The Planck Energy Identity in the Quantum Lattice Model

This work isolates the identity E_P = m_P c^2 = ħ / t_P within the Quantum Lattice Model (QLM) and presents it as a standalone result. In this framework, Planck energy arises directly from the covariant phase–flow relation E = ħ dθ/dτ under a saturated proper-time tick, rather than from a primitive dimensional combination of {ħ, G, c}. The conventional expression E_P = sqrt(ħ c^5 / G) is recovered as an algebraically equivalent derived form. The derivation shows that Planck energy, Planck mass, and the relativistic energy–mass relation close exactly to a single primitive reduced-action throughput per Planck time. The result is presented in a minimal form, without requiring the full development of the broader framework. The identity is situated within the Quantum Lattice Model, where it arises as part of a larger reduced-action lattice structure built from the primitive set {ħ, ℓ_P, t_P}.