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

I present Euclidean Condensate Theory (ECT), a framework in which Lorentzian spacetime, quantum dynamics, gravity, and large parts of gauge and matter phenomenology are investigated as emergent consequences of spontaneous O(4)→O(3) symmetry breaking in a scalar condensate on a four-dimensional Euclidean manifold. The manuscript is organised into four Parts. Part I develops the foundations of the theory: the Euclidean Φ-medium, the ordered vacuum branch, the emergence of Lorentzian signature and causal structure, the matching relations for the characteristic propagation speed, Newton’s constant, and the pre-quantum action scale, and the structural branching into geometric and coherent sectors. Part II develops the macroscopic branch: generalised Einstein equations with ordered-branch corrections, cosmology without a separate inflationary sector, a benchmark route to Hubble-tension alleviation, JWST early-structure implications, and galactic phenomenology including the baryonic Tully–Fisher relation, the radial acceleration relation, and rotation-curve fits across 165 SPARC galaxies without particle dark matter. Part III develops the coherent branch: winding sectors, reflection positivity and the Hilbert-space bridge, canonical structure, decoherence, the quantum–classical boundary, the Principle of Euclidean Stationarity, entanglement and delayed-choice phenomena, vacuum-response effects, and the black-hole information programme. Part IV summarises the derivational architecture, compares ECT with neighbouring programmes, and states falsifiers, limitations, and open problems explicitly. A central feature of the work is methodological honesty: results are separated throughout into structural results, closure-dependent results, and open problems, rather than being presented at a single level of confidence. ECT is therefore not presented as a completed final theory, but as a testable unifying framework for emergent spacetime physics. All numerical code, fitting scripts, and figure-generation code are publicly available at:https://github.com/chufelo/ECT-preprint-code