General Relativity admits two extreme solutions that appear, at first sight, to be unrelated. De Sitter space describes a universe with no matter and a positive cosmological constant, expanding exponentially without bound. The Schwarzschild solution describes the opposite extreme: all mass concentrated at a single point, spacetime contracted to a singularity. Between these extremes, the Friedmann equation governs the observed universe — an expanding geometry whose rate of expansion is modulated by the density of matter and vacuum energy.
The present paper shows that these three are not independent results but three consequences of a single information-theoretic counting principle. When the universe is modelled as a closed system of n bits, partitioned at each moment between free spacetime fabric and composite matter structures, the scale factor perceived by an internal observer is the fraction of the bit budget that remains independently addressable. De Sitter and Schwarzschild emerge as the two limiting cases of this fraction.
No metric tensor is postulated. No force law is imposed. No cosmological constant is introduced as a free parameter. The expansion history of the universe is the geometric reading of information conservation.
The paper is structured as follows. Section 2 derives the relational scale factor from the counting argument and identifies the two GR extremes. Section 3 maps the framework onto Friedmann variables. Section 4 discusses the results. Section 5 states the three foundational results. Section 6 identifies open problems.