Resolution of the Hadwiger-Nelson Problem via the Information Entropy Postulate

Resolution of the Hadwiger-Nelson Problem via the Information Entropy Postulate Author Note: This work formally closes the long-standing problem of the chromatic number of the plane by applying the Information Entropy Postulate (PEI) to the stability of informational fields. Abstract I demonstrate that the chromatic number of the plane, $\chi(\mathbb{R}^2)$, is exactly 7. While classical combinatorics remained divided between 5, 6, and 7, I show that within the PEI framework, any configuration with fewer than 7 colors is dynamically unstable. By modeling the plane as a multi-sheeted nodal structure and using the conservation of nodal angular momentum ($J_z$), I prove that the 7-color hexagonal tiling is the unique global stationary solution that satisfies informational reversibility and avoids entropy saturation. (Caution ! TXT, PDF & Simulation is FRENCH Language !