Explanation of transitionRadius in IndisputableMonolith.Astrophysics.GalacticRotationCurveFromRS
(1) In plain English, the declaration defines a function that maps each natural number k to the real number obtained by raising the golden ratio phi to the power k.
(2) In Recognition Science this supplies the radii at which galactic rotation curves change regime. The module states there are five canonical regimes (rigid-body inner, rising, flat, declining, truncation) and places each transition one rung higher on the phi-ladder, yielding a parameter-free structural prediction.
(3) The formal statement is written as noncomputable def transitionRadius (k : ℕ) : ℝ := phi ^ k. The noncomputable keyword indicates a pure mathematical definition over the reals rather than an executable program; the argument k is a natural number and the result is a real number. It relies on the constant phi imported from Constants.
(4) Visible supporting declarations in the same module are rotationRegime_count establishing exactly five regimes, transitionRadius_ratio proving consecutive radii scale by exactly phi, transitionRadius_pos proving every radius is positive, the structure GalacticRotationCert that packages these facts, and the concrete certificate galacticRotationCert that witnesses them. The module reports zero sorry and zero axioms.
(5) The declaration supplies only the mathematical definition and its immediate algebraic properties; it does not derive the five regimes from deeper RS axioms, does not prove any link to observed galactic data, and does not establish the physical mechanism that selects phi-powers as the transition locations.