{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VXTHLY3ME72LXDEUQAEQ22TFZ2","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"069d95b8888a1cc84f16f4d90d7253f2b384d74b513677a240b4cbecc635004a","cross_cats_sorted":["astro-ph.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2012-07-31T15:21:22Z","title_canon_sha256":"a6dfede90d60ebd48f5c17400ea3e0c379ec4a46a7ef4561139b996b84867a06"},"schema_version":"1.0","source":{"id":"1207.7285","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.7285","created_at":"2026-05-18T03:07:32Z"},{"alias_kind":"arxiv_version","alias_value":"1207.7285v4","created_at":"2026-05-18T03:07:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.7285","created_at":"2026-05-18T03:07:32Z"},{"alias_kind":"pith_short_12","alias_value":"VXTHLY3ME72L","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VXTHLY3ME72LXDEU","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VXTHLY3M","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:e9cb762d4a0b2b23ac310b892dad609df3e9f881e5915e1e9e4b0a1f2bde1a91","target":"graph","created_at":"2026-05-18T03:07:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We provide an analytic solution to the general wavelength integro-differential equation describing the damping of tensor modes of gravitational waves due to free streaming neutrinos in the early universe. Our result is expressed as a series of spherical Bessel functions whose coefficients are functions of the reduced wave number $Q$.","authors_text":"Ben A. Stefanek, Wayne W. Repko","cross_cats":["astro-ph.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2012-07-31T15:21:22Z","title":"An analytic description of the damping of gravitational waves by free streaming neutrinos"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.7285","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8018fdaae4c2726dc73b4f70df00bdff460d3666a2c280af6b03a525f4cff53c","target":"record","created_at":"2026-05-18T03:07:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"069d95b8888a1cc84f16f4d90d7253f2b384d74b513677a240b4cbecc635004a","cross_cats_sorted":["astro-ph.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2012-07-31T15:21:22Z","title_canon_sha256":"a6dfede90d60ebd48f5c17400ea3e0c379ec4a46a7ef4561139b996b84867a06"},"schema_version":"1.0","source":{"id":"1207.7285","kind":"arxiv","version":4}},"canonical_sha256":"ade675e36c27f4bb8c9480090d6a65cebaf5321dc4d58dd3482790dcb83366fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ade675e36c27f4bb8c9480090d6a65cebaf5321dc4d58dd3482790dcb83366fc","first_computed_at":"2026-05-18T03:07:32.033747Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:32.033747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jt8vHwIlAYN9P/hWeBVMI+vvWb+1cpklKzpDWgNbqsL+ggE+BTTlhFjyU+wLinSPfxrzuOwWmkNuQOAjXKpjAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:32.034243Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.7285","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8018fdaae4c2726dc73b4f70df00bdff460d3666a2c280af6b03a525f4cff53c","sha256:e9cb762d4a0b2b23ac310b892dad609df3e9f881e5915e1e9e4b0a1f2bde1a91"],"state_sha256":"4a43b52deedff9fedc4fb0211be9d6d6855680f20ac09e311d63931ca8794e49"}