Category-theoretic functorial invariants built from directed path algebras on templexes yield separable homology and semigroup structures that detect chaos and tipping points from data.
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DNS runs of NS-governed Rayleigh-Bénard convection produce alternating vortical or zonal final states as time-step shrinks, implying small numerical noise controls turbulence statistics and creating a paradox for the neglect of disturbances.
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Functorial invariants for chaos topology from data
Category-theoretic functorial invariants built from directed path algebras on templexes yield separable homology and semigroup structures that detect chaos and tipping points from data.
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A paradox of the Navier-Stokes turbulence
DNS runs of NS-governed Rayleigh-Bénard convection produce alternating vortical or zonal final states as time-step shrinks, implying small numerical noise controls turbulence statistics and creating a paradox for the neglect of disturbances.