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Here we test and establish the universality of this transition along two qualitatively different microscopic axes: lattice geometry, by studying square, triangular, and honeycomb $2\\mathrm{D}$ bilayers as well as $1\\mathrm{D}$ ladders, and a symmetry-preserving rescaling $\\lambda$ of the interlayer couplings relative to the intralayer ones. 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Here we test and establish the universality of this transition along two qualitatively different microscopic axes: lattice geometry, by studying square, triangular, and honeycomb $2\\mathrm{D}$ bilayers as well as $1\\mathrm{D}$ ladders, and a symmetry-preserving rescaling $\\lambda$ of the interlayer couplings relative to the intralayer ones. Comb"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"the transition persists across all four lattice geometries and over a wide range of λ with critical exponents consistent within error, providing strong evidence for a genuine non-equilibrium universality class. The Bogoliubov theory recovers the previously identified scaling a_Z^* ∝ L in the long-range interacting regime α < d+2, and yields an analytical scaling a_Z^* ∝ L^{2/(α-d)} for the critical aspect ratio with system size for α>d+2","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The Bogoliubov instability analysis combined with discrete truncated Wigner simulations accurately captures the full quantum many-body dynamics without significant corrections from higher-order terms or unaccounted finite-size effects.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The dynamical squeezing phase transition in bilayer XXZ spin models is universal across lattice geometries and interlayer coupling rescalings, with a new sub-linear scaling for short-range interactions.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A dynamical squeezing phase transition persists across all lattice geometries and coupling strengths in power-law spin models.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"72ddeb22d4d8ed202d8ce80c53de6658b3e2928c240726bcfb076f3885715c39"},"source":{"id":"2605.13969","kind":"arxiv","version":1},"verdict":{"id":"cbf75922-d411-4a4d-84fb-0db167dc56f4","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T05:59:08.223906Z","strongest_claim":"the transition persists across all four lattice geometries and over a wide range of λ with critical exponents consistent within error, providing strong evidence for a genuine non-equilibrium universality class. 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