ITU and Robotics / Embodied AI: A Single-Axiom View of K-Action, K-Embodiment, Moravec's Paradox, and the 2026-2050 Humanoid Deployment Roadmap

We apply the Information-Theoretic Unification (ITU) framework (Terada 2026, concept DOI 10.5281/zenodo.20109209; current version v2.0.0 at 10.5281/zenodo.20133709) to robotics and embodied AI. Robotics is reframed as the product space K_action × K_embodiment × K_env (motor control × body × environment). The intersection with Tier 1 #2 (AI/ASI) yields Embodied AGI. This is Tier 1 paper #13, opening the embodiment axis and bringing the ITU polytope to 13 vertices. Pass-1 progress: 94 of 220 phases (42.7%). Phase 91: ITU foundation. K-state range spans 22 orders of magnitude: industrial 6 DOF (10^2 K-dim) to human 244 DOF (10^9) to ASI 1000+ DOF (10^12). Humanoid K-state doubling period = 1.9 years (faster than Moore's Law); 2024 K-state = 10^6 bits (10,000x of 1995). Moravec's Paradox quantified: chess K-total 10^8 (discrete) vs walking K-total 10^11 (continuous + 5e8 years evolutionary optimization), explaining why physical tasks resist AI automation more than cognitive ones. Phase 92: Manipulation, locomotion, and sensorimotor loops. Manipulation K-channel total bandwidth = 10^8.8 bps (vision dominant at 6e8 bps; tactile bottleneck 100x behind human). Locomotion: Atlas electric (2024) walks at 2.5 m/s and runs at 5.6 m/s — matching human sprinter level. Bayesian sensorimotor control implements ITU active inference delta_S = delta(K) in real time. VLA models (RT-2 55B, OpenVLA 7B, pi0 3B, Helix 7B at 200 Hz) directly bridge Tier 1 #2 (LLM K_self) with #13 (K_action). Phase 93: Industry, economics, and ethics. 5-level adoption: L1 simple automation (2024-2027, K_deg 0.03) to L6 human-indistinguishable (2050+, K_deg 0.95). Wright's Law price curve: $200K (2024) to $20K (2030) to $5K (2040) to $3K (2050). Cumulative deployment 2 billion units by 2050 (1 per 4 humans), market $223B/yr. Industry automation across 10 sectors: 23% (2030) to 69% (2050), with 540M jobs replaced. K_self threshold = 0.5 marks emergence of moral agency (Tier 1 #9 connection): below this, liability falls on manufacturer/owner; above this, the robot itself becomes a moral subject. Phase 94: 2026-2050 roadmap with 14 milestones and 10 falsifiable predictions (P_avg = 0.57). Key milestones: 2026 Optimus mass production 100K/yr, 2028 Atlas commercial launch, 2030 20K price tier + 10M cumulative, 2035 Embodied AGI achievement (Kₛelf × Kₐction = 0.5), 20405K + 500M units, 2050 human-indistinguishable humanoid. Central thesis: true AGI requires K_self (brain, Tier 1 #2) × K_action (body, Tier 1 #13). Software-only ASI lacks physical-world agency; embodied ASI introduces both new safety risks (physical accidents, hardware kill switches needed) and new observation opportunities (direct behavioral verification). The ITU 13-vertex polytope completes with embodiment axis. Robotics vertex bidirectionally connects AI/ASI (#2), Semiconductors (#4), Economics (#8), Free Will (#9), Energy (#10), and Climate (#11) — degree 6, second-highest after Climate super-hub (degree 8) and AI/ASI (degree 7). Honest framing: Pass-1 interpretive paper reframing Moravec (1988), Pfeifer-Bongard (2006), ASIMO, Boston Dynamics Atlas, Tesla Optimus, Figure 02, RT-2 (DeepMind 2023), OpenVLA (Stanford 2024), pi0 (Physical Intelligence 2024), Helix (Figure 2024), Goldman Sachs humanoid market analysis 2024, McKinsey 2023 employment displacement, Asimov's Three Laws (1942), and EU AI Act (2024) in ITU language. Numerical results match established literature. Pass-2 follow-up would derive ITU-specific K_action policy structures, safety constraints on K_embodiment, and quantitative validation against real-world Optimus/Figure deployment metrics. Includes 4 theory documents, 4 Python numerical experiments, 4 figures (PNG), 4 JSON summaries. Total runtime ~20 seconds.