Salem Eid

The Equipoise Principle: Exchange-Invariant Geometry of Bipartite Readings and the Unique K4 Solitonic Closure

This technical note develops the exact mathematical core of the Equipoise Principle: a calculus for positive bipartite readings represented as curves in the logarithmic plane. The logarithmic slope n = d ln S2 / d ln S1 is clock-free but not invariant under exchange of the two pa...

Universal Spectrum and Edge-Crowding Transitions for Discrete Difference Operators

This preprint studies the discrete Euler map E a = a + V((x−ζ)a) built from theLagrange difference operator (Va)_i = Σ_{j≠i} (a_i − a_j)/(x_i − x_j) on m distinctreal nodes. The spectrum of the induced operator on the quotient by constants isuniversal — always {1, …, m−1}, indepe...

Conditional Harmonic Memory in Consecutive Prime Gaps

Let (g_n=p_{n+1}-p_n) denote consecutive prime gaps near a large height (X), with local scale (L=\log X). This paper develops a unified framework for two complementary forms of arithmetic memory. First, in the coordinates (s=g_n+g_{n+1}) and (t=g_n-g_{n+1}), a model that exactly...