{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:KSJRCVCDYF7QXQTXRPGGVFBSQO","short_pith_number":"pith:KSJRCVCD","canonical_record":{"source":{"id":"0811.1093","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2008-11-07T09:13:02Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"f23531e136727213691e24db64a9f740343460633f0a317b444742ee7eb8dc0c","abstract_canon_sha256":"f2d238f17458476663dcc40cec2eff63b264f470b79a59a4c8563ed2a9b671b4"},"schema_version":"1.0"},"canonical_sha256":"5493115443c17f0bc2778bcc6a943283a159f5786bcca106b421fe054e4ded19","source":{"kind":"arxiv","id":"0811.1093","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0811.1093","created_at":"2026-05-18T02:27:19Z"},{"alias_kind":"arxiv_version","alias_value":"0811.1093v1","created_at":"2026-05-18T02:27:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.1093","created_at":"2026-05-18T02:27:19Z"},{"alias_kind":"pith_short_12","alias_value":"KSJRCVCDYF7Q","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"KSJRCVCDYF7QXQTX","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"KSJRCVCD","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:KSJRCVCDYF7QXQTXRPGGVFBSQO","target":"record","payload":{"canonical_record":{"source":{"id":"0811.1093","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2008-11-07T09:13:02Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"f23531e136727213691e24db64a9f740343460633f0a317b444742ee7eb8dc0c","abstract_canon_sha256":"f2d238f17458476663dcc40cec2eff63b264f470b79a59a4c8563ed2a9b671b4"},"schema_version":"1.0"},"canonical_sha256":"5493115443c17f0bc2778bcc6a943283a159f5786bcca106b421fe054e4ded19","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:19.308513Z","signature_b64":"7muDsLpM+JwKg32Egx28DKrITQAnU+J6ujp2x3u2GQPetv7f2EBq2qjTSvH1ROgMOYiVi5r0zeW34oLKGHf+DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5493115443c17f0bc2778bcc6a943283a159f5786bcca106b421fe054e4ded19","last_reissued_at":"2026-05-18T02:27:19.307733Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:19.307733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0811.1093","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:27:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fTLvu5mcaxJo2hGGZOiVpHMN8nF76FZdXsBRmHJlefMuM0TGn/OG3zVy5jN6TjC74dcBd8ZfQW5KXKM8VF3oBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:39:26.570437Z"},"content_sha256":"fa60c9cf3c8e9de40aee5961ccbff66bf242684ad0446f48996d350737aeb46f","schema_version":"1.0","event_id":"sha256:fa60c9cf3c8e9de40aee5961ccbff66bf242684ad0446f48996d350737aeb46f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:KSJRCVCDYF7QXQTXRPGGVFBSQO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Functions holomorphic along holomorphic vector fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CV","authors_text":"Evgeny Poletsky, Gerd Schmalz, Kang-Tae Kim","submitted_at":"2008-11-07T09:13:02Z","abstract_excerpt":"The main result of the paper is the following generalization of Forelli's theorem: Suppose F is a holomorphic vector field with singular point at p, such that F is linearizable at p and the matrix is diagonalizable with the eigenvalues whose ratios are positive reals. Then any function $\\phi$ that has an asymptotic Taylor expansion at p and is holomorphic along the complex integral curves of F is holomorphic in a neighborhood of p.\n  We also present an example to show that the requirement for ratios of the eigenvalues to be positive reals is necessary."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.1093","kind":"arxiv","version":1},"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":"2026-05-18T02:27:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"augyaQC2brqLD4wufhPdHxZVkYlEZDpdErxSFm+GBXYtrgJ1amJQAyELBVEfwjh2YoMhNpiZ60Hh59sC047VCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:39:26.570820Z"},"content_sha256":"1ffa12648e437e98277fa73426b20728c1be7bf2e5f03b58521c23ce78093b66","schema_version":"1.0","event_id":"sha256:1ffa12648e437e98277fa73426b20728c1be7bf2e5f03b58521c23ce78093b66"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KSJRCVCDYF7QXQTXRPGGVFBSQO/bundle.json","state_url":"