{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LQYBIV57UWJUYWZFBDTIMYRKJP","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":"74ca6bf39faceba311d9a057d9ff145e68e7732717b23ed6c80202dfa6408320","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-28T19:45:49Z","title_canon_sha256":"4d26118154c4f4d01c4cc06638baae6a53d3e4e22a3bbf8ad4e53300c7d76114"},"schema_version":"1.0","source":{"id":"1205.6198","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6198","created_at":"2026-05-18T01:57:16Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6198v1","created_at":"2026-05-18T01:57:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6198","created_at":"2026-05-18T01:57:16Z"},{"alias_kind":"pith_short_12","alias_value":"LQYBIV57UWJU","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LQYBIV57UWJUYWZF","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LQYBIV57","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:64a0017d99e81298661502445f7df4a8d742e1a3352dd1797a98bd83abf83246","target":"graph","created_at":"2026-05-18T01:57:16Z","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":"The stability of static solutions of the spherically symmetric, asymptotically flat Einstein-Vlasov system is studied using a Hamiltonian approach based on energy-Casimir functionals. The main result is a coercivity estimate for the quadratic part of the expansion of the natural energy-Casimir functional about an isotropic steady state. The estimate shows in a quantified way that this quadratic part is positive definite on a class of linearly dynamically accessible perturbations, provided the particle distribution of the steady state is a strictly decreasing function of the particle energy and","authors_text":"Gerhard Rein, Mahir Hadzic","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-28T19:45:49Z","title":"Stability for the spherically symmetric Einstein-Vlasov system - a coercivity estimate"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6198","kind":"arxiv","version":1},"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":"sha256:4321de619628d0ce4a44af7ffd09bf7b429926533ee115586d1b69b8f20197c9","target":"record","created_at":"2026-05-18T01:57:16Z","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":"74ca6bf39faceba311d9a057d9ff145e68e7732717b23ed6c80202dfa6408320","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-28T19:45:49Z","title_canon_sha256":"4d26118154c4f4d01c4cc06638baae6a53d3e4e22a3bbf8ad4e53300c7d76114"},"schema_version":"1.0","source":{"id":"1205.6198","kind":"arxiv","version":1}},"canonical_sha256":"5c301457bfa5934c5b2508e686622a4bc50c453a9ce16382ee9fe1c452a3bcbf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c301457bfa5934c5b2508e686622a4bc50c453a9ce16382ee9fe1c452a3bcbf","first_computed_at":"2026-05-18T01:57:16.480142Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:57:16.480142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lUk2yD2HOA6Pp0x/8hblcB9jPbSfR6iTA3+Qduf59PRmpmmFUdVUSk1/Xs2jEG29XfsUXVJFTiA9Oma4GdSVAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:57:16.480623Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.6198","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4321de619628d0ce4a44af7ffd09bf7b429926533ee115586d1b69b8f20197c9","sha256:64a0017d99e81298661502445f7df4a8d742e1a3352dd1797a98bd83abf83246"],"state_sha256":"20c2e99e38d45a9e4019eff2c1d2c36ed12d2c7f920f24ae027f70fc61d559a8"}