A Relational Least Action Principle Hilbert‐Space: Origin of Gravity

Following Einstein-Rosen (ER) who first recognized it in 1935, we rectify a structural limitation in the Schwarzschild metric. Originally only half of the Newton-Kepler equation was used to derive that metric. Parallel to ER, we substitute the full Newton-Kepler equation instead. Our modification yields a dual-part Schwarzschild metric. However, we offer a different reinterpretation to ER’s bridge/sheets hypersurfaces construct, commonly known as wormholes. We note this modification implicitly introduces discrete spacetime, in the form of hypersurfaces, into general relativity (GR). Under a single relational principle we develope the resulting modified metric into a relational graviatational model. In this model gravity emerges as the effect of the interaction of its dual-part with discrete spacetime. Under equilibrium/nonequilibrium conditions this interaction results in a dynamical repulsive gravity as well as GR’s attractive gravity. This relational interaction prevents central singularity formation. The resulting dynamics is encoded in an energy imbalance geometry. This geometric/ergodynamic reinterpretation of gravity lead to a Hilbert-space formulation of gravity. This relational interaction dynamics result in a confinement-based cosmological diagnostic, and a kinematical Hilbert space of shell degrees of freedom. Junction and Hamiltonian constraints are imposed via group averaging. We embed entropy directly into toroidal geometry. That yields oper- ational observables including orbital invariants, gravitational wave echoes, and shadow modulation. The resulting framework reproduces classical tests results, gives matching numerical estimates for observed cosmological densities, and provides a singularity-free bounce metric. We argue information theoretic functionals (ITF), cannot serve as generators of dynamics, or gravitational interaction. ITF’s are dimensionless state maps without operator action. As such, their role is diagnostic, not dynamical. By contrast, relational least action principle provides a universal generator. This universal generator is applicable across mechanics, field theory, relativity, and quantum dynamics. The Hilbert‐space embedding and equilibrium projection theorem show how standard quantum evolution emerges from this structure. This completes the shift from infor- mational interpretations to a physically grounded, operator‐level account of gravitational dynamics.