linking_selection_principle
plain-language theorem explainer
The linking selection principle asserts that if a sphere in D dimensions admits a circle-linking invariant and the selection hypothesis holds, then D equals 3. Researchers deriving spatial dimensions from the Recognition Science functional equation would cite this as the forward direction of the Draft V1 main theorem. The proof is a direct one-line application of the hypothesis definition via modus ponens.
Claim. If a sphere in dimension $D$ admits circle linking (i.e., SphereAdmitsCircleLinking $D$) and the linking selection principle hypothesis holds, then $D = 3$.
background
This module mirrors theorem statements from Draft_v1.tex by re-exporting proved results or supplying explicit hypothesis interfaces for external mathematics such as Alexander duality. LinkingInvariantHypothesis $D$ is defined as SphereAdmitsCircleLinking $D$, the existence of an integer-valued loop-linking invariant. LinkingSelectionPrincipleHypothesis $D$ is the implication from that predicate to $D=3$, now supplied by the bridge alexander_duality_circle_linking rather than left as an axiom.
proof idea
The proof is a one-line term wrapper that applies the selection hypothesis directly to the linking invariant hypothesis.
why it matters
This supplies the forward direction of the paper proposition that (T), (K), (S) imply D=3. It sits inside the Recognition Science forcing chain at T8, where the eight-tick octave and phi fixed point force three spatial dimensions. The declaration closes one interface in the Draft V1 audit surface without introducing new global axioms.
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