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We find that for phase transition strength $\\alpha > 1$, the forward motion of bubble walls becomes the primary source, whereas for $\\alpha < 1$, the dominant contribution to the density perturbation comes from the delay of vacuum decay. Additionally, the power spectrum of density perturbations generated by the phase transition exhibits a slope of $k^3$ at small wavenumbers and $k^{-1.5}$ at large wavenumbers. 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Furthermore, we calculated "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"For phase transition strength α > 1, forward motion of bubble walls is the primary source of density perturbation, while for α < 1, the dominant contribution comes from the delay of vacuum decay; the density perturbation power spectrum has slope k^3 at small k and k^{-1.5} at large k; GW spectrum has k^3 and k^{-2}.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The lattice simulations accurately capture the non-linear dynamics of bubble wall motion and vacuum decay without significant numerical artifacts or missing physical effects like friction or plasma interactions.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"3D simulations of cosmological first-order phase transitions find density perturbation spectra with k^3 and k^{-1.5} slopes and GW spectra with k^3 and k^{-2}, confirming slow transitions can produce PBHs.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Lattice simulations show bubble wall motion dominates density perturbations for strong first-order phase transitions while vacuum decay delays dominate for weak ones.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"7a54e918fb8c1cefe2d1ed8efb80c919a5cf86765abad96ba1a389dc3575880f"},"source":{"id":"2502.20166","kind":"arxiv","version":4},"verdict":{"id":"0ccac975-86a6-4e3c-89c9-1fbf5929b1ae","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-23T02:30:30.540831Z","strongest_claim":"For phase transition strength α > 1, forward motion of bubble walls is the primary source of density perturbation, while for α < 1, the dominant contribution comes from the delay of vacuum decay; the density perturbation power spectrum has slope k^3 at small k and k^{-1.5} at large k; GW spectrum has k^3 and k^{-2}.","one_line_summary":"3D simulations of cosmological first-order phase transitions find density perturbation spectra with k^3 and k^{-1.5} slopes and GW spectra with k^3 and k^{-2}, confirming slow transitions can produce PBHs.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The lattice simulations accurately capture the non-linear dynamics of bubble wall motion and vacuum decay without significant numerical artifacts or missing physical effects like friction or plasma interactions.","pith_extraction_headline":"Lattice simulations show bubble wall motion dominates density perturbations for strong first-order phase transitions while vacuum decay delays dominate for weak ones."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.20166/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":111,"sample":[{"doi":"","year":null,"title":"As more and more bubbles form and collide, the initially uniform spatial structure is disrupted, resulting in an asymmetric energy distribution","work_id":"30212fe1-0d5e-4c74-ae7d-a74628ca4377","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1982,"title":"S. 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