A Unified Framework for Witness Cosmology: Information, Cosmology, and the Cosmological Constant

We introduce the witness number density n_w as a physical quantity and propose, to the best of our knowledge, the first unified equation linking the dark energy density to the thermodynamic cost of information preservation: ρ_Λ = λ(a) n_w (k_B T ln 2). This equation is dimensionally consistent, it constrains the present-day witness density to n_w^0 ≈ 2.3 × 10^13 m^-3 from observations, and it factorizes the cosmological constant problem into a thermal factor T_0/T_Pl ~ 10^-32 and a density factor N_w/N_max ~ 10^-30, whose product matches the observed value to within 20%. The framework rests on a foundational axiom: the universe is a witnessed contract with sixteen structural elements organized into five functional groups. From this axiom, we deduce: (i) the unified equation above; (ii) a beta function for the information–geometry coupling, β(λ) = 4λ, which yields the running coupling λ(a) ∝ a^4; and (iii) a complete mapping of the sixteen structural elements onto physical counterparts. The inferred witness density lies close to the number density of ultralight dark matter particles with mass m ~ 0.1 meV, suggesting a possible physical identification. The framework predicts a finite lifetime for the universe, bounded by the named term. We emphasize that this is not a quantum field theory derivation; the derivation is information-theoretic. We discuss the predictions, limitations, and open questions. This paper is self-contained and supersedes preliminary versions of these results that appeared earlier, which should be regarded as historical precursors. Main contributions:(1) Introduction of the witness number density n_w as a physical quantity, measurable in m^-3, with an inferred present-day value of n_w^0 ≈ 2.3 × 10^13 m^-3.(2) Proposal of the unified equation ρ_Λ = λ(a) n_w (k_B T ln 2), which is the first equation linking dark energy density to the thermodynamic cost of information preservation.(3) Derivation of the beta function β(λ) = 4λ from the information-theoretic structure of the witnessed contract.(4) Exact factorization of the cosmological constant problem into a thermal factor and a density factor.(5) Complete mapping of the sixteen structural elements onto physical counterparts.