{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:CQSYV6J2YB7SX5B3SEJYAFWQSR","short_pith_number":"pith:CQSYV6J2","schema_version":"1.0","canonical_sha256":"14258af93ac07f2bf43b91138016d0947a34e9dab8580affdaf180f25ab4db17","source":{"kind":"arxiv","id":"0706.0138","version":2},"attestation_state":"computed","paper":{"title":"A quasianalyticity property for monogenic solutions of small divisor problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"David Sauzin (IMCCE), Stefano Marmi (SNS PISA)","submitted_at":"2007-06-01T12:08:01Z","abstract_excerpt":"We discuss the quasianalytic properties of various spaces of functions suitable for one-dimensional small divisor problems. These spaces are formed of functions C^1-holomorphic on certain compact sets K_j of the Riemann sphere (in the Whitney sense), as is the solution of a linear or non-linear small divisor problem when viewed as a function of the multiplier (the intersection of K_j with the unit circle is defined by a Diophantine-type condition, so as to avoid the divergence caused by roots of unity). It turns out that a kind of generalized analytic continuation through the unit circle is po"},"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":"0706.0138","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2007-06-01T12:08:01Z","cross_cats_sorted":[],"title_canon_sha256":"93487985af6e051fd99082d1d0cae58d6a2e6cb3523028cfc35ac5579734c3ec","abstract_canon_sha256":"d780df926f946d858369748219cdb79082cfc5f14262b5996ab9e084daf970c5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:15.457973Z","signature_b64":"cJ17MJKqBowBjRjM2qKrlbZpgyP/jLVMr1w9mAoNV5HyxkMqvgu8tw9dG/VAr8//4F5cLHE8PfNPjiC/BUgeBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14258af93ac07f2bf43b91138016d0947a34e9dab8580affdaf180f25ab4db17","last_reissued_at":"2026-05-18T04:27:15.457481Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:15.457481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A quasianalyticity property for monogenic solutions of small divisor problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"David Sauzin (IMCCE), Stefano Marmi (SNS PISA)","submitted_at":"2007-06-01T12:08:01Z","abstract_excerpt":"We discuss the quasianalytic properties of various spaces of functions suitable for one-dimensional small divisor problems. These spaces are formed of functions C^1-holomorphic on certain compact sets K_j of the Riemann sphere (in the Whitney sense), as is the solution of a linear or non-linear small divisor problem when viewed as a function of the multiplier (the intersection of K_j with the unit circle is defined by a Diophantine-type condition, so as to avoid the divergence caused by roots of unity). It turns out that a kind of generalized analytic continuation through the unit circle is po"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.0138","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":"0706.0138","created_at":"2026-05-18T04:27:15.457556+00:00"},{"alias_kind":"arxiv_version","alias_value":"0706.0138v2","created_at":"2026-05-18T04:27:15.457556+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.0138","created_at":"2026-05-18T04:27:15.457556+00:00"},{"alias_kind":"pith_short_12","alias_value":"CQSYV6J2YB7S","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"CQSYV6J2YB7SX5B3","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"CQSYV6J2","created_at":"2026-05-18T12:25:55.427421+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/CQSYV6J2YB7SX5B3SEJYAFWQSR","json":"https://pith.science/pith/CQSYV6J2YB7SX5B3SEJYAFWQSR.json","graph_json":"https://pith.science/api/pith-number/CQSYV6J2YB7SX5B3SEJYAFWQSR/graph.json","events_json":"https://pith.science/api/pith-number/CQSYV6J2YB7SX5B3SEJYAFWQSR/events.json","paper":"https://pith.science/paper/CQSYV6J2"},"agent_actions":{"view_html":"https://pith.science/pith/CQSYV6J2YB7SX5B3SEJYAFWQSR","download_json":"https://pith.science/pith/CQSYV6J2YB7SX5B3SEJYAFWQSR.json","view_paper":"https://pith.science/paper/CQSYV6J2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0706.0138&json=true","fetch_graph":"https://pith.science/api/pith-number/CQSYV6J2YB7SX5B3SEJYAFWQSR/graph.json","fetch_events":"https://pith.science/api/pith-number/CQSYV6J2YB7SX5B3SEJYAFWQSR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CQSYV6J2YB7SX5B3SEJYAFWQSR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CQSYV6J2YB7SX5B3SEJYAFWQSR/action/storage_attestation","attest_author":"https://pith.science/pith/CQSYV6J2YB7SX5B3SEJYAFWQSR/action/author_attestation","sign_citation":"https://pith.science/pith/CQSYV6J2YB7SX5B3SEJYAFWQSR/action/citation_signature","submit_replication":"https://pith.science/pith/CQSYV6J2YB7SX5B3SEJYAFWQSR/action/replication_record"}},"created_at":"2026-05-18T04:27:15.457556+00:00","updated_at":"2026-05-18T04:27:15.457556+00:00"}