{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:5EMAH6ZM3VH6G3P4UQGS75TVBP","short_pith_number":"pith:5EMAH6ZM","canonical_record":{"source":{"id":"1302.5796","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-02-23T13:12:43Z","cross_cats_sorted":[],"title_canon_sha256":"ee0ec6f8f6ea3d9ffee9e303e6c7ce63315eff709d02a6bd6a37a9a0b00a24a4","abstract_canon_sha256":"208b49e594b151cbab8d63e6bba459e85c03d3d03eedeec219e376d406bce9f4"},"schema_version":"1.0"},"canonical_sha256":"e91803fb2cdd4fe36dfca40d2ff6750bfb0dd91f7e1e9e26dc50f2790ecd8e2b","source":{"kind":"arxiv","id":"1302.5796","version":7},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.5796","created_at":"2026-07-05T00:18:02Z"},{"alias_kind":"arxiv_version","alias_value":"1302.5796v7","created_at":"2026-07-05T00:18:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5796","created_at":"2026-07-05T00:18:02Z"},{"alias_kind":"pith_short_12","alias_value":"5EMAH6ZM3VH6","created_at":"2026-07-05T00:18:02Z"},{"alias_kind":"pith_short_16","alias_value":"5EMAH6ZM3VH6G3P4","created_at":"2026-07-05T00:18:02Z"},{"alias_kind":"pith_short_8","alias_value":"5EMAH6ZM","created_at":"2026-07-05T00:18:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:5EMAH6ZM3VH6G3P4UQGS75TVBP","target":"record","payload":{"canonical_record":{"source":{"id":"1302.5796","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-02-23T13:12:43Z","cross_cats_sorted":[],"title_canon_sha256":"ee0ec6f8f6ea3d9ffee9e303e6c7ce63315eff709d02a6bd6a37a9a0b00a24a4","abstract_canon_sha256":"208b49e594b151cbab8d63e6bba459e85c03d3d03eedeec219e376d406bce9f4"},"schema_version":"1.0"},"canonical_sha256":"e91803fb2cdd4fe36dfca40d2ff6750bfb0dd91f7e1e9e26dc50f2790ecd8e2b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:18:02.741116Z","signature_b64":"MiC1X4/rP+p5lPspsBRZ7f+BId+PP9ktG2iS3qpsFu+EoVByNsXGd8GNlX8wN/V5DRWSUObWa8hiacr8TR7OAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e91803fb2cdd4fe36dfca40d2ff6750bfb0dd91f7e1e9e26dc50f2790ecd8e2b","last_reissued_at":"2026-07-05T00:18:02.740636Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:18:02.740636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.5796","source_version":7,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:18:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"djlFzxYnLk8pVG/+S6B/k+L9QXHrER+ZAguDJ6jg2gsioFwV5Fm4Zluk7+hDFiG69fE3+2stHOlI89F1B38qAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T05:57:10.808344Z"},"content_sha256":"a01015e07dfbbe49e9538d4d046b57bc7a9a736ec152da97f8688bf930b67903","schema_version":"1.0","event_id":"sha256:a01015e07dfbbe49e9538d4d046b57bc7a9a736ec152da97f8688bf930b67903"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:5EMAH6ZM3VH6G3P4UQGS75TVBP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Hartogs extension phenomenon for holomorphic parabolic and reductive geometries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Benjamin McKay (University College Cork)","submitted_at":"2013-02-23T13:12:43Z","abstract_excerpt":"Every holomorphic effective parabolic or reductive geometry on a domain over a Stein manifold extends uniquely to the envelope of holomorphy of the domain. This result completes the open problems of my earlier paper on extension of holomorphic geometric structures on complex manifolds. We use this result to classify the Hopf manifolds which admit holomorphic reductive geometries, and to classify the Hopf manifolds which admit holomorphic parabolic geometries. Every Hopf manifold which admits a holomorphic parabolic geometry with a given model admits a flat one. We classify flat holomorphic par"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5796","kind":"arxiv","version":7},"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/1302.5796/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:18:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sazhYsJykMz48RbkR0nJ0D7sHuVJu0AVupzL7Ygv9QA7krg4iP0j06RGV3qPF6nHl1sK28IQtlosvWVfkCLNAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T05:57:10.808989Z"},"content_sha256":"e82b9c0674707435843f7fa085308627a4a778973e20938fe3884355277e9b9d","schema_version":"1.0","event_id":"sha256:e82b9c0674707435843f7fa085308627a4a778973e20938fe3884355277e9b9d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5EMAH6ZM3VH6G3P4UQGS75TVBP/bundle.json","state_url":"https