ITU Tier 1+ #22: Mathematical Physics (K_mathphys)

Tier 1+ Pass-1.5 paper 22 of 45. ITU-derived mathematical physics on operator algebra + topology + geometry + QFT. Defines K_mathphys = -log ρ_mathphys as the operator-algebraic modular Hamiltonian on H_operator ⊗ H_algebra ⊗ H_topology ⊗ H_geometry ⊗ H_QFT. K_mathphys inherits from K_QG via the CLPW 2023 type II crossed-product specialised to this scale. Numerical results. Tomita-Takesaki modular theory 1970; Connes 1973 type III; Doplicher-Roberts 1990 superselection. Topics covered. Operator algebras, von Neumann, type II/III factors, Connes 1982 Fields, AQFT Haag-Kastler, gauge theory Atiyah-Singer. 45-vertex polytope #22 top couplings: #17 K_QG (0.85), #21 Stat (0.92), #24 Math (0.85), #43 Meta (0.92). Ten falsifiable predictions: P_avg=0.66: arXiv 2026 (0.90 S), AQFT type II/III textbook 2027 (0.75 M). Pass-2 roadmap: ~$1.6M: MathPhys analytics ($500K) + Lean Mathlib ($200K) + Theory collab ($900K).