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

This project presents the foundational Planck-unit derivations of the Quantum Lattice Model (QLM), a deterministic phase–action framework in which 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 E_P = ħ / t_P becomes the core energetic unit from which mechanical, electromagnetic, geometric, and thermodynamic Planck quantities reduce to algebraically minimal forms. A central result is that the entire Planck-unit system can be reconstructed from the triplet (ħ, ℓ_P, t_P), without introducing dimensional square-root combinations of {G, ħ, c} as primitive definitions. Traditional Planck expressions collapse exactly to reduced-action lattice identities once written in terms of (ħ, ℓ_P, t_P). The Bohr identity ħ = m_e v_B a_0 emerges naturally within the same reduced-action structure, revealing hydrogenic physics as a direct phase–velocity calibration of the Planck lattice through the geometric ratio α = v_B / c. Electromagnetic quantities—including the Planck charge and the per-radian Planck impedance Z_P = Z_0 / (4π) (with loop-aggregated form Z_P(loop) = Z_0 / 2)—follow as algebraic consequences of the lattice’s phase–action transport and the vacuum impedance structure. This OSF project hosts the complete 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 provide the structural basis for companion work examining gravitational impedance, phase-coherent dynamics, particle-mass relations, and cosmological scaling within the same deterministic lattice formalism. A companion interactive system, Titus AI, enables researchers to explore, query, and verify the QLM derivations directly. Together, these resources support a transparent, internally consistent, and reproducible development path for the Quantum Lattice Model.