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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"},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","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."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","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."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"A dynamical squeezing phase transition persists across all lattice geometries and coupling strengths in power-law spin models."}],"snapshot_sha256":"72ddeb22d4d8ed202d8ce80c53de6658b3e2928c240726bcfb076f3885715c39"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Recent work has identified a dynamical squeezing phase transition in power-law interacting bilayer XXZ spin models, separating a fully collective phase with Heisenberg-limited squeezing from a partially-collective phase with universal critical scaling. 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