Paper II [meskanen2002] demonstrated that gravitational collapse, analysed through the execution trace of a computational simulation, converges to a zero-entropy state at the classical singularity. The present paper asks what happens when we begin at that point and move in the opposite direction. We present a purely statistical, information-theoretic model, exactly solvable as an Ehrenfest process [ehrenfest1907], that reproduces the qualitative onset of spatial extent and a fully predictable classification of structure-abundance curves, without any hard-coded physical laws, equations of motion, metric tensors, or imposed initial irregularities. We show that the abundance of any fixed structural pattern falls into one of three combinatorially determined regimes. We further show that a specific, simply-derived transform of the model’s underlying variable reproduces the de Sitter scale factor exactly, under a linear identification of bit-flip time with cosmological time. This resolves an apparent shape mismatch between the model’s entropy curve and cosmological expansion.
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