WindowNeutralPattern
A record type holding an 8-tuple of reals whose sum is zero, encoding a neutral modulation pattern over one 8-tick cycle. Device modelers and biophysics researchers cite it when constructing RS-coherent PBM hardware specifications. The definition is a direct structure declaration that packages the values map and the sum-zero constraint with no further lemmas.
claimA window-neutral pattern is a function $v : [8] → ℝ$ such that $∑_{k=0}^7 v(k) = 0$.
background
The module formalizes photobiomodulation devices whose energy rungs follow the φ-ladder E(n) = E_base · φ^n, with rung 6 yielding the therapeutic wavelength ≈766 nm. The eight-tick cycle is the octave period fixed by Recognition Science (T7). Neutrality of the modulation pattern prevents net recognition strain accumulation, consistent with the Recognition Composition Law.
proof idea
Structure definition that directly introduces the fields values : Fin 8 → ℝ and neutral : sum values = 0. No upstream lemmas are invoked; the declaration itself supplies the type used by rs_neutral_pattern and PBMDeviceSpec.
why it matters in Recognition Science
Supplies the modulation_pattern field inside PBMDeviceSpec, the top-level RS-coherent device specification whose every component derives from φ. It realizes the 8-beat neutrality condition stated in the module doc, closing the link between the eight-tick octave (T7) and practical light-therapy hardware. No open scaffolding remains at this node.
scope and limits
- Does not prescribe explicit values for the eight entries.
- Does not impose positivity or boundedness constraints.
- Does not derive frequencies or wavelengths from the pattern.
- Does not prove existence of nontrivial solutions.
formal statement (Lean)
231structure WindowNeutralPattern where
232 values : Fin 8 → ℝ
233 neutral : Finset.univ.sum values = 0
234
235/-- The RS pattern constitutes a valid window-neutral pattern. -/