Quantum Lattice Model: Reduced-Action Foundations and Planck-Unit Derivations

This work presents the foundational Planck-unit derivations of the Quantum Lattice Model (QLM), a deterministic phase–action framework formulated as a first-principles theoretical preprint. In QLM, all Planck-scale quantities arise from a single primitive rule: each lattice tick advances one radian of phase and transports one quantum of reduced action, ħ. From this starting point, the fundamental per-radian Planck energy EP = ħ / tP emerges as the core energetic unit from which mechanical, electromagnetic, geometric, and thermodynamic Planck quantities collapse to minimal algebraic forms. A central result is that the entire Planck-unit system can be reconstructed from the primitive triplet (ħ, ℓP, tP), without invoking dimensional combinations of G, c, and without treating ħ as a derived dimensional constant rather than a fundamental per-radian action. Within the same reduced-action structure, the Bohr identity ħ = me vB a0 emerges naturally, revealing hydrogenic physics as a direct phase-velocity calibration of the Planck lattice. Electromagnetic constants, including the Planck charge and the Planck impedance ZP = Z0 / 2, arise as geometric consequences of phase–action transport on the lattice rather than as independent physical postulates. This record hosts the full manuscript, symbolic derivations, dimensional analyses, CODATA-validated numerical evaluations, and supplemental materials establishing the reduced-action Planck-unit system that underlies the broader QLM framework. These foundations support companion work on gravitational impedance, phase-coherent dynamics, particle-mass structure, and cosmological scaling.