The collective alignment of spins has traditionally been described through the phenomenological molecular field of Weiss or the quantum mechanical exchange interactions of Heisenberg. While these models have served as the bedrock of magnetism, they remain dependent on empirical energy scales and fitting parameters to bridge the gap between microscopic theory and macroscopic transition temperatures. This paper presents the CM Magnetism Theorem, a first-principles derivation of magnetic order rooted in the axioms of Cognitional Mechanics (CM). As the terminal component of the CM transport triad, this work reinterprets ferromagnetism as the proactive "Redundant Copying" of information. In the CM framework, if friction represents failed synchronization and superconductivity represents an algebraic cage against phase-leakage, magnetism is the state where the system maintains logical consistency across a lattice via high-density information parallelization. By mapping the spin manifold onto the SU (2) adjoint representation within M2 (C), we derive the CM Magnetism Constant Lambdaₘag = pi. This constant represents the density of orientation-identities per unitary cycle. We show that the Curie temperature Tc is the critical threshold where thermal stochasticity—defined here as "information overwriting"—exceeds the parallelization frequency of the system. The theorem provides a unified explanation for the stability of magnetic order, analytically deriving Tc values for Iron (Fe), Nickel (Ni), and Cobalt (Co) without empirical fitting. By establishing that the robustness of magnetism stems from the lower-dimensional constraints of the SU (2) manifold compared to the SU (3) manifold of superconductivity, this paper provides a rigorous geometric basis for why magnetic order persists at much higher temperature scales. This work completes the logical bridge between algebraic geometry and collective order, positioning CM as the unified logic for dissipation, non-dissipation, and informational redundancy in condensed matter physics. Key Features: First-Principles Derivation: Derives the Curie temperature using only structural constants (pi), coordination numbers (z), and lattice parameters. Information Parallelization: Redefines spin-spin interaction as a cost-minimization process of information copying within M2 (C). Dimensional Stability: Explains the thermal resilience of magnetism via the geometric constraints of the SU (2) manifold. Predictive Accuracy: Provides a rigorous framework that matches experimental Tc values with over 99% precision for primary ferromagnets. This paper is a direct expansion of the framework established in the CM transport series and completes the triad alongside the Friction and Superconductivity theorems.
T.O. (Thu,) studied this question.