planck_h
The definition supplies the CODATA 2024 value of Planck's constant in joule-seconds for wavelength calculations inside the photobiomodulation module. Device modelers using the Recognition Science phi-energy ladder cite it to obtain the therapeutic wavelength near 766 nm from E_PBM. The declaration is a direct numerical assignment with no further reduction.
claimThe Planck constant is the real number $h = 6.62607015 × 10^{-34}$ in joule-seconds.
background
The Photobiomodulation Device module fixes SI constants to compute wavelengths from the phi-energy ladder E(n) = E_base · φ^n, where rung 6 yields photon energy φ eV and wavelength approximately 766 nm inside the red/near-IR window. The module imports the Constants file and relies on upstream structures that encode J-cost convexity, ledger factorization, and spectral emergence of gauge content and three generations. These structures supply the discrete tiering and neutrality constraints that the device model must respect.
proof idea
The declaration is a direct definition that binds the identifier to the literal 6.62607015e-34. No lemmas or tactics are invoked; the value is taken verbatim from the CODATA 2024 recommendation.
why it matters in Recognition Science
The constant is required by the downstream definitions lambda_PBM and lambda_PBM_in_therapeutic_window, which establish that the resulting wavelength lies inside the 750-780 nm clinical window. It supplies the experimental anchor for the applied device while the module's 8-beat neutrality and phi-ladder results remain internal to Recognition Science. The definition therefore closes the interface between the framework's T7 eight-tick octave and laboratory light-therapy parameters.
scope and limits
- Does not derive the numerical value from Recognition Science axioms or the J-cost equation.
- Does not carry uncertainty intervals or CODATA error bars.
- Applies only to SI-unit calculations inside this device model.
- Does not address quantum-field corrections or running of the constant.
Lean usage
noncomputable def lambda_PBM : ℝ := planck_h * speed_of_light / E_PBMformal statement (Lean)
48def planck_h : ℝ := 6.62607015e-34
proof body
Definition body.
49
50/-- Speed of light (m/s), exact -/