SRE Dynamics: Rigorous Reconstruction of Maxwell's Field Equations via Purely Dimensionless Graph Cohomology and Global Evolutionary Steps

This paper presents a formal, background-independent topological reconstruction of Maxwell's field equations entirely decoupled from continuum space-time manifolds, continuous physical constants, and empirical differential metrics. Grounded in Status-Relational Entropy (SRE) Dynamics, macroscopic time is fundamentally discarded and re-indexed as the emergent statistical consequence of global, synchronous evolutionary steps (S). By mapping physical field interactions as localized algebraic projections of a singular synchronized network intersection kernel onto the 1-chain (edge) and 2-chain (cycle) discrete complex layers, we mathematically derive Faraday's law and the Ampere-Maxwell relation as exact topological tautologies required to maintain matrix condition stability. Furthermore, we prove that fundamental physical constants (e, h, Z0) and the fine-structure constant (alpha) emerge natively as discrete graph-cohomological invariants and spectral radius ceilings of the underlying network complex. To break circular verification loops inherent to finite-difference schemes, an independent, non-cyclic cross-validation protocol is established. This metric matches the spatial dual-divergence of the dynamically evolved electric field against a static, structural invariant derived strictly from the Laplacian null space and boundary drive shock tensors. Parametric scanning across multi-loop non-planar bipartite graphs demonstrates that the topologic validation residual collapses identically to the machine double-precision limit (<= 5.68e-14) across infinite state-refresh cycles, rigorously securing the dynamic gauge-invariance and mathematical exactness of un-extended causal electrodynamics.