{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:OYT267E5UI6UTR2FT7SQY6XFW3","short_pith_number":"pith:OYT267E5","schema_version":"1.0","canonical_sha256":"7627af7c9da23d49c7459fe50c7ae5b6c9cbf7f46bd9f01b3cbf3ce706932089","source":{"kind":"arxiv","id":"1610.02112","version":1},"attestation_state":"computed","paper":{"title":"Thermodynamics of gravitational clustering phenomena: $N$-body self-gravitating gas on the sphere $\\mathbb{S}^{3}\\subset\\mathbb{R}^{4}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO"],"primary_cat":"cond-mat.stat-mech","authors_text":"F. Tello-Ortiz, L. Velazquez","submitted_at":"2016-10-07T01:10:45Z","abstract_excerpt":"This work is devoted to the thermodynamics of gravitational clustering, a collective phenomenon with a great relevance in the $N$-body cosmological problem. We study a classical self-gravitating gas of identical non-relativistic particles defined on the sphere $\\mathbb{S}^{3}\\subset \\mathbb{R}^{4}$ by considering gravitational interaction that corresponds to this geometric space. The analysis is performed within microcanonical description of an isolated Hamiltonian system by combining continuum approximation and steepest descend method. According to numerical solution of resulting equations, t"},"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":"1610.02112","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-10-07T01:10:45Z","cross_cats_sorted":["astro-ph.CO"],"title_canon_sha256":"8924cb90048ff59bfd2ae20966f8cb19f1d8960ecfda9bf75f1de321288057ad","abstract_canon_sha256":"82890eccd0155098a131d3f96655ca43729675f059e97b03f0341f4251781a5a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:33.276963Z","signature_b64":"IagH1QWEXnO9GJsHIGy8zR1pdSDx05LTB8XArG6HTbyAXVqEMRHEUD2ASfT1d+USECiU6PBOQICnjnyIBVeKCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7627af7c9da23d49c7459fe50c7ae5b6c9cbf7f46bd9f01b3cbf3ce706932089","last_reissued_at":"2026-05-18T01:00:33.276397Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:33.276397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Thermodynamics of gravitational clustering phenomena: $N$-body self-gravitating gas on the sphere $\\mathbb{S}^{3}\\subset\\mathbb{R}^{4}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO"],"primary_cat":"cond-mat.stat-mech","authors_text":"F. Tello-Ortiz, L. Velazquez","submitted_at":"2016-10-07T01:10:45Z","abstract_excerpt":"This work is devoted to the thermodynamics of gravitational clustering, a collective phenomenon with a great relevance in the $N$-body cosmological problem. We study a classical self-gravitating gas of identical non-relativistic particles defined on the sphere $\\mathbb{S}^{3}\\subset \\mathbb{R}^{4}$ by considering gravitational interaction that corresponds to this geometric space. The analysis is performed within microcanonical description of an isolated Hamiltonian system by combining continuum approximation and steepest descend method. According to numerical solution of resulting equations, t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02112","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1610.02112","created_at":"2026-05-18T01:00:33.276501+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.02112v1","created_at":"2026-05-18T01:00:33.276501+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.02112","created_at":"2026-05-18T01:00:33.276501+00:00"},{"alias_kind":"pith_short_12","alias_value":"OYT267E5UI6U","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_16","alias_value":"OYT267E5UI6UTR2F","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_8","alias_value":"OYT267E5","created_at":"2026-05-18T12:30:36.002864+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/OYT267E5UI6UTR2FT7SQY6XFW3","json":"https://pith.science/pith/OYT267E5UI6UTR2FT7SQY6XFW3.json","graph_json":"https://pith.science/api/pith-number/OYT267E5UI6UTR2FT7SQY6XFW3/graph.json","events_json":"https://pith.science/api/pith-number/OYT267E5UI6UTR2FT7SQY6XFW3/events.json","paper":"https://pith.science/paper/OYT267E5"},"agent_actions":{"view_html":"https://pith.science/pith/OYT267E5UI6UTR2FT7SQY6XFW3","download_json":"https://pith.science/pith/OYT267E5UI6UTR2FT7SQY6XFW3.json","view_paper":"https://pith.science/paper/OYT267E5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.02112&json=true","fetch_graph":"https://pith.science/api/pith-number/OYT267E5UI6UTR2FT7SQY6XFW3/graph.json","fetch_events":"https://pith.science/api/pith-number/OYT267E5UI6UTR2FT7SQY6XFW3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OYT267E5UI6UTR2FT7SQY6XFW3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OYT267E5UI6UTR2FT7SQY6XFW3/action/storage_attestation","attest_author":"https://pith.science/pith/OYT267E5UI6UTR2FT7SQY6XFW3/action/author_attestation","sign_citation":"https://pith.science/pith/OYT267E5UI6UTR2FT7SQY6XFW3/action/citation_signature","submit_replication":"https://pith.science/pith/OYT267E5UI6UTR2FT7SQY6XFW3/action/replication_record"}},"created_at":"2026-05-18T01:00:33.276501+00:00","updated_at":"2026-05-18T01:00:33.276501+00:00"}