ARIE-ARIADNE LE'DETSAMBALI

We present a complete proof architecture for a negative answer to the Borel unfriendly-partition problem. Starting from the tail-equivalence relation E₀ on the space of binary sequ…

This article develops the boundary blow-up component of the supplied σ₂-Sobolev trace proof dossier. Starting from normalized subcritical minimizing sequences, we formulate the con…

This article isolates the variational and geometric core of the σ₂-Sobolev trace problem developed in the supplied proof dossier. For n ≥ 5, we consider conformal metrics on the Eu…

We develop an exact structural formulation of the vorticity dynamics for the three-dimensional incompressible Navier–Stokes equations. Writing ω=ρξ with |ξ|=1, we derive the amplit…

We study Gallai's path-decomposition problem for the point–triple Levi graph Ln(m,3). Its bipartition consists of the points of … and the 3-subsets of … , with incidence as adjacen…

We study exact simulation of finite-dimensional quantum communication and bipartite quantum correlations by classical protocols with unlimited shared randomness and a finite classi…

This revision uses the current official FormalConjectures/ErdosProblems/1.lean source. The source marks the principal theorem erdos1 as research open and leaves it with sorry. The…

We study the Lean 4 formalization of Erdős Problem 1, the distinct subset sums problem. The principal Erdős conjecture remains open in the formal-conjectures development considered…

We study the two conductor-30 identities conjectured by Rogers and Yuttanan for the four-dimensional lattice sum F(b,c). The identities relate F(2,15) and F(2,5/3) to the Mahler-me…

Let P⊂R^2be a convex n-gon of area A, and let λ1^N (P)denote the first nonzero eigenvalue of the Laplacian with Neumann boundary conditions. We investigate the conjecture that the…