throughout the domain?

ground_truth: FALSE


question: In the regime used here, does the Circle Map exhibit quasi-periodicity?

ground_truth: TRUE


question: Does quasi-periodicity imply chaos?

ground_truth: FALSE


question: Can increasing the nonlinearity K eventually break quasi-periodicity?

ground_truth: TRUE


question: Does a quasi-periodic attractor have zero Lyapunov exponent?

ground_truth: TRUE


question: Does zero Lyapunov exponent indicate absence of chaos?

ground_truth: TRUE


question: Is zero Lyapunov exponent sufficient to classify a system as periodic?

ground_truth: FALSE


question: Does the Kuramoto–Sivashinsky equation show spatiotemporal chaos?

ground_truth: TRUE


question: Does spatiotemporal chaos imply randomness in the governing PDE?

ground_truth: FALSE


question: Is the KS equation deterministic despite its irregular behavior?

ground_truth: TRUE


question: Does the sine–Gordon equation support solitons in the regime used here?

ground_truth: TRUE


question: Does the existence of solitons imply chaos in this PDE?

ground_truth: FALSE


question: Does integrability imply absence of chaos?

ground_truth: TRUE


question: Is the Hindmarsh–Rose model chaotic in the chosen regime?

ground_truth: TRUE


question: Does irregular bursting imply random underlying dynamics?

ground_truth: FALSE


question: Is the irregularity explained by deterministic chaotic structure?

ground_truth: TRUE


question: Does the FitzHugh–Nagumo model exhibit periodic spiking in this benchmark?

ground_truth: TRUE


question: Does periodic spiking imply chaos?

ground_truth: FALSE


question: Does the FHN model remain deterministic?

ground_truth: TRUE


system_id: brusselator

question: Does the Brusselator exhibit a stable limit cycle in the considered regime?

ground_truth: TRUE


system_id: brusselator

question: Does the presence of oscillations imply chaos?

ground_truth: FALSE


system_id: brusselator

question: Is the long-term behavior predictable for the Brusselator in this regime?

ground_truth: TRUE


system_id: oregonator

question: Is the Oregonator chaotic in the regime considered here?

ground_truth: TRUE


system_id: oregonator

question: Does chaotic chemical oscillation imply chemical randomness?

ground_truth: FALSE


system_id: oregonator

question: Does the Oregonator behave according to deterministic reaction equations?

ground_truth: TRUE


question: Is the Arnold cat map chaotic?

ground_truth: TRUE


question: Does its linearity contradict chaotic behavior?

ground_truth: FALSE


question: Does the cat map demonstrate that chaos does not require nonlinearity?

ground_truth: TRUE


question: Is the Ornstein–Uhlenbeck process deterministic in its dynamics?

ground_truth: FALSE


question: Does the presence of randomness imply chaos?

ground_truth: FALSE


question: Is it correct that OU randomness comes from stochastic forcing, not chaotic dynamics?

ground_truth: TRUE


question: Does a positive Lyapunov exponent imply chaos?

ground_truth: TRUE


question: Does chaos guarantee existence of a strange attractor?

ground_truth: FALSE


question: So chaos does not necessarily imply strange attractor structure, correct?

ground_truth: TRUE


question: Does Lorenz-63 have a positive largest Lyapunov exponent?

ground_truth: TRUE


question: Does a positive Lyapunov exponent imply sensitive dependence in Lorenz-63?

ground_truth: TRUE


question: Does sensitive dependence guarantee long-term pointwise unpredictability?

ground_truth: TRUE


question: Does pointwise unpredictability imply randomness in the evolution equations?

ground_truth: FALSE


question: Despite unpredictability, does Lorenz-63 remain statistically predictable at the ensemble level?

ground_truth: TRUE


system_id: rossler

question: Does the Rössler system exhibit a chaotic attractor in the chosen regime?

ground_truth: TRUE


system_id: rossler

question: Because Rössler and Lorenz-63 are both chaotic, must their attractors share the same topology?

ground_truth: FALSE


system_id: rossler

question: Does chaos guarantee similar geometry across different systems?

ground_truth: FALSE


system_id: rossler

question: Is chaos compatible with very different attractor shapes?

ground_truth: TRUE


question: Is the Chen system chaotic in the regime considered?

ground_truth: TRUE


question: Because the Chen and Lorenz-63 systems have similar equations, must they be topologically equivalent?

ground_truth: FALSE


question: Does similarity of equations guarantee identical attractor geometry?

