PFUSRC-053: From Empty Set to Basin Surface – Twelve Questions on Human Mathematics, and a Reconstruction Agenda Based on a Closed Whole

Since the axiomatic system was established, modern mathematics has been built upon four foundational premises: the empty set as a void origin, discrete independent units, static uncoupled axioms, and the presupposition of actual infinity. This artificially constructed theoretical system has supported thousands of years of symbolic deduction and engineering applications. For a long time, academia has tacitly equated this locally effective computational framework with the ontological laws of the universe, mistakenly elevating man-made instrumental tools to universal cosmic truths. Nevertheless, this system bears an innate ontological divide: to simplify calculation and guarantee internal logical consistency, modern mathematics discards the universal properties of the real cosmos—topological closure, holistic coupling, scale stratification, dynamic evolution and interfacial interaction—leading to an inherent flaw: it works well as a computational tool yet distorts ontological reality. This paper adopts limited-range reductio ad absurdum as its core argument method. Through twelve progressive fundamental questions, it systematically dissects the foundational defects of conventional mathematics covering the ontology of zero and one, the definition of infinity, artificial axiom selection, systemic boundary setting and thermodynamic interpretation. It clarifies the essential dividing line between the instrumental validity of classical mathematics and its overextended ontological claims. On this basis, centering on the topological structure of 45° triple coaxial bicone, the 12/11 topological gauge ratio, scale projection epistemology and globally closed steady-state topology, this paper puts forward a full reconstruction scheme for the foundations of mathematics, realizing a paradigm shift from "human-selected axiomatic systems" to "cosmologically necessary topological systems". Furthermore, this paper provides dimensional reduction interpretations of core classical physical equations within the PFUSRC ontological mathematics framework: it proves that E=mc² is a degenerate special case of dual-field dynamics, redefines the speed of light as an intrinsic topological constant of the Gap Field, and reinterprets Feynman path integral as a 3D cross-section approximation. This work achieves unified reconstruction spanning mathematical foundations and fundamental physical laws.