{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:7M2RPVMCIPTPIJAJR3MS5KMNLU","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":"2884a2d4e39516023c3f6224fedb4f668abcdcd751bb3a3387607fe87e1d97e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2009-02-24T18:53:56Z","title_canon_sha256":"d62e4cdc44929076a180698fb45523d3c5120f3550480925405e642356c6e330"},"schema_version":"1.0","source":{"id":"0902.4215","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.4215","created_at":"2026-05-18T01:34:42Z"},{"alias_kind":"arxiv_version","alias_value":"0902.4215v4","created_at":"2026-05-18T01:34:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.4215","created_at":"2026-05-18T01:34:42Z"},{"alias_kind":"pith_short_12","alias_value":"7M2RPVMCIPTP","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"7M2RPVMCIPTPIJAJ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"7M2RPVMC","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:5f171dc2eed7fa72c73fdaff61bf82c55cf715b8a6d312e2801c274b3e05cc7c","target":"graph","created_at":"2026-05-18T01:34:42Z","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":"Let S be a smooth real surface in C^2 and let p\\in S be a point at which the tangent plane is a complex line. How does one determine whether or not S is locally polynomially convex at such a p --- i.e. at a CR singularity ? Even when the order of contact of T_p(S) with S at p equals 2, no clean characterisation exists; difficulties are posed by parabolic points. Hence, we study non-parabolic CR singularities. We show that the presence or absence of Bishop discs around certain non-parabolic CR singularities is completely determined by a Maslov-type index. This result subsumes all known facts ab","authors_text":"Gautam Bharali","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2009-02-24T18:53:56Z","title":"The local polynomial hull near a degenerate CR singularity -- Bishop discs revisited"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.4215","kind":"arxiv","version":4},"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":"sha256:2be78aa207299f8358c186cc4d409c4cc99a4ad889da04e14efc262492d4aa08","target":"record","created_at":"2026-05-18T01:34:42Z","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":"2884a2d4e39516023c3f6224fedb4f668abcdcd751bb3a3387607fe87e1d97e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2009-02-24T18:53:56Z","title_canon_sha256":"d62e4cdc44929076a180698fb45523d3c5120f3550480925405e642356c6e330"},"schema_version":"1.0","source":{"id":"0902.4215","kind":"arxiv","version":4}},"canonical_sha256":"fb3517d58243e6f424098ed92ea98d5d3ffef43c296016f4d7436b03004223fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb3517d58243e6f424098ed92ea98d5d3ffef43c296016f4d7436b03004223fc","first_computed_at":"2026-05-18T01:34:42.504135Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:42.504135Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GQO4HUYj0OKL9o/hevi0vv0btvPtGZQXyzSl67tJKHbpk3bBUV/1k71/yBYZOurGVCMQQ9hJ8BcpTwFE0/oFBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:42.504694Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.4215","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2be78aa207299f8358c186cc4d409c4cc99a4ad889da04e14efc262492d4aa08","sha256:5f171dc2eed7fa72c73fdaff61bf82c55cf715b8a6d312e2801c274b3e05cc7c"],"state_sha256":"359c0876d5f1c7894617dd8eff9e0cb577495bd394e481c1c97132e9e3ad3f58"}