Starting from the zero-entropy state and increasing entropy through minimal single-bit changes, we ask what geometric and structural features emerge? Do they resemble those of the observed universe?
The key insight is that space itself is not a background structure into which matter is placed. Space emerges relationally from the density of the minimal detectable substructures of information. When entropy is zero, no structures exist and the universe is a single unextended point. As entropy increases, minimal structures proliferate, and their uniform distribution across the bitstring is perceived by an internal observer as spatial expansion. Expansion is the geometric reading of entropy increase.
This reframing has three immediate consequences.
First, it resolves the initial conditions problem without appeal to quantum fluctuations or fine-tuning. The zero-entropy initial state is one of the two shortest-description configurations (the all-zero and all-one bitstrings) in the entire space of 2L bitstrings, and is unique once a symmetry-breaking convention fixes which of the two is taken as the origin.
Second, it provides a native mechanism for matter formation. As entropy increases, higher-order structures emerge, and — as shown in Section 3 — the qualitative shape of their abundance curve is fixed in advance by the combinatorial composition of the pattern being counted, not by any physical input.
Third, and most significantly, the model’s underlying relaxation variable admits an exact reparametrisation under which it reproduces the de Sitter scale factor precisely (Section 5.3), rather than merely resembling it qualitatively.
The paper is structured as follows. Section 2 describes the bitstring setup, the exact Ehrenfest solution governing its evolution, the fabric filter, and the recursive density filters that extract hierarchical matter structures. Section 3 presents the numerical results and the three-regime classification of structural abundance. Section 4 establishes the filter-independence of this classification across any filter definitions. Section 5 interprets the findings and compares them with standard cosmological approaches, including the exact de Sitter correspondence. Section 6 concludes.