1. Introduction

1.1 The Conceptual Crisis of Gravity

Gravity occupies a unique and unsettled position in fundamental physics. In classical theory, it is modeled as a force acting at a distance, while in general relativity it is reinterpreted as a manifestation of spacetime geometry. Although both descriptions are empirically successful within their respective domains, they are conceptually incompatible and provide no unified account of what gravity is.

The force-based description relies on instantaneous interactions governed by prescribed laws, whereas the geometric description replaces forces entirely with curvature and geodesic motion. Neither framework explains why gravity should exist in the first place, nor why it should exhibit the specific qualitative features observed across scales. General relativity, in particular, presupposes the existence of spacetime geometry and gravitational interaction, offering no criterion for when gravitational behavior should emerge, weaken, or fail.

Effective and modified gravity models extend or approximate these theories, but they inherit the same foundational assumption: gravity is always present and must be encoded either as a force or as geometry. This implicit assumption obscures the deeper question of whether gravity is a necessary structure of nature or a contingent dynamical phenomenon.

1.2 Why Emergence Is Not Enough

In response to these limitations, a variety of emergent-gravity proposals have been developed, suggesting that gravity arises from underlying microscopic degrees of freedom, thermodynamic principles, or collective behavior. While these approaches relax the assumption of fundamentality, they typically retain an implicit notion of gravitational existence. Emergence is invoked as an explanatory label rather than a mathematically precise condition.

Most emergent frameworks focus on reproducing known gravitational equations or phenomenology, but they do not specify the conditions under which gravity should fail to appear. In particular, they lack an explicit criterion distinguishing regimes where gravitational behavior exists from those where it does not. As a result, emergence alone does not resolve the conceptual problem; it merely relocates it to a deeper level without defining a sharp existence boundary.

Without a time-dependent, dynamical condition for gravitational existence, emergent models remain descriptive rather than generative. They explain how gravity might look once assumed, but not why it should arise at all, nor why it may appear intermittently or conditionally.

1.3 Scope and Structure of This Work

This work addresses the existence problem of gravity directly. We do not assume gravity as a force, a geometric property, or a universal interaction. Instead, we ask under what dynamical and temporal conditions gravitational behavior can arise from a minimal inertial system with dissipation and memory.

The framework developed here is intentionally limited in scope. We do not attempt to quantize gravity, modify general relativity, or propose a new metric theory. We do not claim universality across all physical regimes. Rather, we construct a controlled setting in which gravitational phenomenology—specifically bound orbits—can be studied without presupposing its existence.

For this reason, the present work defines a framework rather than a model. A model specifies outcomes given assumptions; a framework specifies the conditions under which certain classes of outcomes can exist at all. By focusing on temporal closure and inertial dynamics, we provide a foundation that can support multiple models while remaining agnostic about force laws and geometry.