RotorPitch
RotorPitch aliases the integer pitch parameter kappa from the spiral field structure for use in log-spiral rotor geometry. Flight modelers cite it when constructing reports on φ-scaled propulsion paths. The declaration performs a direct type alias to the upstream Params record with no computation or lemmas required.
claimThe rotor pitch is the integer parameter $k$ in the record that sets the log-spiral radius scaling $r(θ)=r_0·φ^{(k·θ)/(2π)}$.
background
The Flight.Geometry module supplies the purely geometric layer for the spiral-field model, including the φ-tetrahedral angle and log-spiral rotor paths derived from the RS constant φ. No physical claims appear here. RotorPitch re-exports the parameter structure whose doc-comment records the radius formula $r(θ)=r_0·φ^{(κ·θ)/(2π)}$ with integer pitch κ. Upstream parameter records from ILG and Masses modules supply the base scale r0 and related constants such as alpha and Clag.
proof idea
The declaration is a one-line abbreviation that directly aliases the Params structure from the SpiralField module.
why it matters in Recognition Science
RotorPitch supplies the pitch type for the geometric scaffold in the flight subtheory. It is referenced by the FlightReport definition that summarizes theorems on φ-geometry. This fits the Recognition framework's use of φ for self-similar scaling and log-spiral constructions in the forcing chain. It enables downstream display of model status without closing any open questions.
scope and limits
- Does not assign specific integer values to the pitch parameter.
- Does not prove properties of the log-spiral path.
- Does not include dynamical equations or forces.
- Does not reference the full set of ILG parameters beyond the alias.
formal statement (Lean)
36abbrev RotorPitch := IndisputableMonolith.Spiral.SpiralField.Params
proof body
Definition body.
37
38/-- Rotor radial path: log-spiral scaling on the φ lattice.
39
40`r(θ) = r0 · φ^{(κ·θ)/(2π)}`. -/