The FCHP Mathematical Basis of Panspatial Genesis Finsler Coherence Hyperfractal Phaspace as the Generative Topology Of Life, Form and Dimensional Emergence

This paper develops the mathematical basis of Finsler Coherence Hyperfractal Phaspace
(FCHP) as the generative topological framework underlying Panspatial Genesis. The central thesis is that FCHP is not a passive geometric container but a coherence-active, anisotropic, recursively structured phaspace whose intrinsic laws govern the emergence of organized form.

Within this framework, Noetherian Finsler Numbers (NFN) provide the quantized local units of directed coherence topology, while the Coherence Directional Gradient (CDG) functions as the primary organizing operator through which chirality, torsion, negentropic stabilization, and irreversible emergence are structured.

The paper establishes the conceptual and mathematical foundations required to show that life-capable organization is not accidental within such a space, but arises as an intrinsic stability regime of the topology itself. In this sense, Panspatial Genesis is presented not as a metaphor but as a theorem of structured coherence space.