Dynamical Morphisms on Causal Sets: Benincasa-Dowker Kernels, Goldstino Vacuum Energy, and a Mechanism Toward the Fine-Structure Constant

A causal-set formulation of topological mismatch dark energy in which spacetime is a Poisson-sprinkled stochastic causal order and matter lives as continuous spinor fibers over the discrete base. The work uses the Benincasa–Dowker nonlocal d’Alembertian as the canonical Lorentz-invariant-in-the-mean kernel, promotes the discrete–continuum morphisms (Phi and R) to auxiliary dynamical fields, and defines the vacuum by integrating them out at a Parisi–Wu stochastic-quantization fixed point, yielding a leading volume term in the reduced effective action with a cosmological-constant stress tensor. It also proposes a dynamical origin for the fine-structure constant by treating the electromagnetic coupling as an equilibrium value selected by minimizing a gauge-operator spectrum mismatch, and it includes a toy spectral calculation showing the selected coupling concentrates in sensible ranges rather than scattering across orders of magnitude. Additional components include a Volkov–Akulov Goldstino sector tied to the mismatch energy density, a demonstration that the zero-temperature Lorentz-invariant vacuum has vanishing shear and bulk viscosities (excluding dissipative tired-light behavior), Lorentz-covariant definitions of response rates using local invariant scalars, and appendices with scaling estimates, parameter benchmarks, a Gaussian morphism-integral estimate of the vacuum functional coefficient, and an observational and numerical validation roadmap.