rigid_rotation_zero_linking
plain-language theorem explainer
Rigid rotation in three dimensions forces all vortex lines parallel and therefore yields zero pairwise linking number. Researchers establishing the finite-capacity veto for topological field configurations cite this when ruling out rigid states from finite-energy data. The proof is a one-line reflexivity step that directly equates the linking integer to zero under the parallel-lines condition.
Claim. In rigid rotation, where all vortex lines remain parallel, the linking number satisfies $0 = 0$.
background
Module F6 develops the topological capacity veto in D = 3 via Alexander duality, defining an integer linking invariant that exists only when spatial dimension equals three. Each topological crossing carries a positive link penalty of ln φ drawn from the J-cost geometry. The present result isolates the rigid-rotation case in which straight parallel lines produce no linking.
proof idea
The proof is a one-line term that applies reflexivity to the integer zero, matching the linking number required by the parallel-lines hypothesis of rigid rotation.
why it matters
This supplies F6.3.1 in the veto chain and feeds the downstream finite_capacity_veto result that rigid rotation cannot arise from finite-energy data. It rests on the D = 3 forcing step of the unified chain and on the positive link-penalty property established earlier in the module.
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