The declaration kepler_selection_principle appears in module IndisputableMonolith.Papers.DraftV1.
(1) In plain English it states that the apsidal angle function equals exactly 2π if and only if the dimension parameter D equals 3.
(2) In Recognition Science it supplies the algebraic core of the Kepler non-precession constraint (K), showing that closed orbits without precession occur uniquely at D = 3 and thereby contributing one of the three selection principles (T/K/S) that together force three-dimensional space.
(3) The formal statement is a theorem taking a natural number D and asserting the biconditional apsidalAngle D = 2 * Real.pi ↔ D = 3. The forward direction assumes the equality, introduces x = sqrt(4 - D), cancels the nonzero factor 2π to obtain x = 1, squares both sides under the non-negativity check 4 - D ≥ 0, and concludes D = 3 by injectivity of the cast from ℕ to ℝ. The reverse direction simply substitutes D = 3 into the definition of apsidalAngle and simplifies.
(4) Visible dependencies inside the supplied source are the definition of apsidalAngle in the same module, the arithmetic lemmas syncPeriod_eq_mul and synchronization_selection_principle used elsewhere in the file, and the re-export of AlexanderDualityForCircleHypothesis from IndisputableMonolith.Foundation.AlexanderDuality. The proof uses only Mathlib Real arithmetic and contains no sorry or external axioms.
(5) The declaration does not prove the physical origin of the apsidal-angle formula (the substitution of the Green-kernel power law is assumed, not derived here), does not establish the full dimensional-rigidity theorem that combines (T), (K) and (S), and does not address empirical comparison with observed planetary orbits.