ITU Tier 1+ #11: Climate Information Theory (K_climate)

Tier 1+ Pass-1.5 paper 11 of 45. ITU-derived climate science on atmosphere + ocean + cryosphere + biosphere + carbon cycle. Defines K_climate = -log ρ_climate as the operator-algebraic modular Hamiltonian on H_atmosphere ⊗ H_ocean ⊗ H_cryosphere ⊗ H_biosphere ⊗ H_carbon. K_climate inherits from K_QG via the CLPW 2023 type II crossed-product specialised to this scale. Numerical results. IPCC AR6 2021-23, 1.5C overshoot likely, CO2 422 ppm 2024.5, Antarctic sea ice record low 2023. Topics covered. IPCC AR6 2021-23, COP28 UAE 2023.12 fossil fuel transition, CO2 422 ppm, Antarctic sea ice 2023 record low, ocean heat uptake. 45-vertex polytope #11 top couplings: #10 K_energy (0.92), #18 Astrobio (0.85), #14 Comm (0.85), #39 Politics (0.85). Ten falsifiable predictions: P_avg=0.65: arXiv 2026 (0.90 S), 1.5C breached 2027 (0.85 S), Net-zero G20 2070 (0.45 W). Pass-2 roadmap: ~$1.6M: Climate analytics ($500K) + Lean Mathlib ($200K) + IPCC+IEA collab ($900K).