Abstract Contemporary Artificial Intelligence is facing a crisis of scale and interpretability. Traditional Large Language Models (LLMs) rely on additive complexity, resulting in opaque "black boxes" that struggle with real-time updates and logic. This paper introduces the C.L.E.A.R. (Contrainte Logique Émergente & Herméneutique) framework, a paradigm of Subtractive Intelligence. Building upon the Lottery Ticket Hypothesis, we apply extreme structural pressure to induce Grokking, forcing the network to abandon statistical approximation for algorithmic generalization. We demonstrate the extraction of deterministic "Logical Kernels" (< 100 KB) capable of resolving axiomatic paradoxes through emergent periodic wave-functions. Furthermore, we outline the D.R.E.S. protocol, a decentralized distribution model inspired by Federated Learning that guarantees user privacy by extracting pure logic devoid of training data. Code and Resources C.L.E.A.R. Framework: https://github.com/Maxenonyme/C.L.E.A.R Axiomatic Duality Experiments: https://github.com/Maxenonyme/Axiomatic-Duality-Grokking
Maxence Berthomieu (Fri,) studied this question.