Spectral Non-Linearity and Topological Constraints on the Continuum: A Formal and Methodological Addendum to the Primary Logical Infrastructure (PLI)

This technical treatise develops a further formal and methodological extension of the Primary Logical Infrastructure (PLI) framework. By introducing the discrete non-linear p-Laplacian operator, this paper formulates a mathematical language to evaluate the localized relational density and capacity limits of a pre-geometric substrate. Through the integration of the combinatorial Cheeger constant and the spectral gap decay dynamics, it proposes a non-divergent algebraic resolution to gravitational singularities and macroscopic spacetime emergence, arguing that relativistic physical collapses correspond to topological bottlenecks of the underlying network. Finally, this work delineates the exact discrete-to-continuum correspondence through kernel-weighted constructions, setting a methodological boundary for the scope of computational monism within contemporary quantum gravity and spacetime functionalism.