ITU Tier 1+ #4: Semiconductor Scaling (K_semi)

Tier 1+ Pass-1.5 paper 4 of 45. Operator-algebraic semiconductor-scaling theory unifying Moore's law + EUV + supply chain. Defines K_semi = -log ρ_semi as the operator-algebraic modular Hamiltonian on H_lithography ⊗ H_device ⊗ H_yield ⊗ H_supply. K_semi inherits from K_QG via the CLPW 2023 type II crossed-product specialised to this scale. Numerical results. Moore's law transistor density 1971-2024, TSMC N2 2025, EUV lithography 13.5nm, Dennard scaling end. Topics covered. TSMC 2nm 2025, ASML High-NA EUV 2023, CHIPS Act 2022.8.9 $52B, Samsung GAA, Intel 18A, Huawei 7nm Mate 60 Pro. 45-vertex polytope #4 top couplings: #3 K_crypto (0.85), #13 K_robot (0.85), #14 K_comm (0.85). Ten falsifiable predictions: P_avg=0.65: arXiv 2026 (0.90 S), TSMC N2 production 2025 (0.85 S), Sub-1nm by 2030 (0.55 M). Pass-2 roadmap: ~$1.5M: Semi analytics ($500K) + Lean Mathlib ($200K) + Foundry partnerships ($800K). Copyright © 2026 Munehiro Terada / Roboken. Licensed under CC-BY-4.0.