The Dark Energy Equation of State from the Planck Loop as a Local Schwarzschild Horizon

The dark energy equation of state is predicted to be a constant, w = −1 + ln 2/(30π) = −0.9926. The prediction rests on one identification and one rule, both stated before any number is computed. The identification is that every Planck scale loop of quantum geometry is a local Schwarzschild horizon. The Planck scale is the smallest at which the inside and the outside of a horizon can be separated. The rule is that a quantity carried across the horizon to an exterior observer loses the fraction ε = ln 2/(30π) of its states. The three factors of ε are the entropy of one binary choice, the thirty channels of the sedenion level, and the phase π of a half turn. The prediction is consistent with every present constant w constraint that includes supernovae. It is refuted by an established evolving equation of state, or by a constant w at or below −1 once σ(w) < 0.005. Two further hypotheses give the count of levels from the Planck length to the de Sitter radius as 44.66, against 44.72 from the measured Λ. They are a scale factor eπ per Cayley–Dickson level and a one bit cost for the loss of commutativity. So Λ, which is 10¹²² times smaller than its Planck value, follows from counting to within a factor of 1.4, with no epoch chosen. With the sedenion zero divisor fraction 2/5 and a baryonic ratio 1/14, the present cosmological budget closes within 0.5σ of Planck 2018.