{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:KJLBEC2IQSFWFVKLXOCPVQZ5KP","short_pith_number":"pith:KJLBEC2I","canonical_record":{"source":{"id":"2301.07662","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-01-18T17:11:53Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"7bc85182c7529c7703a91a6ee76f8e970ea70eda687e5eabc73d00e7f4693ee7","abstract_canon_sha256":"04a61d5213263467370c38a3b47004f694e2a0a6377a25eaef0b3b689bcf5956"},"schema_version":"1.0"},"canonical_sha256":"5256120b48848b62d54bbb84fac33d53f96270b7ca2d080b6d76abb27987a1f1","source":{"kind":"arxiv","id":"2301.07662","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2301.07662","created_at":"2026-07-05T11:40:46Z"},{"alias_kind":"arxiv_version","alias_value":"2301.07662v1","created_at":"2026-07-05T11:40:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.07662","created_at":"2026-07-05T11:40:46Z"},{"alias_kind":"pith_short_12","alias_value":"KJLBEC2IQSFW","created_at":"2026-07-05T11:40:46Z"},{"alias_kind":"pith_short_16","alias_value":"KJLBEC2IQSFWFVKL","created_at":"2026-07-05T11:40:46Z"},{"alias_kind":"pith_short_8","alias_value":"KJLBEC2I","created_at":"2026-07-05T11:40:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:KJLBEC2IQSFWFVKLXOCPVQZ5KP","target":"record","payload":{"canonical_record":{"source":{"id":"2301.07662","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-01-18T17:11:53Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"7bc85182c7529c7703a91a6ee76f8e970ea70eda687e5eabc73d00e7f4693ee7","abstract_canon_sha256":"04a61d5213263467370c38a3b47004f694e2a0a6377a25eaef0b3b689bcf5956"},"schema_version":"1.0"},"canonical_sha256":"5256120b48848b62d54bbb84fac33d53f96270b7ca2d080b6d76abb27987a1f1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:40:46.850039Z","signature_b64":"IFLCAP9uYqQl05RatmPl7UqUr40MxB/JqOtKDjGxGWHEt8qPpVjLBNT1Ufljc/RymZONkucUSY7HKLpAekk5Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5256120b48848b62d54bbb84fac33d53f96270b7ca2d080b6d76abb27987a1f1","last_reissued_at":"2026-07-05T11:40:46.849543Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:40:46.849543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2301.07662","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:40:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0GAsUBkQN1UmWUKpzEax7gaiEE82nTsP9iXmAtrwXBNTu4C2dLjVB0HXUkY/95jU3UaDfCzXbHavDY4W/X9HAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T05:13:02.119972Z"},"content_sha256":"eb9ae73e5749826c6ec716512bb035489a2b7cb96bb361f6e71f6f35a74f3d8c","schema_version":"1.0","event_id":"sha256:eb9ae73e5749826c6ec716512bb035489a2b7cb96bb361f6e71f6f35a74f3d8c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:KJLBEC2IQSFWFVKLXOCPVQZ5KP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Damping versus oscillations for a gravitational Vlasov-Poisson system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Christopher Straub, Gerhard Rein, Mahir Hadzic, Matthew Schrecker","submitted_at":"2023-01-18T17:11:53Z","abstract_excerpt":"We consider a family of isolated inhomogeneous steady states to the gravitational Vlasov-Poisson system with a point mass at the centre. They are parametrised by the polytropic index $k>1/2$, so that the phase space density of the steady state is $C^1$ at the vacuum boundary if and only if $k>1$. We prove the following sharp dichotomy result: if $k>1$ the linear perturbations Landau damp and if $1/2< k\\le1$ they do not.\n  The above dichotomy is a new phenomenon and highlights the importance of steady state regularity at the vacuum boundary in the discussion of long-time behaviour of the pertur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.07662","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/2301.07662/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:40:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q91wTQYnul2cMXdbclOLowc0f7YcYEVTWk+Lwj/QvTKi+vrMz8quJ+aSzBjNkWX74dzg3Atq4Ak10NXBOMrHDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T05:13:02.120538Z"},"content_sha256":"6756ea1d0245e91b76fc51ecc345f97ea58a0e9fdd2074596c5fcf0a3539216e","schema_version":"1.0","event_id":"sha256:6756ea1d0245e91b76fc51ecc345f97ea58a0e9fdd2074596c5fcf0a3539216e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KJLBEC2IQSFWFVKLXOCPVQZ5KP/bundle.json","state_url":"https://pith.