13. Limitations and Open Problems

13.1 What This Framework Does Not Claim

This work does not claim to replace existing gravitational theories within their established domains of empirical success. In particular, it does not assert that Newtonian gravity or general relativity are incorrect as effective descriptions of observed phenomena.

Rather, the framework presented here operates at a different conceptual level. It addresses the conditions under which gravitational behavior exists at all, not the precise form of force laws or spacetime dynamics once such behavior is already assumed.

Specifically, this work does not claim:

• A derivation of Einstein’s field equations,
• A metric or geometric description of spacetime,
• A universal force law valid across all regimes,
• Immediate experimental falsification of established models.

The intent is foundational clarification, not phenomenological replacement.

13.2 Numerical and Conceptual Boundaries

The present results rely on numerical simulations of a simplified inertial emergent system. While the simulations demonstrate robust qualitative behavior, they are subject to inherent numerical limitations.

These include:

• Finite grid resolution and domain size,
• Discretization effects and timestep constraints,
• Idealized boundary conditions,
• Simplified forms of damping and screening.

Conceptually, the closure functional $\mathcal{C}[\Psi(t)]$ is presently defined operationally rather than analytically. While its empirical extraction is well-defined, its mathematical structure remains only partially characterized.

As such, the framework should be regarded as a controlled exploration of a principle rather than a complete theory.

13.3 What Must Be Proven Next

Several critical steps are required to elevate this framework from a validated conceptual structure to a fully established physical theory.

These include:

• A rigorous mathematical characterization of the closure functional,
• Analytical criteria for phase boundaries and critical thresholds,
• Proofs of stability and uniqueness for closed dynamical phases,
• Extension beyond two-body configurations,
• Connection to observational or experimental signatures.

Of particular importance is the identification of invariant signatures of temporal closure that could, in principle, be tested beyond numerical simulation.

Until such developments are completed, the framework should be understood as an opening of a new line of inquiry rather than a finished endpoint.

These limitations are not weaknesses of the approach, but a reflection of its foundational nature. Any theory that seeks to redefine the conditions of physical existence must first establish its boundaries with precision.