Ludovic Tagnon

Closing the per-field reduction: collar contraction, the stretched road, and a certified minimax for the complex sin²-algorithm

We prove a per-field periodicity theorem for the complex sin²-algorithm: for every cubic field K of signature (1, 1) and every order of K, with constants γ = 51/50, m₀ = 10, κ = 1 independent of the field and state, the selected greedy orbit of every admissible initial state is e...

Closing the per-field reduction: collar contraction, the stretched road, and a certified minimax for the complex sin²-algorithm

We prove a per-field periodicity theorem for the complex sin²-algorithm: for every cubic field K of signature (1, 1) and every order of K, with constants γ = 51/50, m₀ = 10, κ = 1 independent of the field and state, the selected greedy orbit of every admissible initial state is e...