USP Field Theory — The Frequency–Radius Law (f ≈ c / 2πr)

This release introduces and formalizes the USP Frequency–Radius Law, the flagship equation of USP Field Theory. The law states: f \approx \frac{c}{2\pi r} It ties a structure’s natural oscillation frequency directly to its radius, unifying particles, atoms, stars, and black holes under a single resonance rule. Origins: Derived from the resonance ceiling principle (USPs resonate near ). Scaling: Valid across 50+ orders of magnitude — from USPs to electrons, protons, atoms, stars, and black holes. Collapse thresholds: Δf > f_threshold predicts when electrons, atoms, or stars lose stability. Analogy: Like drum skins, small radii vibrate faster, large radii slower — an intuitive law consistent with oscillator physics. Implications: Provides a unified resonance framework for mass, energy, and force. Collapse thresholds can be tested in atomic/stellar experiments. Serves as the defining equation of USP Field Theory, analogous to in relativity. This release includes both the formal document and visual outreach material (poster) presenting the law in an accessible, intuitive way.