Bell Correlations from Joint Phase Dynamics in Dual-Frame Theory: Distance-Dependent Suppression and the Continuum Limit

This paper presents a geometric, admissibility-based account of Bell correlations within Dual-Frame Theory (DFT). The central claim is structural rather than dynamical: violations of Bell inequalities do not require nonlocal or superluminal causal influence, but instead diagnose a failure of state-based (Σ₁) descriptions to preserve the full set of admissible joint continuations encoded at the trajectory or configuration level (Σ₂). For bipartite systems with binary outcomes, a quotient construction identifies a single gauge-invariant relative phaseΔθ ∈ S¹ as the joint configuration coordinate relevant to Bell scenarios. Measurement settings act as contextual frame rotations on this manifold, local outcomes remain stochastic, and no-signaling is preserved, yet not all joint outcome pairs are admissible. From this admissibility geometry, the standard cosine correlator and the Tsirelson bound emerge as geometric ceilings imposed by the structure of the quotient space rather than as axioms of Hilbert-space kinematics. A stability-based harmonic selection argument shows that binary coarse-graining on S¹ naturally yields a first-harmonic correlator as the empirically robust form. A concrete worked example is provided in an appendix, demonstrating how higher Fourier harmonics are intrinsically suppressed under dichotomic measurement maps and generic coarse-graining. Possible deviations from ideal admissibility—such as relative-phase diffusion or noise—are treated separately as phenomenological perturbations. Existing loophole-free Bell experiments are used to place stringent upper bounds on any such admissibility degradation, implying that standard quantum predictions are recovered in the ideal limit. The work reframes Bell correlations as diagnostics of representational insufficiency rather than as evidence for nonlocal dynamics. Its contribution is foundational and interpretive: it clarifies how correlations stronger than classical factorization can arise from joint geometric constraints while remaining fully compatible with relativistic causality.