ITU Tier 1+ #5: Cancer Information Theory (K_cancer)

Tier 1+ Pass-1.5 paper 5 of 45. ITU-derived cancer biology with K_cancer modular Hamiltonian on genome/tumor/immune/microenv/therapy. Defines K_cancer = -log ρ_cancer as the operator-algebraic modular Hamiltonian on H_genome ⊗ H_tumor ⊗ H_immune ⊗ H_microenv ⊗ H_therapy. K_cancer inherits from K_QG via the CLPW 2023 type II crossed-product specialised to this scale. Numerical results. Hanahan-Weinberg 2011 hallmarks; checkpoint inhibitor response (Routy-Sivan 2018 Science); CAR-T solid-tumor trials 2024. Topics covered. Hanahan-Weinberg hallmarks, Yamanaka 2006 OSKM, PD-1/PD-L1 checkpoint, CAR-T Carl June 2010, AlphaFold protein folding 2020/2024. 45-vertex polytope #5 top couplings: #6 K_aging (0.95), #27 Microbiome (0.92), #29 Dev (0.92), #31 K_qbio (0.92). Ten falsifiable predictions: P_avg=0.66: arXiv 2026 (0.90 S), Pan-cancer biomarker 2028 (0.65 M), CAR-T solid tumor approval 2027 (0.55 M). Pass-2 roadmap: ~$1.7M: Cancer analytics ($600K) + Lean Mathlib ($200K) + Oncology partnership ($900K).