Emergence of FLRW Cosmology from Discrete Horizon Layering

We construct a horizon-based reconstruction algorithm in which the ordered growth history of a spherically symmetric black-hole horizon defines an effective expanding interior geometry. Adopting an external-observer perspective, horizon evolution is organized as a discrete sequence of completed updates registered on a stretched horizon at Planck-scale proper distance outside the Schwarzschild radius. The update sequence is used solely as a causal-ordering and bookkeeping convention, rather than as a claim about microscopic mass quantization. Using only the completed-update ordering, the horizon area-information relation, and an information-limited stacking rule that reconstructs radial depth from the cumulative update history, we show that a homogeneous and isotropic interior continuum envelope emerges. Coarse-grained homogeneity is implemented by requiring that equal enclosed update fractions correspond to equal enclosed volume fractions on constant-time slices, which fixes the radial weighting of successive layers and removes the central density divergence that would arise from naive Schwarzschild-radius layering. The maximally symmetric continuum descriptor of the reconstruction is therefore FLRW. A minimal stacking convention that identifies areal radius with accumulated stacked proper depth selects the spatially flat representative within the reconstruction class. Strict edge matching of the reconstructed outer radius to the instantaneous horizon size, together with scale-free fractional rescaling, yields a rigid coasting expansion law in the reconstructed interior. No bulk stress-energy tensor, Einstein field equations, or microscopic model of horizon degrees of freedom is assumed. The result should be read as a constructive existence proof: given a minimal and explicit set of horizon-based structural inputs, a spatially flat coasting cosmology emerges as the natural continuum description of the coarse-grained horizon update history.