lambda_PBM
plain-language theorem explainer
The definition supplies the wavelength for the Recognition Science photobiomodulation device as the ratio of Planck's constant times speed of light to the φ-scaled energy rung. Device designers and biophysics modelers cite it when specifying RS-coherent light sources. The declaration is realized by direct substitution of the module's energy definition and the two physical constants.
Claim. $λ_{PBM} := hc / E_{PBM}$ (meters), where $E_{PBM} = φ · eV$ and $eV$ is the electron-volt to joule conversion.
background
The module develops an RS-coherent photobiomodulation device based on the φ-energy ladder. Energy at rung n satisfies E(n) = E_base · φ^n with E_base = φ^{-5} eV from the biophase scale; rung 6 therefore yields the photobiomodulation energy E_PBM = φ eV. This energy lies inside the red/near-IR clinical window (600–850 nm) where therapeutic efficacy is strongest. The wavelength is obtained from the standard Planck relation using the exact values of h and c supplied by the module.
proof idea
The declaration is a direct definition that composes the Planck constant, speed of light, and the photobiomodulation energy E_PBM.
why it matters
This supplies the wavelength parameter for the canonical RS device specification and for the theorems establishing that the wavelength falls inside the 750–780 nm therapeutic window. It instantiates the φ-ladder prediction at rung 6 and connects to the eight-tick neutrality constraint in the modulation pattern. It closes the link between the abstract energy ladder and concrete device hardware.
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