Epistemic Singularities: The Failure of Local Reconstruction in Non-Analytical Spacetimes

General Relativity is classically formulated on smooth (C∞) manifolds, where the existence and uniqueness of geodesic evolution are guaranteed by the well-posedness of hyperbolic partial differential equations. However, we identify a specific class of smooth but non-analytic regimes, termed “Flat Points”, where this global determinism decouples from local reconstructibility. At a Flat Point, the metric derivatives may vanish to all orders, rendering the Taylor series expansion informationally vacuous despite the manifold remaining geometrically regular. We define this phenomenon as an “Epistemic Singularity”: a locus where the local jet data fails to encode the extension of the worldline, effectively creating a horizon of local predictability. We argue that in these informationally degenerate regimes, the transition from derivative-based classical trajectories to path-integral formulations arises not solely from quantum scales, but as a necessary mechanism for information completion in non-analytic spacetimes.