SDRIS: Topological Regularity of a Recursive Vacuum Bulk

Abstract: We present a finite-dimensional dynamical system inspired by the SDRIS bulk model with fixed recursion depth N=408, formulated as an arithmetic-weighted cascade with coupled transport and storage variables. The model implements a two-fluid structure consisting of a transient flow component and a persistent bulk storage component, coupled through divisor-dependent dissipation and optional non-local redistribution on an arithmetic graph. We show that layers indexed by composite integers act as efficient energy sinks with long-term storage capacity, while prime-indexed layers exhibit minimal dissipation and support long-lived coherent modes. For bounded forcing and finite spectral cut-off, the system defines a deterministic system of ordinary differential equations admitting a globally stable attractor of reduced effective dimension. Numerical experiments demonstrate robust convergence toward structured steady states with spectra dominated by prime-supported modes, largely independent of initial conditions and forcing details. The present work provides a mathematically explicit implementation of qualitative mechanisms previously discussed in SDRIS bulk models, established purely at the level of finite-dimensional ODEs. Methodology: The simulation implements a discretized recursive vacuum on a compact arithmetic lattice (N=408). Key mechanisms include: Arithmetic Dissipation: Damping coefficients scaled by the divisor function $\tau(n)$. Two-Fluid Coupling: Separation into transmissive (Flow) and storage (Spin) energy sectors. Non-Local Redistribution: Energy transfer along divisor graphs rather than spatial proximity. Software: The reference implementation (Python) used to generate the results is included as supplementary material (two Python notebooks: SDRIS_TwoFluid_ReferenceImp.ipynb and SDRIS_TwoFluid_ReferenceImp.ipynb).