Information-driven cosmology: The Číhal invariant and the Hanák constant

We present an information-theoretic cosmological framework where the expansion of the Universe is governed by an informational feedback law linking the Hubble parameter, information density, and entropy flow. The study identifies two emergent quantities: the Číhal invariant H a = \text{const.} and the Hanák constant ξ_H = 1/2, representing an energy–entropy balance between gravitational dynamics and informational flux. Using observational H(z) and BAO data extended with Planck and JWST anchors, the model reproduces the late-time effective equation of state w_{\rm eff} ≈ -0.42 and yields H_0 = 61.0 ± 0.6 {\rm km s^{-1} Mpc^{-1}}. Thermodynamic validation confirms ξ_H stability within ±0.01 across redshift. All figures and LaTeX source files accompany this Zenodo record.