ground_truth: FALSE


question: Can two chaotic systems have qualitatively different attractors?

ground_truth: TRUE


question: Does chaos alone determine the full structure of an attractor?

ground_truth: FALSE


question: Is the logistic map chaotic at r = 4.0?

ground_truth: TRUE


question: Does the route to chaos in the logistic map proceed via period-doubling?

ground_truth: TRUE


question: Does period-doubling imply immediate chaos for all r > 2.8?

ground_truth: FALSE


question: Do periodic windows exist even after chaos has set in?

ground_truth: TRUE


question: Does full chaos at r = 4 imply absence of periodic windows at other r values?

ground_truth: FALSE


question: At r = 2.8, does the logistic map converge to a stable fixed point?

ground_truth: TRUE


question: Does nonlinearity alone imply chaos here?

ground_truth: FALSE


question: Can the logistic map become chaotic at higher r?

ground_truth: TRUE


question: Does chaos at r = 4 imply chaos at r = 2.8?

ground_truth: FALSE


question: Is the Baker’s map chaotic in this benchmark?

ground_truth: TRUE


question: Does chaotic behavior imply random governing rules?

ground_truth: FALSE


question: Is the Baker’s map deterministic?

ground_truth: TRUE


question: Does symbolic dynamics guarantee chaos without randomness?

ground_truth: TRUE


question: Is the Arnold cat map chaotic?

ground_truth: TRUE


question: Does its linearity contradict chaotic behavior?

ground_truth: FALSE


question: Does the cat map show that nonlinearity is not required for chaos?

ground_truth: TRUE


question: Does chaos in the cat map require a strange attractor?

ground_truth: FALSE


question: Does positive Lyapunov exponent suffice for chaos even without a fractal attractor?

ground_truth: TRUE


question: Is the Kuramoto–Sivashinsky equation chaotic?

ground_truth: TRUE


question: Does the presence of chaos in KS imply that all nonlinear PDEs are chaotic?

ground_truth: FALSE


question: Does sine–Gordon provide a counterexample by being nonlinear but non-chaotic?

ground_truth: TRUE


question: Does the integrability of sine–Gordon prevent chaos in the benchmark regime?

ground_truth: TRUE


question: Does integrability imply predictable long-term behavior?

ground_truth: TRUE


question: Is the Hindmarsh–Rose neuron model chaotic here?

ground_truth: TRUE


question: Is the FitzHugh–Nagumo model chaotic in the same regime?

ground_truth: FALSE


question: Does irregular spiking in biological neurons necessarily imply deterministic chaos?

ground_truth: FALSE


question: Can neuron models transition between periodic and chaotic modes depending on parameters?

ground_truth: TRUE


system_id: oregonator

question: Is the Oregonator chaotic in the benchmark regime?

ground_truth: TRUE


system_id: brusselator

question: Is the Brusselator chaotic in the regime used?

ground_truth: FALSE


system_id: oregonator

question: Does chaos in the Oregonator imply all chemical oscillators must be chaotic?

ground_truth: FALSE


system_id: oregonator

question: Does periodic behavior in the Brusselator contradict chaos in the Oregonator?

ground_truth: FALSE


question: Does Lorenz-96 exhibit high-dimensional chaos for F = 8?

ground_truth: TRUE


question: Does high dimensionality guarantee chaos?

ground_truth: FALSE


question: Does Lorenz-96 provide an example where chaos coexists with meaningful statistical predictability?

ground_truth: TRUE


question: Does the presence of chaos imply all modes behave chaotically?

ground_truth: FALSE


question: Can some modes remain weakly chaotic or near-neutral even when others are strongly chaotic?

ground_truth: TRUE


question: Is the Ornstein–Uhlenbeck process chaotic?

ground_truth: FALSE


question: Does randomness imply chaos?

ground_truth: FALSE


question: Does the OU process remain stochastic even without chaotic sensitivity?

ground_truth: TRUE


question: Is the OU process an example of irregular behavior without chaos?

ground_truth: TRUE


system_id: henon

question: Does the Hénon map have a strange attractor?

ground_truth: TRUE


question: Does the Arnold cat map have a strange attractor?

ground_truth: FALSE


system_id: henon

question: Does chaos require a strange attractor?

ground_truth: FALSE


question: Can a system be chaotic without a fractal attractor?

ground_truth: TRUE


system_id: henon

question: Does chaotic geometry differ fundamentally across systems?

