«Quantum Gravity via Alpha-Triad: A Unified Formalism for Loop Quantum Gravity, Graviton, and Discrete Time»

We present a unified formalism for quantum gravity based on the Alpha-Triad — three dimensionless constants (α₁, α₂, α₃) satisfying the normalization condition α₁² + α₂² + α₃² = 1. Within this framework: Loop quantum gravity acquires minimal area Amin⁡=α1⋅lP2Amin=α1⋅lP2 and minimal volume Vmin⁡=α2⋅lP3Vmin=α2⋅lP3, allowing geometric quantization of spacetime. The graviton is interpreted as an excitation of the α-field, with mass and spin determined by the combination of α₁ and α₂, and the number of polarizations given by α₃. The problem of time is resolved via discretization of time with step Δt=α3⋅tPΔt=α3⋅tP, where α₃(t) evolves dynamically. The central result is the Wheeler–DeWitt equation in the α-representation: H^αΨ=(α1⋅H^GR+α2⋅H^QM+α3⋅H^int)Ψ=0,H^αΨ=(α1⋅H^GR+α2⋅H^QM+α3⋅H^int)Ψ=0, which naturally unifies the geometric (GR) and quantum-field (QM) components. A computational calculator for modified Planck units is provided. For α₁ ≈ 0,618 and α₂ ≈ 0,786, the results closely match standard Planck scales, confirming the model's plausibility. This publication continues the series of works by the «Resonance Group» aimed at building a unified physical reality based on the Alpha-Triad and O-Matrix.