{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:2DGEHU24Q7PYQ4UK4SSDTQE3SE","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":"8481a50c0d8b39226ccee6e574bb584e83a5c7e2186b34e12819744ca9bdc1cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-07-08T18:02:29Z","title_canon_sha256":"ad6faaecc87b8745f7cedcebd487bd18a7ab56685596a3740e53e7c922c1915f"},"schema_version":"1.0","source":{"id":"1107.1687","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.1687","created_at":"2026-05-18T04:18:35Z"},{"alias_kind":"arxiv_version","alias_value":"1107.1687v1","created_at":"2026-05-18T04:18:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.1687","created_at":"2026-05-18T04:18:35Z"},{"alias_kind":"pith_short_12","alias_value":"2DGEHU24Q7PY","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"2DGEHU24Q7PYQ4UK","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"2DGEHU24","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:9a4f59702d6bc53e6aacafa9a3688fd8c308ad267fa25b5fd60bf187c3209a18","target":"graph","created_at":"2026-05-18T04:18:35Z","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":"We consider the Szeg\\\"o kernel for domains \\Omega in C^2 given by \\Omega = {(z,w): Im w > b(Re z)} where b is a non-convex quartic polynomial with positive leading coefficient. Such domains are not pseudoconvex. We describe the subset of \\bar{\\Omega} \\times \\bar{\\Omega} on which the kernel and all its derivatives are finite. In particular, we show that there are points off the diagonal of the boundary at which the Szeg\\\"o kernel is infitie as well as points on the diagonal at which it is finite.","authors_text":"Jennifer Halfpap, Michael Gilliam","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-07-08T18:02:29Z","title":"The Szeg\\\"o kernel for certain non-pseudoconvex domains in C^2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1687","kind":"arxiv","version":1},"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":"sha256:77140b91e0e48907479ef5fbd9540d5b74dfc8052653c9022d73c18c05376959","target":"record","created_at":"2026-05-18T04:18:35Z","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":"8481a50c0d8b39226ccee6e574bb584e83a5c7e2186b34e12819744ca9bdc1cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-07-08T18:02:29Z","title_canon_sha256":"ad6faaecc87b8745f7cedcebd487bd18a7ab56685596a3740e53e7c922c1915f"},"schema_version":"1.0","source":{"id":"1107.1687","kind":"arxiv","version":1}},"canonical_sha256":"d0cc43d35c87df88728ae4a439c09b912f2e3559080f7660a1097aab2c63dc7d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d0cc43d35c87df88728ae4a439c09b912f2e3559080f7660a1097aab2c63dc7d","first_computed_at":"2026-05-18T04:18:35.215860Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:35.215860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vhdqdHK1yqcKdbWPxtFBSYBPic5CKZyBZYC4hW0NvlxKIcdtS54oCL08AU+9GyUZmj5Mz6DN9cChXTUeysOpBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:35.216431Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.1687","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77140b91e0e48907479ef5fbd9540d5b74dfc8052653c9022d73c18c05376959","sha256:9a4f59702d6bc53e6aacafa9a3688fd8c308ad267fa25b5fd60bf187c3209a18"],"state_sha256":"a3b0973c4eb3f2558b40aec9927f793baa781bb58ff86a6fc4c1a8ce512e0619"}