{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:D6GPFKP337W3T23XCPDIIQUPS4","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":"98e3c3e82609822e285ed0930ae35ee8bb60ce39f0c7511dac46f00efc6ce448","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-12-08T09:20:26Z","title_canon_sha256":"c6b8acabb014a7513c6c7ae56eaa4069dc072b577ed0524d3eeb7f59efbd89ec"},"schema_version":"1.0","source":{"id":"1112.1789","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1789","created_at":"2026-05-18T04:06:45Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1789v1","created_at":"2026-05-18T04:06:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1789","created_at":"2026-05-18T04:06:45Z"},{"alias_kind":"pith_short_12","alias_value":"D6GPFKP337W3","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"D6GPFKP337W3T23X","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"D6GPFKP3","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:3265efe2ac5a56cbd59930a2f51be967ddb17028148d5aabe008bbc426dff4a2","target":"graph","created_at":"2026-05-18T04:06:45Z","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":"The goal of this paper is to give a detailed analytical description of the global dynamics of N points interacting through the singular logarithmic potential and subject to the following symmetry constraint: at each instant they form an orbit of the dihedral group of order 2l. The main device in order to achieve our results is a technique very popular in Celestial Mechanics, usually referred to as \"McGehee transformation\". After performing this change of coordinates that regularizes the total collision, we study the rest-points of the flow, the invariant manifolds and we derive interesting inf","authors_text":"Alessandro Portaluri, Francesco Paparella","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-12-08T09:20:26Z","title":"Global dynamics of stationary, dihedral, nearly-parallel vortex filaments"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1789","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:acbce1b4f932e8d61d656c8b5061a613561e3051e1483e42c0f52811b18138a2","target":"record","created_at":"2026-05-18T04:06:45Z","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":"98e3c3e82609822e285ed0930ae35ee8bb60ce39f0c7511dac46f00efc6ce448","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-12-08T09:20:26Z","title_canon_sha256":"c6b8acabb014a7513c6c7ae56eaa4069dc072b577ed0524d3eeb7f59efbd89ec"},"schema_version":"1.0","source":{"id":"1112.1789","kind":"arxiv","version":1}},"canonical_sha256":"1f8cf2a9fbdfedb9eb7713c684428f9724ee4c70aaa6c89000b4100e4a6273db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f8cf2a9fbdfedb9eb7713c684428f9724ee4c70aaa6c89000b4100e4a6273db","first_computed_at":"2026-05-18T04:06:45.659129Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:45.659129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N5LEDHArziJf6X2PbUP0n6m/RvV83qjgwsHQFtCc5XlJCX94Fm+nTXRtFlx4a9ItkvjQ97mTAvUyy2TceS1NDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:45.659629Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.1789","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:acbce1b4f932e8d61d656c8b5061a613561e3051e1483e42c0f52811b18138a2","sha256:3265efe2ac5a56cbd59930a2f51be967ddb17028148d5aabe008bbc426dff4a2"],"state_sha256":"26b56eef680166b8beec5e27adc9390acd37da0efd0f5dcf8f78b2f4c88e01af"}