{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:W2UC46AG7IP5PW5KX6MC5ZVFTS","short_pith_number":"pith:W2UC46AG","schema_version":"1.0","canonical_sha256":"b6a82e7806fa1fd7dbaabf982ee6a59cb57a3d757ea0cd60dbcb95501f707d4a","source":{"kind":"arxiv","id":"1803.07845","version":1},"attestation_state":"computed","paper":{"title":"Stationary phase methods and the splitting of separatrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alberto Enciso, Alejandro Luque, Daniel Peralta-Salas","submitted_at":"2018-03-21T10:46:48Z","abstract_excerpt":"Using stationary phase methods, we provide an explicit formula for the Melnikov function of the one and a half degrees of freedom system given by a Hamiltonian system subject to a rapidly oscillating perturbation. Remarkably, the Melnikov function turns out to be computable without an explicit knowledge of the separatrix and in the case of non-analytic systems. This is related to a priori stable systems coupled with low regularity perturbations. It also applies to perturbations controlled by wave-type equations, so in particular we also illustrate this result with the motion of charged particl"},"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":"1803.07845","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-03-21T10:46:48Z","cross_cats_sorted":[],"title_canon_sha256":"e8a00cc1384a13fb2784b13a48dc78c18e7348f3b3346dc5c3be1d7b36206f4b","abstract_canon_sha256":"ed44756d3653829b9c87208cb4f1707ce840e3c8bc5732873675d7709d6c4ac1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:13.933298Z","signature_b64":"CDUOGC3OnvZszah2PvEfFmWyjtguiT7015vGR1jRUrmM65yvrVYaHgA9SGH+x+j0KMIVYkHaANxc/Ss9ALGrDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6a82e7806fa1fd7dbaabf982ee6a59cb57a3d757ea0cd60dbcb95501f707d4a","last_reissued_at":"2026-05-17T23:50:13.932497Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:13.932497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stationary phase methods and the splitting of separatrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alberto Enciso, Alejandro Luque, Daniel Peralta-Salas","submitted_at":"2018-03-21T10:46:48Z","abstract_excerpt":"Using stationary phase methods, we provide an explicit formula for the Melnikov function of the one and a half degrees of freedom system given by a Hamiltonian system subject to a rapidly oscillating perturbation. Remarkably, the Melnikov function turns out to be computable without an explicit knowledge of the separatrix and in the case of non-analytic systems. This is related to a priori stable systems coupled with low regularity perturbations. It also applies to perturbations controlled by wave-type equations, so in particular we also illustrate this result with the motion of charged particl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07845","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1803.07845","created_at":"2026-05-17T23:50:13.932620+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.07845v1","created_at":"2026-05-17T23:50:13.932620+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.07845","created_at":"2026-05-17T23:50:13.932620+00:00"},{"alias_kind":"pith_short_12","alias_value":"W2UC46AG7IP5","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_16","alias_value":"W2UC46AG7IP5PW5K","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_8","alias_value":"W2UC46AG","created_at":"2026-05-18T12:32:59.047623+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/W2UC46AG7IP5PW5KX6MC5ZVFTS","json":"https://pith.science/pith/W2UC46AG7IP5PW5KX6MC5ZVFTS.json","graph_json":"https://pith.science/api/pith-number/W2UC46AG7IP5PW5KX6MC5ZVFTS/graph.json","events_json":"https://pith.science/api/pith-number/W2UC46AG7IP5PW5KX6MC5ZVFTS/events.json","paper":"https://pith.science/paper/W2UC46AG"},"agent_actions":{"view_html":"https://pith.science/pith/W2UC46AG7IP5PW5KX6MC5ZVFTS","download_json":"https://pith.science/pith/W2UC46AG7IP5PW5KX6MC5ZVFTS.json","view_paper":"https://pith.science/paper/W2UC46AG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.07845&json=true","fetch_graph":"https://pith.science/api/pith-number/W2UC46AG7IP5PW5KX6MC5ZVFTS/graph.json","fetch_events":"https://pith.science/api/pith-number/W2UC46AG7IP5PW5KX6MC5ZVFTS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W2UC46AG7IP5PW5KX6MC5ZVFTS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W2UC46AG7IP5PW5KX6MC5ZVFTS/action/storage_attestation","attest_author":"https://pith.science/pith/W2UC46AG7IP5PW5KX6MC5ZVFTS/action/author_attestation","sign_citation":"https://pith.science/pith/W2UC46AG7IP5PW5KX6MC5ZVFTS/action/citation_signature","submit_replication":"https://pith.science/pith/W2UC46AG7IP5PW5KX6MC5ZVFTS/action/replication_record"}},"created_at":"2026-05-17T23:50:13.932620+00:00","updated_at":"2026-05-17T23:50:13.932620+00:00"}