Euclidean Condensate Theory (ECT): Emergence of Spacetime, Quantum Mechanics, and Gravity from Spontaneous O(4) Symmetry Breaking

Euclidean Condensate Theory (ECT) is developed as a framework in which spacetime, quantum mechanics, and gravity emerge from spontaneous symmetry breaking of a single scalar condensate on a four-dimensional Euclidean manifold. In this picture, Lorentzian signature, time, the causal cone, and the effective gravitational and quantum structures arise on the ordered branch rather than being introduced as independent starting postulates. The same framework also relates the effective values of key physical constants, including the speed of light, Newton's constant, and the quantum action scale, to condensate parameters. The theory is organised around one underlying architecture applied across domains that are usually treated separately: quantum dynamics and gravity; a pre-geometric route to the interaction sectors and fermionic structure; the dark sector, including galaxy rotation curves, the baryonic Tully–Fisher relation, late-time acceleration, and the cosmological-constant problem; the horizon, flatness, and monopole problems without inflation; and structural aspects of the measurement problem and black-hole information problem. It also leads to testable consequences, including an ultra-weak fifth-force channel and an ultralight Goldstone-like boson sector. Throughout, derived results, effective descriptions conditional on closure assumptions, and sharply stated open problems are kept explicitly separate. ECT is presented not as a finished ultraviolet completion, but as a unified and testable research programme with explicit falsifiers. All numerical code is publicly available at https://github.com/chufelo/ECT-preprint-code. Companion article: An accessible overview is available at https://doi.org/10.5281/zenodo.19430795