{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:TAW4J6LQJIJON764IHJJU2GJ5B","short_pith_number":"pith:TAW4J6LQ","canonical_record":{"source":{"id":"1508.07520","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-30T01:19:19Z","cross_cats_sorted":[],"title_canon_sha256":"9ba1367dad67ca8ba0d2fd50a8055201e4b0db490ac1ac4a829521e249159707","abstract_canon_sha256":"5f3d03e6b22b6e3e2af5a3ccfda03034a85e56d6433e8b98e4ff80a0f7831fc5"},"schema_version":"1.0"},"canonical_sha256":"982dc4f9704a12e6ffdc41d29a68c9e846789a35b05b537ac038f05e2caebcea","source":{"kind":"arxiv","id":"1508.07520","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.07520","created_at":"2026-05-18T00:40:28Z"},{"alias_kind":"arxiv_version","alias_value":"1508.07520v2","created_at":"2026-05-18T00:40:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07520","created_at":"2026-05-18T00:40:28Z"},{"alias_kind":"pith_short_12","alias_value":"TAW4J6LQJIJO","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TAW4J6LQJIJON764","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TAW4J6LQ","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:TAW4J6LQJIJON764IHJJU2GJ5B","target":"record","payload":{"canonical_record":{"source":{"id":"1508.07520","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-30T01:19:19Z","cross_cats_sorted":[],"title_canon_sha256":"9ba1367dad67ca8ba0d2fd50a8055201e4b0db490ac1ac4a829521e249159707","abstract_canon_sha256":"5f3d03e6b22b6e3e2af5a3ccfda03034a85e56d6433e8b98e4ff80a0f7831fc5"},"schema_version":"1.0"},"canonical_sha256":"982dc4f9704a12e6ffdc41d29a68c9e846789a35b05b537ac038f05e2caebcea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:28.937461Z","signature_b64":"Z5wuV3kg5H/yB785yc8R1Q+oLFgzmkleQKJQW2BXndGc3zKjCvxl2tRRMORgWnyocze5WPLkvBgRGQlE9HDSBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"982dc4f9704a12e6ffdc41d29a68c9e846789a35b05b537ac038f05e2caebcea","last_reissued_at":"2026-05-18T00:40:28.936943Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:28.936943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.07520","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":"2026-05-18T00:40:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z0UhMbC5TzoOcXMwLqx8v4o/tZ6zzC4lKV16Raa+BXsUxOGdJtM2Xy8X5W3FJdZNq0IA8qwHC9jawseZs5W/BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:43:27.482110Z"},"content_sha256":"94901f325f2a166a337c1be61f87f2329375a475c783c56f203ff67b2b16edae","schema_version":"1.0","event_id":"sha256:94901f325f2a166a337c1be61f87f2329375a475c783c56f203ff67b2b16edae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:TAW4J6LQJIJON764IHJJU2GJ5B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence, stability, and symmetry of relative equilibria with a dominant vortex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alanna Hoyer-Leitzel, Anna Barry","submitted_at":"2015-08-30T01:19:19Z","abstract_excerpt":"We analyze existence, stability, and symmetry of point vortex relative equilibria with one dominant vortex and N vortices with infinitesimal circulation. The dimension of the problem can be reduced by taking an infinitesimal circulation limit, resulting in the so-called (1+N)-vortex problem. In this work, we first generalize the reduction to allow for circulations of varying signs and weights. We then prove that symmetric configurations require equality of two circulation parameters in the (1+3)-vortex problem and show that there are stable asymmetric relative equilibria. In a number of exampl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07520","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":"2026-05-18T00:40:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uQGyo3VRcXjUYHn4veMHxhtlN19c1tMwh4Ih7VAoME7OpwX6Ps8xQZXbD0P8+MvqMaGyqXWdSM6buD/Ele4sCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:43:27.482487Z"},"content_sha256":"cef0400af5b65f20f49454ee4d0b35e243f0cf24f64fe14598dbe3b288353af7","schema_version":"1.0","event_id":"sha256:cef0400af5b65f20f49454ee4d0b35e243f0cf24f64fe14598dbe3b288353af7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TAW4J6LQJIJON764IHJJU2GJ5B/bundle.json","state_url":"https://pith.science/pith