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We prove that $M_t$ is not locally polynomially convex if $t<1$. The local hull contains a ball centred at the origin if $t<\\sqrt{3}/2$. We also prove that $M_t$"},"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":"1909.04085","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-09-09T18:16:12Z","cross_cats_sorted":[],"title_canon_sha256":"fb1d9527bff1c10d218ef6985efa2a3254c72ce51336e6345a7af37c3326b9e3","abstract_canon_sha256":"b6b6d523195f1a4a3410e2ad411d4eade39d16ec2a80f17ce3a0b4032e74c055"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:06:35.498417Z","signature_b64":"2eKyUgXsEzfTbCRcgCdf8I6Ac/j8Xpp+tF8X4DCysrNIvGbYtDxlyWf+ZY77iqT0+X7pAAp5lySWyF73BIQBAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"275d9096be4ed98aff690317dc20ac0b36d577a3765b3eab387f71e73606bdd3","last_reissued_at":"2026-07-05T10:06:35.498010Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:06:35.498010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Certain real surfaces in $\\mathbb{C}^2$ with isolated singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Sushil Gorai","submitted_at":"2019-09-09T18:16:12Z","abstract_excerpt":"Under certain geometric condition, the surfaces in $\\mathbb{C}^2$ with isolated CR singularity at the origin and with cubic lowest degree homogeneous term in its graph near the origin, can be reduced, up to biholomorphism of $\\mathbb{C}^2$, to a one parameter family of the form \\[ M_t:=\\left\\{(z,w)\\in\\mathbb{C}^2: w=z^2\\overline{z}+tz\\overline{z}^2+\\dfrac{t^2}{3} \\overline{z}^3+o(|z|^3)\\right\\},\\;\\; t\\in (0,\\infty) \\] near the origin. We prove that $M_t$ is not locally polynomially convex if $t<1$. The local hull contains a ball centred at the origin if $t<\\sqrt{3}/2$. We also prove that $M_t$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.04085","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1909.04085/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1909.04085","created_at":"2026-07-05T10:06:35.498066+00:00"},{"alias_kind":"arxiv_version","alias_value":"1909.04085v3","created_at":"2026-07-05T10:06:35.498066+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.04085","created_at":"2026-07-05T10:06:35.498066+00:00"},{"alias_kind":"pith_short_12","alias_value":"E5OZBFV6J3MY","created_at":"2026-07-05T10:06:35.498066+00:00"},{"alias_kind":"pith_short_16","alias_value":"E5OZBFV6J3MYV73J","created_at":"2026-07-05T10:06:35.498066+00:00"},{"alias_kind":"pith_short_8","alias_value":"E5OZBFV6","created_at":"2026-07-05T10:06:35.498066+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.30792","citing_title":"Carleman Approximation for certain sets with an isolated singularity","ref_index":9,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/E5OZBFV6J3MYV73JAML5YIFMBM","json":"https://pith.science/pith/E5OZBFV6J3MYV73JAML5YIFMBM.json","graph_json":"https://pith.science/api/pith-number/E5OZBFV6J3MYV73JAML5YIFMBM/graph.json","events_json":"https://pith.science/api/pith-number/E5OZBFV6J3MYV73JAML5YIFMBM/events.json","paper":"https://pith.science/paper/E5OZBFV6"},"agent_actions":{"view_html":"https://pith.science/pith/E5OZBFV6J3MYV73JAML5YIFMBM","download_json":"https://pith.science/pith/E5OZBFV6J3MYV73JAML5YIFMBM.json","view_paper":"https://pith.science/paper/E5OZBFV6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1909.04085&json=true","fetch_graph":"https://pith.science/api/pith-number/E5OZBFV6J3MYV73JAML5YIFMBM/graph.json","fetch_events":"https://pith.science/api/pith-number/E5OZBFV6J3MYV73JAML5YIFMBM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E5OZBFV6J3MYV73JAML5YIFMBM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E5OZBFV6J3MYV73JAML5YIFMBM/action/storage_attestation","attest_author":"https://pith.science/pith/E5OZBFV6J3MYV73JAML5YIFMBM/action/author_attestation","sign_citation":"https://pith.science/pith/E5OZBFV6J3MYV73JAML5YIFMBM/action/citation_signature","submit_replication":"https://pith.science/pith/E5OZBFV6J3MYV73JAML5YIFMBM/action/replication_record"}},"created_at":"2026-07-05T10:06:35.498066+00:00","updated_at":"2026-07-05T10:06:35.498066+00:00"}