We present a constructive theory of universal parameterization (UPF) for formal deductive systems (FDS). The central object is an explicitly constructed countable tower of basic systems Bₙ, based on Gentzen's sequent calculus LK. We prove that for any FDS P of finite complexity m, there exist n ≤ 4m² + 2 and a finite parameter α of length O(m³ log m) such that P is strictly isomorphic to U(n, α) — the parameterized version of Bₙ. The isomorphism is defined as an equivalence of derivation categories with explicit translating functors. We provide a complete parameterization algorithm and prove its correctness.
Daniel Osipenkov (2026) studied this question.