Dynamic Phase Resonances in Hexagonal Close-Packed Media: Sub-Nodal Pressure Gradients and the Mechanical Casimir Boundary (Part VII)

This paper establishes a deterministic mechanical resolution to the Casimir effect, replacing quantum-electrodynamical zero-point fluctuations with the rigid geometry of the Hexagonal Close-Packed (3HCP) matrix. Within the UMM v9.5 framework, parallel boundaries are modeled as geometric filters that restrict sub-nodal harmonic updates of the 144-resonance grid. The exclusion of specific integer cell arrangements creates a localized drop in internal lattice pressure. By calculating the finite-difference Quantum of Conjunction (δρe) divergence, the author derives the classic inverse-fourth-power attractive force from pure contact mechanics and hardware-level grid stability. Creative Commons Attribution Non Commercial No Derivatives 4.0 International