Champ P: Physical and Geometric Foundations of a Universal Scalar Field

This work introduces the Champ P (Planck Field), a theoretical framework aiming to unify gravity, quantum mechanics, and thermodynamics through a universal scalar field defined on a compact manifold of type (S3×S3)/Z3(S³×S³)/ℤ₃(S3×S3)/Z3. The model explores the coupling between this field and the Standard Model via its topological and geometrical properties, highlighting the emergence of fermionic generations from the homology structure of the manifold. By combining the approaches of Caldeira–Leggett, Lindblad dynamics, and the Wheeler–DeWitt equation, the Champ P provides a coherent description of matter–energy interactions, quantum decoherence, and gravitational curvature at the Planck scale. This framework suggests new perspectives on dark matter, vacuum fluctuations, and the entropic nature of time, contributing to the ongoing search for a unified physical theory.