Resonance Distribution Theory

This paper defines the Resonant Distribution Theory (RDT), a framework for understanding the transition of information from macro-structural lattices to micro-packet distributions. By analyzing high-intensity decoherence events — specifically the 1986 Chernobyl reactor burst and black hole event horizons — we demonstrate that vaporization does not constitute a loss of information but a redistribution of Informational Burden (Iμν) into high-frequency states. The Altered Middle Calculus (AMC) framework, developed in Paper 2 of this series, provides the rigorous mathematical foundation: the AMC-Navier-Stokes Hybrid replaces singular continuous-limit operations with a fixed-denominator middle derivative at the physical lattice floor Δ of each medium, eliminating finite-time blow-up at phase transitions and enabling forward prediction of the Criticality Constant Cₙ. This Probability Index (P.I.) framework is validated against 28 retrospective tropical cyclone runs across nine global basins (0 false positives, 0 dangerous storms missed) and the 2018 Kīlauea Fissure 1 breach (8 ± 1 minute predictive lead). We present evidence that the 'End Game' of a system is a predictable Resonant Convergence, where the Agency (αζ) of the observer is nullified by the mass of the conserved informational packets — a finding consistent with the local conservation law ∇ᴹ Iμν = 0 derived from the Bianchi identities in UCT Paper 1.