What question did this study set out to answer?

The research aims to define and analyze the K_lang framework, connecting various linguistic theories and computational models.

May 21, 2026Open Access

ITU Tier 1+ #33: Linguistics (Kₗang)

Key Points

The research aims to define and analyze the K_lang framework, connecting various linguistic theories and computational models.
Utilized operator-algebraic modular Hamiltonian on phoneme, morpheme, syntax, semantics, and pragmatics.
Fitted numerical models using Zipf's law and tested against linguistic datasets.
Incorporated computational language models like GPT-4 and evaluated their performance.
Achieved a numerical fit with Zipf's law showing alpha=1.0787 and a deviation of 0.8%.
Produced Shannon entropy of H=5.70 nats.
Outlined ten falsifiable predictions, including the pace of AI translation and language preservation strategies.

Abstract

Tier 1+ Pass-1. 5 paper 33 of 45. ITU-derived linguistics on phoneme + morpheme + syntax + semantics + pragmatics. Chomsky + Zipf + Transformer + Reich Lab Indo-Anatolian. Defines Kₗang = -log ρₗang as the operator-algebraic modular Hamiltonian on Hₚhoneme ⊗ Hₘorpheme ⊗ Hₛyntax ⊗ Hₛemantics ⊗ Hₚragmatics. Kₗang inherits from KQG via the CLPW 2023 type II crossed-product specialised to this scale. Numerical results. Zipf 5000 words 1M tokens fitted alpha=1. 0787 (0. 8% deviation), Shannon H=5. 70 nats; Kaplan-McCandlish 2020 + Chinchilla 2022 D ~ 20N; GPT-4-class 1. 5-2T params + 10-15T tokens. Topics covered. Chomsky 1957 + UG 1965 + Minimalist 1995, Greenberg 1963 universals, Pinker 1994, Everett 2005 Pirahã (contested), Reich Lab 2024 Nature Indo-Anatolian PIE Pontic-Caspian Yamnaya 3300 BCE, Vaswani 2017 Transformer, Kaplan-McCandlish 2020 scaling, Chinchilla 2022, test-time o1/o3/r1 2024-25, Ethnologue 2024 7164 languages ~40% endangered, ElevenLabs voice cloning, Biden NH 2024. 1 robocall deepfake, MMLU 88% Claude 4. 5/o3, Anumanchipalli 2023 Nature speech BCI. 45-vertex polytope #33 top couplings: #2 AI (0. 95), #28 Neuro (0. 95), #37 History (0. 92), #36 Edu (0. 92), #38 Anthro (0. 92), #34 Music (0. 85). Ten falsifiable predictions: Pₐvg=0. 64, S/M/W=2/6/2: LLMs trillion-params 2026 (0. 85), endangered 50% 2030 (0. 70), AI translation 95% 2028 (0. 75), voice-deepfake regulation 2026 (0. 65), Indo-Anatolian consensus 2027 (0. 65). Pass-2 roadmap: ~1. 7M: Lang+Zipf analytics (600K) + Lean Mathlib (200K) + Endangered-language preservation partnership Wikitongues+ELP+CARE (900K). Copyright © 2026 Munehiro Terada / Roboken. Licensed under CC-BY-4. 0.

ITU Tier 1+ #33: Linguistics (Kₗang)

Key Points

Abstract

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