ITU Tier 1+ #27: Microbiome (K_microbe)

Tier 1+ Pass-1.5 paper 27 of 45. ITU-derived microbiome on gut + skin + oral + immune + metabolic. Defines K_microbe = -log ρ_microbe as the operator-algebraic modular Hamiltonian on H_gut ⊗ H_skin ⊗ H_oral ⊗ H_immune ⊗ H_metabolic. K_microbe inherits from K_QG via the CLPW 2023 type II crossed-product specialised to this scale. Numerical results. Human Microbiome Project 2007-, FMT C. difficile 2013 Nature, Akkermansia + Bifidobacterium PD-1 response. Topics covered. HMP 2007, FMT Borody C diff, Routy-Sivan 2018 cancer immunotherapy, Gopalakrishnan 2018, GLP-1 microbiome interaction, IBD dysbiosis. 45-vertex polytope #27 top couplings: #5 Cancer (0.92), #6 Aging (0.92), #31 K_qbio (0.92), #29 Dev (0.85). Ten falsifiable predictions: P_avg=0.66: arXiv 2026 (0.90 S), Microbiome companion diagnostic 2027 (0.65 M), IBD FMT Phase 3 2026 (0.55 M). Pass-2 roadmap: ~$1.6M: Microbe analytics ($500K) + Lean Mathlib ($200K) + Clinical collab ($900K).