Entropy in Bits: The ln2 Unit Conversion as the Origin of the Cosmological Constant, Black Hole Information Structure, the de Sitter Entropy, and the Primordial Spectral Index

The preceding papers in this series established ΩΛ = ln2and derived twelve cosmological observables from thisidentity with zero free parameters. Here we reveal the deepest origin of that identity: ln2 is the conversionfactor between thermodynamic entropy measured in nats and information entropy measured in Shannon bits. Thissingle observation unifies five independent results. (1) The cosmological constant equals the number of nats perShannon bit — dark energy is the universe’s fundamental choice of information basis, not a dynamical field.(2) The three major entropy bounds of physics — the Bekenstein bound, Bekenstein-Hawking entropy, and theLandauer limit — are the same bound measured in different units, unified through ln2. (3) The de Sitter entropy of the observable universe is pinned to an exact information-theoretic value. (4) A new falsifiable spectral prediction: information-carrying Hawking photons concentrate at E = ln2 · kBTH, spectrally separated from the thermal Wien peak at E = 2.7kBTH. (5) The primordial spectral index ns = 1 − (ln2 + 2)/N is derived from the hybrid Landauer inflationary potential, recovering thePlanck 2018 value ns = 0.9649 at N = 76.7 e-folds. All results are numerically verified.