{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:KDYETZTZ2LEB54CBVLTBJHKY2I","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"7a743895d0e3258b26023b97158ab1d6c95ca896b1b8bbebb69e41e2c1461e34","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.CV","submitted_at":"2007-11-03T06:02:48Z","title_canon_sha256":"91ada3c8f2f8714d2e0005f79bd49afd694b41faafc2bdfbc4c98b7f404267f2"},"schema_version":"1.0","source":{"id":"0711.0429","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0711.0429","created_at":"2026-05-18T03:15:56Z"},{"alias_kind":"arxiv_version","alias_value":"0711.0429v2","created_at":"2026-05-18T03:15:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0711.0429","created_at":"2026-05-18T03:15:56Z"},{"alias_kind":"pith_short_12","alias_value":"KDYETZTZ2LEB","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"KDYETZTZ2LEB54CB","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"KDYETZTZ","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:b733f2d83ea69871c1feeabe9e24a6c2c28b96769dde040bf32f42fa9fa48461","target":"graph","created_at":"2026-05-18T03:15:56Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The D'Angelo finite type is shown to be equivalent to the Kohn finite ideal type on smooth, pseudoconvex domains in complex n space. This is known as the Kohn Conjecture. The argument uses Catlin's notion of a boundary system as well as methods from subanalytic and semialgebraic geometry. When a subset of the boundary contains only two level sets of the Catlin multitype, a lower bound for the subelliptic gain in the \\bar\\partial-Neumann problem is obtained in terms of the D'Angelo type, the dimension of the ambient space, and the level of forms.","authors_text":"Andreea C. Nicoara","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"math.CV","submitted_at":"2007-11-03T06:02:48Z","title":"Equivalence of types and Catlin boundary systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.0429","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:19c0ca6943d14d82d0e344a3b5465e0f6de584a991923332c6f5c66fc4805b00","target":"record","created_at":"2026-05-18T03:15:56Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"7a743895d0e3258b26023b97158ab1d6c95ca896b1b8bbebb69e41e2c1461e34","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.CV","submitted_at":"2007-11-03T06:02:48Z","title_canon_sha256":"91ada3c8f2f8714d2e0005f79bd49afd694b41faafc2bdfbc4c98b7f404267f2"},"schema_version":"1.0","source":{"id":"0711.0429","kind":"arxiv","version":2}},"canonical_sha256":"50f049e679d2c81ef041aae6149d58d207aee1bedc0de7096aab0369e6149722","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50f049e679d2c81ef041aae6149d58d207aee1bedc0de7096aab0369e6149722","first_computed_at":"2026-05-18T03:15:56.205674Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:56.205674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NN/33Wmj7qtDvJIlZtGu6otw1QQ+sp5T7jIAq3WIVC++TaNbd3T9MToEr7glb79j3/S7X+fLys5vpeLrhaQtAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:56.206609Z","signed_message":"canonical_sha256_bytes"},"source_id":"0711.0429","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19c0ca6943d14d82d0e344a3b5465e0f6de584a991923332c6f5c66fc4805b00","sha256:b733f2d83ea69871c1feeabe9e24a6c2c28b96769dde040bf32f42fa9fa48461"],"state_sha256":"000526f80fc3cdfa2eb69f33c4ffa018fa341abd51ccac4527301fa6c67629e1"}