{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:KW33HLFWVRU2KTU4XFWWAL4ADC","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":"51c0a77d0ba4c0187f4da2814910c73829a173a01499b119c9b88f0e3d4404fb","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2010-10-20T20:00:00Z","title_canon_sha256":"07123fd333025a00c61e6beb7769905a94b80f4be21dec84734be7f802874609"},"schema_version":"1.0","source":{"id":"1010.4301","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.4301","created_at":"2026-05-18T02:05:00Z"},{"alias_kind":"arxiv_version","alias_value":"1010.4301v1","created_at":"2026-05-18T02:05:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.4301","created_at":"2026-05-18T02:05:00Z"},{"alias_kind":"pith_short_12","alias_value":"KW33HLFWVRU2","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KW33HLFWVRU2KTU4","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KW33HLFW","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:a2f0cc98f716678021be8c3fe17cfb3356cedcb2f1f1ef1ea3aa8fab710eec6a","target":"graph","created_at":"2026-05-18T02:05:00Z","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":"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","authors_text":"Emmanuel Van Hese, Herwig Dejonghe, Maarten Baes","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2010-10-20T20:00:00Z","title":"On the universality of the global slope -- anisotropy inequality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.4301","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":"sha256:9cd5b6aeb9fdf5aa2c1ad7b26900a222a15fc6802f8c41f6b1164c4497c95244","target":"record","created_at":"2026-05-18T02:05:00Z","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":"51c0a77d0ba4c0187f4da2814910c73829a173a01499b119c9b88f0e3d4404fb","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2010-10-20T20:00:00Z","title_canon_sha256":"07123fd333025a00c61e6beb7769905a94b80f4be21dec84734be7f802874609"},"schema_version":"1.0","source":{"id":"1010.4301","kind":"arxiv","version":1}},"canonical_sha256":"55b7b3acb6ac69a54e9cb96d602f80189564ae0f1429153653632594b1fe9739","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55b7b3acb6ac69a54e9cb96d602f80189564ae0f1429153653632594b1fe9739","first_computed_at":"2026-05-18T02:05:00.381934Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:05:00.381934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6iuU/L9Xq1NITiJZkiDiXy4mnpAeSVWLFi6kisgBv/RNSp6Fuk0YdhOpYhZG794wbV4WUPWvuY0ilAzUvovABw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:05:00.382692Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.4301","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9cd5b6aeb9fdf5aa2c1ad7b26900a222a15fc6802f8c41f6b1164c4497c95244","sha256:a2f0cc98f716678021be8c3fe17cfb3356cedcb2f1f1ef1ea3aa8fab710eec6a"],"state_sha256":"c52973005202c50a7f68b56d9341035ac02050549c871b6eb553b41d03c91c2f"}