{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:TSJFWES2MZVFXLEWND7OOMJP6U","short_pith_number":"pith:TSJFWES2","schema_version":"1.0","canonical_sha256":"9c925b125a666a5bac9668fee7312ff508522c4e8ba40d7f0c79c865cc1d2b60","source":{"kind":"arxiv","id":"2412.15192","version":1},"attestation_state":"computed","paper":{"title":"Accurate method for ultralight axion CMB and matter power spectra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.CO","authors_text":"Daniel Grin, Rayne Liu, Wayne Hu","submitted_at":"2024-12-19T18:57:34Z","abstract_excerpt":"Ultralight axions (ULAs) with masses $10^{-33} \\lesssim m/{\\rm eV} \\lesssim 10^{-12}$ are well motivated in string-inspired models and can be part or all of the dark energy or the dark matter in this range. Since the ULA field oscillates at a frequency $m$ that can be much larger than the expansion rate $H$, accurate and efficient calculation of cosmological observables requires an effective time averaged treatment. While these are well established for $m\\gg 10 H_{\\rm eq}$, the Hubble rate at matter radiation equality, here we extend and develop these techniques to cover the mass range $10^{-3"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2412.15192","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2024-12-19T18:57:34Z","cross_cats_sorted":[],"title_canon_sha256":"2fbe91b66ed88dfdce7cf05c1810200da5d9b9c658ddce433a1d257a8bcb1b00","abstract_canon_sha256":"09e5e213dc0bf5714300111ff42df454042f04abde5004a3dc28455a8b70e189"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:51:58.984746Z","signature_b64":"ktc5AZ2T/G3/F8OssgrPpK0lYpQNbaThBrsshwBzfWWZ+zN7l8hw3qC9l3KkjPBLbJzyrNRnE3f0umFae9o9DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c925b125a666a5bac9668fee7312ff508522c4e8ba40d7f0c79c865cc1d2b60","last_reissued_at":"2026-07-05T09:51:58.984296Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:51:58.984296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Accurate method for ultralight axion CMB and matter power spectra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.CO","authors_text":"Daniel Grin, Rayne Liu, Wayne Hu","submitted_at":"2024-12-19T18:57:34Z","abstract_excerpt":"Ultralight axions (ULAs) with masses $10^{-33} \\lesssim m/{\\rm eV} \\lesssim 10^{-12}$ are well motivated in string-inspired models and can be part or all of the dark energy or the dark matter in this range. Since the ULA field oscillates at a frequency $m$ that can be much larger than the expansion rate $H$, accurate and efficient calculation of cosmological observables requires an effective time averaged treatment. While these are well established for $m\\gg 10 H_{\\rm eq}$, the Hubble rate at matter radiation equality, here we extend and develop these techniques to cover the mass range $10^{-3"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.15192","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.15192/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2412.15192","created_at":"2026-07-05T09:51:58.984360+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.15192v1","created_at":"2026-07-05T09:51:58.984360+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.15192","created_at":"2026-07-05T09:51:58.984360+00:00"},{"alias_kind":"pith_short_12","alias_value":"TSJFWES2MZVF","created_at":"2026-07-05T09:51:58.984360+00:00"},{"alias_kind":"pith_short_16","alias_value":"TSJFWES2MZVFXLEW","created_at":"2026-07-05T09:51:58.984360+00:00"},{"alias_kind":"pith_short_8","alias_value":"TSJFWES2","created_at":"2026-07-05T09:51:58.984360+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2606.06410","citing_title":"The Atacama Cosmology Telescope: Probing new signatures of ultralight axions with gravitational lensing","ref_index":68,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TSJFWES2MZVFXLEWND7OOMJP6U","json":"https://pith.science/pith/TSJFWES2MZVFXLEWND7OOMJP6U.json","graph_json":"https://pith.science/api/pith-number/TSJFWES2MZVFXLEWND7OOMJP6U/graph.json","events_json":"https://pith.science/api/pith-number/TSJFWES2MZVFXLEWND7OOMJP6U/events.json","paper":"https://pith.science/paper/TSJFWES2"},"agent_actions":{"view_html":"https://pith.science/pith/TSJFWES2MZVFXLEWND7OOMJP6U","download_json":"https://pith.science/pith/TSJFWES2MZVFXLEWND7OOMJP6U.json","view_paper":"https://pith.science/paper/TSJFWES2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.15192&json=true","fetch_graph":"https://pith.science/api/pith-number/TSJFWES2MZVFXLEWND7OOMJP6U/graph.json","fetch_events":"https://pith.science/api/pith-number/TSJFWES2MZVFXLEWND7OOMJP6U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TSJFWES2MZVFXLEWND7OOMJP6U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TSJFWES2MZVFXLEWND7OOMJP6U/action/storage_attestation","attest_author":"https://pith.science/pith/TSJFWES2MZVFXLEWND7OOMJP6U/action/author_attestation","sign_citation":"https://pith.science/pith/TSJFWES2MZVFXLEWND7OOMJP6U/action/citation_signature","submit_replication":"https://pith.science/pith/TSJFWES2MZVFXLEWND7OOMJP6U/action/replication_record"}},"created_at":"2026-07-05T09:51:58.984360+00:00","updated_at":"2026-07-05T09:51:58.984360+00:00"}