Mathematical Foundations and Simulation Models of the Harmonic Framework of Reality (Corrected Edition)

This paper presents the complete mathematical foundations of the Harmonic Framework of Reality and describes the simulation models used to derive, test, and visualise its core predictions. We derive the unified energy law E = m c² (v/c) ^ (± ln (P) /ln (27) ) from first principles, showing how classical kinetic energy (½mv²) emerges as the n=2 case and momentum as the n=1 case, while using the dimensionless ratio v/c to resolve unit ambiguities. We derive the temporal mass equation Tm = k·2q·m·v^ (n-1) ·a, the threshold for inertial collapse, and the Tau field envelope Ψ_τ (r, t) = ε (t) sin (ω_τ t) exp (–λ (t) r²) that governs aperture breathing and entry windows. We present the harmonic ladder (27 Hz to 864 Hz, 32 harmonics) and derive the numbers 32 and 230 from the 19: 13: 4 ratio. We provide Python code for three key simulations: (1) the light formation model (wave induced sonoluminescence), (2) the 64 frequency handshake engine (coherence tracking and energy harvesting), and (3) the harmonic lens for LIGO data analysis. All code is presented in plain text for direct replication. The simulations confirm the predicted coherence stability of the Tau lattice and provide a template for searching the 27 Hz line in gravitational wave data. An important clarification is made: the full 32 frequency harmonic stack (27 Hz to 864 Hz) yields n ≈ 54. 65, corresponding to the 32 dimensional manifold, while the muon g 2 32 harmonic comb is a distinct prediction (sidebands at the precession frequency) and is not simulated by the handshake engine. A previous version of this paper contained a computational error; the corrected calculations are presented here.