The Operational Geometry of Coherence: A Deterministic Framework Beyond Spacetime

This article presents a framework in which spacetime is not fundamental but conditional. General Relativity remains exactly valid wherever the coherence field Ξ is high, enabling a smooth Lorentzian manifold. When Ξ ≈ const, the Einstein–Hilbert term is active and the full structure of GR is recovered, including all confirmed weak- and strong-field predictions. When Ξ → 0, coherence collapses, the prefactor of the Einstein–Hilbert term vanishes, and the manifold description ceases to apply. Geometry does not break; it deactivates. Beyond this threshold, the structure of reality is governed by interaction strengths among modal components rather than by metric distances among spacetime points, forming a coherence geometry. The transition between these regimes is dynamical and measurable: modal amplitudes determine the total dynamical content E, phase alignment determines Ξ, and the coherence matrix C₍ᵢⱼ₎ specifies the organisational structure in the non-manifold domain. This framework explains both the emergence and the breakdown of spacetime without modifying Einstein's equations where they have been validated and yields falsifiable observational predictions, including the universal radio → optical/UV → X-ray ordering in coherence-collapse events.