Information Constraint Theory (ICT): Structural Derivation of Galactic Scale Factors and the Al-Kilani Constant K

This paper presents Information Constraint Theory (ICT), a novel framework for understanding galactic dynamics and large-scale cosmic structure. ICT posits that spacetime obeys intrinsic informational constraints, with a fundamental structural constant $K = \phi \cdot \pi \cdot e$. From this first principle, we derive the Al-Kilani Gradient Law and the scaling factor $\eta \approx 42$, providing a parameter-free explanation for observed galaxy rotation curves without invoking dark matter. The manuscript includes: An axiomatic foundation of ICT Structural derivation of galactic scale factors A rigorous mathematical formulation of the density gradient Comparative context with MOND and RAR Predictions validated against the SPARC database ($\chi^2_\mathrm{red} \approx 1.02$) ICT offers a mathematically self-consistent, physics-first framework, bridging fundamental constants with observable galactic behavior. This work establishes a foundation for further theoretical and computational exploration of the universe as an informationally constrained system.