THFR-E3: Experimental Constraints on Finite-Speed Hidden-Influence Models and the Premetric Bell/EPR Architecture of THFR

Bell experiments constrain local/common-cause explanations of quantum correlations under the corresponding assumptions. A distinct experimental program tests a more specific class of models in which the observed nonlocal correlations are explained by a hidden causal influence propagating in a preferred frame between spatially separated events at a finite superluminal speed c<v<∞. Yin et al. obtained a lower bound of order 104c for the corresponding finite-speed preferred-frame model; Bancal et al. showed that, for the finite-speed causal-influence model class they studied, choosing an arbitrarily large but finite v does not remove the problem of operational superluminal signalling; Santamaria Amato et al. demonstrated a tabletop feasibility speed-bound scheme in the CMB frame; Li, Hu, Deng, and Scarani proposed cluster-state witnesses for a more direct test of finite-speed hidden-influence models. The present work examines how this experimentally tested model class relates to the current Bell/EPR interpretation of the Theory of Harmonic Field Resonance (THFR). The central structural comparison is that, in THFR, the Bell/EPR correlation is not modelled as a hidden influence propagating from one already realized detector event to another through effective spacetime. Therefore, experimental lower bounds on finite-speed hidden influence are not lower bounds on a fundamental “THFR Bell speed.” For the purposes of this work, a structural class of Bell/EPR models compatible with the current THFR causal architecture is defined. At the level of the Bell-binding mechanism, this class is disjoint by construction from the finite-speed hidden-influence class, because the latter requires a finite superluminal propagation parameter v and a corresponding influence-cone structure, whereas the THFR class does not employ such objects for Bell binding. The established correspondence has the epistemic status EXTERNAL STRUCTURAL CORRESPONDENCE. The work is a theoretical model-class comparison and does not present a quantitative derivation of Bell statistics from the mathematical apparatus of THFR.