Information Uni cation Theory: Contribution to the Solution of the Core-Cusp Problem

We present the Information Uni cation Theory (TURI), positing informationas the primordial physical substrate. Starting from a cyclic universe with constantentropy (∆Scycle = 0), we derive a universal density pro le ρ(r) = ρ0sech8(r/rc)possessing a structural additivity property via convolution.This pro le structurally solves the "Core-Cusp" problem: the condition dρ/dr|r→0 =0 generates a at core consistent with observations (SPARC, Lelli et al., 2016), contrary to the singularities of the ΛCDM model. The enclosed mass convergence rigorously reproduces Keplerian laws (V ∝ 1/R). The parameter P = |T×Vrot×mabs|quanti es the compositional homogeneity of the medium (HyperLEDA, Makarov etal., 2014).Application to some massive galaxies suggests the preservation of the sech8 structure at the baryonic level, opening the way to the universality of this distributionfor both dark and baryonic matter. Our pro le strictly preserves Newtonian gravity(V 2(R) = GM(R)/R)withoutforcedmodi cation, revealing that dark and baryonicmatter constitute manifestations of a single fundamental informational substrate.