Explanation of kepler_selection_principle
(1) In plain English, the declaration states that the apsidal angle function Δθ(D) — defined as 2π divided by the square root of (4 − D) — equals exactly 2π if and only if the natural number D equals 3. The proof proceeds by assuming the equality, showing that the denominator must be 1 (via cancellation and non-negativity of the radicand), solving for D, and verifying the converse by direct substitution.
(2) It matters in Recognition Science because it encodes the (K) Kepler non-precession constraint of Draft_v1.tex. Combined with the (S) synchronization-selection principle and the (T) linking-selection principle, it contributes to the dimensional-rigidity argument that forces D = 3 as the unique dimension satisfying all three constraints simultaneously.
(3) The formal statement is theorem kepler_selection_principle (D : ℕ) : apsidalAngle D = 2 * Real.pi ↔ D = 3. It is a biconditional. The forward direction uses algebraic cancellation on the real numbers, positivity of π, and the fact that √(4 − D) = 1 implies D = 3 after casting from ℝ back to ℕ. The reverse direction substitutes D = 3 to obtain √1 = 1 and recovers equality.
(4) Visible dependencies in the supplied source: it is defined in the same module as apsidalAngle and is invoked by dimensional_rigidity_main and no_higher_dimensional_alternative. The module imports IndisputableMonolith.Foundation.AlexanderDuality (supplying alexander_duality_circle_linking for the (T) constraint) and re-exports synchronization_selection_principle for the (S) constraint. The proof relies only on Mathlib real arithmetic (no external hypotheses or sorry).
(5) It does not prove the origin of the closed-form apsidal-angle expression from the Green-kernel power law, nor the full physical derivation of the (K) constraint from recognition geometry. It also leaves the placeholder hypotheses (RGConditionsForDualityHypothesis, CentralPotentialDerivationHypothesis, RobustnessHypothesis) unformalized and does not establish the complete (T/K/S) conjunction without supplying the linking hypothesis.