A Recursive Framework for Modeling Existence: Integrating the Riemann Hypothesis via Vacuum Lattice Harmonic

This work presents a recursive mathematical framework for modeling existence, unifying thermodynamic conservation, multi-universal structures, and number theory. At its core is the Vacuum Lattice Harmonic (VLH), a spinning 4D lattice geometry embedded in an $M$-dimensional brane manifold scaffolded by dark matter. The VLH provides a falsifiable, first-law governed model of existence that extends beyond general relativity and interprets universes as bounded solutions connected through conserved energy perturbations. A central result of this framework is a reformulation of the Riemann Hypothesis (RH): the completed Riemann xi-function $\xi(s)$ arises naturally as the VLH partition function. RH emerges as a thermodynamic equilibrium condition, enforced either through positivity of “work” moments (Li’s criterion) or spectral self-adjointness (Hilbert–Pólya). This reframes RH not as an isolated conjecture, but as a natural outcome of conservation principles within the VLH lattice. The paper also explores interpretive extensions, such as mapping Robert Monroe’s experiential “locales” onto stable lattice positions, showing how subjective phenomena can be analytically framed within the same conserved system. The framework is designed to be falsifiable: any unresolved scientific or mathematical query must resolve within first-law confines, or the model fails. For RH specifically, testing reduces to verifying VLH kernel duality and the positivity of Li–Keiper coefficients.