DER IV: Deterministic Spinor Geometry and the Physical Measurement Bridge to EPR Correlations

This work presents DER IV, the fourth instalment in the Deterministic Emergent Reasoning (DER) programme. The framework develops a fully deterministic, non-probabilistic description of EPR-type correlations based on a single global spinor field (“one-body principle”). Detector settings (α,β)(\alpha, \beta)(α,β) are not external random variables but emergent boundary conditions of the same global configuration. As a result, statistical independence (SI) is not definable within the ontology and Bell’s joint-assignment structure does not arise.

Physical detector clicks are modelled as sign-thresholded projections of bilinear covariants of the global spinor. A deterministic evolution law for the spinor phase is given, together with a numerical scheme reproducing the −cos⁡(α−β)-\cos(\alpha - \beta)−cos(α−β) correlation without sampling, noise, or hidden variables.

Appendix D formally shows the impossibility of embedding DER into any local hidden-variable (LHV) representation. Additional sections detail the measurement bridge, the non-jointness axiom, the global structure of detector orientations, and a deterministic threshold model for real detectors (SNSPD/APD/TES). The paper concludes that DER occupies a domain outside Bell’s probabilistic framework while remaining physically coherent and experimentally testable.