16 papers
Optimal Finite Interval Discrepancy via Binary Refinement
Arthur F. Ramos, David B. Hulak, Ruy J. G. B. de Queiroz
DeLeo, Henderschedt, and Wells introduced a finite-horizon version of the classical de Bruijn--Erdos interval discrepancy problem. Starting from the unit interval, one repeatedly s…
Topological Semantics for Scoped Computational Paths
Arthur Freitas Ramos, Ruy J. G. B. de Queiroz, Anjolina Grisi de Oliveira +1
Computational paths record equality as explicit finite traces of primitive steps. We give a topological semantics for a scoped rewrite presentation whose steps have continuous geom…
Multiplier obstructions for Legendre pairs of length 333
Arthur F. Ramos, David B. Hulak, Ruy J. G. B. de Queiroz
A Legendre pair of length 333 would yield a Hadamard matrix of order 668, the smallest order presently unresolved by the Hadamard conjecture. We study the structured case in which…
From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game
Arthur F. Ramos, Tulio Soria
We present a metagame analysis of the competitive Pokemon Trading Card Game, machine-checked in Lean 4 over real tournament data. The headline game-theoretic results, including Nas…
Formalizing Singer Sidon Constructions and Sidon Set Infrastructure in Lean 4
David B. Hulak, Arthur F. Ramos, Ruy J. G. B. de Queiroz
ErdÅs Problem 30 asks for sharp asymptotics of the Sidon extremal function , and Singer's construction is the classical source of lower-bound examples matching the main term…
Certified Qualitative Analysis of the SIR ODE and Reusable Scalar Lemmas in Isabelle/HOL
David B. Hulak, Arthur F. Ramos, Ruy J. G. B. de Queiroz
We present a mechanically checked Isabelle/HOL bridge from the Picard-Lindelof flow infrastructure in the Archive of Formal Proofs (AFP) to selected qualitative facts for the mass-…