Zeraoulia Rafik

Minimal Real Generalized Trisecants

Ranestad, Seigal, and Wang asked whether, for every admissible triple (d,n,m)(d,n,m), there exists a smooth, irreducible, non-degenerate real projective variety of dimension mm, codimension nn, and degree dd, whose maximum number of real points in a transverse complementary linea...

A Global Lyapunov Resolution of the Zeraoulia–Sprott HIV-Therapy Conjecture

We study the autonomous three-dimensional HIV dynamics model formed by the concentrations of CD4 lymphocytes, CD8 lymphocytes, and the HIV-1 viral load. Zeraoulia and Sprott conjectured, on the basis of numerical evidence, that the system is nonchaotic for every positive choice o...

A local concentration correction in Hua and Yang's cellular Kakeya reduction

This technical note concerns equation (9.5c0), page 40, of Hua and Yang's Cellular Maximal-Density Factoring and a Conditional Repair of the Streamlined Three-Dimensional Kakeya Reduction, arXiv:2608.18870v3 (26 August 2026). A singleton fine tube inside one coarse tube gives an...

Boundary Matching Multiplicity from Orthogonal Signings: Determinant Bounds, Stability, and Refined Cube Certificates

Let W be a Hermitian matrix supported on a graph G and satisfying W² = αI. Across a cut V(G) = S ⊔ T, the identity BB* = αI − A² gives a rank certificate. This manuscript develops local Hall-profile bounds via principal Gram matrices and quadratic effective rank, an elementary Ca...

Technical Corrections and Missing Justifications in a Streamlined Proof of the Three-Dimensional Kakeya Set Conjecture

This technical note examines version 1 of Guth, Wang and Zahl, A streamlined proof of the Kakeya set conjecture in R^3 (arXiv:2601.14411v1). It records parameter and bookkeeping defects in Theorem 7.3(B), supplies a self-contained proof of the omitted shaded slab estimate in Lemm...

Technical Corrections and Missing Justifications in a Streamlined Proof of the Three-Dimensional Kakeya Set Conjecture

This technical note examines version 1 of Guth, Wang and Zahl, A streamlined proof of the Kakeya set conjecture in R^3 (arXiv:2601.14411v1). It records parameter and bookkeeping defects in Theorem 7.3(B), supplies a self-contained proof of the omitted shaded slab estimate in Lemm...