= Hofer nondegeneracy from rational Lagrangian displacement
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Assume the lower bound $e(L)\geq\gamma(L)/2$ for a closed <rational Lagrangian submanifold>, with matching energy convention. A nonidentity Hamiltonian map displaces a sufficiently small ball about some moved point. Inside that ball place a <Lagrangian torus> formed from equal-area circles. Its <least positive Liouville period> is positive, so the map's norm is at least half this period. This proves positivity of the distance between different maps without appealing to nondegeneracy itself.
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