{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:IQSLYLXJJQB2KYABDMNHEHUQW4","short_pith_number":"pith:IQSLYLXJ","canonical_record":{"source":{"id":"1905.05297","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-05-13T21:40:54Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"9f23993a1fbdf0604139058a155bf86ca4019fdfd313e5b4cb83d763f63acab9","abstract_canon_sha256":"ff1091735f261e584375c1491553ee417891bc099c92c60bc0abc7d9b96c543d"},"schema_version":"1.0"},"canonical_sha256":"4424bc2ee94c03a560011b1a721e90b71c9aea617adb8d8e9ddefd7019edaf99","source":{"kind":"arxiv","id":"1905.05297","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.05297","created_at":"2026-05-17T23:46:16Z"},{"alias_kind":"arxiv_version","alias_value":"1905.05297v1","created_at":"2026-05-17T23:46:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.05297","created_at":"2026-05-17T23:46:16Z"},{"alias_kind":"pith_short_12","alias_value":"IQSLYLXJJQB2","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"IQSLYLXJJQB2KYAB","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"IQSLYLXJ","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:IQSLYLXJJQB2KYABDMNHEHUQW4","target":"record","payload":{"canonical_record":{"source":{"id":"1905.05297","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-05-13T21:40:54Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"9f23993a1fbdf0604139058a155bf86ca4019fdfd313e5b4cb83d763f63acab9","abstract_canon_sha256":"ff1091735f261e584375c1491553ee417891bc099c92c60bc0abc7d9b96c543d"},"schema_version":"1.0"},"canonical_sha256":"4424bc2ee94c03a560011b1a721e90b71c9aea617adb8d8e9ddefd7019edaf99","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:16.927875Z","signature_b64":"Ld76PC5yJJTPCN8h9eWNONjAN50akbi+T4vB+4bKGrQINPPObTta8Eb6wZptJ0fqLWZDix8Hi6LCBeUX59uvDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4424bc2ee94c03a560011b1a721e90b71c9aea617adb8d8e9ddefd7019edaf99","last_reissued_at":"2026-05-17T23:46:16.927281Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:16.927281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.05297","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:46:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tn7WiVjGRj/t/fE7xZP+g0eexxEpj1eZsFlldfJYPpUbo4a9WgxINOeaAsdiOWCY/QZqtXKMAY6Lz5Oe/OIkAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:47:17.497694Z"},"content_sha256":"c038e94524f71cdd3ad29018edd340198d0d9bc3206200f249a345445b40d744","schema_version":"1.0","event_id":"sha256:c038e94524f71cdd3ad29018edd340198d0d9bc3206200f249a345445b40d744"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:IQSLYLXJJQB2KYABDMNHEHUQW4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Morse index and stability of the planar N-vortex problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"Alessandro Portaluri, Qin Xing, Xijun Hu","submitted_at":"2019-05-13T21:40:54Z","abstract_excerpt":"This paper concerns the investigation of the stability properties of relative equilibria which are rigidly rotating vortex configurations sometimes called vortex crystals, in the N-vortex problem. Such a configurations can be characterized as critical point of the Hamiltonian function restricted on the constant angular impulse hypersurface in the phase space (topologically a pseudo-sphere whose coefficients are the circulation strengths of the vortices). Relative equilibria are generated by the circle action on the so-called shape pseudo-sphere (which generalize the standard shape sphere appea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.05297","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:46:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yxitz9eBMosGBzEJXW77vgrmjaI4PGTkBXOIBdw3Pdjf+jdutAkWe1eJN7CfC33EjzY226Yw2jO5+7iNxHfDBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:47:17.498041Z"},"content_sha256":"30cb39be07f6f658827cd76072531a6b7c98402d38a853a0516576dcc321084e","schema_version":"1.0","event_id":"sha256:30cb39be07f6f658827cd76072531a6b7c98402d38a853a0516576dcc321084e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IQSLYLXJJQB2KYABDMNHEHUQW4/bundle.json","state_url":"https://pith.science/pith/IQSLYLXJJQB2KYABDMNHEHUQW4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IQSLYLXJJQB2KYABDMNHEHUQW4/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":"2026-05-28T06:47:17Z","links":{"resolver":"https://pith.science/pith/IQSLYLXJJQB2KYABDMNHEHUQW4","bundle":"https://pith.science/pith/IQSLYLXJJQB2KYABDMNHEHUQW4/bundle.json","state":"https://pith.science/pith/IQSLYLXJJQB2KYABDMNHEHUQW4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IQSLYLXJJQB2KYABDMNHEHUQW4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:IQSLYLXJJQB2KYABDMNHEHUQW4","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":"ff1091735f261e584375c1491553ee417891bc099c92c60bc0abc7d9b96c543d","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-05-13T21:40:54Z","title_canon_sha256":"9f23993a1fbdf0604139058a155bf86ca4019fdfd313e5b4cb83d763f63acab9"},"schema_version":"1.0","source":{"id":"1905.05297","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.05297","created_at":"2026-05-17T23:46:16Z"},{"alias_kind":"arxiv_version","alias_value":"1905.05297v1","created_at":"2026-05-17T23:46:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.05297","created_at":"2026-05-17T23:46:16Z"},{"alias_kind":"pith_short_12","alias_value":"IQSLYLXJJQB2","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"IQSLYLXJJQB2KYAB","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"IQSLYLXJ","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:30cb39be07f6f658827cd76072531a6b7c98402d38a853a0516576dcc321084e","target":"graph","created_at":"2026-05-17T23:46:16Z","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":"This paper concerns the investigation of the stability properties of relative equilibria which are rigidly rotating vortex configurations sometimes called vortex crystals, in the N-vortex problem. Such a configurations can be characterized as critical point of the Hamiltonian function restricted on the constant angular impulse hypersurface in the phase space (topologically a pseudo-sphere whose coefficients are the circulation strengths of the vortices). Relative equilibria are generated by the circle action on the so-called shape pseudo-sphere (which generalize the standard shape sphere appea","authors_text":"Alessandro Portaluri, Qin Xing, Xijun Hu","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-05-13T21:40:54Z","title":"Morse index and stability of the planar N-vortex problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.05297","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:c038e94524f71cdd3ad29018edd340198d0d9bc3206200f249a345445b40d744","target":"record","created_at":"2026-05-17T23:46:16Z","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":"ff1091735f261e584375c1491553ee417891bc099c92c60bc0abc7d9b96c543d","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-05-13T21:40:54Z","title_canon_sha256":"9f23993a1fbdf0604139058a155bf86ca4019fdfd313e5b4cb83d763f63acab9"},"schema_version":"1.0","source":{"id":"1905.05297","kind":"arxiv","version":1}},"canonical_sha256":"4424bc2ee94c03a560011b1a721e90b71c9aea617adb8d8e9ddefd7019edaf99","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4424bc2ee94c03a560011b1a721e90b71c9aea617adb8d8e9ddefd7019edaf99","first_computed_at":"2026-05-17T23:46:16.927281Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:16.927281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ld76PC5yJJTPCN8h9eWNONjAN50akbi+T4vB+4bKGrQINPPObTta8Eb6wZptJ0fqLWZDix8Hi6LCBeUX59uvDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:16.927875Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.05297","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c038e94524f71cdd3ad29018edd340198d0d9bc3206200f249a345445b40d744","sha256:30cb39be07f6f658827cd76072531a6b7c98402d38a853a0516576dcc321084e"],"state_sha256":"f30b41c0370b3764d32f7cd1aa3d84b4f11ebfdcdd8a4eae3b8dc93d9a4ad060"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4mJo/WiOznY4Nqcqe2PV91A4Y9kg+kMstn8NvPB3y/atyxgsyWisMiHlQmgCQX47eFMnyFsRYpAJa7/0ljtuAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T06:47:17.499988Z","bundle_sha256":"99a07d8199866deb4df95877920e68b312b41fc3db0c2c83685c88fc6321bf80"}}