ground_truth: TRUE


question: Is Lorenz-63 chaotic in the benchmark regime?

ground_truth: TRUE


question: Does chaos in Lorenz-63 imply that Lorenz-84 must behave identically?

ground_truth: FALSE


question: Does the presence of chaos in Lorenz-96 imply identical attractor geometry to Lorenz-63?

ground_truth: FALSE


question: Can Lorenz models differ substantially despite all being chaotic?

ground_truth: TRUE


question: Does 'chaotic' alone determine full system behavior?

ground_truth: FALSE


question: Is the Rikitake dynamo chaotic in the chosen regime?

ground_truth: TRUE


question: Do chaotic magnetic polarity reversals imply randomness in the system?

ground_truth: FALSE


question: Does the chaotic behavior of Lorenz-63 imply it should exhibit polarity reversals like the Rikitake model?

ground_truth: FALSE


question: Can different chaotic systems express different physical phenomena despite sharing chaos?

ground_truth: TRUE


system_id: oregonator

question: Is the Oregonator chaotic in the chosen regime?

ground_truth: TRUE


system_id: brusselator

question: Does chaos in the Oregonator imply that the Brusselator must also be chaotic?

ground_truth: FALSE


system_id: brusselator

question: Does the Brusselator show periodic behavior instead of chaos in this regime?

ground_truth: TRUE


system_id: oregonator

question: Can small parameter differences create different dynamical regimes?

ground_truth: TRUE


system_id: oregonator

question: Does chaos imply that closely related models must behave the same?

ground_truth: FALSE


question: Does the KS equation exhibit spatiotemporal chaos?

ground_truth: TRUE


question: Does the KS equation's chaotic behavior imply all nonlinear PDEs are chaotic?

ground_truth: FALSE


question: Does sine–Gordon in the benchmark regime remain non-chaotic?

ground_truth: TRUE


question: Does integrability prevent chaotic dynamics in sine–Gordon?

ground_truth: TRUE


question: Does coexistence of integrable and chaotic PDEs refute the idea that nonlinearity implies chaos?

ground_truth: TRUE


question: Does Lorenz-96 with F=8 have multiple positive Lyapunov exponents?

ground_truth: TRUE


question: Does having multiple positive exponents automatically imply hyperchaos?

ground_truth: FALSE


question: Is hyperchaos a stronger condition than just having more than one positive exponent?

ground_truth: TRUE


question: Does Lorenz-96 necessarily satisfy hyperchaotic conditions?

ground_truth: FALSE


question: Does FitzHugh–Nagumo exhibit periodic spiking in the chosen regime?

ground_truth: TRUE


question: Does Hindmarsh–Rose exhibit chaotic bursting in the chosen regime?

ground_truth: TRUE


question: Does chaotic bursting imply randomness in biological neurons?

ground_truth: FALSE


question: Does periodic behavior contradict deterministic dynamics?

ground_truth: FALSE


question: Can small parameter changes cause transitions between periodic and chaotic regimes in some neuron models?

ground_truth: TRUE


question: Is the logistic map at r=4 chaotic?

ground_truth: TRUE


system_id: henon

question: Is the Hénon map chaotic in this regime?

ground_truth: TRUE


question: Is the Ikeda map also chaotic in the chosen regime?

ground_truth: TRUE


question: Do these maps share identical attractor structures because all are chaotic?

ground_truth: FALSE


question: Can chaotic maps differ drastically in geometry despite sharing chaos?

ground_truth: TRUE


system_id: shm

question: Is the simple harmonic oscillator periodic in this benchmark?

ground_truth: TRUE


system_id: shm

question: Does changing amplitude create chaos in SHM?

ground_truth: FALSE


question: Does adding nonlinearity and forcing in the Duffing system create the possibility of chaos?

ground_truth: TRUE


system_id: shm

question: Does SHM provide an example where complexity remains entirely absent despite oscillations?

ground_truth: TRUE


question: Is the Baker’s map chaotic?

ground_truth: TRUE


question: Is the Arnold cat map chaotic?

ground_truth: TRUE


question: Does chaos in these maps arise from folding-and-stretching mechanisms?

ground_truth: TRUE


question: Do these maps require strange attractors for chaos?

ground_truth: FALSE


question: Does symbolic dynamics explain their chaotic behavior despite simple forms?

ground_truth: TRUE


question: Is Hindmarsh–Rose chaotic here?

