General Quantum Occupancy Theory -- Vol IV - Comparative Calculations -- PART 1 -- GQOT versus the Standard Model -- A Framework for Discrete vs. Continuous Derivations

Description: The epistemological validity of a foundational physical theory rests on its ability to analytically derive observable phenomena with a minimal parameter footprint. Legacy Quantum Chromodynamics (QCD) cannot analytically derive quark confinement from its continuous Lagrangian, relying instead on phenomenological patches, running couplings, and multiple free parameters (e. g. , the Lund String Model) to match empirical data. In Volume IV, Part 1 of the General Quantum Occupancy Theory (GQOT), we present rigorous comparative calculations demonstrating that the parameterized Standard Model is merely the continuous, statistical shadow of GQOT’s discrete graph efficiency. By redefining Physical Action as the discrete integer count of bipartite edge-swaps within a finite adjacency matrix, GQOT replaces continuous differential equations with pure combinatorics. Utilizing a single scale-invariant kinematic anchor (hg = 75 Planck lengths) derived strictly from discrete spatial projection limits, this paper natively derives established empirical constants without continuous phenomenological tuning. Key derivations include: Quark Confinement & Hadronisation: The exact 1. 26 fm confinement limit and ~ 4. 2 x 10^-24 s decay timescale are derived natively as the mathematical point of absolute Informational Stenosis, triggered when the algorithmic cost of stretching a V=3 motif exceeds the topological cost of printing an anti-node pair. The Emergence of Inertia: Classical Force (F=ma) is proven to be a macroscopic illusion. Inertia is mathematically defined as "Algorithmic Rigidity, " emerging flawlessly from the linear regime of the hyperbolic tangent (tanh) saturation curve. The paper demonstrates the exact cubic suppression (chi³ / 3) of topological deviation that guarantees classical macroscopic behavior. Resolution of the Proton Radius Puzzle: The exact muonic hydrogen measurement (0. 840 fm) is derived strictly as the topological equilibrium of the K4 tetrahedral motif (Vweak / Vₛtrong = 2/3). Furthermore, the discrepancy with electron scattering measurements (0. 875 fm) is structurally resolved via the overlapping diffuse halos of fractional Rendered Trace Spectrums (0 < tau < 1). The Proton Mass: The macroscopic mass of the proton (~ 0. 940 GeV) is analytically bridged to the discrete combinatorial geometry to within 0. 2% accuracy. This framework formally bridges the discrete combinatorial bedrock of Quantum Information Theory with the continuous language of legacy physics, proving that continuous Lagrangian mechanics are the emergent macroscopic result of a bipartite matrix minimizing its computational edge-swaps. Updates v2 Fixed errors in the bibliography and also a minor error in the formatting of the table of contents.