The Geometry of the Relational Vacuum: The Constitution of Mass, Charge, and Spacetime from the Direction-Neutral Equilibrium Matrix of the Icosidodecahedron (Volume IV)

This supplementary monograph (Volume IV) marks the formal and didactically optimized completion of the parameter-free geometric framework established in Volume I. It expands the structural bridge model from foundational spacetime metrics directly into the domain of quantum electrodynamics (ED) by providing a rigorous, parameter-free derivation of the Sommerfeld fine-structure constant (). The framework explicitly isolates the unperturbed vacuum base state at zero energy. By restricting the mathematical framework to this absolute cosmic gauge state, the model successfully deduces the fundamental coupling constant before dynamical high-energy interactions or the "running" of coupling products occur. Physical interactions are modeled not as content within an independent space, but as the scale-invariant manifest of the vacuum's self-stabilizing feedback loops. Methodological & Combinatorial Core: The Discrete Base Synchronization Phase (): The framework models the interaction between a stationary particle (electron) and a passing wave (photon) as a sequential locking process. The photon systematically resolves the spatial hardware constraints of the icosahedral symmetry group () through a cumulative chain of discrete phase steps (). The Statistical Phase Elongation (): In the physical vacuum, the information transfer is subject to continuous sub-Planckian quantum fluctuations (Feynman diagrams). The three-dimensional expansion of orthogonal space creates an informational interaction surface of exactly 360 channels, filtered through the microscopic bottleneck of four decagon gate planes (), yielding an ideal redundancy investment of of a cycle. The Postulate of Spacelike CPT-Dichotomy: Under the static zero-energy constraint, the dynamic component of time reversal () loses operational relevance within the resting filter. The remaining binary, raumlike CPT-dichotomies of Charge () and Parity () form a pure integer cascade brake (), establishing a strict, parameter-free vacuum loss factor of exactly . In the final additive synthesis, the discrete hardware resonance and the fractional phase shift merge seamlessly on an identical dimensional scale of pure radians, yielding an uncompromised, parameter-free convergence with international CODATA reference datasets: Characterized as a structural bridge model, the work provides precise, risk-exposed predictions for future space-based atomic interferometry (orbital quantum metrology) and opens mathematical avenues for structural engineering solutions regarding the de-coherence of qubits in quantum computing architectures. Document Series Context: Volume I: The Spacetime Filter Matrix (Zenodo DOI: 10.5281/zenodo.20692491) Volume II: The Cybernetic Monadology Volume III: The Neural Symmetry & Inversion Volume IV: The Geometry of the Relational Vacuum (This Publication)