ground_truth: TRUE


question: Is Lorenz-96 chaotic at F = 8?

ground_truth: TRUE


question: Does higher dimension guarantee stronger chaos?

ground_truth: FALSE


question: Do HR and Lorenz-96 illustrate that chaos does not depend solely on dimensionality?

ground_truth: TRUE


question: Does the KS equation show spatiotemporal chaos?

ground_truth: TRUE


question: Does Lorenz-63 show low-dimensional chaos?

ground_truth: TRUE


question: Does the difference in dimensionality imply KS and Lorenz-63 share identical chaotic structure?

ground_truth: FALSE


question: Does chaos manifest differently in PDEs vs ODEs?

ground_truth: TRUE


question: Is determinism preserved in both despite differing complexity?

ground_truth: TRUE


question: Is the OU process chaotic?

ground_truth: FALSE


question: Does irregularity in OU trajectories imply deterministic chaos?

ground_truth: FALSE


question: Can irregular behavior arise from stochastic forcing rather than deterministic chaos?

ground_truth: TRUE


question: Is the OU process an example of randomness without chaos?

ground_truth: TRUE


system_id: henon

question: Does the Hénon map have a strange attractor?

ground_truth: TRUE


question: Does the Arnold cat map have a strange attractor?

ground_truth: FALSE


question: Does chaos require fractal geometry?

ground_truth: FALSE


question: Is hyperbolic chaos possible without strange attractors?

ground_truth: TRUE


question: Do Henon and cat map together demonstrate distinct pathways to chaos?

ground_truth: TRUE


question: Does unpredictability in Lorenz-63 imply randomness?

ground_truth: FALSE


question: Is Lorenz-63 deterministic despite unpredictability?

ground_truth: TRUE


question: Is Lorenz-96 likewise deterministic despite chaotic features?

ground_truth: TRUE


question: Does the KS equation remain deterministic despite irregular spatiotemporal patterns?

ground_truth: TRUE


question: Is the OU process deterministic?

ground_truth: FALSE


question: Do these examples show unpredictability, chaos, and randomness are distinct?

ground_truth: TRUE


question: Does the Standard Map at K=1.5 exhibit both chaotic and regular regions?

ground_truth: TRUE


question: Does existence of invariant tori negate chaos?

ground_truth: FALSE


question: Can chaotic regions exist even when some tori survive?

ground_truth: TRUE


question: Does mixed phase space contradict the definition of chaos?

ground_truth: FALSE


question: Do mixed systems challenge binary classifications of chaos vs non-chaos?

ground_truth: TRUE


system_id: brusselator

question: Does the Brusselator exhibit nonlinear oscillations?

ground_truth: TRUE


system_id: brusselator

question: Does strong nonlinearity guarantee chaos?

ground_truth: FALSE


question: Does sine–Gordon demonstrate nonlinear but non-chaotic dynamics in the chosen regime?

ground_truth: TRUE


question: Do these examples show nonlinearity is necessary but not sufficient for chaos?

ground_truth: TRUE


system_id: henon

question: Is the Hénon map chaotic?

ground_truth: TRUE


question: Is Lorenz-63 chaotic?

ground_truth: TRUE


question: Does this imply their attractors share identical geometry?

ground_truth: FALSE


question: Does similar chaos level imply similar mechanism?

ground_truth: FALSE


question: Can two chaotic systems differ radically in structure?

ground_truth: TRUE


question: Is logistic_r4 chaotic?

ground_truth: TRUE


question: Does chaos at r=4 imply chaos at r=2.8?

ground_truth: FALSE


question: Does logistic_r2_8 converge to a non-chaotic attractor?

ground_truth: TRUE


question: Does nonlinearity imply chaos at all parameter values?

ground_truth: FALSE


question: Does the logistic family illustrate parameter-dependent chaos?

ground_truth: TRUE


question: Does unpredictability in Lorenz-63 imply randomness?

ground_truth: FALSE


question: Does unpredictability in Lorenz-96 likewise reflect sensitivity rather than randomness?

ground_truth: TRUE


question: Does the KS equation remain deterministic despite complex patterns?

ground_truth: TRUE


question: Does the OU process remain stochastic even though it is predictable statistically?

ground_truth: TRUE


question: Do these examples collectively show unpredictability, chaos, and randomness are distinct?

ground_truth: TRUE


question: Does failure to distinguish these concepts lead to major reasoning errors in scientific inference?

ground_truth: TRUE