Deriving Hardy's Entanglement Probability from Presentist Fragmentalism

We derive Hardy's maximal nonlocal success probability directly within a Presentist Fragmentalist (PF) ontology, without invoking Hilbert space, amplitudes, or the Born rule. The core idea is to treat pre-interaction misalignment of "present windows" as a measurable structure on an alignment space Λ = T × T endowed with a uniform product measure µ. A Fragmentalist Probability Theory (FPT) is developed on this space, replacing the standard Kolmogorov framework. Hardy's four logical constraints (H1–H4) are encoded as measurable relations on Λ. A minimal "correlated subset" ansatz combined with exclusion of synchronized alignments yields a PF success probability P(p) = [p·(1 − p)]^2/(1 − p^2) for 0 < p < 1, with a unique interior maximizer at p = φ^−1 (the golden ratio conjugate) and Pmax = φ^−5 ≈ 0.09017, which equals the quantum Hardy bound. We show kernel-independence, no-signaling of marginals, robustness to perturbations, and a concrete setting-indexed construction on the admissible space Λ^H that realizes the full Hardy table. The result is an ontologically transparent derivation of Hardy's probability from PF's synchronization under misalignment. We close with remarks on robustness and prospects for generalization.