device_matches_octave
The theorem establishes that the canonical RS-coherent photobiomodulation device operates with precisely eight ticks per modulation cycle. Researchers modeling light therapy devices aligned with recognition science would cite this to confirm consistency with the eight-tick octave forced by three spatial dimensions. The proof is a direct reflexivity on the device specification definition.
claimLet rs_device denote the canonical recognition-science photobiomodulation device with all parameters derived from φ. Then its number of ticks per modulation cycle equals 8.
background
The module formalizes a photobiomodulation device operating in coherence with the φ-ladder, where energy rungs satisfy E(n) = E_base · φ^n and rung 6 yields a therapeutic wavelength near 766 nm. The rs_device definition supplies the canonical specification with wavelength, rs_neutral_pattern modulation, and frequencies θ = φ^3 Hz, α = φ^5 Hz, γ = φ^8 Hz, all with zero free parameters. This setting draws from the upstream rs_device declaration, which states that the device is the canonical RS-coherent PBM device with parameters derived from φ.
proof idea
The proof is a one-line reflexivity that directly matches the ticks_per_cycle field in the rs_device definition to the constant 8.
why it matters in Recognition Science
This declaration confirms alignment of the photobiomodulation device with the eight-tick octave (T7) forced by D = 3 spatial dimensions in the recognition chain. It supports the module's 8-beat pattern neutrality result that prevents accumulation of recognition strain. The theorem closes the link from the forcing chain to applied device parameters, enabling downstream claims on brainwave entrainment within EEG bands.
scope and limits
- Does not derive the value 8 from the forcing chain inside this module.
- Does not address physical realizability or clinical trial data for the device.
- Does not compute explicit numerical frequencies beyond the octave match.
formal statement (Lean)
344theorem device_matches_octave : rs_device.ticks_per_cycle = 8 := rfl
proof body
Term-mode proof.
345
346end Photobiomodulation
347end Applied
348end IndisputableMonolith