ITU Tier 1+ #24: Pure Mathematics (K_math)

Tier 1+ Pass-1.5 paper 24 of 45. ITU-derived pure mathematics unifying logic + structure + proof + metamath. Defines K_math = -log ρ_math as the operator-algebraic modular Hamiltonian on H_axiom ⊗ H_logic ⊗ H_structure ⊗ H_proof ⊗ H_metamath. K_math inherits from K_QG via the CLPW 2023 type II crossed-product specialised to this scale. Numerical results. Wiles 1994 Fermat, Perelman 2002-3 Poincare/Geometrization Fields refused 2006, Mochizuki 2012 IUT contested. Topics covered. Wiles Fermat, Perelman Poincare-Geometrization, Mochizuki IUT contested, RH unproven Clay $1M, Yang-Mills mass gap Clay, P vs NP. 45-vertex polytope #24 top couplings: #17 K_QG (0.95), #22 MathPhys (0.92), #25 Holo (0.92), #43 Meta (0.95). Ten falsifiable predictions: P_avg=0.65: arXiv 2026 (0.90 S), RH LLM-assisted attempt 2030 (0.30 W), Lean Mathlib ITU lib 2027 (0.65 M). Pass-2 roadmap: ~$2M: Math analytics ($700K) + Lean Mathlib ($300K) + Math research collab ($1M).