Fire a single particle at a barrier with two slits. An interference pattern emerges even when particles are sent one at a time. Introduce which-path detection and the pattern disappears. Quantum mechanics predicts these outcomes with extraordinary accuracy. What it does not provide is a widely accepted physical account of the underlying mechanism. We present Binding Geometry, a framework that proposes such a mechanism. In this view, a particle corresponds to a locally jammed region within a frustrated geometric lattice. Each particle carries delocalized geometric slack—void degrees of freedom distributed through the surrounding structure. Because this slack is a property of geometry rather than a localized object, it can extend through both slits simultaneously. Overlapping slack configurations give rise to interference. Introducing a detector adds constraints to the local geometry, forcing the slack to localize into a single configuration and suppressing interference. This behaviour is one instance of a broader proposal: physical reality can be understood as a packing problem in which degrees of freedom arrange under geometric constraints. The structure of those constraints determines coordination numbers, phase thresholds, and the numerical values of physical constants. Established physical theories accurately describe the observable consequences of this packing. Binding Geometry aims to describe the underlying structure from which those consequences arise. The framework leaves all experimentally verified equations of the Standard Model and General Relativity intact. It instead addresses a class of open questions left unresolved by current theory, including the origin of the fine-structure constant, the smallness of the cosmological constant, the existence of three particle generations, and the physical interpretation of quantum measurement. Binding Geometry has been examined across more than forty domains spanning physics, computation, and biology (enumerated in Supplement B), where thresholds and transition points consistently align with predictions derived from packing geometry. The framework also yields falsifiable predictions, including the persistence of evolving dark energy in continued DESI releases and a correlated drift between cosmological parameters and the fine-structure constant.