ITU Tier 1+ #21: Statistical Mechanics (K_stat)

Tier 1+ Pass-1.5 paper 21 of 45. ITU-derived statistical mechanics on microstate + ensemble + phase + transition + entropy. Defines K_stat = -log ρ_stat as the operator-algebraic modular Hamiltonian on H_microstate ⊗ H_ensemble ⊗ H_phase ⊗ H_transition ⊗ H_entropy. K_stat inherits from K_QG via the CLPW 2023 type II crossed-product specialised to this scale. Numerical results. Boltzmann entropy S = k log W; Ising model 2D; phase transitions universality; non-equilibrium Jarzynski 1997. Topics covered. Boltzmann 1872, Gibbs 1902, Ising 1925, Onsager 1944 2D Ising exact, Jarzynski 1997, fluctuation theorems, KPZ universality. 45-vertex polytope #21 top couplings: #17 K_QG (0.92), #22 MathPhys (0.92), #20 SM (0.85), #24 Math (0.92). Ten falsifiable predictions: P_avg=0.66: arXiv 2026 (0.90 S), Non-equilibrium statistical mechanics textbook 2027 (0.75 M). Pass-2 roadmap: ~$1.6M: Stat analytics ($500K) + Lean Mathlib ($200K) + Theory collab ($900K).