Black Hole Formation from Shannon Entropy and the Ghidan 1/0 Bit-Qubit Framework

This preprint presents a first-principles derivation of the black-hole collapse radius using the Ghidan 1/0 Bit-Qubit framework combined with Shannon entropy and energy-density encoding limits. Instead of treating gravity and horizon formation as purely geometric effects of spacetime curvature, the model interprets physical systems as informational structures requiring finite encoding capacity. Collapse occurs when the informational demand imposed by energy density equals or exceeds the maximum Shannon entropy capacity available within a region. Using the Ghidan exterior informational law χ(r)=1−κ/r and an energy-based informational compression constant, we derive an informational collapse radius: r_c = γE and show that when γ = 2G/c⁴, this naturally reproduces the Schwarzschild radius: r_c = 2GM/c² without assuming spacetime curvature or Einstein field equations as primitives. Two collapse regimes are identified: Entropy-density collapse (local informational saturation) Integrated informational collapse (macroscopic limit equivalent to GR) Numerical validation across stellar black holes, Sagittarius A*, and M87* shows close agreement between predicted informational collapse radii and observed horizon scales. This work establishes a metric-free informational foundation for gravitational collapse and suggests that classical spacetime geometry may represent an emergent large-scale limit of deeper information-processing constraints in physical reality. The paper forms part of the Ghidan 1/0 Bit-Qubit research program, which models physical observables as outcomes of finite informational processing capacity rather than spacetime primitives. Supporting derivations of the exterior χ(r)=1−κ/r law and κ determination from redshift data are provided in companion works.