The declaration linking_selection_principle in module IndisputableMonolith.Papers.DraftV1 is a short theorem that concludes D = 3.
(1) In plain English it says: if the linking-selection hypothesis holds for a given natural number D (i.e., the statement “linking invariant implies D = 3” is assumed) and the linking invariant itself is supplied for that D, then D must equal 3. The proof is simply the application of the hypothesis function to the invariant witness.
(2) In Recognition Science the result supplies one leg of the dimensional-rigidity argument in Draft_v1.tex. Together with the synchronization-selection and Kepler-selection principles also present in the same module, it contributes to showing that only D = 3 simultaneously satisfies the topological (T), arithmetic (S) and dynamical (K) constraints that the framework derives from the Law of Logic.
(3) The formal statement is read as follows: the parameters are a natural number D, a hypothesis h of type LinkingSelectionPrincipleHypothesis D (itself defined as LinkingInvariantHypothesis D → D = 3), and a witness hLink of type LinkingInvariantHypothesis D. The conclusion D = 3 is obtained by the single line h hLink. No further computation or unfolding is required inside the theorem body.
(4) Visible dependencies in the supplied source are the two preceding definitions LinkingSelectionPrincipleHypothesis and LinkingInvariantHypothesis, both of which delegate to SphereAdmitsCircleLinking imported from IndisputableMonolith.Foundation.AlexanderDuality. The underlying biconditional is supplied by the theorem alexander_duality_circle_linking in that module, which itself rests on the concrete definition CircleReducedCohomologyNontrivial and the reflexivity proof circle_reduced_cohomology_iff.
(5) The declaration does not prove the linking invariant hypothesis itself, nor does it establish the full (T/K/S) conjunction required for the main dimensional-rigidity theorem dimensional_rigidity_main. It likewise does not contain the external Alexander-duality isomorphism or any cohomology computations beyond the named identification already present in the AlexanderDuality module.