Ontological Singularity Interpretation: In Search of a New Mathematics for Fundamental Physics

We outline a conceptual framework in which the entire physical universe---spacetime, fields, and particles---is interpreted as the boundary projection of an ontological singularity $\Omega$, a pre-spatiotemporal, structureless source. Photons are identified as the unique fixed points of this projection, characterized by their null proper time and their direct inheritance of the timeless nature of $\Omega$. This single postulate offers a unified ontological perspective on the core structures of quantum mechanics: the uncertainty principle reflects the impossibility of simultaneously localizing a boundary point in two complementary ways of approaching $\Omega$; non-commutativity emerges from the intrinsic algebraic structure of the projection; entanglement corresponds to multiple boundary points sharing a single source in $\Omega$; the measurement problem dissolves because measurement accesses pre-existing source information rather than collapsing a wavefunction. The framework extends to gravitation (spacetime as boundary geometry, gravitons as its quantized fluctuations), to the gauge groups $U(1)$, $SU(2)$, $SU(3)$ (interpreted as the simplest symmetry structures emerging from the projection), and to cosmology (dark energy as the residual tension of the temporal projection direction, offering a fresh perspective on the vacuum catastrophe). The framework is not a complete theory but a conceptual model pointing toward the need for a novel mathematical structure: a continuous geometry that inherently forbids exact localization, distinct from both classical continua and discrete lattices. The aim of this paper is to articulate this vision and to stimulate the search for the appropriate mathematical language that could turn it into a predictive physical theory.