The Universal Generative Principle (UGP) is a deterministic arithmetic framework defined over integer ridges Rₙ = 2ⁿ - 16. It produces, from first principles and without free parameters, a unique canonical seed---the triple (1, 73, 823) ---whose orbit under the Generative Triple Evolution (GTE) map is rigidly determined. We present ugp-lean, a machine-checked Lean 4 formalization of the UGP/GTE framework comprising more than 400 modules, all zero sorry. This version reflects the Turing-universality and vacuity remediation (Rounds 98-100 + Phase 1-3 remediation, 2026-07-06): a genuine Turing-universality route via register-machine (Minsky 1967 2-counter machine) simulation is established and machine-certified; a vacuous proof stub (True AND True) previously used for this purpose has been removed; the unsound Cook-independent algebraic universality route has been retracted (NAND functional completeness is a finite Boolean result, not a Turing-universality certificate, and the two routes are now clearly distinguished) ; 17 additional vacuous/tautological proofs across the library have been corrected or honestly rescoped (SPEC₄08) ; the axiom inventory has been audited to 98 disclosed named axioms with a reproducible counting methodology; and a stale Rule-110 theorem name was corrected throughout. Canonical current state (post-graduation commit 89e0d81): 435 lean files, 98 disclosed named axioms (all named, none hidden), zero sorry throughout, zero standard Lean/Mathlib logical axioms beyond propext/Classical. choice/Quot. sound. All core algebraic uniqueness, structural richness, and computational universality results remain fully machine-certified. Remaining open formalizations (GH convergence, entanglement area law, Page-Wootters Born bridge, cobordism/quark/vertex bridges) are explicitly labeled as open in the paper and repository.
Nova Spivack (Mon,) studied this question.