Unity of Space, Time, and Electromagnetism in the ZEBTS Theory

This article demonstrates that the Zero‑Energy Boundary Theory of Space‑Time (ZEBTS) provides a mathematically complete and fully derived Theory of Everything. Using only the Spectral Theorem, the Kato–Rellich theorem, Stone’s theorem, and the axioms defining the χ‑operator, the work proves that space, time, electromagnetism, the metric, the fine‑structure constant, and charge quantisation all emerge as spectral and topological projections of a single self‑adjoint operator 𝐷 𝜒 with compact resolvent. Space arises from the nodal structure of eigenfunctions; time emerges from the unitary evolution generated by 𝐷 𝜒 ; electromagnetism is produced by the non‑commutativity of the χ‑Boundary algebra; and the metric is induced by the resolvent kernel. Maxwell’s equations, the Schrödinger equation, the Bianchi identity, and charge conservation are shown to be topological invariants of the χ‑Boundary, not postulated laws. The fine‑structure constant 𝛼 = 1 / 𝜆 137 is derived as a spectral eigenvalue, while charge quantisation follows from the topology of the χ‑Boundary gauge sector. The χ‑signature 𝑆 𝜒 provides three quantitative, falsifiable predictions, each parametrically distinct from known physical corrections, establishing ZEBTS as an empirically testable framework. The global novelty of this work is the complete derivation chain: Spectral Theorem → χ‑operator → χ‑Boundary → physical observables. No physical assumptions are introduced. The article concludes that ZEBTS is a rigorous, falsifiable, and structurally complete Theory of Everything.