Spectral Analysis and Low-Rank Structural Transitions Emergent from Dimensionless Causal Metric Networks under SRE Dynamics

This study investigates a coordinates-free relational matrix framework governed by Status-Relational Entropy (SRE) Dynamics. Operating under the protocol of SRE User Guide, we simulate a zero-dark-energy cosmological boundary coupled with an evolving variable speed of light parameterized by the global baud rate ceiling . We demonstrate that the discrete progression of a one-dimensional sequence breaks the low-rank degeneracy of the inner-product feature space. By implementing a mathematically rigorous double centering operator, we isolate authentic structural dimensions from macroscopic metric expansion artifacts. The computational model is evaluated via an empirical pipeline driven by un-scalized spectroscopic dataset slices from the Sloan Digital Sky Survey (SDSS DR19). The empirical results demonstrate that the effective rank exhibits a discrete jump from to near the epoch of , indicating a structural transition in the causal network. Concurrently, tracking the first-order discrete difference of the maximum eigenvalue reveals an isolated peak, mapping a localized network mutation rather than a continuous micro-derivative. The potential influences of statistical fluctuations, sample limitations, and survey selection effects are discussed to separate matrix algorithmic behavior from intrinsic cosmological invariants.