MMS-A18 - A Converged Parameter Basin for the Entropic Spacetime Field

The Entropic Spacetime Field (ESF) is a thermodynamic framework in which spacetime is treated as an active medium whose large-scale geometry emerges from entropy production, transport, saturation and persistence within an underlying ripplefield microstructure. In previous papers (MMS-A16, MMS-A17), ESF was shown to reproduce a viable background cosmology with delayed entropy activation and to naturally transition from linear perturbations to non-linear, filament-dominated dynamics at late times. This paper presents a converged parameter basin for ESF that simultaneously satisfies early-universe safety, intermediate-redshift expansion constraints, late-time structure formation and non-linear stability. A systematic parameter scan identifies a robust region of ESF parameter space in which (i) a controlled 4–5% intermediate-redshift deficit in the Hubble expansion rate is produced, alleviating the Hubble tension without disrupting early-universe observables; (ii) entropy perturbations become localised and persistent on filamentary scales (≈4–10 Mpc) through diffusion and non-linear reinforcement; and (iii) late-time geometric memory generates effective gravitational wells capable of flattening galaxy rotation curves without non-baryonic dark matter. The converged ESF basin exhibits stable non-linear plateaus in entropy density, clear scale separation between large-scale suppression and small-scale enhancement, and no runaway behaviour across void, filament, cluster and supercluster modes. The resulting phenomenology yields concrete, falsifiable predictions, including excess weak lensing convergence at filament edges decoupled from baryonic tracers, sharpened filament profiles and scale-dependent late-time clustering. This work establishes a self-consistent late-time regime for ESF and provides a quantitative foundation for observational testing using existing and forthcoming weak lensing, galaxy survey and rotation curve data.