The CM Friction Theorem: An Analytic Derivation of the Coefficient of Friction via Non-Commutative Phase Interference

This paper presents a groundbreaking analytic derivation of the coefficient of friction (mu) rooted in the principles of Cognitional Mechanics (CM). In a departure from classical stochastic models such as the Prandtl-Tomlinson and Frenkel-Kontorova frameworks, this work redefines friction as a deterministic phenomenon emerging from non-commutative phase interference. By modeling the interface interaction as an operator M_int acting upon a state trajectory Phi(t), we derive the CM geometric constant K = sqrt(3) from the adjoint Casimir of the su(3) algebra. The coefficient of friction is shown to be a structural invariant of the algebraic manifold, represented as the ratio of integrated "logical stress" (unitary leakage) to the spectral expectation of the normal load. The theorem provides a unified description of diverse friction regimes, providing a first-principles explanation for structural superlubricity through ergodic phase averaging. By establishing a direct link between informational consistency and mechanical resistance, this work positions CM as a rigorous, predictive framework for modern tribology and condensed matter physics. Key Features: Analytic Derivation: Derives mu without empirical fitting parameters. Geometric Invariance: Establishes K = sqrt(3) as a universal constant in M3(C) interface algebra. Deterministic Framework: Eliminates stochastic "mayoi" (deliberation) in state transitions. Information-Physics Equivalence: Connects friction to Landauer’s principle via logical stress density. This paper is an application of the foundation laid in "A Wave-Representational Formulation of Cognitional Mechanics: From Algebraic Finality to Process Visibility" (DOI: 10.5281/zenodo.18203826).