phi_energy_rung
plain-language theorem explainer
The phi-energy ladder defines photon energy at rung n as E_base multiplied by phi to the power n. Photobiomodulation researchers cite it to locate therapeutic wavelengths on the recognition coherence ladder. The declaration is a direct definition using the base energy and golden-ratio exponentiation.
Claim. $E(n) = E_0 · ϕ^n$, where $E_0 = ϕ^{-5}$ eV converted to joules.
background
The Applied.PhotobiomodulationDevice module formalizes RS-coherent light therapy using the phi-energy ladder for photon energies. E_base supplies the recognition coherence quantum as phi to the negative five times the eV-to-joule factor, drawn from upstream constants.
proof idea
This is a direct definition that multiplies E_base by the real power of phi to n. No lemmas are applied.
why it matters
This definition underpins the therapeutic wavelength calculations, feeding E_PBM_is_rung_6 which equates rung 6 to phi eV, plus the positivity and step lemmas. It realizes the phi-ladder scaling from the Recognition Science framework, connecting to the eight-tick octave and rung-6 therapeutic window.
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