{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:3JP3VE33L77YOHH2VX2PBVZH7P","short_pith_number":"pith:3JP3VE33","schema_version":"1.0","canonical_sha256":"da5fba937b5fff871cfaadf4f0d727fbcfa48163f8b0ddd23840d57127f15b42","source":{"kind":"arxiv","id":"0911.3665","version":1},"attestation_state":"computed","paper":{"title":"Slow Diffusive Gravitational Instability Before Decoupling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.CO","authors_text":"Todd A. Thompson","submitted_at":"2009-11-18T21:58:38Z","abstract_excerpt":"Radiative diffusion damps acoustic modes at large comoving wavenumber (k) before decoupling (``Silk damping''). In a simple WKB analysis, neglecting moments of the temperature distribution beyond the quadrupole, damping appears in the acoustic mode as a term of order ik^2/(taudot) where taudot is the scattering rate per unit conformal time. Although the Jeans instability is stabilized on scales smaller than the adiabatic Jeans length, I show that the medium is linearly unstable to first order in (1/taudot) to a slow diffusive mode. At large comoving wavenumber, the characteristic growth rate b"},"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":"0911.3665","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2009-11-18T21:58:38Z","cross_cats_sorted":[],"title_canon_sha256":"7afa239a282510c599d0a7d0b4fbfac3d609769e5e72b9b0c189935a315315c6","abstract_canon_sha256":"7ac603feee9bfe3805d0967365e48e21b775a7eaa789f12ab1070c502cb11ff0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:34:04.642916Z","signature_b64":"g7x2e70nIXZ8skwb4KhUO8/lycLDxT+/BjZwk9OdywVLmF3uwC7ZiutpL4LlcINY1lAVfPSsrpVJFLFFMSNnCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da5fba937b5fff871cfaadf4f0d727fbcfa48163f8b0ddd23840d57127f15b42","last_reissued_at":"2026-05-18T02:34:04.642198Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:34:04.642198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Slow Diffusive Gravitational Instability Before Decoupling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.CO","authors_text":"Todd A. Thompson","submitted_at":"2009-11-18T21:58:38Z","abstract_excerpt":"Radiative diffusion damps acoustic modes at large comoving wavenumber (k) before decoupling (``Silk damping''). In a simple WKB analysis, neglecting moments of the temperature distribution beyond the quadrupole, damping appears in the acoustic mode as a term of order ik^2/(taudot) where taudot is the scattering rate per unit conformal time. Although the Jeans instability is stabilized on scales smaller than the adiabatic Jeans length, I show that the medium is linearly unstable to first order in (1/taudot) to a slow diffusive mode. At large comoving wavenumber, the characteristic growth rate b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.3665","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":""},"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":"0911.3665","created_at":"2026-05-18T02:34:04.642304+00:00"},{"alias_kind":"arxiv_version","alias_value":"0911.3665v1","created_at":"2026-05-18T02:34:04.642304+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.3665","created_at":"2026-05-18T02:34:04.642304+00:00"},{"alias_kind":"pith_short_12","alias_value":"3JP3VE33L77Y","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_16","alias_value":"3JP3VE33L77YOHH2","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_8","alias_value":"3JP3VE33","created_at":"2026-05-18T12:25:58.018023+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3JP3VE33L77YOHH2VX2PBVZH7P","json":"https://pith.science/pith/3JP3VE33L77YOHH2VX2PBVZH7P.json","graph_json":"https://pith.science/api/pith-number/3JP3VE33L77YOHH2VX2PBVZH7P/graph.json","events_json":"https://pith.science/api/pith-number/3JP3VE33L77YOHH2VX2PBVZH7P/events.json","paper":"https://pith.science/paper/3JP3VE33"},"agent_actions":{"view_html":"https://pith.science/pith/3JP3VE33L77YOHH2VX2PBVZH7P","download_json":"https://pith.science/pith/3JP3VE33L77YOHH2VX2PBVZH7P.json","view_paper":"https://pith.science/paper/3JP3VE33","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0911.3665&json=true","fetch_graph":"https://pith.science/api/pith-number/3JP3VE33L77YOHH2VX2PBVZH7P/graph.json","fetch_events":"https://pith.science/api/pith-number/3JP3VE33L77YOHH2VX2PBVZH7P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3JP3VE33L77YOHH2VX2PBVZH7P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3JP3VE33L77YOHH2VX2PBVZH7P/action/storage_attestation","attest_author":"https://pith.science/pith/3JP3VE33L77YOHH2VX2PBVZH7P/action/author_attestation","sign_citation":"https://pith.science/pith/3JP3VE33L77YOHH2VX2PBVZH7P/action/citation_signature","submit_replication":"https://pith.science/pith/3JP3VE33L77YOHH2VX2PBVZH7P/action/replication_record"}},"created_at":"2026-05-18T02:34:04.642304+00:00","updated_at":"2026-05-18T02:34:04.642304+00:00"}