{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:GKYXYCTKYPVZRRQ6DXYMAWREJR","short_pith_number":"pith:GKYXYCTK","canonical_record":{"source":{"id":"1104.0014","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2011-03-31T20:01:58Z","cross_cats_sorted":["astro-ph.GA","math-ph","math.MP"],"title_canon_sha256":"20f939ff27745d487efbb147300ab2cf3b241f8116052a1a701a6245e21573d3","abstract_canon_sha256":"1e01b7e17708070494f4615587dfbbcc0872bfd46c8f273b944db06e5ea88193"},"schema_version":"1.0"},"canonical_sha256":"32b17c0a6ac3eb98c61e1df0c05a244c77b2738f2c51accd70d82d90b04ca4db","source":{"kind":"arxiv","id":"1104.0014","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.0014","created_at":"2026-05-18T04:17:14Z"},{"alias_kind":"arxiv_version","alias_value":"1104.0014v2","created_at":"2026-05-18T04:17:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0014","created_at":"2026-05-18T04:17:14Z"},{"alias_kind":"pith_short_12","alias_value":"GKYXYCTKYPVZ","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GKYXYCTKYPVZRRQ6","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GKYXYCTK","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:GKYXYCTKYPVZRRQ6DXYMAWREJR","target":"record","payload":{"canonical_record":{"source":{"id":"1104.0014","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2011-03-31T20:01:58Z","cross_cats_sorted":["astro-ph.GA","math-ph","math.MP"],"title_canon_sha256":"20f939ff27745d487efbb147300ab2cf3b241f8116052a1a701a6245e21573d3","abstract_canon_sha256":"1e01b7e17708070494f4615587dfbbcc0872bfd46c8f273b944db06e5ea88193"},"schema_version":"1.0"},"canonical_sha256":"32b17c0a6ac3eb98c61e1df0c05a244c77b2738f2c51accd70d82d90b04ca4db","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:17:14.869864Z","signature_b64":"HlgbK1S4+eqZBr11BrGLGTDoXDgpZlpaDOlIv+2iU85E9aDpVAsT0hIUNxokHGtUTHY8nLNTA7i8fWOvhWgjDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32b17c0a6ac3eb98c61e1df0c05a244c77b2738f2c51accd70d82d90b04ca4db","last_reissued_at":"2026-05-18T04:17:14.869210Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:17:14.869210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.0014","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:17:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KUjbdEPA/n4LcscWnoFhtuhXT8yM6Qs9rU4TuTrnqFFxf0WlA3ZjDO3GD8iVmkpSsjoXLqtZ17KWXsKlXi65CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T15:31:52.675400Z"},"content_sha256":"0eab0e8af2a568b5f16b3ce36ad6f0e0708fe5d7473a732cb1baf457cd1c14eb","schema_version":"1.0","event_id":"sha256:0eab0e8af2a568b5f16b3ce36ad6f0e0708fe5d7473a732cb1baf457cd1c14eb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:GKYXYCTKYPVZRRQ6DXYMAWREJR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Constraints on velocity anisotropy of spherical systems with separable augmented densities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.GA","math-ph","math.MP"],"primary_cat":"astro-ph.CO","authors_text":"J. An (NAOC)","submitted_at":"2011-03-31T20:01:58Z","abstract_excerpt":"If the augmented density of a spherical anisotropic system is assumed to be multiplicatively separable to functions of the potential and the radius, the radial function, which can be completely specified by the behavior of the anisotropy parameter alone, also fixes the anisotropic ratios of every higher-order velocity moment. It is inferred from this that the non-negativity of the distribution function necessarily limits the allowed behaviors of the radial function. This restriction is translated into the constraints on the behavior of the anisotropy parameter. We find that not all radial vari"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0014","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:17:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KqO7qE2eUJ3ZPHRIX2Sp36x+X3xRf4XOp9hOpNIthnDtARO9hWAgOkokm1JatCxv1By8aqpecuhl/04YP4WYDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T15:31:52.675750Z"},"content_sha256":"e4876de7c5b7791bb7a5b38340ed141adfec2131195251af260c05ab3be3ab6f","schema_version":"1.0","event_id":"sha256:e4876de7c5b7791bb7a5b38340ed141adfec2131195251af260c05ab3be3ab6f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GKYXYCTKYPVZRRQ6DXYMAWREJR/bundle.json","state_url":"https://pith.science/pith/GKYXYCTKYPVZRRQ6DXYMAWREJR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GKYXYCTKYPVZRRQ6DXYMAWREJR/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":"2026-06-09T15:31:52Z","links":{"resolver":"https://pith.science/pith/GKYXYCTKYPVZRRQ6DXYMAWREJR","bundle":"https://pith.science/pith/GKYXYCTKYPVZRRQ6DXYMAWREJR/bundle.json","state":"https://pith.science/pith/GKYXYCTKYPVZRRQ6DXYMAWREJR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GKYXYCTKYPVZRRQ6DXYMAWREJR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GKYXYCTKYPVZRRQ6DXYMAWREJR","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":"1e01b7e17708070494f4615587dfbbcc0872bfd46c8f273b944db06e5ea88193","cross_cats_sorted":["astro-ph.GA","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2011-03-31T20:01:58Z","title_canon_sha256":"20f939ff27745d487efbb147300ab2cf3b241f8116052a1a701a6245e21573d3"},"schema_version":"1.0","source":{"id":"1104.0014","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.0014","created_at":"2026-05-18T04:17:14Z"},{"alias_kind":"arxiv_version","alias_value":"1104.0014v2","created_at":"2026-05-18T04:17:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0014","created_at":"2026-05-18T04:17:14Z"},{"alias_kind":"pith_short_12","alias_value":"GKYXYCTKYPVZ","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GKYXYCTKYPVZRRQ6","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GKYXYCTK","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:e4876de7c5b7791bb7a5b38340ed141adfec2131195251af260c05ab3be3ab6f","target":"graph","created_at":"2026-05-18T04:17:14Z","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":"If the augmented density of a spherical anisotropic system is assumed to be multiplicatively separable to functions of the potential and the radius, the radial function, which can be completely specified by the behavior of the anisotropy parameter alone, also fixes the anisotropic ratios of every higher-order velocity moment. It is inferred from this that the non-negativity of the distribution function necessarily limits the allowed behaviors of the radial function. This restriction is translated into the constraints on the behavior of the anisotropy parameter. We find that not all radial vari","authors_text":"J. An (NAOC)","cross_cats":["astro-ph.GA","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2011-03-31T20:01:58Z","title":"Constraints on velocity anisotropy of spherical systems with separable augmented densities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0014","kind":"arxiv","version":2},"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":"sha256:0eab0e8af2a568b5f16b3ce36ad6f0e0708fe5d7473a732cb1baf457cd1c14eb","target":"record","created_at":"2026-05-18T04:17:14Z","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":"1e01b7e17708070494f4615587dfbbcc0872bfd46c8f273b944db06e5ea88193","cross_cats_sorted":["astro-ph.GA","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2011-03-31T20:01:58Z","title_canon_sha256":"20f939ff27745d487efbb147300ab2cf3b241f8116052a1a701a6245e21573d3"},"schema_version":"1.0","source":{"id":"1104.0014","kind":"arxiv","version":2}},"canonical_sha256":"32b17c0a6ac3eb98c61e1df0c05a244c77b2738f2c51accd70d82d90b04ca4db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32b17c0a6ac3eb98c61e1df0c05a244c77b2738f2c51accd70d82d90b04ca4db","first_computed_at":"2026-05-18T04:17:14.869210Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:17:14.869210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HlgbK1S4+eqZBr11BrGLGTDoXDgpZlpaDOlIv+2iU85E9aDpVAsT0hIUNxokHGtUTHY8nLNTA7i8fWOvhWgjDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:17:14.869864Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.0014","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0eab0e8af2a568b5f16b3ce36ad6f0e0708fe5d7473a732cb1baf457cd1c14eb","sha256:e4876de7c5b7791bb7a5b38340ed141adfec2131195251af260c05ab3be3ab6f"],"state_sha256":"f389cf61b74f210a939b6f53a5afee8fa30c76ce402e7bafea37f28172fb59e8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"npKvGhcInR1KCYSBzirAwl+ali7zysjeqvzee6D74PK8USd6BSa1HjoxuoTLmuYf3tBLmv7lKKMLvcHbxKy+BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T15:31:52.677764Z","bundle_sha256":"651b11acc7110399d54d5e3ad7e53c3d7aa35e2bb14057680f6fb42fb3f04af4"}}