The Spatial Autodynamicity Field Ψ: A Technical Supplement to SGCU Version 2.0

This paper is a technical supplement to the SGCU Version 2.0 thought experiment (DOI: 10.5281/zenodo.20695406). It focuses exclusively on the newly introduced physical quantity Ψ – spatial autodynamicity – postulated as the intrinsic property of the only fundamental entity: three‑dimensional continuous space. Ψ is a second‑order symmetric tensor field that reduces to a scalar Ψ(t) in a homogeneous universe. Using an action S = \int d^4x \sqrt{-g(\Psi)} [\frac12 \partial_\mu \Psi \partial^\mu \Psi - V(\Psi)] + S_{\text{top}}[\Psi], we derive Ψ’s behaviour on three scales: (i) cosmological – Ψ(t) drives dynamic dark energy (predictions w_0\approx-0.96,\; w_a\approx-0.15), a cyclic bounce via a unification phase transition, primordial gravitational waves r\approx0.0012, and an ultra‑low‑frequency gravitational wave background; (ii) macroscopic gravity – the smooth part of Ψ is mapped to the metric g_{\mu\nu}= \mathcal{G}_{\mu\nu}[\Psi], and in the long‑wavelength limit general relativity emerges as an effective theory; (iii) microscopic quantum scale – topological defects of Ψ (vortices → U(1), trefoil knots → SU(3), chiral twists → SU(2)) generate Standard Model particles through quantised excitations, while quantum wavefunctions and measurement collapse correspond to fluctuations and decoherence of Ψ. We thereby show that general relativity and quantum mechanics are not contradictory but two effective descriptions of the same Ψ field at different resolutions. All falsifiable predictions are listed. Open mathematical problems are explicitly stated to invite collaboration. This supplement is intended for readers with a background in theoretical physics and mathematics.