Proving Light as an Emergent Logical Residual in Causal Information Networks: A Formal Derivation Using SRE-Dynamics Operators 1-10 (A Complete Axiomatic Integration Showcase)

This paper provides a rigorous formal derivation establishing "Light" not as an independent material wave, but as an emergent topological manifold woven from the logical residuals (information discrepancies) between asynchronously evolving nodes within a discrete causal network. By deploying the full suite of SRE-Dynamics Operators 1–10, we deconstruct the material ontology of both light and matter, redefining "nodes" as stacks of self-compensating internal causal loops whose cumulative path-depth manifests macroscopically as rest mass. Through the application of Operator 1 (Local Graph Expansion) and Operator 10 (Homological Firewall), we demonstrate how the injection of new variables at the evolutionary frontier drives dimensional expansion while maintaining global algebraic connectivity (λ₂ > 0). We further establish that the macroscopic frequency (f) and the speed of light (c) are not fundamental constants but protocol-level emergences: frequency is mapped to the eigenvalue spacing (Δλ) of a localized cross-spectral matrix, while c is defined as the system's "Global Baud Rate" or sampling ceiling, regulated by local topological density. The inclusion of the Commercial Core Operators (7–9) provides the final systemic closure, proving the "Zero-Flux Escape Theorem" for energy conservation and the "Spacetime Solidification" mechanism through the anchoring of global Betti number variation (Δβ₁ ≡ 0). This mathematical framework successfully resolves long-standing quantum paradoxes—such as wave-particle duality and entanglement—by reducing them to the interplay between global fiber bundles and localized truncation acts within a non-background, random-access indexing space. Ultimately, this showcase establishes light as the metabolic computational cost projected onto the physical rendering layer required to achieve causal consensus between independent evolutionary manifolds.