We present the Universal Generative Principle (UGP)~ as a unifying vocabulary that subsumes the premises of nine universal meta-laws (ML-1 through ML-9). The UGP framework, grounded in the Perfect Self-Containment (PSC) foundational principle, provides a single substrate—Generative Triple Evolution (GTE, 225 machine-checked modules)—from which each meta-law follows as a structural consequence. For ML-2 (Natural Gradient Flows), ML-4 (Hydrodynamics), ML-5 (Gauge Fields), and ML-6 (Geometric Flows/GR), we show that UGP's axioms subsume the premises of the classical results of Jaynes~(1957), Yau~(1991), Yang–Mills~(1954), and Jacobson~(1995) respectively; the proofs of those results stand as cited, and the UGP contribution is showing they are instances of the same framework. For ML-7 (Zipf's Law), we provide a complete, rigorous derivation with a finite-rank Euler–Maclaurin error bound, validated on 21 diverse corpora. For ML-3 (Arrow of Time) and ML-8 (Basin Selection by Conserved Charge), machine-checked backing is available in the NEMS programme~(Papers~36, 78, 09, 17, 22). For ML-9 (Attractor Thermodynamics), a Lean-verified entropy witness exists in -lean~( \_entropy\_prefix8\_gt\_prefix9, zero sorry).