{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:O4D7KR3MYDDG4SMAMORUUZDL5L","short_pith_number":"pith:O4D7KR3M","schema_version":"1.0","canonical_sha256":"7707f5476cc0c66e498063a34a646bead6f3c7664a56fd415c81a942ec07e1b5","source":{"kind":"arxiv","id":"math/0509173","version":1},"attestation_state":"computed","paper":{"title":"Elliptic CR-manifolds and shear invariant ODE with additional symmetries","license":"","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CV","authors_text":"Gerd Schmalz, Vladimir Ezhov","submitted_at":"2005-09-07T23:22:06Z","abstract_excerpt":"We classify the ODEs that correspond to elliptic CR-manifolds with maximal isotropy. It follows that the dimension of the isotropy group of an elliptic CR-manifold can be only 10 (for the quadric), 4 (for the listed examples) or less. This is in contrast with the situation of hyperbolic CR-manifolds, where the dimension can be 10 (for the quadric), 6 or 5 (for semi-quadrics) or less than 4. We also prove that, for all elliptic CR-manifolds with non-linearizable istropy group, except for two special manifolds, the points with non-linearizable isotropy form exactly some complex curve on the mani"},"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":"math/0509173","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CV","submitted_at":"2005-09-07T23:22:06Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"3d264c9b50240d9dc4c7ba6afe66e1778a78979c402a976cc0e5ba19f4fbc97d","abstract_canon_sha256":"ec40e85366637b59aa5a62968f6ed24c6250efaa32996df46c30d4e508094150"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:08.722365Z","signature_b64":"Efljr6iq60wUIMOLu6XmiEIuu3GTTZIKSX7jud3VNLqArUgQiGAD4I6kAYyE/0WSFNe71GsNW77jn6wPIC26Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7707f5476cc0c66e498063a34a646bead6f3c7664a56fd415c81a942ec07e1b5","last_reissued_at":"2026-05-18T02:27:08.721466Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:08.721466Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Elliptic CR-manifolds and shear invariant ODE with additional symmetries","license":"","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CV","authors_text":"Gerd Schmalz, Vladimir Ezhov","submitted_at":"2005-09-07T23:22:06Z","abstract_excerpt":"We classify the ODEs that correspond to elliptic CR-manifolds with maximal isotropy. It follows that the dimension of the isotropy group of an elliptic CR-manifold can be only 10 (for the quadric), 4 (for the listed examples) or less. This is in contrast with the situation of hyperbolic CR-manifolds, where the dimension can be 10 (for the quadric), 6 or 5 (for semi-quadrics) or less than 4. We also prove that, for all elliptic CR-manifolds with non-linearizable istropy group, except for two special manifolds, the points with non-linearizable isotropy form exactly some complex curve on the mani"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0509173","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":"math/0509173","created_at":"2026-05-18T02:27:08.721588+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0509173v1","created_at":"2026-05-18T02:27:08.721588+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0509173","created_at":"2026-05-18T02:27:08.721588+00:00"},{"alias_kind":"pith_short_12","alias_value":"O4D7KR3MYDDG","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_16","alias_value":"O4D7KR3MYDDG4SMA","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_8","alias_value":"O4D7KR3M","created_at":"2026-05-18T12:25:53.335082+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/O4D7KR3MYDDG4SMAMORUUZDL5L","json":"https://pith.science/pith/O4D7KR3MYDDG4SMAMORUUZDL5L.json","graph_json":"https://pith.science/api/pith-number/O4D7KR3MYDDG4SMAMORUUZDL5L/graph.json","events_json":"https://pith.science/api/pith-number/O4D7KR3MYDDG4SMAMORUUZDL5L/events.json","paper":"https://pith.science/paper/O4D7KR3M"},"agent_actions":{"view_html":"https://pith.science/pith/O4D7KR3MYDDG4SMAMORUUZDL5L","download_json":"https://pith.science/pith/O4D7KR3MYDDG4SMAMORUUZDL5L.json","view_paper":"https://pith.science/paper/O4D7KR3M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0509173&json=true","fetch_graph":"https://pith.science/api/pith-number/O4D7KR3MYDDG4SMAMORUUZDL5L/graph.json","fetch_events":"https://pith.science/api/pith-number/O4D7KR3MYDDG4SMAMORUUZDL5L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O4D7KR3MYDDG4SMAMORUUZDL5L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O4D7KR3MYDDG4SMAMORUUZDL5L/action/storage_attestation","attest_author":"https://pith.science/pith/O4D7KR3MYDDG4SMAMORUUZDL5L/action/author_attestation","sign_citation":"https://pith.science/pith/O4D7KR3MYDDG4SMAMORUUZDL5L/action/citation_signature","submit_replication":"https://pith.science/pith/O4D7KR3MYDDG4SMAMORUUZDL5L/action/replication_record"}},"created_at":"2026-05-18T02:27:08.721588+00:00","updated_at":"2026-05-18T02:27:08.721588+00:00"}