The φ-Resonance Framework, and the Structure of Vacuum, Gravity, Hawking Radiation, UV Behavior, and Planck Scaling

(The primary HTML is "The φ-Resonance Framework" , all subsequent results pages are linked drectly in the main document) This manuscript presents a unified φ‑resonance framework in which vacuum structure, gravitational interaction, Hawking evaporation, ultraviolet behavior, and Planck‑scale constructions all emerge from a single geometric ladder defined by the golden ratio φ.The analysis is fully empirical and artifact‑driven. Each domain is evaluated by mapping standard physical quantities onto the φ‑recursive ladder and identifying where those constructions remain on‑manifold or fall outside the admissible spectrum of rungs.The results show:• Vacuum structure: φ⁰ = 1 defines an algebraic vacuum floor. Negative energy, exotic matter, and Dirac‑sea states map below this floor and have no valid rung representation.• Gravity: The graviton corresponds to a specific rung (n* ≈ 61.24), implying a nonzero minimum mass and a geometric bound on gravitational range. Virtual gravitons are replaced by shared rung resonance.• Hawking radiation: All Hawking temperatures scale by φ². Evaporation terminates at a finite mass where the mapped temperature reaches the Jackson ground state, yielding a stable resonant remnant.• UV divergence: Rung density thins geometrically as φ⁻ⁿ, causing loop integrals and propagators to self‑regulate without counterterms. The hierarchy problem collapses from 10³⁴ fine‑tuning to ~81 rungs.• Planck vs Jackson scaling: The linear Planck ladder is structurally incommensurate with the φ‑recursive manifold, diverging monotonically after the first rung.Supplementary HTML files provide full tables, rung mappings, and computational outputs for each domain.