All Fundamental Physical Constants Derived from Five Basic Entities and Hyperbolic-Cubic Geometry

A geometric approach within the Theory of Hyperbolic Unity (THUI) isproposed, in which 39 fundamental physical constants — including the gravitationalconstant G, the fine-structure constant α, the cosmological constant Λ, the Hubbleconstant H0, masses of Standard Model particles, and others — are analyticallyderived from five basic entities: the Planck length ℓPl, the golden ratio ϕ, the numberπ, the base of the natural logarithm e, and the resonance number 1729. The constants emerge as geometric harmonics of the 1729 resonance within adual vacuum structure consisting of a local cubic layer with metric R3 (providingdiscreteness and regularization of divergences) and a nonlocal hyperbolic layer {5, 3, 3}(accounting for infinity and nonlocality). Statistical analysis of 22 verified constants yields a joint probability of randomcoincidence less than 10−198 (significance > 30σ), ruling out any numerologicalinterpretation. The approach achieves analytical unification without extra dimensions, arbitraryparameters, or infinite renormalizations. Testable predictions include a vacuum resonancefrequency of 1729 Hz (accessible to laboratory verification), a finite radius of theobservable Universe, and black hole entropy values.