A Compton-Normalized Information Scale for a Dynamical Spherical Blackbody Model: CMB-Scale Geometry, Horizon Thermodynamics, and Vacuum-Energy Comparison

We present a model connecting a dynamically rotating and expanding spherical geometry with the quantum scales of the electron. The spherical boundary is treated as a genuinely dynamical surface whose radius changes with time while the sphere rotates. For the information-scale calculation, an instantaneous configuration is represented by an equivalent static spherical shell at the selected radius. This is a geometric representation of the dynamical surface at one instant and does not imply that the underlying dynamics stop. The fiducial radius used in the numerical calculation is approximately 4.4 times 10 to the 26 metres. This value is taken from the characteristic cosmic microwave background scale. It is not assumed to be the exact global radius of the entire universe. The actual global scale could be larger because of spatial topology, curvature, or other geometric effects. Since the relevant surface area grows with the square of the radius, any larger global radius would increase the resulting scale accordingly. The spherical shell is characterized by its surface area and enclosed three dimensional volume. The ratio between the surface area and the enclosed volume is inversely proportional to the radius. The microscopic normalization is based on the electron. The electron rest energy is used as the energy scale, while the Compton wavelength is used as the characteristic quantum length scale of the electron. The Compton wavelength is not chosen arbitrarily. It arises naturally in Compton scattering and characterizes the electron photon interaction scale. The calculation combines the macroscopic spherical surface area with Newtons gravitational constant, the electron mass, the electron Compton wavelength, and the electron rest energy. This procedure produces a characteristic scale of approximately 2.014 times 10 to the 119. The horizon thermodynamic correspondence used in the associated spherical model contains an additional factor of two through the energy, temperature and entropy relation. Applying this factor produces a final model dependent scale of approximately 4.029 times 10 to the 119. This quantity is not claimed to be a measured number of information bits and is not presented as an established microscopic entropy of the electron. It is proposed as a characteristic information and energy scale resulting from the combination of the macroscopic spherical geometry with the microscopic quantum scales of the electron. The construction is compared with black hole horizon entropy, Hawking temperature, and the large hierarchy associated with quantum field theoretic vacuum energy estimates. These comparisons are intended as scale comparisons and do not establish an identity between the quantities. The model further explores the hypothesis that a three dimensional region bounded by a dynamically evolving spherical surface may approach a maximum entropy information configuration when represented by its corresponding instantaneous static boundary geometry. The results are presented as a mathematical model and a hypothesis for further investigation. They do not by themselves establish that the universe is an ideal blackbody, that the calculated scale is the actual information content of the electron, or that the model replaces standard cosmology or quantum field theory.