From Relation to Gauge Geometry. Presymplectic Reduction and Localization of Bilocal Constraint Orbits

In previous work, the radial sector of bilocal phase spacewas shown to generate a distinguished relational time coordinatethrough the geometry of constraint orbits. The present paper investigates the complementary angular sector.We show that the angular sector admits a natural presymplectic reduction whose reduced phase space is a symplectic orbit carrying a Hamiltonian group action. Localizing this reduced internal geometry over spacetime naturally produces a connection, covariant momenta, and the Yang–Mills curvature. The resulting construction leads from the geometry ofconstraint orbits to Yang--Mills-type structures withoutintroducing gauge fields as fundamental objects.