PBMDeviceSpec
plain-language theorem explainer
The photobiomodulation device specification structure assembles wavelength, modulation pattern, and frequency parameters for an RS-coherent light therapy device, with wavelength constrained to the 750-780 nm therapeutic window and frequencies aligned to EEG bands. Applied physicists modeling φ-derived biophotonic devices would reference this specification. The definition directly encodes the eight-tick cycle and window-neutral sum constraint without further derivation steps.
Claim. A structure specifying a device with wavelength $λ ∈ ℝ$ where $750 × 10^{-9} < λ < 780 × 10^{-9}$, modulation pattern $p : {0,…,7} → ℝ$ with $∑ p(k) = 0$, frequencies $f_θ, f_α, f_γ$ satisfying the band inequalities $4 < f_θ < 8$, $8 < f_α < 13$, $30 < f_γ < 100$ and ordering $f_θ < f_α < f_γ$, and exactly eight ticks per cycle.
background
This module develops the Recognition Science model for photobiomodulation devices coherent with the φ-ladder. The φ-energy ladder is defined by $E(n) = E_{base} · φ^n$ with base energy $φ^{-5}$ eV, so that rung 6 produces $φ$ eV and wavelength approximately 766 nm in the red/near-IR range. WindowNeutralPattern requires a function from the finite set of eight ticks to reals whose sum is zero, enforcing neutrality to prevent recognition strain accumulation.
proof idea
The declaration is a structure definition that lists the required fields and attaches the positivity, band, and ordering constraints as field propositions. It depends on the WindowNeutralPattern structure for the modulation field. No proof tactics are involved; the structure is populated downstream by explicit φ-power assignments in the canonical device definition.
why it matters
This structure serves as the type for the canonical RS-coherent device definition, which supplies concrete φ-derived values for wavelength, pattern, and frequencies. It realizes the applied photobiomodulation specification within the framework, incorporating the eight-tick octave and φ-ladder to predict the 766 nm therapeutic window. The construction closes the formal device model with zero free parameters, though clinical efficacy remains an open empirical question.
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