4 papers
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…
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…
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…
Formalizing Singer Sidon Constructions and Sidon Set Infrastructure in Lean 4
David B. Hulak, Arthur F. Ramos, Ruy J. G. B. de Queiroz
Erdős 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.…