Relational Existence, Topological Self-Consistency, and the Origin of Fermions in the Floriano Unified Theory

We present the foundational principle of the Floriano Unified Theory (TUF): the Principle of Relational Existence, according to which no particle can exist in isolation because its projection from the atemporal hyperspace Ξ depends exclusively on the holonomies generated by its interactions with neighbouring particles. The resulting self-consistency condition — that the patterns of Ξ which project must be precisely those that generate the holonomies selecting them — leads to a rigid topological structure. We show that the compact space S¹ with N_θ = 207 discrete positions has universal cover S³, whose topology is uniquely guaranteed by the Poincaré theorem proved by Perelman (2003). The isomorphism S³ ≅ SU(2) yields the electroweak isospin group without postulating it. The factorisation 207 = 9 × 23 and the subgroup Z₉ ⊂ Z₂₀₇ generate exactly 9 zero modes — the 9 charged fermions of the Standard Model. The factor 23, a Heegner number, fixes the muon mass scale as the unique arithmetically exceptional solution of the self-consistency condition.

This paper is the ontological foundation (Paper 0) of the TUF series. The formal developments in the following works are consequences of the Principle of Relational Existence stated here:

- Paper 1 — Fermion mass spectrum: https://doi.org/10.5281/zenodo.18988060
- Paper 2 — Why exactly three generations: https://doi.org/10.5281/zenodo.18991190
- Paper 3 — Dark matter as excited holonomy modes: https://doi.org/10.5281/zenodo.18991306