://pith.science/pith/5EMAH6ZM3VH6G3P4UQGS75TVBP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5EMAH6ZM3VH6G3P4UQGS75TVBP/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":"2026-07-07T05:57:10Z","links":{"resolver":"https://pith.science/pith/5EMAH6ZM3VH6G3P4UQGS75TVBP","bundle":"https://pith.science/pith/5EMAH6ZM3VH6G3P4UQGS75TVBP/bundle.json","state":"https://pith.science/pith/5EMAH6ZM3VH6G3P4UQGS75TVBP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5EMAH6ZM3VH6G3P4UQGS75TVBP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:5EMAH6ZM3VH6G3P4UQGS75TVBP","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":"208b49e594b151cbab8d63e6bba459e85c03d3d03eedeec219e376d406bce9f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-02-23T13:12:43Z","title_canon_sha256":"ee0ec6f8f6ea3d9ffee9e303e6c7ce63315eff709d02a6bd6a37a9a0b00a24a4"},"schema_version":"1.0","source":{"id":"1302.5796","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.5796","created_at":"2026-07-05T00:18:02Z"},{"alias_kind":"arxiv_version","alias_value":"1302.5796v7","created_at":"2026-07-05T00:18:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5796","created_at":"2026-07-05T00:18:02Z"},{"alias_kind":"pith_short_12","alias_value":"5EMAH6ZM3VH6","created_at":"2026-07-05T00:18:02Z"},{"alias_kind":"pith_short_16","alias_value":"5EMAH6ZM3VH6G3P4","created_at":"2026-07-05T00:18:02Z"},{"alias_kind":"pith_short_8","alias_value":"5EMAH6ZM","created_at":"2026-07-05T00:18:02Z"}],"graph_snapshots":[{"event_id":"sha256:e82b9c0674707435843f7fa085308627a4a778973e20938fe3884355277e9b9d","target":"graph","created_at":"2026-07-05T00:18:02Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1302.5796/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Every holomorphic effective parabolic or reductive geometry on a domain over a Stein manifold extends uniquely to the envelope of holomorphy of the domain. This result completes the open problems of my earlier paper on extension of holomorphic geometric structures on complex manifolds. We use this result to classify the Hopf manifolds which admit holomorphic reductive geometries, and to classify the Hopf manifolds which admit holomorphic parabolic geometries. Every Hopf manifold which admits a holomorphic parabolic geometry with a given model admits a flat one. We classify flat holomorphic par","authors_text":"Benjamin McKay (University College Cork)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-02-23T13:12:43Z","title":"The Hartogs extension phenomenon for holomorphic parabolic and reductive geometries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5796","kind":"arxiv","version":7},"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:a01015e07dfbbe49e9538d4d046b57bc7a9a736ec152da97f8688bf930b67903","target":"record","created_at":"2026-07-05T00:18:02Z","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":"208b49e594b151cbab8d63e6bba459e85c03d3d03eedeec219e376d406bce9f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-02-23T13:12:43Z","title_canon_sha256":"ee0ec6f8f6ea3d9ffee9e303e6c7ce63315eff709d02a6bd6a37a9a0b00a24a4"},"schema_version":"1.0","source":{"id":"1302.5796","kind":"arxiv","version":7}},"canonical_sha256":"e91803fb2cdd4fe36dfca40d2ff6750bfb0dd91f7e1e9e26dc50f2790ecd8e2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e91803fb2cdd4fe36dfca40d2ff6750bfb0dd91f7e1e9e26dc50f2790ecd8e2b","first_computed_at":"2026-07-05T00:18:02.740636Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:18:02.740636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MiC1X4/rP+p5lPspsBRZ7f+BId+PP9ktG2iS3qpsFu+EoVByNsXGd8GNlX8wN/V5DRWSUObWa8hiacr8TR7OAw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:18:02.741116Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.5796","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a01015e07dfbbe49e9538d4d046b57bc7a9a736ec152da97f8688bf930b67903","sha256:e82b9c0674707435843f7fa085308627a4a778973e20938fe3884355277e9b9d"],"state_sha256":"e13cde0658818e480b0a2354bb67d5efdf6869311be8a7c136340249187d87ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HGWA//AchpWao8cx4IGHdKxsqdQsbhRoeqnA4H94QUjwXIW4hQyaNQa20m7iz4OgA+OImXEBI6Xw0Ki6YD15CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T05:57:10.812571Z","bundle_sha256":"1aa0fbe31d4ebdd622c2b986040fc54c29b5f02f3853296110fdb67640888d37"}}