{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:VOR4OAZSZJH62BZOGCLOGSNFYJ","short_pith_number":"pith:VOR4OAZS","schema_version":"1.0","canonical_sha256":"aba3c70332ca4fed072e3096e349a5c26bd28cc6ce4710428009f77ded027630","source":{"kind":"arxiv","id":"1801.03343","version":1},"attestation_state":"computed","paper":{"title":"Some remarks on the optimality of the Bruno-R{\\\"u}ssmann condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Abed Bounemoura (CEREMADE)","submitted_at":"2018-01-10T12:27:11Z","abstract_excerpt":"We prove that the Bruno-R{\\\"u}ssmann condition is optimal for the analytic preservation of a quasi-periodic invariant curve for an analytic twist map. The proof is based on Yoccoz's corresponding result for analytic circle diffeomorphisms and the uniqueness of invariant curves with a given irrational rotation number. We also prove a similar result for analytic Tonelli Hamiltonian flow with n = 2 degrees of freedom; for n $\\ge$ 3 we only obtain a weaker result which recovers and slightly improves a theorem of Bessi."},"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":"1801.03343","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-01-10T12:27:11Z","cross_cats_sorted":[],"title_canon_sha256":"6d2ef07d203ab192c96d1680bc2363d119cf1c71b1324a96618365143222f4c5","abstract_canon_sha256":"5b1734ef060f0a73da70ae78545721883c4e5d01d8f2256cb0359244472d5a48"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:17.339961Z","signature_b64":"+HlzQtkyNC0ppS+3S1j43uQ6+D2vEU/XpZLjZvVME3AY0blpRSFTHh7PjDwkW0xv2H4rkVN9aZqw93YTZmKNAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aba3c70332ca4fed072e3096e349a5c26bd28cc6ce4710428009f77ded027630","last_reissued_at":"2026-05-18T00:26:17.339454Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:17.339454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some remarks on the optimality of the Bruno-R{\\\"u}ssmann condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Abed Bounemoura (CEREMADE)","submitted_at":"2018-01-10T12:27:11Z","abstract_excerpt":"We prove that the Bruno-R{\\\"u}ssmann condition is optimal for the analytic preservation of a quasi-periodic invariant curve for an analytic twist map. The proof is based on Yoccoz's corresponding result for analytic circle diffeomorphisms and the uniqueness of invariant curves with a given irrational rotation number. We also prove a similar result for analytic Tonelli Hamiltonian flow with n = 2 degrees of freedom; for n $\\ge$ 3 we only obtain a weaker result which recovers and slightly improves a theorem of Bessi."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.03343","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":"1801.03343","created_at":"2026-05-18T00:26:17.339535+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.03343v1","created_at":"2026-05-18T00:26:17.339535+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.03343","created_at":"2026-05-18T00:26:17.339535+00:00"},{"alias_kind":"pith_short_12","alias_value":"VOR4OAZSZJH6","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_16","alias_value":"VOR4OAZSZJH62BZO","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_8","alias_value":"VOR4OAZS","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/VOR4OAZSZJH62BZOGCLOGSNFYJ","json":"https://pith.science/pith/VOR4OAZSZJH62BZOGCLOGSNFYJ.json","graph_json":"https://pith.science/api/pith-number/VOR4OAZSZJH62BZOGCLOGSNFYJ/graph.json","events_json":"https://pith.science/api/pith-number/VOR4OAZSZJH62BZOGCLOGSNFYJ/events.json","paper":"https://pith.science/paper/VOR4OAZS"},"agent_actions":{"view_html":"https://pith.science/pith/VOR4OAZSZJH62BZOGCLOGSNFYJ","download_json":"https://pith.science/pith/VOR4OAZSZJH62BZOGCLOGSNFYJ.json","view_paper":"https://pith.science/paper/VOR4OAZS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.03343&json=true","fetch_graph":"https://pith.science/api/pith-number/VOR4OAZSZJH62BZOGCLOGSNFYJ/graph.json","fetch_events":"https://pith.science/api/pith-number/VOR4OAZSZJH62BZOGCLOGSNFYJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VOR4OAZSZJH62BZOGCLOGSNFYJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VOR4OAZSZJH62BZOGCLOGSNFYJ/action/storage_attestation","attest_author":"https://pith.science/pith/VOR4OAZSZJH62BZOGCLOGSNFYJ/action/author_attestation","sign_citation":"https://pith.science/pith/VOR4OAZSZJH62BZOGCLOGSNFYJ/action/citation_signature","submit_replication":"https://pith.science/pith/VOR4OAZSZJH62BZOGCLOGSNFYJ/action/replication_record"}},"created_at":"2026-05-18T00:26:17.339535+00:00","updated_at":"2026-05-18T00:26:17.339535+00:00"}