Unified Informational Theory: Contribution to Solving the Core-Cusp Problem

Abstract We present the Unified Informational Theory (TURI), positing information as the primordial physical substrate. Starting from a cyclic universe with constant entropy (ΔS cycle = 0), we derive a universal profile of density ρ(r)=ρ₀sech⁸(r/r c ) possessing a structural additivity property by convolution. This profile structurally solves the "Core-Cusp" problem: the condition dρ/dr|_(r→0) = 0 generates a flat core consistent with observations [1], unlike the singularities of the ΛCDM model. The convergence of the enclosed mass rigorously reproduces the Keplerian laws (V∝ √(1/R)). the parameter P = |T×V_rot×mabs| quantifies the compositional homogeneity of the medium [2]. The application to a few massive galaxies suggests the preservation of the sech⁸ structure at the baryonic level, paving the way for the universality of this distribution for dark and baryonic matter. Our profile strictly preserves Newtonian gravity (V²(R) = G.M(R)/R) without forced modification, revealing that dark and baryonic matter constitute manifestations of a single fundamental informational substrate.