{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:4ERM7Q64XP7PTEN2ARZGUF35I7","short_pith_number":"pith:4ERM7Q64","schema_version":"1.0","canonical_sha256":"e122cfc3dcbbfef991ba04726a177d47c6107f9076f6890d64c26e8c1fef07ba","source":{"kind":"arxiv","id":"1804.07479","version":3},"attestation_state":"computed","paper":{"title":"Hamiltonian boundary value problems, conformal symplectic symmetries, and conjugate loci","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.DG","authors_text":"Christian Offen, Robert I McLachlan","submitted_at":"2018-04-20T07:48:51Z","abstract_excerpt":"In this paper we continue our study of bifurcations of solutions of boundary-value problems for symplectic maps arising as Hamiltonian diffeomorphisms. These have been shown to be connected to catastrophe theory via generating functions and ordinary and reversal phase space symmetries have been considered. Here we present a convenient, coordinate free framework to analyse separated Lagrangian boundary value problems which include classical Dirichlet, Neumann and Robin boundary value problems. The framework is then used to {prove the existence of obstructions arising from} conformal symplectic "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1804.07479","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-04-20T07:48:51Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"f1079adaa813c8325a65a42ee7da92d292b5ef434e86e5fd46a524ca82b18d7a","abstract_canon_sha256":"2c66be4f1dec942db9be94ee989c5a8d9e523324e7a467a1756bd8a3a0f97981"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:52:41.880517Z","signature_b64":"XFxfdEU/GjbKKO2C5n14bwBnLWU5kSJiyIkzuJvcws+AXs+jMgITmDYy5mrE4KlJFQXLbahwNfQ7Sl07NRy0Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e122cfc3dcbbfef991ba04726a177d47c6107f9076f6890d64c26e8c1fef07ba","last_reissued_at":"2026-07-05T06:52:41.880007Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:52:41.880007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hamiltonian boundary value problems, conformal symplectic symmetries, and conjugate loci","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.DG","authors_text":"Christian Offen, Robert I McLachlan","submitted_at":"2018-04-20T07:48:51Z","abstract_excerpt":"In this paper we continue our study of bifurcations of solutions of boundary-value problems for symplectic maps arising as Hamiltonian diffeomorphisms. These have been shown to be connected to catastrophe theory via generating functions and ordinary and reversal phase space symmetries have been considered. Here we present a convenient, coordinate free framework to analyse separated Lagrangian boundary value problems which include classical Dirichlet, Neumann and Robin boundary value problems. The framework is then used to {prove the existence of obstructions arising from} conformal symplectic "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07479","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1804.07479/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1804.07479","created_at":"2026-07-05T06:52:41.880066+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.07479v3","created_at":"2026-07-05T06:52:41.880066+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.07479","created_at":"2026-07-05T06:52:41.880066+00:00"},{"alias_kind":"pith_short_12","alias_value":"4ERM7Q64XP7P","created_at":"2026-07-05T06:52:41.880066+00:00"},{"alias_kind":"pith_short_16","alias_value":"4ERM7Q64XP7PTEN2","created_at":"2026-07-05T06:52:41.880066+00:00"},{"alias_kind":"pith_short_8","alias_value":"4ERM7Q64","created_at":"2026-07-05T06:52:41.880066+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4ERM7Q64XP7PTEN2ARZGUF35I7","json":"https://pith.science/pith/4ERM7Q64XP7PTEN2ARZGUF35I7.json","graph_json":"https://pith.science/api/pith-number/4ERM7Q64XP7PTEN2ARZGUF35I7/graph.json","events_json":"https://pith.science/api/pith-number/4ERM7Q64XP7PTEN2ARZGUF35I7/events.json","paper":"https://pith.science/paper/4ERM7Q64"},"agent_actions":{"view_html":"https://pith.science/pith/4ERM7Q64XP7PTEN2ARZGUF35I7","download_json":"https://pith.science/pith/4ERM7Q64XP7PTEN2ARZGUF35I7.json","view_paper":"https://pith.science/paper/4ERM7Q64","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.07479&json=true","fetch_graph":"https://pith.science/api/pith-number/4ERM7Q64XP7PTEN2ARZGUF35I7/graph.json","fetch_events":"https://pith.science/api/pith-number/4ERM7Q64XP7PTEN2ARZGUF35I7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4ERM7Q64XP7PTEN2ARZGUF35I7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4ERM7Q64XP7PTEN2ARZGUF35I7/action/storage_attestation","attest_author":"https://pith.science/pith/4ERM7Q64XP7PTEN2ARZGUF35I7/action/author_attestation","sign_citation":"https://pith.science/pith/4ERM7Q64XP7PTEN2ARZGUF35I7/action/citation_signature","submit_replication":"https://pith.science/pith/4ERM7Q64XP7PTEN2ARZGUF35I7/action/replication_record"}},"created_at":"2026-07-05T06:52:41.880066+00:00","updated_at":"2026-07-05T06:52:41.880066+00:00"}