{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:23WCL7IWAVNYFVFF7XSZXZ6SKP","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":"900b5cd40c6f092146f7fed70242c1d1a786862991642a67453b3dbc4a4206d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2008-05-23T18:18:05Z","title_canon_sha256":"17b74cc97b2b15a55fe355350472a0a9b9a910434ba7617ff03de6a3b115aa09"},"schema_version":"1.0","source":{"id":"0805.3678","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0805.3678","created_at":"2026-05-18T04:14:06Z"},{"alias_kind":"arxiv_version","alias_value":"0805.3678v3","created_at":"2026-05-18T04:14:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0805.3678","created_at":"2026-05-18T04:14:06Z"},{"alias_kind":"pith_short_12","alias_value":"23WCL7IWAVNY","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"23WCL7IWAVNYFVFF","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"23WCL7IW","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:00be32600fc9455d471d0b4628e420fb0779bb0b6f4d237f0a2b94bcb6654972","target":"graph","created_at":"2026-05-18T04:14:06Z","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":"In this note we prove Poincar\\'e type inequalities for a family of kinetic equations. We apply this inequality to the variational solution of a linear kinetic model.","authors_text":"Pascal Azerad (I3M), St\\'ephane Brull (IMT)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2008-05-23T18:18:05Z","title":"In\\'egalit\\'es de Poincar\\'e cin\\'etiques"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.3678","kind":"arxiv","version":3},"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":"sha256:8cd7ff3abf99dccd2393ee1a2c5bd299b913d15a2451a1e1ec4a2d972566eb3f","target":"record","created_at":"2026-05-18T04:14:06Z","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":"900b5cd40c6f092146f7fed70242c1d1a786862991642a67453b3dbc4a4206d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2008-05-23T18:18:05Z","title_canon_sha256":"17b74cc97b2b15a55fe355350472a0a9b9a910434ba7617ff03de6a3b115aa09"},"schema_version":"1.0","source":{"id":"0805.3678","kind":"arxiv","version":3}},"canonical_sha256":"d6ec25fd16055b82d4a5fde59be7d253d4846773f7fe2448d30d6a48c23c262c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6ec25fd16055b82d4a5fde59be7d253d4846773f7fe2448d30d6a48c23c262c","first_computed_at":"2026-05-18T04:14:06.095564Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:06.095564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AFPd/gccogoO0p6u2gxH2k0ziiFloo/dGV5Tiw/ipa2k0cbl2lhVsck2H61v6MVq2hIeuQXeKqJ3rSVfpV/wAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:06.095972Z","signed_message":"canonical_sha256_bytes"},"source_id":"0805.3678","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8cd7ff3abf99dccd2393ee1a2c5bd299b913d15a2451a1e1ec4a2d972566eb3f","sha256:00be32600fc9455d471d0b4628e420fb0779bb0b6f4d237f0a2b94bcb6654972"],"state_sha256":"2c0e526e55bf2b2f964066e2617401d76e2aec164cb1f1a93cc0842182d0f81f"}