The Zero Group Set - Ontological Mathematics

Zero serves different roles across mathematics, physics, and philosophical interpretation. This paper organizes selected uses into a Zero Group Set, understood as a comparative taxonomy. It distinguishes arithmetic identities and annihilators from roots, zero maps, limiting values, geometric reference points, and physical ground states. Within the coherence framework, it retains seven proposed classes: Arithmetic Zero, Factorial Zero, Exponential Zero, Zeta Naught, Tower Zero, Dimensional Zero, and Symmetry Zero. Their ontological readings are stated separately from conventional mathematical definitions and empirical claims. The central proposal is that the varied uses of zero provide a vocabulary for examining absence, balance, potential, and coherence. Establishing a common mechanism of emergence require further definitions and derivations; the present contribution is the taxonomy and the distinctions needed to use it consistently. Keywords zero; ontological mathematics; coherence; identity; vacuum; Explainer video Watch on YouTube (Roots of Reality): https://www.youtube.com/watch?v=gQLV2gHwljw The video, its thumbnail and description are included in this record.