K. Fathi

Odd-Cycle Frustration in Competitive Networks: An Exact Topology Characterization

This release gives an exact support-topology characterization for a class of competitive generalized Lotka–Volterra communities whose coexistence equilibrium is permanent and globally asymptotically stable, yet cannot be made evolutionarily stable by any positive projective scali...

Dimensional Thresholds and Exact Obstructions for Evolutionary Stability under Replicator Equivalences

Stefano Allesina asked whether every globally stable interior equilibrium of a replicator equation becomes an evolutionarily stable strategy (ESS) after a common-payoff shift and positive projective rescaling. This preprint gives an exact obstruction theory and determines the dim...

Comparison Packets and Deletion-Radius Lifting for Diameter-Two Ulam Anticodes: A computer-assisted proof of the full k = 2 conjecture for n ≥ 5

This record contains the manuscript, LaTeX source, and reproducibility materials for a computer-assisted solution of the diameter-two case of the Devlin–Douhovnikoff Ulam anticode conjecture. For permutations pi and sigma in S_n, the Ulam distance is d_U(pi,sigma) = n - LCS(pi,si...

Comparison Stability for Permutation Deletion Shadows: Closing the 38-Order Condorcet Frontier

This paper develops an information-theoretic and order-theoretic method for studying directional deletion shadows of Condorcet domains. For a family D of linear orders, let ∂ᵢD denote the family obtained by deleting alternative i. The directional contraction conjecture asks wheth...