lambda_PBM
The definition computes the therapeutic wavelength for an RS-coherent photobiomodulation device as the ratio of Planck's constant times the speed of light to the PBM energy fixed at φ eV. Biophysicists and device engineers working inside the Recognition Science framework cite it when specifying the operating wavelength of φ-ladder light therapy. The definition is a direct algebraic substitution of the module constants with no additional lemmas required.
claim$λ_{PBM} := hc / E_{PBM}$ where $E_{PBM} = φ · (1 eV)$ converted to joules.
background
The Photobiomodulation Device module formalizes an RS-coherent light therapy device built on the φ-energy ladder. Energies follow E(n) = E_base · φ^n with the biophase scale E_coh = φ^{-5} eV; rung 6 therefore yields E_PBM = φ eV. The constants planck_h and speed_of_light are the exact CODATA values for h and c. The definition converts this energy into the corresponding wavelength in meters.
proof idea
One-line definition that substitutes the product of planck_h and speed_of_light divided by E_PBM.
why it matters in Recognition Science
This definition supplies the wavelength parameter for the canonical RS-coherent device rs_device and feeds the downstream theorems that locate the wavelength inside the 750-780 nm therapeutic window and the tighter 766 nm approximation. It realizes the concrete device prediction from the φ-ladder (rung 6) inside the Recognition Science framework and closes the link between abstract energy rungs and applied hardware specifications.
scope and limits
- Does not derive E_PBM from the forcing chain or Recognition Composition Law.
- Does not compute numerical values or error bounds.
- Does not incorporate modulation patterns or entrainment frequencies.
- Does not address clinical outcomes or biological mechanisms.
formal statement (Lean)
142noncomputable def lambda_PBM : ℝ := planck_h * speed_of_light / E_PBM
proof body
Definition body.
143