/TAW4J6LQJIJON764IHJJU2GJ5B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TAW4J6LQJIJON764IHJJU2GJ5B/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":"2026-06-02T22:43:27Z","links":{"resolver":"https://pith.science/pith/TAW4J6LQJIJON764IHJJU2GJ5B","bundle":"https://pith.science/pith/TAW4J6LQJIJON764IHJJU2GJ5B/bundle.json","state":"https://pith.science/pith/TAW4J6LQJIJON764IHJJU2GJ5B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TAW4J6LQJIJON764IHJJU2GJ5B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TAW4J6LQJIJON764IHJJU2GJ5B","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":"5f3d03e6b22b6e3e2af5a3ccfda03034a85e56d6433e8b98e4ff80a0f7831fc5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-30T01:19:19Z","title_canon_sha256":"9ba1367dad67ca8ba0d2fd50a8055201e4b0db490ac1ac4a829521e249159707"},"schema_version":"1.0","source":{"id":"1508.07520","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.07520","created_at":"2026-05-18T00:40:28Z"},{"alias_kind":"arxiv_version","alias_value":"1508.07520v2","created_at":"2026-05-18T00:40:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07520","created_at":"2026-05-18T00:40:28Z"},{"alias_kind":"pith_short_12","alias_value":"TAW4J6LQJIJO","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TAW4J6LQJIJON764","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TAW4J6LQ","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:cef0400af5b65f20f49454ee4d0b35e243f0cf24f64fe14598dbe3b288353af7","target":"graph","created_at":"2026-05-18T00:40:28Z","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":"We analyze existence, stability, and symmetry of point vortex relative equilibria with one dominant vortex and N vortices with infinitesimal circulation. The dimension of the problem can be reduced by taking an infinitesimal circulation limit, resulting in the so-called (1+N)-vortex problem. In this work, we first generalize the reduction to allow for circulations of varying signs and weights. We then prove that symmetric configurations require equality of two circulation parameters in the (1+3)-vortex problem and show that there are stable asymmetric relative equilibria. In a number of exampl","authors_text":"Alanna Hoyer-Leitzel, Anna Barry","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-30T01:19:19Z","title":"Existence, stability, and symmetry of relative equilibria with a dominant vortex"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07520","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":"sha256:94901f325f2a166a337c1be61f87f2329375a475c783c56f203ff67b2b16edae","target":"record","created_at":"2026-05-18T00:40:28Z","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":"5f3d03e6b22b6e3e2af5a3ccfda03034a85e56d6433e8b98e4ff80a0f7831fc5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-30T01:19:19Z","title_canon_sha256":"9ba1367dad67ca8ba0d2fd50a8055201e4b0db490ac1ac4a829521e249159707"},"schema_version":"1.0","source":{"id":"1508.07520","kind":"arxiv","version":2}},"canonical_sha256":"982dc4f9704a12e6ffdc41d29a68c9e846789a35b05b537ac038f05e2caebcea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"982dc4f9704a12e6ffdc41d29a68c9e846789a35b05b537ac038f05e2caebcea","first_computed_at":"2026-05-18T00:40:28.936943Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:28.936943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z5wuV3kg5H/yB785yc8R1Q+oLFgzmkleQKJQW2BXndGc3zKjCvxl2tRRMORgWnyocze5WPLkvBgRGQlE9HDSBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:28.937461Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.07520","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94901f325f2a166a337c1be61f87f2329375a475c783c56f203ff67b2b16edae","sha256:cef0400af5b65f20f49454ee4d0b35e243f0cf24f64fe14598dbe3b288353af7"],"state_sha256":"11c7c3e247806fbf0f83b175ce937a277621832384314d6ae8ff6f9d6aef859e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mO/NXX6L1M3Y3E0gTEkzExm1wz3+cgEB6zzBmZJai77ZOoxWpD4de2qN9B4pPhZ2MVstZikQvF1y0mJkYQYVDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T22:43:27.484618Z","bundle_sha256":"6945398e60e4e0e45113d39052288c2e9188378fa076d1f7c6c563a3ae3aee7c"}}