{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:Z6HZVVCIUCGKPOXYESGUBFV2Q3","short_pith_number":"pith:Z6HZVVCI","schema_version":"1.0","canonical_sha256":"cf8f9ad448a08ca7baf8248d4096ba86d58b2e40fc43e22557b1f769f185fa53","source":{"kind":"arxiv","id":"1405.0866","version":3},"attestation_state":"computed","paper":{"title":"A General Mechanism of Diffusion in Hamiltonian Systems: Qualitative Results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.CD"],"primary_cat":"math.DS","authors_text":"Marian Gidea, Rafael de la Llave, Tere Seara","submitted_at":"2014-05-05T11:58:13Z","abstract_excerpt":"We present a general mechanism to establish the existence of diffusing orbits in a large class of nearly integrable Hamiltonian systems. Our approach relies on successive applications of the `outer dynamics' along homoclinic orbits to a normally hyperbolic invariant manifold. The information on the outer dynamics is encoded by a geometrically defined map, referred to as the `scattering map'.\n  We find pseudo-orbits of the scattering map that keep advancing in some privileged direction. Then we use the recurrence property of the `inner dynamics', restricted to the normally hyperbolic invariant "},"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":"1405.0866","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-05-05T11:58:13Z","cross_cats_sorted":["math-ph","math.MP","nlin.CD"],"title_canon_sha256":"da1a592de8319b648778f7b26d0e08724e5810af39a3d3429bd3acddb339a76c","abstract_canon_sha256":"5bae315241b82589cc6c32d8e77ceb4d4321477567d0c04bb2c87ffaa3daa7a5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:50.505618Z","signature_b64":"yN+EA2h0M8XsxB7BLL0skk760EUCgUOnqdNjWoocMf2sS7tW/+w1gSex/kekTjEXW/d/QEA/3rMgc2hgD7H6BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf8f9ad448a08ca7baf8248d4096ba86d58b2e40fc43e22557b1f769f185fa53","last_reissued_at":"2026-05-18T00:45:50.505013Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:50.505013Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A General Mechanism of Diffusion in Hamiltonian Systems: Qualitative Results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.CD"],"primary_cat":"math.DS","authors_text":"Marian Gidea, Rafael de la Llave, Tere Seara","submitted_at":"2014-05-05T11:58:13Z","abstract_excerpt":"We present a general mechanism to establish the existence of diffusing orbits in a large class of nearly integrable Hamiltonian systems. Our approach relies on successive applications of the `outer dynamics' along homoclinic orbits to a normally hyperbolic invariant manifold. The information on the outer dynamics is encoded by a geometrically defined map, referred to as the `scattering map'.\n  We find pseudo-orbits of the scattering map that keep advancing in some privileged direction. Then we use the recurrence property of the `inner dynamics', restricted to the normally hyperbolic invariant "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0866","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":""},"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":"1405.0866","created_at":"2026-05-18T00:45:50.505093+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.0866v3","created_at":"2026-05-18T00:45:50.505093+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0866","created_at":"2026-05-18T00:45:50.505093+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z6HZVVCIUCGK","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z6HZVVCIUCGKPOXY","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z6HZVVCI","created_at":"2026-05-18T12:28:59.999130+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/Z6HZVVCIUCGKPOXYESGUBFV2Q3","json":"https://pith.science/pith/Z6HZVVCIUCGKPOXYESGUBFV2Q3.json","graph_json":"https://pith.science/api/pith-number/Z6HZVVCIUCGKPOXYESGUBFV2Q3/graph.json","events_json":"https://pith.science/api/pith-number/Z6HZVVCIUCGKPOXYESGUBFV2Q3/events.json","paper":"https://pith.science/paper/Z6HZVVCI"},"agent_actions":{"view_html":"https://pith.science/pith/Z6HZVVCIUCGKPOXYESGUBFV2Q3","download_json":"https://pith.science/pith/Z6HZVVCIUCGKPOXYESGUBFV2Q3.json","view_paper":"https://pith.science/paper/Z6HZVVCI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.0866&json=true","fetch_graph":"https://pith.science/api/pith-number/Z6HZVVCIUCGKPOXYESGUBFV2Q3/graph.json","fetch_events":"https://pith.science/api/pith-number/Z6HZVVCIUCGKPOXYESGUBFV2Q3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z6HZVVCIUCGKPOXYESGUBFV2Q3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z6HZVVCIUCGKPOXYESGUBFV2Q3/action/storage_attestation","attest_author":"https://pith.science/pith/Z6HZVVCIUCGKPOXYESGUBFV2Q3/action/author_attestation","sign_citation":"https://pith.science/pith/Z6HZVVCIUCGKPOXYESGUBFV2Q3/action/citation_signature","submit_replication":"https://pith.science/pith/Z6HZVVCIUCGKPOXYESGUBFV2Q3/action/replication_record"}},"created_at":"2026-05-18T00:45:50.505093+00:00","updated_at":"2026-05-18T00:45:50.505093+00:00"}