science/pith/KJLBEC2IQSFWFVKLXOCPVQZ5KP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KJLBEC2IQSFWFVKLXOCPVQZ5KP/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-11T05:13:02Z","links":{"resolver":"https://pith.science/pith/KJLBEC2IQSFWFVKLXOCPVQZ5KP","bundle":"https://pith.science/pith/KJLBEC2IQSFWFVKLXOCPVQZ5KP/bundle.json","state":"https://pith.science/pith/KJLBEC2IQSFWFVKLXOCPVQZ5KP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KJLBEC2IQSFWFVKLXOCPVQZ5KP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:KJLBEC2IQSFWFVKLXOCPVQZ5KP","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":"04a61d5213263467370c38a3b47004f694e2a0a6377a25eaef0b3b689bcf5956","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-01-18T17:11:53Z","title_canon_sha256":"7bc85182c7529c7703a91a6ee76f8e970ea70eda687e5eabc73d00e7f4693ee7"},"schema_version":"1.0","source":{"id":"2301.07662","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2301.07662","created_at":"2026-07-05T11:40:46Z"},{"alias_kind":"arxiv_version","alias_value":"2301.07662v1","created_at":"2026-07-05T11:40:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.07662","created_at":"2026-07-05T11:40:46Z"},{"alias_kind":"pith_short_12","alias_value":"KJLBEC2IQSFW","created_at":"2026-07-05T11:40:46Z"},{"alias_kind":"pith_short_16","alias_value":"KJLBEC2IQSFWFVKL","created_at":"2026-07-05T11:40:46Z"},{"alias_kind":"pith_short_8","alias_value":"KJLBEC2I","created_at":"2026-07-05T11:40:46Z"}],"graph_snapshots":[{"event_id":"sha256:6756ea1d0245e91b76fc51ecc345f97ea58a0e9fdd2074596c5fcf0a3539216e","target":"graph","created_at":"2026-07-05T11:40:46Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2301.07662/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a family of isolated inhomogeneous steady states to the gravitational Vlasov-Poisson system with a point mass at the centre. They are parametrised by the polytropic index $k>1/2$, so that the phase space density of the steady state is $C^1$ at the vacuum boundary if and only if $k>1$. We prove the following sharp dichotomy result: if $k>1$ the linear perturbations Landau damp and if $1/2< k\\le1$ they do not.\n  The above dichotomy is a new phenomenon and highlights the importance of steady state regularity at the vacuum boundary in the discussion of long-time behaviour of the pertur","authors_text":"Christopher Straub, Gerhard Rein, Mahir Hadzic, Matthew Schrecker","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-01-18T17:11:53Z","title":"Damping versus oscillations for a gravitational Vlasov-Poisson system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.07662","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:eb9ae73e5749826c6ec716512bb035489a2b7cb96bb361f6e71f6f35a74f3d8c","target":"record","created_at":"2026-07-05T11:40:46Z","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":"04a61d5213263467370c38a3b47004f694e2a0a6377a25eaef0b3b689bcf5956","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-01-18T17:11:53Z","title_canon_sha256":"7bc85182c7529c7703a91a6ee76f8e970ea70eda687e5eabc73d00e7f4693ee7"},"schema_version":"1.0","source":{"id":"2301.07662","kind":"arxiv","version":1}},"canonical_sha256":"5256120b48848b62d54bbb84fac33d53f96270b7ca2d080b6d76abb27987a1f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5256120b48848b62d54bbb84fac33d53f96270b7ca2d080b6d76abb27987a1f1","first_computed_at":"2026-07-05T11:40:46.849543Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:40:46.849543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IFLCAP9uYqQl05RatmPl7UqUr40MxB/JqOtKDjGxGWHEt8qPpVjLBNT1Ufljc/RymZONkucUSY7HKLpAekk5Cw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:40:46.850039Z","signed_message":"canonical_sha256_bytes"},"source_id":"2301.07662","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb9ae73e5749826c6ec716512bb035489a2b7cb96bb361f6e71f6f35a74f3d8c","sha256:6756ea1d0245e91b76fc51ecc345f97ea58a0e9fdd2074596c5fcf0a3539216e"],"state_sha256":"4f4e78b34272e0a6b7bc4fa107d09e822311b9b6676f72c3df8dafcc3f1b1d14"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d5ewqP3GMSV7nWHwgzk+sh1M2kMb3mnf3n5MgjeOEyfx9iCie0PHbv/B78pf/wCF8rKcJdzqipc9mOKzl0PuCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T05:13:02.124959Z","bundle_sha256":"2ef5aa931ee17b69486ad3ef7b89d3eaa6e08c24c254fd241011ab48bf762ac9"}}