A SRE-Dynamics Inspired Topological Paradigm for Composite Elementary Particles and Relational Space Emergence

This paper presents a rigorous qualitative probabilistic formulation for the topological logic configuration and emergent geometry of composite elementary particles within the framework of Status-Relational Entropy (SRE) Dynamics. Stripping away all absolute spatiotemporal and energy priors, this non-background independent paradigm defines elementary particles as discrete, irreducible Internal Causal Loops driven by the Minimum Observational Step (l_min). By evaluating a 2x2 localized cross-spectral Hermitian operator mapping two coupled internal loops, we demonstrate that as the cross-coherence coefficient rho approaches unity, the generalized spectral ensemble spontaneously transitions from the Wigner Surmise to a continuous Poisson process. Under full-rank expansion, this spectral collapse triggers a three-in-one emergent manifestation at the macro-layer: the collapse of relational distance to zero via mutual information maximization, the generation of a logical pressure gradient (rendered as the strong interaction force) at the numerical truncation boundary epsilon = 10^-7, and a combinatorial explosion of Secondary Causal Feedback Paths. This step-wise jump in cumulative loop depth non-fittingly dictates the structural delta of particle rest masses, achieving a mathematically honest unification of composite particle physics and relational metric space.