Non-Orthogonal Universal Construction for the Prouhet–Tarry–Escott Problem

📧 Contact: sasa.jov.ubl@gmail.com. Among universal constructions valid for all degrees $k$, the classical solution of Prouhet based on the Thue--Morse sequence occupies a central position.. Its defining feature is an underlying orthogonality that enforces a highly regular and sparse internal structure. This raises a fundamental structural question that has received little explicit attention: Why not consider universal non-orthogonal construction while preserving the cardinality $2^k$? In this paper, we answer this question affirmatively by exhibiting an explicit non-orthogonal recursive construction.The loss of orthogonality allows for substantially richer local configurations.In particular, the resulting sets may contain desired longer consecutive integer runs than those permitted by the Thue--Morse construction, while still satisfying all moment identities up to degree $k$ and preserving the classical bound $2^k$. 📘 Cite as: Saša Jovičević (2026), Non-Orthogonal Universal Construction for the Prouhet–Tarry–Escott Problem, Zenodo.