Research Proposal

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On the Ontological Foundations of Mathematics: A Unified Theory of Phenomenal Layers, Essence Classes, and Sequential-Positional Fields

• September 2026

• DOI: 

• 10.13140/RG.2.2.13314.03524

• Xiaohui Zou

This paper establishes a rigorous ontological and formal foundation for mathematics based on the framework of Rongzhi Xue (Rongzhixue, the study of wisdom convergence). We distinguish sharply between the phenomenal layer (W, T, L: physical, intentional, and linguistic phenomena constrained by space-time-matter-energy) and the essence layer (LYFXW: li, yi, fa, xu, wei), and prove that the latter constitutes a single equivalence class under the Law of Identity-Difference. Crucially, we demonstrate that what are traditionally called "spaces" in mathematicsCartesian, Hilbert, factor, Euclidean, hyperbolic (BolyaiLobachevsky), and Rie-mannianare not physical spaces at all, but rather abstract sequential-positional fields (F), i.e., structures of order, position, formal relation, and essential information. We formalize this distinction, give explicit isomorphisms and counterexamples, and resolve the category error that has historically conflated phenomenal space with mathematical structure. The resulting Φ-Architecture (four-layer information architecture) and x = p(W) metric calculus provide a complete, formally sound basis for mathematics, physics, computation, and humanmachine symbiosis.

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