Preonic First Principles and the Bell Correlations: Deriving E(a,b) = −cos(θ_ab) from the Symmetry Constraints on Spin-½ Preonic Aggregates

Abstract

Bell-type experiments are the most precisely tested quantum mechanical predictions and the most frequently cited evidence for non-locality in physics. This paper derives the quantum mechanical correlation function E(a,b) = −cos(θ_ab) for spin-½ particle pairs in the singlet state from the first principles of Quantum-Geometry Dynamics (QGD). Reversing earlier claims that QGD satisfies Bell's theorem through source-correlation alone, this version explicitly acknowledges that source-correlation is fully compatible with Factorizability. Instead, QGD denies Factorizability via the instantaneous, non-local p-gravity coupling (m_a · m_b · k) operative between the two measurement events—a mechanism whose defense is formally offloaded to companion papers (P2, P47), freeing this paper to focus strictly on the geometric derivation. The derivation proceeds in two stages. The first establishes four symmetry constraints that any preonic account of spin-½ must satisfy: rotational isotropy of preonic space, the zero-total-momentum condition defining the singlet state, the binary outcome constraint, and the conservation of intrinsic momentum. These constraints are shown to be jointly sufficient to uniquely determine the correlation function given a specified measurement weighting function P(+1|θ). The second stage demonstrates that if the p-gravity binding structure of a spin-½ aggregate naturally enforces an internal angular distribution of f(α) ∝ (1 + cos α), yielding the weighting P(+1|θ) = cos²(θ/2), the exact −cos(θ_ab) correlation and the Tsirelson bound of 2√2 follow directly. The full derivation of this distribution from p-gravity equilibrium is stated formally as a conditional structural constraint requiring a companion calculation, rather than a completed closed-form proof. Three physical extensions beyond the idealized case are incorporated: (i) measurement is restricted to objects (P6), meaning only total mass and resultant momentum are accessible to the detector; (ii) p-gravity coupling geometry is mass-velocity-regime dependent; and (iii) the n-gravity field of distant matter introduces a systematic, testable deviation E(a,b) = −cos(θ_ab) + ε, distinguishing QGD from standard quantum mechanics. The account is compared with Bohmian mechanics, retrocausal models, and the many-worlds interpretation. Finally, the refutation of top-down causation (P19) formally closes the option that macro-level autonomy in the experimenter's settings could generate the correlations by a non-preonic route. Continuous functions are treated throughout as finite prescriptions (P36), and no new axioms or free parameters are introduced.