https://pith.science/pith/KSJRCVCDYF7QXQTXRPGGVFBSQO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KSJRCVCDYF7QXQTXRPGGVFBSQO/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":"2026-06-02T22:39:26Z","links":{"resolver":"https://pith.science/pith/KSJRCVCDYF7QXQTXRPGGVFBSQO","bundle":"https://pith.science/pith/KSJRCVCDYF7QXQTXRPGGVFBSQO/bundle.json","state":"https://pith.science/pith/KSJRCVCDYF7QXQTXRPGGVFBSQO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KSJRCVCDYF7QXQTXRPGGVFBSQO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:KSJRCVCDYF7QXQTXRPGGVFBSQO","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":"f2d238f17458476663dcc40cec2eff63b264f470b79a59a4c8563ed2a9b671b4","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2008-11-07T09:13:02Z","title_canon_sha256":"f23531e136727213691e24db64a9f740343460633f0a317b444742ee7eb8dc0c"},"schema_version":"1.0","source":{"id":"0811.1093","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0811.1093","created_at":"2026-05-18T02:27:19Z"},{"alias_kind":"arxiv_version","alias_value":"0811.1093v1","created_at":"2026-05-18T02:27:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.1093","created_at":"2026-05-18T02:27:19Z"},{"alias_kind":"pith_short_12","alias_value":"KSJRCVCDYF7Q","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"KSJRCVCDYF7QXQTX","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"KSJRCVCD","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:1ffa12648e437e98277fa73426b20728c1be7bf2e5f03b58521c23ce78093b66","target":"graph","created_at":"2026-05-18T02:27:19Z","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 main result of the paper is the following generalization of Forelli's theorem: Suppose F is a holomorphic vector field with singular point at p, such that F is linearizable at p and the matrix is diagonalizable with the eigenvalues whose ratios are positive reals. Then any function $\\phi$ that has an asymptotic Taylor expansion at p and is holomorphic along the complex integral curves of F is holomorphic in a neighborhood of p.\n  We also present an example to show that the requirement for ratios of the eigenvalues to be positive reals is necessary.","authors_text":"Evgeny Poletsky, Gerd Schmalz, Kang-Tae Kim","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2008-11-07T09:13:02Z","title":"Functions holomorphic along holomorphic vector fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.1093","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:fa60c9cf3c8e9de40aee5961ccbff66bf242684ad0446f48996d350737aeb46f","target":"record","created_at":"2026-05-18T02:27:19Z","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":"f2d238f17458476663dcc40cec2eff63b264f470b79a59a4c8563ed2a9b671b4","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2008-11-07T09:13:02Z","title_canon_sha256":"f23531e136727213691e24db64a9f740343460633f0a317b444742ee7eb8dc0c"},"schema_version":"1.0","source":{"id":"0811.1093","kind":"arxiv","version":1}},"canonical_sha256":"5493115443c17f0bc2778bcc6a943283a159f5786bcca106b421fe054e4ded19","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5493115443c17f0bc2778bcc6a943283a159f5786bcca106b421fe054e4ded19","first_computed_at":"2026-05-18T02:27:19.307733Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:19.307733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7muDsLpM+JwKg32Egx28DKrITQAnU+J6ujp2x3u2GQPetv7f2EBq2qjTSvH1ROgMOYiVi5r0zeW34oLKGHf+DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:19.308513Z","signed_message":"canonical_sha256_bytes"},"source_id":"0811.1093","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa60c9cf3c8e9de40aee5961ccbff66bf242684ad0446f48996d350737aeb46f","sha256:1ffa12648e437e98277fa73426b20728c1be7bf2e5f03b58521c23ce78093b66"],"state_sha256":"5687e2939da7b76fa6e4fc6fef7388656492aa223ed95efe2c417a0a84d90c96"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z6sHrBYAAXYczHA2KGqA7/oiGrriTZkprzfb6/mWyRX6x6CyYvoANAZDuO/WpTVhGTSpbY/JzZwbrgPYS6ZDDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T22:39:26.572795Z","bundle_sha256":"061ac602ebfa782fed443a83b701f88b213ebd5f572546cdd0f839d0b554da83"}}