{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:VTNLWX2V24HSRED6H2QQ6TN5UA","short_pith_number":"pith:VTNLWX2V","schema_version":"1.0","canonical_sha256":"acdabb5f55d70f28907e3ea10f4dbda00fca8bdeac78a060d32150da44fe71b2","source":{"kind":"arxiv","id":"1610.01701","version":2},"attestation_state":"computed","paper":{"title":"Reflection symmetries of Isolated Self-consistent Stellar Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.GA","authors_text":"J. An, J. L. Sanders, N. W. Evans","submitted_at":"2016-10-06T01:01:07Z","abstract_excerpt":"Isolated, steady-state galaxies correspond to equilibrium solutions of the Poisson--Vlasov system. We show that (i) all galaxies with a distribution function depending on energy alone must be spherically symmetric and (ii) all axisymmetric galaxies with a distribution function depending on energy and the angular momentum component parallel to the symmetry axis must also be reflection-symmetric about the plane $z=0$. The former result is Lichtenstein's Theorem, derived here by a method exploiting symmetries of solutions of elliptic partial differential equations, while the latter result is new."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1610.01701","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.GA","submitted_at":"2016-10-06T01:01:07Z","cross_cats_sorted":[],"title_canon_sha256":"03f65fef1460c6ee4c3e18b7783ac1379e55762b2150541994efa9f8526a7545","abstract_canon_sha256":"b9d66be3314f7140cf08c945aa626d14471828106e9decadb57f9ffa0e87cba3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:43.681398Z","signature_b64":"FNhKHFV6t8dzv/AueKFV4w3G5EtdLrwiAsXsF9pJV/W0WExdQo670BjmN3L+HXAs8y9yQKEqK/V0LIN6KV0XCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"acdabb5f55d70f28907e3ea10f4dbda00fca8bdeac78a060d32150da44fe71b2","last_reissued_at":"2026-05-18T00:51:43.680662Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:43.680662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Reflection symmetries of Isolated Self-consistent Stellar Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.GA","authors_text":"J. An, J. L. Sanders, N. W. Evans","submitted_at":"2016-10-06T01:01:07Z","abstract_excerpt":"Isolated, steady-state galaxies correspond to equilibrium solutions of the Poisson--Vlasov system. We show that (i) all galaxies with a distribution function depending on energy alone must be spherically symmetric and (ii) all axisymmetric galaxies with a distribution function depending on energy and the angular momentum component parallel to the symmetry axis must also be reflection-symmetric about the plane $z=0$. The former result is Lichtenstein's Theorem, derived here by a method exploiting symmetries of solutions of elliptic partial differential equations, while the latter result is new."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01701","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1610.01701","created_at":"2026-05-18T00:51:43.680785+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.01701v2","created_at":"2026-05-18T00:51:43.680785+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.01701","created_at":"2026-05-18T00:51:43.680785+00:00"},{"alias_kind":"pith_short_12","alias_value":"VTNLWX2V24HS","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_16","alias_value":"VTNLWX2V24HSRED6","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_8","alias_value":"VTNLWX2V","created_at":"2026-05-18T12:30:48.956258+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VTNLWX2V24HSRED6H2QQ6TN5UA","json":"https://pith.science/pith/VTNLWX2V24HSRED6H2QQ6TN5UA.json","graph_json":"https://pith.science/api/pith-number/VTNLWX2V24HSRED6H2QQ6TN5UA/graph.json","events_json":"https://pith.science/api/pith-number/VTNLWX2V24HSRED6H2QQ6TN5UA/events.json","paper":"https://pith.science/paper/VTNLWX2V"},"agent_actions":{"view_html":"https://pith.science/pith/VTNLWX2V24HSRED6H2QQ6TN5UA","download_json":"https://pith.science/pith/VTNLWX2V24HSRED6H2QQ6TN5UA.json","view_paper":"https://pith.science/paper/VTNLWX2V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.01701&json=true","fetch_graph":"https://pith.science/api/pith-number/VTNLWX2V24HSRED6H2QQ6TN5UA/graph.json","fetch_events":"https://pith.science/api/pith-number/VTNLWX2V24HSRED6H2QQ6TN5UA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VTNLWX2V24HSRED6H2QQ6TN5UA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VTNLWX2V24HSRED6H2QQ6TN5UA/action/storage_attestation","attest_author":"https://pith.science/pith/VTNLWX2V24HSRED6H2QQ6TN5UA/action/author_attestation","sign_citation":"https://pith.science/pith/VTNLWX2V24HSRED6H2QQ6TN5UA/action/citation_signature","submit_replication":"https://pith.science/pith/VTNLWX2V24HSRED6H2QQ6TN5UA/action/replication_record"}},"created_at":"2026-05-18T00:51:43.680785+00:00","updated_at":"2026-05-18T00:51:43.680785+00:00"}