Markov property for singular stochastic partial differential equations

Prove the Markov property for general singular stochastic partial differential equations close to criticality, including the 4_{4-} stochastic quantisation equation for sufficiently small > 0.

Background

The paper places its local well-posedness theory in the broader program of constructing restartable dynamics for singular stochastic partial differential equations. Such dynamics require an appropriate nonlinear state space and, ultimately, a Markov process describing the evolution after restarting from a later state. Existing work has established this framework for particular models, but the authors identify the Markov property as unresolved for general singular SPDEs near criticality, specifically citing the 4_{4-} stochastic quantisation equation for small > 0. This question is distinct from the paper's principal theorem, which establishes local well-posedness and convergence for a class of nonlinear heat equations with random initial conditions.