rs_device
The canonical RS-coherent photobiomodulation device assembles wavelength, modulation pattern, and brainwave frequencies directly from the golden ratio φ with no free parameters. Applied researchers in biophysics cite it when specifying a light-therapy device whose parameters sit on the φ-ladder and obey the eight-tick octave. The definition is a record literal that wires together pre-proved wavelength, positivity, band-membership, and distinct-mode lemmas.
claimThe canonical RS-coherent photobiomodulation device is the structure whose operating wavelength is $hc/E$ meters, modulation pattern is the neutral 8-window pattern, theta frequency is $φ^3$ Hz, alpha frequency is $φ^5$ Hz, gamma frequency is $φ^8$ Hz, and modulation cycle contains exactly 8 ticks, with all positivity, therapeutic-window, and distinct-band conditions satisfied.
background
PBMDeviceSpec is the structure that records an RS-coherent photobiomodulation device; every field is required to be derived from φ. The module sets the φ-energy ladder $E(n)=E_0·φ^n$ with $E_0=φ^{-5}$ eV, so rung 6 yields the therapeutic wavelength ≈766 nm inside the 600–850 nm clinical window. Upstream lemmas supply the concrete wavelength (lambda_PBM), its positivity and window membership, the three distinct frequency bands, and the octave definition (ratio 2) that fixes the tick count at 8.
proof idea
The definition is a direct record construction. It populates wavelength_m with lambda_PBM, modulation_pattern with the neutral pattern, the three frequencies with the corresponding powers of φ, ticks_per_cycle with 8, and supplies the matching lemmas lambda_PBM_pos, lambda_PBM_in_therapeutic_window, phi_cubed_in_theta_band, phi_fifth_in_alpha_band, phi_eighth_in_gamma_band, and modes_span_distinct_bands for the remaining fields.
why it matters in Recognition Science
This definition supplies the concrete device instance that realizes the eight-tick octave (T7) in an applied setting. The immediate parent is the theorem device_matches_octave, which confirms ticks_per_cycle = 8 by reflexivity. It closes the zero-parameter specification for a φ-derived PBM device and links the forcing-chain octave directly to a therapeutic wavelength and EEG-band entrainment.
scope and limits
- Does not establish clinical efficacy or safety data.
- Does not derive the therapeutic window bounds from the recognition equation.
- Does not address hardware implementation or power-delivery details.
- Does not claim uniqueness among all possible RS-coherent devices.
Lean usage
theorem device_matches_octave : rs_device.ticks_per_cycle = 8 := rflformal statement (Lean)
325noncomputable def rs_device : PBMDeviceSpec := {
proof body
Definition body.
326 wavelength_m := lambda_PBM
327 modulation_pattern := rs_neutral_pattern
328 theta_freq_Hz := phi ^ 3
329 alpha_freq_Hz := phi ^ 5
330 gamma_freq_Hz := phi ^ 8
331 ticks_per_cycle := 8
332
333 wavelength_pos := lambda_PBM_pos
334 wavelength_therapeutic := lambda_PBM_in_therapeutic_window
335 ticks_is_eight := rfl
336 theta_in_band := phi_cubed_in_theta_band
337 alpha_in_band := phi_fifth_in_alpha_band
338 gamma_in_band := phi_eighth_in_gamma_band
339 modes_ordered := modes_span_distinct_bands
340}
341
342/-- The device uses exactly 8 ticks per modulation cycle,
343 matching the fundamental recognition octave (T7: D=3 → 8 ticks). -/