{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1998:MHOIQTWXEV753DVTB56HRPGIG7","short_pith_number":"pith:MHOIQTWX","canonical_record":{"source":{"id":"gr-qc/9812061","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"1998-12-17T14:09:32Z","cross_cats_sorted":[],"title_canon_sha256":"7e53a1e4498d0f5ae218aa5514e94966b41491c04ca1a1bb5ff98ab5a94ddcf3","abstract_canon_sha256":"48c607aa3a27c620bd08518727f379f7c7e715263564ab050634041046d3c105"},"schema_version":"1.0"},"canonical_sha256":"61dc884ed7257fdd8eb30f7c78bcc837ed609bf8374e907cd241c2f7429ac071","source":{"kind":"arxiv","id":"gr-qc/9812061","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/9812061","created_at":"2026-05-18T01:39:18Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/9812061v1","created_at":"2026-05-18T01:39:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/9812061","created_at":"2026-05-18T01:39:18Z"},{"alias_kind":"pith_short_12","alias_value":"MHOIQTWXEV75","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"MHOIQTWXEV753DVT","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"MHOIQTWX","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1998:MHOIQTWXEV753DVTB56HRPGIG7","target":"record","payload":{"canonical_record":{"source":{"id":"gr-qc/9812061","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"1998-12-17T14:09:32Z","cross_cats_sorted":[],"title_canon_sha256":"7e53a1e4498d0f5ae218aa5514e94966b41491c04ca1a1bb5ff98ab5a94ddcf3","abstract_canon_sha256":"48c607aa3a27c620bd08518727f379f7c7e715263564ab050634041046d3c105"},"schema_version":"1.0"},"canonical_sha256":"61dc884ed7257fdd8eb30f7c78bcc837ed609bf8374e907cd241c2f7429ac071","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:39:18.218119Z","signature_b64":"NmevhtDByoiTkzx+jDDUJTmFq+AkH2Ri6hyFmcTttwTQl8jUWjI3XZYebasPXX0VY6XDIwQNXb6DD+VkZNR2Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61dc884ed7257fdd8eb30f7c78bcc837ed609bf8374e907cd241c2f7429ac071","last_reissued_at":"2026-05-18T01:39:18.217290Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:39:18.217290Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"gr-qc/9812061","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":"2026-05-18T01:39:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"taUST3UPwL8A3jfdTY2GVwUqQU71o4YyDPskJXivlTfa9GZnsH7u9TsYyG2pAlIdzVDdXlg/mKOTtDRx6k2qAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T16:02:57.761995Z"},"content_sha256":"506a8dbecdafeb9883fd0964cc66011af49dd6125212a830947e4cf1985738d8","schema_version":"1.0","event_id":"sha256:506a8dbecdafeb9883fd0964cc66011af49dd6125212a830947e4cf1985738d8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1998:MHOIQTWXEV753DVTB56HRPGIG7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Compact support of spherically symmetric equilibria in non-relativistic and relativistic galactic dynamics","license":"","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Alan D. Rendall, Gerhard Rein","submitted_at":"1998-12-17T14:09:32Z","abstract_excerpt":"Equilibrium states in galactic dynamics can be described as stationary solutions of the Vlasov-Poisson system, which is the non-relativistic case, or of the Vlasov-Einstein system, which is the relativistic case. To obtain spherically symmetric stationary solutions the distribution function of the particles (stars) on phase space is taken to be a function of the particle energy and angular momentum. We give a new condition on this function which guarantees that the resulting steady state has finite mass and compact support both for the non-relativistic and the relativistic case. The condition "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/9812061","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:39:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BseTs/UvAuOx+C6V59mR6qtXSemcsxIAprlW6n1cjup38N4jmJg6twOvHmYfx8ZH7Ht5MjSSesDTzRRkhSQ/CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T16:02:57.762686Z"},"content_sha256":"5a284a90a324c7bd77833d21355c01ab7078356e85a9a5b5351da7f7eed058dc","schema_version":"1.0","event_id":"sha256:5a284a90a324c7bd77833d21355c01ab7078356e85a9a5b5351da7f7eed058dc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MHOIQTWXEV753DVTB56HRPGIG7/bundle.json","state_url":"https://pith.science/pith/MHOIQTWXEV753DVTB56HRPGIG7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MHOIQTWXEV753DVTB56HRPGIG7/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":"2026-06-10T16:02:57Z","links":{"resolver":"https://pith.science/pith/MHOIQTWXEV753DVTB56HRPGIG7","bundle":"https://pith.science/pith/MHOIQTWXEV753DVTB56HRPGIG7/bundle.json","state":"https://pith.science/pith/MHOIQTWXEV753DVTB56HRPGIG7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MHOIQTWXEV753DVTB56HRPGIG7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:MHOIQTWXEV753DVTB56HRPGIG7","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":"48c607aa3a27c620bd08518727f379f7c7e715263564ab050634041046d3c105","cross_cats_sorted":[],"license":"","primary_cat":"gr-qc","submitted_at":"1998-12-17T14:09:32Z","title_canon_sha256":"7e53a1e4498d0f5ae218aa5514e94966b41491c04ca1a1bb5ff98ab5a94ddcf3"},"schema_version":"1.0","source":{"id":"gr-qc/9812061","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/9812061","created_at":"2026-05-18T01:39:18Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/9812061v1","created_at":"2026-05-18T01:39:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/9812061","created_at":"2026-05-18T01:39:18Z"},{"alias_kind":"pith_short_12","alias_value":"MHOIQTWXEV75","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"MHOIQTWXEV753DVT","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"MHOIQTWX","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:5a284a90a324c7bd77833d21355c01ab7078356e85a9a5b5351da7f7eed058dc","target":"graph","created_at":"2026-05-18T01:39:18Z","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":"Equilibrium states in galactic dynamics can be described as stationary solutions of the Vlasov-Poisson system, which is the non-relativistic case, or of the Vlasov-Einstein system, which is the relativistic case. To obtain spherically symmetric stationary solutions the distribution function of the particles (stars) on phase space is taken to be a function of the particle energy and angular momentum. We give a new condition on this function which guarantees that the resulting steady state has finite mass and compact support both for the non-relativistic and the relativistic case. The condition ","authors_text":"Alan D. Rendall, Gerhard Rein","cross_cats":[],"headline":"","license":"","primary_cat":"gr-qc","submitted_at":"1998-12-17T14:09:32Z","title":"Compact support of spherically symmetric equilibria in non-relativistic and relativistic galactic dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/9812061","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":"sha256:506a8dbecdafeb9883fd0964cc66011af49dd6125212a830947e4cf1985738d8","target":"record","created_at":"2026-05-18T01:39:18Z","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":"48c607aa3a27c620bd08518727f379f7c7e715263564ab050634041046d3c105","cross_cats_sorted":[],"license":"","primary_cat":"gr-qc","submitted_at":"1998-12-17T14:09:32Z","title_canon_sha256":"7e53a1e4498d0f5ae218aa5514e94966b41491c04ca1a1bb5ff98ab5a94ddcf3"},"schema_version":"1.0","source":{"id":"gr-qc/9812061","kind":"arxiv","version":1}},"canonical_sha256":"61dc884ed7257fdd8eb30f7c78bcc837ed609bf8374e907cd241c2f7429ac071","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61dc884ed7257fdd8eb30f7c78bcc837ed609bf8374e907cd241c2f7429ac071","first_computed_at":"2026-05-18T01:39:18.217290Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:39:18.217290Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NmevhtDByoiTkzx+jDDUJTmFq+AkH2Ri6hyFmcTttwTQl8jUWjI3XZYebasPXX0VY6XDIwQNXb6DD+VkZNR2Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:39:18.218119Z","signed_message":"canonical_sha256_bytes"},"source_id":"gr-qc/9812061","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:506a8dbecdafeb9883fd0964cc66011af49dd6125212a830947e4cf1985738d8","sha256:5a284a90a324c7bd77833d21355c01ab7078356e85a9a5b5351da7f7eed058dc"],"state_sha256":"110d6da1e455c4e91da798f5c2fc15758e25feabe29442c89f5f04537457e10d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fGOuvc2+4ZU1qU8podXBnJlopYb7TKyQXdrX9SzKZOHWIek9mb7TFiGWQnLXBT8fQCqCk9CVSOTTcqWUsWRkDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T16:02:57.767055Z","bundle_sha256":"9d3a4751805bc87363e0f54b1188fe5bf1716ba330c910fe2d3cc53eef5a4027"}}