{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:KW33HLFWVRU2KTU4XFWWAL4ADC","short_pith_number":"pith:KW33HLFW","schema_version":"1.0","canonical_sha256":"55b7b3acb6ac69a54e9cb96d602f80189564ae0f1429153653632594b1fe9739","source":{"kind":"arxiv","id":"1010.4301","version":1},"attestation_state":"computed","paper":{"title":"On the universality of the global slope -- anisotropy inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"astro-ph.CO","authors_text":"Emmanuel Van Hese, Herwig Dejonghe, Maarten Baes","submitted_at":"2010-10-20T20:00:00Z","abstract_excerpt":"Recently, some intriguing results have lead to speculations whether the central density slope -- velocity dispersion anisotropy inequality (An & Evans) actually holds at all radii for spherical dynamical systems. We extend these studies by providing a complete analysis of the global slope -- anisotropy inequality for all spherical systems in which the augmented density is a separable function of radius and potential. We prove that these systems indeed satisfy the global inequality if their central anisotropy is $\\beta_0\\leq 1/2$. Furthermore, we present several systems with $\\beta_0 > 1/2$ for"},"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":"1010.4301","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2010-10-20T20:00:00Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"07123fd333025a00c61e6beb7769905a94b80f4be21dec84734be7f802874609","abstract_canon_sha256":"51c0a77d0ba4c0187f4da2814910c73829a173a01499b119c9b88f0e3d4404fb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:05:00.382692Z","signature_b64":"6iuU/L9Xq1NITiJZkiDiXy4mnpAeSVWLFi6kisgBv/RNSp6Fuk0YdhOpYhZG794wbV4WUPWvuY0ilAzUvovABw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55b7b3acb6ac69a54e9cb96d602f80189564ae0f1429153653632594b1fe9739","last_reissued_at":"2026-05-18T02:05:00.381934Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:05:00.381934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the universality of the global slope -- anisotropy inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"astro-ph.CO","authors_text":"Emmanuel Van Hese, Herwig Dejonghe, Maarten Baes","submitted_at":"2010-10-20T20:00:00Z","abstract_excerpt":"Recently, some intriguing results have lead to speculations whether the central density slope -- velocity dispersion anisotropy inequality (An & Evans) actually holds at all radii for spherical dynamical systems. We extend these studies by providing a complete analysis of the global slope -- anisotropy inequality for all spherical systems in which the augmented density is a separable function of radius and potential. We prove that these systems indeed satisfy the global inequality if their central anisotropy is $\\beta_0\\leq 1/2$. Furthermore, we present several systems with $\\beta_0 > 1/2$ for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.4301","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":"1010.4301","created_at":"2026-05-18T02:05:00.382063+00:00"},{"alias_kind":"arxiv_version","alias_value":"1010.4301v1","created_at":"2026-05-18T02:05:00.382063+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.4301","created_at":"2026-05-18T02:05:00.382063+00:00"},{"alias_kind":"pith_short_12","alias_value":"KW33HLFWVRU2","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"KW33HLFWVRU2KTU4","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"KW33HLFW","created_at":"2026-05-18T12:26:09.077623+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/KW33HLFWVRU2KTU4XFWWAL4ADC","json":"https://pith.science/pith/KW33HLFWVRU2KTU4XFWWAL4ADC.json","graph_json":"https://pith.science/api/pith-number/KW33HLFWVRU2KTU4XFWWAL4ADC/graph.json","events_json":"https://pith.science/api/pith-number/KW33HLFWVRU2KTU4XFWWAL4ADC/events.json","paper":"https://pith.science/paper/KW33HLFW"},"agent_actions":{"view_html":"https://pith.science/pith/KW33HLFWVRU2KTU4XFWWAL4ADC","download_json":"https://pith.science/pith/KW33HLFWVRU2KTU4XFWWAL4ADC.json","view_paper":"https://pith.science/paper/KW33HLFW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1010.4301&json=true","fetch_graph":"https://pith.science/api/pith-number/KW33HLFWVRU2KTU4XFWWAL4ADC/graph.json","fetch_events":"https://pith.science/api/pith-number/KW33HLFWVRU2KTU4XFWWAL4ADC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KW33HLFWVRU2KTU4XFWWAL4ADC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KW33HLFWVRU2KTU4XFWWAL4ADC/action/storage_attestation","attest_author":"https://pith.science/pith/KW33HLFWVRU2KTU4XFWWAL4ADC/action/author_attestation","sign_citation":"https://pith.science/pith/KW33HLFWVRU2KTU4XFWWAL4ADC/action/citation_signature","submit_replication":"https://pith.science/pith/KW33HLFWVRU2KTU4XFWWAL4ADC/action/replication_record"}},"created_at":"2026-05-18T02:05:00.382063+00:00","updated_at":"2026-05-18T02:05:00.382063+00:00"}