{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4PVBGG4GWGWPTEBTMJDA77XIJM","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":"3024832844d5705ab0995e217e95c4edb4e168562181adaf5706d11044544434","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-07-10T13:08:20Z","title_canon_sha256":"7174f1747f297a8d734d4a35e5d57a050691ee11c6b3f770b44c760b91c0ec36"},"schema_version":"1.0","source":{"id":"1507.02883","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02883","created_at":"2026-05-18T01:32:52Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02883v2","created_at":"2026-05-18T01:32:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02883","created_at":"2026-05-18T01:32:52Z"},{"alias_kind":"pith_short_12","alias_value":"4PVBGG4GWGWP","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4PVBGG4GWGWPTEBT","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4PVBGG4G","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:c654004561e15d6c7a2f44f95fac47ed4dc6ee3195a2fb84cfccc0d64fb24039","target":"graph","created_at":"2026-05-18T01:32:52Z","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":"In the planar $N$-center problem, for a non-trivial free homotopy class of the configuration space satisfying certain mild condition, we show that there is at least one collision free $T$-periodic solution for any positive $T.$ We use the direct method of calculus of variations and the main difficulty is to show that minimizers under certain topological constraints are free of collision.","authors_text":"Guowei Yu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-07-10T13:08:20Z","title":"Periodic Solutions of the Planar N-Center Problem with topological constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02883","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":"sha256:0927bf4c01f075a601be368287f9a0b705c23a8a72cbb721bf1ab9cd4a82c007","target":"record","created_at":"2026-05-18T01:32:52Z","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":"3024832844d5705ab0995e217e95c4edb4e168562181adaf5706d11044544434","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-07-10T13:08:20Z","title_canon_sha256":"7174f1747f297a8d734d4a35e5d57a050691ee11c6b3f770b44c760b91c0ec36"},"schema_version":"1.0","source":{"id":"1507.02883","kind":"arxiv","version":2}},"canonical_sha256":"e3ea131b86b1acf9903362460ffee84b1ec25e4924f7b1ad81dde52cdf495063","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3ea131b86b1acf9903362460ffee84b1ec25e4924f7b1ad81dde52cdf495063","first_computed_at":"2026-05-18T01:32:52.101744Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:52.101744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3B+Qc0bY6xr/rCdrOY0CwcSba8dxf4qliORyyvqKZe3NDq+475iWvcHb5lLlzCulagktFRNS+GNXiqBJ6KJaBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:52.102205Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.02883","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0927bf4c01f075a601be368287f9a0b705c23a8a72cbb721bf1ab9cd4a82c007","sha256:c654004561e15d6c7a2f44f95fac47ed4dc6ee3195a2fb84cfccc0d64fb24039"],"state_sha256":"8fcdfe25e68648612e03198ba1b943e3439e12a7b24898b042121d74569901b8"}