Horizons as Boundaries of Geometric Representability: A Functionalist Reading of Black Holes in the Spacetime-Emergence Debate

This paper takes up a conceptual question left open by the physics of emergent spacetime: if geometry is an emergent, functional description of a deeper non-spatiotemporal structure of quantum correlations, how should we construe the regimes — black-hole horizons and the classical singularities behind them — where that description visibly fails? Working within the spacetime-functionalism program of Knox, Lam, and Wüthrich, and observing Jaksland and Salimkhani's discipline that "spacetime emergence" names many problems rather than one, the paper defends a deflationary reading: a horizon is a boundary of geometric representability, while the substrate itself remains definite. The argument is set out formally enough to be inspectable, and its central inference is shown to be defeasible — licensing the epistemic reading only on an explicit premise of substrate regularity, which the paper isolates rather than assumes silently. The proposal offers no theory of quantum gravity and no quantitative claim, only a clarification of what it would mean for geometry to have an edge.