What question did this study set out to answer?

This paper aims to unify semiconductor scaling theories, specifically Moore's law and extreme ultraviolet (EUV) lithography, through operator-algebraic methods.

May 21, 2026Open Access

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

Key Points

This paper aims to unify semiconductor scaling theories, specifically Moore's law and extreme ultraviolet (EUV) lithography, through operator-algebraic methods.
Defines K_semi using operator-algebraic modular Hamiltonian concepts, combining multiple frameworks.
Analyzes numerical results regarding Moore's law transistor density from 1971 to 2024, focusing on industry advancements.
Covers topics including TSMC 2nm technology and relevant industry acts, such as the CHIPS Act.
P_avg of ten falsifiable predictions yields 0.65 overall future scaling effectiveness.
Highlights TSMC N2 production anticipated in 2025 with a success likelihood of 0.85.
Projects sub-1nm technology realization by 2030 with a success likelihood of 0.55.

Abstract

Tier 1+ Pass-1. 5 paper 4 of 45. Operator-algebraic semiconductor-scaling theory unifying Moore's law + EUV + supply chain. Defines Kₛemi = -log ρₛemi as the operator-algebraic modular Hamiltonian on Hₗithography ⊗ Hdevice ⊗ Hᵧield ⊗ Hₛupply. Kₛemi inherits from KQG 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 Kcrypto (0. 85), #13 Kᵣobot (0. 85), #14 Kcomm (0. 85). Ten falsifiable predictions: Pₐvg=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.

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

Key Points

Abstract

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