The 3D Energy Relation, Neutrinos, and Temperature in the Trit Framework

The Trit energy space has three orthogonal axes: E_S = mc² (symmetric sector), E_A = pc (antisymmetric sector), E_I = (W_A/Λ_c)mc² (I₂ coupling sector). The total energy satisfies the Pythagorean relation E²_total = (mc²)² + (pc)² + (W_A/Λ_c)²(mc²)². This extends the SR energy-momentum relation with a third term that is zero in free space (W_A/Λ_c < 10⁻²⁵ in all tested systems) and activates at nuclear density. The Pythagorean form — and not any other power — is forced by the Euclidean geometry of T³ = {−1,0,+1}³, which Fermat's Last Theorem guarantees is unique. The mass-energy transformation is a rotation in this 3D space, providing the mechanism that SR states but never explains. Three types of rotation correspond to acceleration (SR), field coupling at W_A ~ Λ_c (Type 2 gravity), and the Grand Flip at the horizon (black hole jet). The tetrahedral angle arccos(1/√3) = 54.74° emerges at the singularity det(X) → 0 as the most symmetric energy state. Neutrinos occupy the (−1,−1,−1) corner of T³ and propagate primarily through the E_I sector. Four neutrino mixing predictions are confirmed at < 0.5%. A new prediction follows: m²_eff = m²_ν(1 + (W_A/Λ_c)²) — environment-dependent effective mass, testable with IceCube-Gen2 near a neutron star merger. Temperature in the Trit is derived from the path integral: k_BT = ħ|φ̇| where φ̇ is the phase rotation rate in energy space. The Hawking temperature T_H = ħc³/(8πGMk_B) and the Unruh temperature T_U = ħa/(2πck_B) follow as exact corollaries — both from the same formula at different horizon geometries. Three open problems are explicitly stated: the derivation of k_B from Trit geometry, the Bose-Einstein distribution from T³ winding, and the full Trit thermal field theory.