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Here we establish that orbital-angular-momentum (OAM) encoding and Gottesman-Kitaev-Preskill (GKP) lattice geometry are structurally coupled: an OAM mode of topological charge $\\ell$ induces a phase-space rotation $\\theta_\\ell=\\ell\\pi/\\ell_{\\max}$, corresponding to a family of twisted GKP stabilizer lattices. 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