rotorPath
RotorPath is the direct abbreviation for the logarithmic spiral radial function in the Flight.Geometry module, expressing r(θ) = r0 · φ^(κθ / 2π) on the φ lattice. Modelers of spiral-field propulsion cite it when invoking the geometric scaffold without reimplementing the scaling. The declaration is a one-line alias to the upstream logSpiral definition.
claimThe rotor radial path is the function $r(θ) = r_0 · φ^{(κ · θ)/(2π)}$, where $r_0$ is the sector-dependent base radius and $φ$ is the golden-ratio constant from Recognition Science.
background
The Flight.Geometry module supplies the purely geometric layer of the spiral-field propulsion model: the φ-tetrahedral angle, log-spiral rotor paths, and math-only lemmas on step ratios, all derived from the RS constant φ with no physical claims. RotorPath re-exports the logSpiral definition, which computes r0 multiplied by φ raised to the exponent (kappa · θ) / (2π). Upstream anchors include the sector-wise r0 offsets in Masses.Anchor and the logSpiral implementation in Spiral.SpiralField.
proof idea
This is a one-line wrapper that aliases the logSpiral definition from IndisputableMonolith.Spiral.SpiralField.
why it matters in Recognition Science
The abbreviation places the rotor radial path inside the Flight.Geometry module, completing the geometric foundation for the φ-tetrahedral / log-spiral scaffold. It supplies the explicit scaling law used by the spiral-field propulsion model and connects directly to the Recognition Science constant φ and the eight-tick octave structure. The declaration fills the geometric layer described in the module documentation.
scope and limits
- Does not introduce physical interpretations or propulsion claims.
- Does not perform numerical evaluation or path simulation.
- Does not depend on empirical data beyond RS constants φ and kappa.
- Does not alter the underlying logSpiral implementation.
formal statement (Lean)
41noncomputable abbrev rotorPath := IndisputableMonolith.Spiral.SpiralField.logSpiral
proof body
Definition body.
42
43namespace SpiralLemmas
44
45open IndisputableMonolith.Spiral
46
47/-- `logSpiral` is nonzero whenever `r0` is nonzero (since φ^x > 0). -/