{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:TRZTZSHQTAQA5QVF5JHQDX7F7E","short_pith_number":"pith:TRZTZSHQ","canonical_record":{"source":{"id":"1108.5625","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-08-29T16:12:51Z","cross_cats_sorted":[],"title_canon_sha256":"6aa54f97dc883a048ca63d5920cb18fdbc8f80f6b7612d890b65cd99c03658f5","abstract_canon_sha256":"b9fec14284bc316f9728293dfb9950e74c568c6f78c4cd8f805ff8c9f2556314"},"schema_version":"1.0"},"canonical_sha256":"9c733cc8f098200ec2a5ea4f01dfe5f91ea59869849567cc78bed5aa12a49dea","source":{"kind":"arxiv","id":"1108.5625","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.5625","created_at":"2026-05-18T04:14:28Z"},{"alias_kind":"arxiv_version","alias_value":"1108.5625v2","created_at":"2026-05-18T04:14:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5625","created_at":"2026-05-18T04:14:28Z"},{"alias_kind":"pith_short_12","alias_value":"TRZTZSHQTAQA","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TRZTZSHQTAQA5QVF","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TRZTZSHQ","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:TRZTZSHQTAQA5QVF5JHQDX7F7E","target":"record","payload":{"canonical_record":{"source":{"id":"1108.5625","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-08-29T16:12:51Z","cross_cats_sorted":[],"title_canon_sha256":"6aa54f97dc883a048ca63d5920cb18fdbc8f80f6b7612d890b65cd99c03658f5","abstract_canon_sha256":"b9fec14284bc316f9728293dfb9950e74c568c6f78c4cd8f805ff8c9f2556314"},"schema_version":"1.0"},"canonical_sha256":"9c733cc8f098200ec2a5ea4f01dfe5f91ea59869849567cc78bed5aa12a49dea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:28.659972Z","signature_b64":"FNvdYJmcG5fkASQ6+Nb5/7CkzCTI41Fi/SgKz/9QE24r7pbGZahmd4EvBf1HKqsIEn+ETAOl7GJXz52/G+f6Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c733cc8f098200ec2a5ea4f01dfe5f91ea59869849567cc78bed5aa12a49dea","last_reissued_at":"2026-05-18T04:14:28.659348Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:28.659348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.5625","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:14:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PiLjRdedBFhhMGJ7oyCPMHD8oSa8oaJEhhGJzp822vGtMzNtTffulZNqa5l/v1YiPZ6JJR67czSgBXwk2l0gCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:13:03.577694Z"},"content_sha256":"37bae2c9daa22d5739e1dd8b7fd298896fe85463dd6337df965f05f7be0adfc7","schema_version":"1.0","event_id":"sha256:37bae2c9daa22d5739e1dd8b7fd298896fe85463dd6337df965f05f7be0adfc7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:TRZTZSHQTAQA5QVF5JHQDX7F7E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the polynomial convexity of the union of more than two totally-real planes in C^2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Sushil Gorai","submitted_at":"2011-08-29T16:12:51Z","abstract_excerpt":"In this paper we shall discuss local polynomial convexity at the origin of the union of finitely many totally-real planes through $0 \\in\\mathbb{C}^2$. The planes, say $P_0,..., P_N$, satisfy a mild transversality condition that enables us to view them in Weinstock normal form, i.e. $P_0=\\mathbb{R}^2$ and $P_j=M(A_j):=(A_j+i\\mathbb{I})\\mathbb{R}^2$, $j=1,...,N$, where each $A_j$ is a $2\\times 2$ matrix with real entries. Weinstock has solved the problem completely for N=1 (in fact, for pairs of transverse, maximally totally-real subspaces in $\\mathbb{C}^n\\, \\forall n\\geq 2$). Using a characteri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5625","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:14:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kybz2f/u91AZa/vaCWRaLJ6/gsvnMHkvVpB9M5R+/CbZbRbuyakiTsTxfWO2imki6P0KYZB7ieIOZgfLna7tBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:13:03.578055Z"},"content_sha256":"50ef0204a8ab43769af805be8212d66853835778beddd95a67cc357d8a80e4a2","schema_version":"1.0","event_id":"sha256:50ef0204a8ab43769af805be8212d66853835778beddd95a67cc357d8a80e4a2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TRZTZSHQTAQA5QVF5JHQDX7F7E/bundle.json","state_url":"https://pith.science/pith/TRZTZSHQTAQA5QVF5JHQDX7F7E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TRZTZSHQTAQA5QVF5JHQDX7F7E/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-30T23:13:03Z","links":{"resolver":"https://pith.science/pith/TRZTZSHQTAQA5QVF5JHQDX7F7E","bundle":"https://pith.science/pith/TRZTZSHQTAQA5QVF5JHQDX7F7E/bundle.json","state":"https://pith.science/pith/TRZTZSHQTAQA5QVF5JHQDX7F7E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TRZTZSHQTAQA5QVF5JHQDX7F7E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TRZTZSHQTAQA5QVF5JHQDX7F7E","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":"b9fec14284bc316f9728293dfb9950e74c568c6f78c4cd8f805ff8c9f2556314","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-08-29T16:12:51Z","title_canon_sha256":"6aa54f97dc883a048ca63d5920cb18fdbc8f80f6b7612d890b65cd99c03658f5"},"schema_version":"1.0","source":{"id":"1108.5625","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.5625","created_at":"2026-05-18T04:14:28Z"},{"alias_kind":"arxiv_version","alias_value":"1108.5625v2","created_at":"2026-05-18T04:14:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5625","created_at":"2026-05-18T04:14:28Z"},{"alias_kind":"pith_short_12","alias_value":"TRZTZSHQTAQA","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TRZTZSHQTAQA5QVF","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TRZTZSHQ","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:50ef0204a8ab43769af805be8212d66853835778beddd95a67cc357d8a80e4a2","target":"graph","created_at":"2026-05-18T04:14:28Z","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":"In this paper we shall discuss local polynomial convexity at the origin of the union of finitely many totally-real planes through $0 \\in\\mathbb{C}^2$. The planes, say $P_0,..., P_N$, satisfy a mild transversality condition that enables us to view them in Weinstock normal form, i.e. $P_0=\\mathbb{R}^2$ and $P_j=M(A_j):=(A_j+i\\mathbb{I})\\mathbb{R}^2$, $j=1,...,N$, where each $A_j$ is a $2\\times 2$ matrix with real entries. Weinstock has solved the problem completely for N=1 (in fact, for pairs of transverse, maximally totally-real subspaces in $\\mathbb{C}^n\\, \\forall n\\geq 2$). Using a characteri","authors_text":"Sushil Gorai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-08-29T16:12:51Z","title":"On the polynomial convexity of the union of more than two totally-real planes in C^2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5625","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":"sha256:37bae2c9daa22d5739e1dd8b7fd298896fe85463dd6337df965f05f7be0adfc7","target":"record","created_at":"2026-05-18T04:14:28Z","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":"b9fec14284bc316f9728293dfb9950e74c568c6f78c4cd8f805ff8c9f2556314","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-08-29T16:12:51Z","title_canon_sha256":"6aa54f97dc883a048ca63d5920cb18fdbc8f80f6b7612d890b65cd99c03658f5"},"schema_version":"1.0","source":{"id":"1108.5625","kind":"arxiv","version":2}},"canonical_sha256":"9c733cc8f098200ec2a5ea4f01dfe5f91ea59869849567cc78bed5aa12a49dea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c733cc8f098200ec2a5ea4f01dfe5f91ea59869849567cc78bed5aa12a49dea","first_computed_at":"2026-05-18T04:14:28.659348Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:28.659348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FNvdYJmcG5fkASQ6+Nb5/7CkzCTI41Fi/SgKz/9QE24r7pbGZahmd4EvBf1HKqsIEn+ETAOl7GJXz52/G+f6Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:28.659972Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.5625","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37bae2c9daa22d5739e1dd8b7fd298896fe85463dd6337df965f05f7be0adfc7","sha256:50ef0204a8ab43769af805be8212d66853835778beddd95a67cc357d8a80e4a2"],"state_sha256":"5b85c0885305020149736e28d1898a0115384a8fbe8ee77f58aab8f172c1190c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1KfoAs64QTZ6T+nA7nzhRr8iEmXZvgdwdwOkRJPzE8xdTc4buoZ3eWzePXMt817i9d5szUN/y+ecSU9C/ZiLCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T23:13:03.580241Z","bundle_sha256":"f131f47d69b3602ee9ea4a32de29bd9bac6bfb6804464b104848057a12d8e98f"}}