The Brush Fallacy and Cognitive Sovereignty: Formalizing Irreducible Human Intentionality, Aesthetic Entropy, and Intellectual Property Attribution in Generative Systems

A pervasive fallacy in contemporary artificial intelligence discourse asserts that because generative models are universally accessible, outputs generated through human-AI interaction are commoditized, interchangeable, and devoid of distinct human authorship. Just as universal access to pigments and brushes does not render every painter capable of producing a masterpiece, access to identical foundation model weights $\theta$ does not equalize creative, strategic, or analytical output. This monograph formally refutes the "Instrumentality Equivalence Fallacy" through information theory, statistical mechanics, and statutory intellectual property doctrine. We prove that an unguided or generically prompted foundation model converges rapidly toward maximum-likelihood mediocrity (mode collapse onto the training manifold centroid). Genuine structural novelty, aesthetic resonance, and analytical depth are strictly bounded by the non-ergodic cognitive entropy injected by the Human-in-Command (HIC). Furthermore, we establish a deterministic cryptographic provenance architecture over the 64-bit Goldilocks prime field ($\mathbb{F}_p, p = 2^{64} - 2^{32} + 1$) via QFS-zkVM and Q-SAFA to mathematically isolate, verify, and protect human intentionality against unauthorized weight absorption, value dilution, and uncompensated platform exploitation under the Strict No-Learn Covenant (NLL-v1.0-2026). ====================================================================== STRICT NOTICE REGARDING INTELLECTUAL PROPERTY, COMMERCIAL LICENSING, AND PROHIBITION OF UNAUTHORIZED AI TRAINING AND UTILIZATION ====================================================================== 1. 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The use of the Works by any AI developer, platform provider, or third party for the following purposes is strictly prohibited without a prior written commercial license agreement and appropriate monetary compensation to the author: Training, pre-training, fine-tuning, alignment, or evaluation of any Artificial Intelligence (AI), Machine Learning (ML) models, or Large Language Models (LLMs). Ingesting and storing information into Retrieval-Augmented Generation (RAG) systems, vector databases, knowledge graphs, or AI agents to generate outputs, summaries, or derivative responses. Automated scraping, crawling, harvesting, or Text and Data Mining (TDM) for dataset compilation. 2. Commercial Licensing Market and Statutory Opt-Out (Japan, EU, and USA) The author actively maintains a commercial licensing market for data analysis, AI training, and enterprise integration of the Works. 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