{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DHBUJOFTFIPCYWBAXM7PK7CATM","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":"6ca2028a7c0c60514b97098ac5ec992185dc2d6b64009a18e4a389947c0a7ddc","cross_cats_sorted":["math.DS","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-04-08T03:09:34Z","title_canon_sha256":"dbbdfa0faf50d66d053d130fe9b1956cbad4ec7e4de4c54f09477d411a053408"},"schema_version":"1.0","source":{"id":"1504.01815","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.01815","created_at":"2026-05-18T02:19:18Z"},{"alias_kind":"arxiv_version","alias_value":"1504.01815v1","created_at":"2026-05-18T02:19:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01815","created_at":"2026-05-18T02:19:18Z"},{"alias_kind":"pith_short_12","alias_value":"DHBUJOFTFIPC","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DHBUJOFTFIPCYWBA","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DHBUJOFT","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:b8f503a5f3b1add7aac92e9bdcbce2f281960f0fe4ebcea32428c2ab2eb1b2e4","target":"graph","created_at":"2026-05-18T02:19:18Z","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 present paper is devoted to studying the Hill-type formula and Krein-type trace formula for ODE, which is a continuous work of our previous work for Hamiltonian systems \\cite{HOW}. Hill-type formula and Krein-type trace formula are given by Hill at 1877 and Krein in 1950's separately. Recently, we find that there is a closed relationship between them \\cite{HOW}. In this paper, we will obtain the Hill-type formula for the $S$-periodic orbits of the first order ODEs. Such a kind of orbits is considered naturally to study the symmetric periodic and quasi-periodic solutions. By some similar id","authors_text":"Penghui Wang, Xijun Hu","cross_cats":["math.DS","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-04-08T03:09:34Z","title":"Hill-type formula and Krein-type trace formula for $S$-periodic solutions in ODEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01815","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":"sha256:87a09ae90c74c3621712db4828af5631baafea0a9c7b1e1d1ed04e786f280440","target":"record","created_at":"2026-05-18T02:19:18Z","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":"6ca2028a7c0c60514b97098ac5ec992185dc2d6b64009a18e4a389947c0a7ddc","cross_cats_sorted":["math.DS","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-04-08T03:09:34Z","title_canon_sha256":"dbbdfa0faf50d66d053d130fe9b1956cbad4ec7e4de4c54f09477d411a053408"},"schema_version":"1.0","source":{"id":"1504.01815","kind":"arxiv","version":1}},"canonical_sha256":"19c344b8b32a1e2c5820bb3ef57c409b27594134e03822adab565610c4cc7cb0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19c344b8b32a1e2c5820bb3ef57c409b27594134e03822adab565610c4cc7cb0","first_computed_at":"2026-05-18T02:19:18.219843Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:18.219843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QKTbPn3QpKWOXVzwrJAZB7/mvfNKeLya6c3Tx+6CKcINxKnw2nAbDfvqcx8MBKw2QaD7RBVcfpoD9VvzHp3OAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:18.220453Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.01815","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87a09ae90c74c3621712db4828af5631baafea0a9c7b1e1d1ed04e786f280440","sha256:b8f503a5f3b1add7aac92e9bdcbce2f281960f0fe4ebcea32428c2ab2eb1b2e4"],"state_sha256":"d6210111028c7d16256e466ad0eaf5091ee4686fbca0c5be9f4e2367e6cc6e69"}