Emergent Metric Structure and Effective Gravity from Geometric Overflow

In earlier developments of Selection Geometry, geometric overflow was introduced as the part of structure that remains inaccessible under observer-dependent realization. It was proposed as a natural source of local mixedness and irreversibility. In this paper, we examine the possible spatial expression of that same structure. We argue that gradients of unrecoverable accessibility within the realized sector may generate an effective metric organization: what is harder to access, distinguish, or reconstruct may appear as more distant within the local representation of reality. On this view, space need not be treated as an externally given background. Instead, it may emerge as a relational geometry produced by observer-dependent reduction. We further suggest that gravity-like behavior may be understood as an effective geometric response to persistent non-closure, rather than as a primitive interaction assumed from the outset. This paper does not claim a full derivation of general relativity or a reconstruction of Einstein’s equations. Its aim is more limited: to identify a structural route by which algebraic non-closure and accessibility constraints can give rise to emergent metric structure and effective gravitational behavior. In this sense, geometric overflow is developed here as a structural bridge from informational asymmetry to spatial form.