{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:UNA6K6M2XPYOMHBJB53MBNVT7R","short_pith_number":"pith:UNA6K6M2","schema_version":"1.0","canonical_sha256":"a341e5799abbf0e61c290f76c0b6b3fc65a38b712e5129ae4cef4bafc4e07850","source":{"kind":"arxiv","id":"1412.2615","version":2},"attestation_state":"computed","paper":{"title":"Normal form of holomorphic vector fields with an invariant torus under Brjuno's A condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Claire Chavaudret (JAD)","submitted_at":"2014-12-08T15:42:00Z","abstract_excerpt":"We consider the holomorphic normalization problem for a holomorphic vector field in the neighborhood of the product of a fixed point and an invariant torus. Supposing that the vector field is a perturbation of a linear part around the fixed point and of a rotation on the invariant torus (the unperturbed vector field is called the quasi-linear part of the perturbed one), it was shown by J.Aurouet that the system is holomorphically linearizable if there are no exact resonances in the quasi-linear part and if the quasi-linear part satisfies to Brjuno's arithmetical condition. In the presence of e"},"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":"1412.2615","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-12-08T15:42:00Z","cross_cats_sorted":[],"title_canon_sha256":"dd89aafac0412451fd4f6fc0f4872d6255de66a8fdac3529adf8286240d3d100","abstract_canon_sha256":"44d51ada5e784fc5348e82b283e3a2b39b4fcd9308d615360c925dbb6a30c945"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:02.823921Z","signature_b64":"Q8S5G/E49bQy8mxZanTQ0DOnnrF7mf7XKtmgk2LBzhauOO1lCUv4HbkaDEMu8UoLkx/IFHiXcINemjiDbVFtDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a341e5799abbf0e61c290f76c0b6b3fc65a38b712e5129ae4cef4bafc4e07850","last_reissued_at":"2026-05-18T01:21:02.823224Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:02.823224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Normal form of holomorphic vector fields with an invariant torus under Brjuno's A condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Claire Chavaudret (JAD)","submitted_at":"2014-12-08T15:42:00Z","abstract_excerpt":"We consider the holomorphic normalization problem for a holomorphic vector field in the neighborhood of the product of a fixed point and an invariant torus. Supposing that the vector field is a perturbation of a linear part around the fixed point and of a rotation on the invariant torus (the unperturbed vector field is called the quasi-linear part of the perturbed one), it was shown by J.Aurouet that the system is holomorphically linearizable if there are no exact resonances in the quasi-linear part and if the quasi-linear part satisfies to Brjuno's arithmetical condition. In the presence of e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2615","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":"1412.2615","created_at":"2026-05-18T01:21:02.823340+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.2615v2","created_at":"2026-05-18T01:21:02.823340+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2615","created_at":"2026-05-18T01:21:02.823340+00:00"},{"alias_kind":"pith_short_12","alias_value":"UNA6K6M2XPYO","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_16","alias_value":"UNA6K6M2XPYOMHBJ","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_8","alias_value":"UNA6K6M2","created_at":"2026-05-18T12:28:52.271510+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/UNA6K6M2XPYOMHBJB53MBNVT7R","json":"https://pith.science/pith/UNA6K6M2XPYOMHBJB53MBNVT7R.json","graph_json":"https://pith.science/api/pith-number/UNA6K6M2XPYOMHBJB53MBNVT7R/graph.json","events_json":"https://pith.science/api/pith-number/UNA6K6M2XPYOMHBJB53MBNVT7R/events.json","paper":"https://pith.science/paper/UNA6K6M2"},"agent_actions":{"view_html":"https://pith.science/pith/UNA6K6M2XPYOMHBJB53MBNVT7R","download_json":"https://pith.science/pith/UNA6K6M2XPYOMHBJB53MBNVT7R.json","view_paper":"https://pith.science/paper/UNA6K6M2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.2615&json=true","fetch_graph":"https://pith.science/api/pith-number/UNA6K6M2XPYOMHBJB53MBNVT7R/graph.json","fetch_events":"https://pith.science/api/pith-number/UNA6K6M2XPYOMHBJB53MBNVT7R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UNA6K6M2XPYOMHBJB53MBNVT7R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UNA6K6M2XPYOMHBJB53MBNVT7R/action/storage_attestation","attest_author":"https://pith.science/pith/UNA6K6M2XPYOMHBJB53MBNVT7R/action/author_attestation","sign_citation":"https://pith.science/pith/UNA6K6M2XPYOMHBJB53MBNVT7R/action/citation_signature","submit_replication":"https://pith.science/pith/UNA6K6M2XPYOMHBJB53MBNVT7R/action/replication_record"}},"created_at":"2026-05-18T01:21:02.823340+00:00","updated_at":"2026-05-18T01:21:02.823340+00:00"}