{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:WLELQZ27DYV2UAL6WN2UNABHVC","short_pith_number":"pith:WLELQZ27","schema_version":"1.0","canonical_sha256":"b2c8b8675f1e2baa017eb375468027a88dbb7c363a1063f3ebf805d5d5cbed12","source":{"kind":"arxiv","id":"1209.3397","version":4},"attestation_state":"computed","paper":{"title":"On asymptotic description of passage through a resonance in quasi-linear Hamiltonian systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Anatoly Neishtadt, Tan Su","submitted_at":"2012-09-15T12:13:31Z","abstract_excerpt":"We consider a quasi-linear Hamiltonian system with one and a half degrees of freedom. The Hamiltonian of this system differs by a small, $\\sim\\varepsilon$, perturbing term from the Hamiltonian of a linear oscillatory system. We consider passage through a resonance: the frequency of the latter system slowly changes with time and passes through 0. The speed of this passage is of order of $\\varepsilon$. We provide asymptotic formulas that describe effects of passage through a resonance with an accuracy $O(\\varepsilon^{\\frac32})$. This is an improvement of known results by Chirikov (1959), Kevorki"},"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":"1209.3397","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-15T12:13:31Z","cross_cats_sorted":[],"title_canon_sha256":"fc4ce80b916be96bc6bd503d39d7e6c53c55efb3cceb19b98b30caebfe482b1d","abstract_canon_sha256":"146bdadc78ff6d353373156f3124666b638954665cc66c5fa720b3f0c49a4b0e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:43.600190Z","signature_b64":"Nc0NsfFntYX86UQXWn/pkZ41Y6eOwDlBSaQC9yBRxwJXk68t3TL5PqvgRl0Hh3PCNM0PABTsG++MQqssVvXQCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b2c8b8675f1e2baa017eb375468027a88dbb7c363a1063f3ebf805d5d5cbed12","last_reissued_at":"2026-05-18T03:41:43.599161Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:43.599161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On asymptotic description of passage through a resonance in quasi-linear Hamiltonian systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Anatoly Neishtadt, Tan Su","submitted_at":"2012-09-15T12:13:31Z","abstract_excerpt":"We consider a quasi-linear Hamiltonian system with one and a half degrees of freedom. The Hamiltonian of this system differs by a small, $\\sim\\varepsilon$, perturbing term from the Hamiltonian of a linear oscillatory system. We consider passage through a resonance: the frequency of the latter system slowly changes with time and passes through 0. The speed of this passage is of order of $\\varepsilon$. We provide asymptotic formulas that describe effects of passage through a resonance with an accuracy $O(\\varepsilon^{\\frac32})$. This is an improvement of known results by Chirikov (1959), Kevorki"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3397","kind":"arxiv","version":4},"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":"1209.3397","created_at":"2026-05-18T03:41:43.599343+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.3397v4","created_at":"2026-05-18T03:41:43.599343+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3397","created_at":"2026-05-18T03:41:43.599343+00:00"},{"alias_kind":"pith_short_12","alias_value":"WLELQZ27DYV2","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_16","alias_value":"WLELQZ27DYV2UAL6","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_8","alias_value":"WLELQZ27","created_at":"2026-05-18T12:27:25.539911+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/WLELQZ27DYV2UAL6WN2UNABHVC","json":"https://pith.science/pith/WLELQZ27DYV2UAL6WN2UNABHVC.json","graph_json":"https://pith.science/api/pith-number/WLELQZ27DYV2UAL6WN2UNABHVC/graph.json","events_json":"https://pith.science/api/pith-number/WLELQZ27DYV2UAL6WN2UNABHVC/events.json","paper":"https://pith.science/paper/WLELQZ27"},"agent_actions":{"view_html":"https://pith.science/pith/WLELQZ27DYV2UAL6WN2UNABHVC","download_json":"https://pith.science/pith/WLELQZ27DYV2UAL6WN2UNABHVC.json","view_paper":"https://pith.science/paper/WLELQZ27","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.3397&json=true","fetch_graph":"https://pith.science/api/pith-number/WLELQZ27DYV2UAL6WN2UNABHVC/graph.json","fetch_events":"https://pith.science/api/pith-number/WLELQZ27DYV2UAL6WN2UNABHVC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WLELQZ27DYV2UAL6WN2UNABHVC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WLELQZ27DYV2UAL6WN2UNABHVC/action/storage_attestation","attest_author":"https://pith.science/pith/WLELQZ27DYV2UAL6WN2UNABHVC/action/author_attestation","sign_citation":"https://pith.science/pith/WLELQZ27DYV2UAL6WN2UNABHVC/action/citation_signature","submit_replication":"https://pith.science/pith/WLELQZ27DYV2UAL6WN2UNABHVC/action/replication_record"}},"created_at":"2026-05-18T03:41:43.599343+00:00","updated_at":"2026-05-18T03:41:43.599343+00:00"}