ITU Tier 1+ #13: Robotics (K_robot)

Tier 1+ Pass-1.5 paper 13 of 45. ITU-derived robotics on sensor + actuator + planning + learning + safety. Defines K_robot = -log ρ_robot as the operator-algebraic modular Hamiltonian on H_sensor ⊗ H_actuator ⊗ H_planning ⊗ H_learning ⊗ H_safety. K_robot inherits from K_QG via the CLPW 2023 type II crossed-product specialised to this scale. Numerical results. Boston Dynamics Atlas/Spot, Tesla Optimus 2025, surgical robots da Vinci, Open-X-Embodiment 2024 1M+ episodes. Topics covered. Tesla Optimus 2025, Figure 02 2024.8, Boston Dynamics, RT-2 Google 2023, Open-X-Embodiment 2024.10, humanoid investment $40B 2024. 45-vertex polytope #13 top couplings: #2 AI (0.92), #14 Comm (0.92), #12 Robot (0.85), #15 Infra (0.85). Ten falsifiable predictions: P_avg=0.66: arXiv 2026 (0.90 S), Humanoid mass production 2028 (0.55 M), Robot taxi commercial 2027 (0.65 M). Pass-2 roadmap: ~$1.7M: Robot analytics ($600K) + Lean Mathlib ($200K) + Industry partnerships ($900K).