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Then $\\tau^3_p$ must identically vanish. In this case we further define an invariant quartic tensor $\\tau^4_p \\colon \\C T_p \\times \\C T_p\n  \\times K^{10}_p\\"},"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":"1704.01808","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-04-06T12:46:03Z","cross_cats_sorted":[],"title_canon_sha256":"5fc727878eedd564970115cc677d3a085a41a9a5edb84cfbac3b68092e51c3c1","abstract_canon_sha256":"9ac0e8d81a9a838e955129bc66e4d49c09a6649b9dff6abc977e754791b4ebf1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:20.785555Z","signature_b64":"hOTyWPKUeSBDc9ZvxvOUPy9wm+aZsB9KpWvCH2+x9QLEUn6DxEHcviihaVXF2aNOJWlw2f0IuNpC/MNdYSelBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f52eb43fc85c24dcff19f1bb7985828cedefc681299a51fcfb3127d694110269","last_reissued_at":"2026-05-18T00:25:20.784800Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:20.784800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A geometric approach to Catlin's boundary systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Dmitri Zaitsev","submitted_at":"2017-04-06T12:46:03Z","abstract_excerpt":"For a point $p$ in a smooth real hypersurface $M\\subset\\C^n$, where the Levi form has the nontrivial kernel $K^{10}_p$, we introduce an invariant cubic tensor $\\tau^3_p \\colon \\C T_p \\times K^{10}_p \\times \\overline{K^{10}_p} \\to \\C\\otimes (T_p/H_p)$, which together with Ebenfelt's tensor $\\psi_3$, constitutes the full set of $3$rd order invariants of $M$ at $p$.\n  Next, in addition, assume $M\\subset\\C^n$ to be {\\em (weakly) pseudoconvex}. Then $\\tau^3_p$ must identically vanish. In this case we further define an invariant quartic tensor $\\tau^4_p \\colon \\C T_p \\times \\C T_p\n  \\times K^{10}_p\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01808","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":"1704.01808","created_at":"2026-05-18T00:25:20.784937+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.01808v2","created_at":"2026-05-18T00:25:20.784937+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.01808","created_at":"2026-05-18T00:25:20.784937+00:00"},{"alias_kind":"pith_short_12","alias_value":"6UXLIP6ILQSN","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_16","alias_value":"6UXLIP6ILQSNZ7YZ","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_8","alias_value":"6UXLIP6I","created_at":"2026-05-18T12:31:03.183658+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/6UXLIP6ILQSNZ7YZ6G5XTBMCRT","json":"https://pith.science/pith/6UXLIP6ILQSNZ7YZ6G5XTBMCRT.json","graph_json":"https://pith.science/api/pith-number/6UXLIP6ILQSNZ7YZ6G5XTBMCRT/graph.json","events_json":"https://pith.science/api/pith-number/6UXLIP6ILQSNZ7YZ6G5XTBMCRT/events.json","paper":"https://pith.science/paper/6UXLIP6I"},"agent_actions":{"view_html":"https://pith.science/pith/6UXLIP6ILQSNZ7YZ6G5XTBMCRT","download_json":"https://pith.science/pith/6UXLIP6ILQSNZ7YZ6G5XTBMCRT.json","view_paper":"https://pith.science/paper/6UXLIP6I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.01808&json=true","fetch_graph":"https://pith.science/api/pith-number/6UXLIP6ILQSNZ7YZ6G5XTBMCRT/graph.json","fetch_events":"https://pith.science/api/pith-number/6UXLIP6ILQSNZ7YZ6G5XTBMCRT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6UXLIP6ILQSNZ7YZ6G5XTBMCRT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6UXLIP6ILQSNZ7YZ6G5XTBMCRT/action/storage_attestation","attest_author":"https://pith.science/pith/6UXLIP6ILQSNZ7YZ6G5XTBMCRT/action/author_attestation","sign_citation":"https://pith.science/pith/6UXLIP6ILQSNZ7YZ6G5XTBMCRT/action/citation_signature","submit_replication":"https://pith.science/pith/6UXLIP6ILQSNZ7YZ6G5XTBMCRT/action/replication_record"}},"created_at":"2026-05-18T00:25:20.784937+00:00","updated_at":"2026-05-18T00:25:20.784937+00:00"}