{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:JZCHRIOGLKHS26OUM22VHDPM2G","short_pith_number":"pith:JZCHRIOG","schema_version":"1.0","canonical_sha256":"4e4478a1c65a8f2d79d466b5538decd19f87960456c53f3ba9ef3ae4a808a2c0","source":{"kind":"arxiv","id":"1811.01649","version":2},"attestation_state":"computed","paper":{"title":"The equivalence theory for infinite type hypersurfaces in $\\mathbb C^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CV","authors_text":"Bernhard Lamel, Ilya Kossovskiy, Peter Ebenfelt","submitted_at":"2018-11-05T12:54:00Z","abstract_excerpt":"We develop a classification theory for real-analytic hypersurfaces in $\\mathbb C^2$ in the case when the hypersurface is of {\\em infinite type} at the reference point. This is the remaining, not yet understood case in $\\mathbb C^2$ in the {\\it Probl\\`eme local}, formulated by H.\\,Poincar\\'e in 1907 and asking for a complete biholomorphic classification of real hypersurfaces in complex space. One novel aspect of our results, appearing in this revised version, is a notion of {\\em smooth normal forms} for real-analytic hypersurfaces. We rely fundamentally on the recently developed CR -- DS techni"},"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":"1811.01649","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-11-05T12:54:00Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"7beada21933f6e2d2f4d49bcd7fe15bd6b6eca6ae0a55c6b3414238fff852bd2","abstract_canon_sha256":"97674dbe4a745924cf71916887a90c6bf44fff47a04836e72270ab15798b7430"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:08.554913Z","signature_b64":"B82s84bgAu4+dLNjIyJkP5/eYG6iOMrhFRi0nUmg37NmgrO98/bBCRoZLwxz7uaVJug1k1HBzPfTHCKi0vpHAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e4478a1c65a8f2d79d466b5538decd19f87960456c53f3ba9ef3ae4a808a2c0","last_reissued_at":"2026-05-17T23:42:08.554448Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:08.554448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The equivalence theory for infinite type hypersurfaces in $\\mathbb C^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CV","authors_text":"Bernhard Lamel, Ilya Kossovskiy, Peter Ebenfelt","submitted_at":"2018-11-05T12:54:00Z","abstract_excerpt":"We develop a classification theory for real-analytic hypersurfaces in $\\mathbb C^2$ in the case when the hypersurface is of {\\em infinite type} at the reference point. This is the remaining, not yet understood case in $\\mathbb C^2$ in the {\\it Probl\\`eme local}, formulated by H.\\,Poincar\\'e in 1907 and asking for a complete biholomorphic classification of real hypersurfaces in complex space. One novel aspect of our results, appearing in this revised version, is a notion of {\\em smooth normal forms} for real-analytic hypersurfaces. We rely fundamentally on the recently developed CR -- DS techni"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01649","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":"1811.01649","created_at":"2026-05-17T23:42:08.554518+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.01649v2","created_at":"2026-05-17T23:42:08.554518+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.01649","created_at":"2026-05-17T23:42:08.554518+00:00"},{"alias_kind":"pith_short_12","alias_value":"JZCHRIOGLKHS","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_16","alias_value":"JZCHRIOGLKHS26OU","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_8","alias_value":"JZCHRIOG","created_at":"2026-05-18T12:32:33.847187+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/JZCHRIOGLKHS26OUM22VHDPM2G","json":"https://pith.science/pith/JZCHRIOGLKHS26OUM22VHDPM2G.json","graph_json":"https://pith.science/api/pith-number/JZCHRIOGLKHS26OUM22VHDPM2G/graph.json","events_json":"https://pith.science/api/pith-number/JZCHRIOGLKHS26OUM22VHDPM2G/events.json","paper":"https://pith.science/paper/JZCHRIOG"},"agent_actions":{"view_html":"https://pith.science/pith/JZCHRIOGLKHS26OUM22VHDPM2G","download_json":"https://pith.science/pith/JZCHRIOGLKHS26OUM22VHDPM2G.json","view_paper":"https://pith.science/paper/JZCHRIOG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.01649&json=true","fetch_graph":"https://pith.science/api/pith-number/JZCHRIOGLKHS26OUM22VHDPM2G/graph.json","fetch_events":"https://pith.science/api/pith-number/JZCHRIOGLKHS26OUM22VHDPM2G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JZCHRIOGLKHS26OUM22VHDPM2G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JZCHRIOGLKHS26OUM22VHDPM2G/action/storage_attestation","attest_author":"https://pith.science/pith/JZCHRIOGLKHS26OUM22VHDPM2G/action/author_attestation","sign_citation":"https://pith.science/pith/JZCHRIOGLKHS26OUM22VHDPM2G/action/citation_signature","submit_replication":"https://pith.science/pith/JZCHRIOGLKHS26OUM22VHDPM2G/action/replication_record"}},"created_at":"2026-05-17T23:42:08.554518+00:00","updated_at":"2026-05-17T23:42:08.554518+00:00"}