Configuration-Dependent Bilocal Constraints and the Emergence of Lorentzian Geometry

This work constitutes the first technical steptoward a relational formulation of gravitybased on the constraint formalism.We consider a bilocal quadratic phase-space constraintwhose structure depends on configuration variablesand show that its geometric consistencyleads to the emergence of a local Lorentzian geometryin the reference sector.The motion of the projected constraint orbitstakes the form of geodesicsof a certain effective structure,without postulating a spacetime metricor a time parameter at the fundamental level.The resulting formalism is interpretedas a relational counterpartof particle motion in curved geometry,providing a natural openingtoward geometrodynamics.