{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:IGPMDTZ6TDPCEWQLXMJ6ZMILCY","short_pith_number":"pith:IGPMDTZ6","schema_version":"1.0","canonical_sha256":"419ec1cf3e98de225a0bbb13ecb10b16351334b4af3aac6a492cbfc681e2be06","source":{"kind":"arxiv","id":"1104.2979","version":2},"attestation_state":"computed","paper":{"title":"There is only one KAM curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Carlo Carminati, David Sauzin (SNS PISA, Imcce), Stefano Marmi (SNS PISA)","submitted_at":"2011-04-15T08:22:21Z","abstract_excerpt":"We consider the standard family of area-preserving twist maps of the annulus and the corresponding KAM curves. Addressing a question raised by Kolmogorov, we show that, instead of viewing these invariant curves as separate objects, each of which having its own Diophantine frequency, one can encode them in a single function of the frequency which is naturally defined in a complex domain containing the real Diophantine frequencies and which is monogenic in the sense of Borel; this implies a remarkable property of quasianalyticity, a form of uniqueness of the monogenic continuation, although real"},"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":"1104.2979","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-04-15T08:22:21Z","cross_cats_sorted":[],"title_canon_sha256":"9477cc3b29969003b00fe32224f018bcace7e81ef7021372eb000d012555c651","abstract_canon_sha256":"5f6f52a156781079fbb1efe5a5b189b841a68c62fa4cd6483ba31b7e7b98e50a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:17:04.261804Z","signature_b64":"KHyukAhykUNzrtjCECjc4jyB5mCBpV+Q6UnGvOiKiyZUpig0g/XNFbeRP4krZ0Z2M/DLtwmmmHPIOD1/1hE4Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"419ec1cf3e98de225a0bbb13ecb10b16351334b4af3aac6a492cbfc681e2be06","last_reissued_at":"2026-05-18T04:17:04.261250Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:17:04.261250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"There is only one KAM curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Carlo Carminati, David Sauzin (SNS PISA, Imcce), Stefano Marmi (SNS PISA)","submitted_at":"2011-04-15T08:22:21Z","abstract_excerpt":"We consider the standard family of area-preserving twist maps of the annulus and the corresponding KAM curves. Addressing a question raised by Kolmogorov, we show that, instead of viewing these invariant curves as separate objects, each of which having its own Diophantine frequency, one can encode them in a single function of the frequency which is naturally defined in a complex domain containing the real Diophantine frequencies and which is monogenic in the sense of Borel; this implies a remarkable property of quasianalyticity, a form of uniqueness of the monogenic continuation, although real"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.2979","kind":"arxiv","version":2},"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":"1104.2979","created_at":"2026-05-18T04:17:04.261343+00:00"},{"alias_kind":"arxiv_version","alias_value":"1104.2979v2","created_at":"2026-05-18T04:17:04.261343+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.2979","created_at":"2026-05-18T04:17:04.261343+00:00"},{"alias_kind":"pith_short_12","alias_value":"IGPMDTZ6TDPC","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"IGPMDTZ6TDPCEWQL","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"IGPMDTZ6","created_at":"2026-05-18T12:26:30.835961+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/IGPMDTZ6TDPCEWQLXMJ6ZMILCY","json":"https://pith.science/pith/IGPMDTZ6TDPCEWQLXMJ6ZMILCY.json","graph_json":"https://pith.science/api/pith-number/IGPMDTZ6TDPCEWQLXMJ6ZMILCY/graph.json","events_json":"https://pith.science/api/pith-number/IGPMDTZ6TDPCEWQLXMJ6ZMILCY/events.json","paper":"https://pith.science/paper/IGPMDTZ6"},"agent_actions":{"view_html":"https://pith.science/pith/IGPMDTZ6TDPCEWQLXMJ6ZMILCY","download_json":"https://pith.science/pith/IGPMDTZ6TDPCEWQLXMJ6ZMILCY.json","view_paper":"https://pith.science/paper/IGPMDTZ6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1104.2979&json=true","fetch_graph":"https://pith.science/api/pith-number/IGPMDTZ6TDPCEWQLXMJ6ZMILCY/graph.json","fetch_events":"https://pith.science/api/pith-number/IGPMDTZ6TDPCEWQLXMJ6ZMILCY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IGPMDTZ6TDPCEWQLXMJ6ZMILCY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IGPMDTZ6TDPCEWQLXMJ6ZMILCY/action/storage_attestation","attest_author":"https://pith.science/pith/IGPMDTZ6TDPCEWQLXMJ6ZMILCY/action/author_attestation","sign_citation":"https://pith.science/pith/IGPMDTZ6TDPCEWQLXMJ6ZMILCY/action/citation_signature","submit_replication":"https://pith.science/pith/IGPMDTZ6TDPCEWQLXMJ6ZMILCY/action/replication_record"}},"created_at":"2026-05-18T04:17:04.261343+00:00","updated_at":"2026-05-18T04:17:04.261343+00:00"}