{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:6LCGIXATOMEX54OC5M7Y66HHK5","short_pith_number":"pith:6LCGIXAT","canonical_record":{"source":{"id":"2011.09637","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2020-11-19T03:59:09Z","cross_cats_sorted":[],"title_canon_sha256":"1cd5cb738d187c443a3d221706ab3e0b5de309fa821bd7c841db8c9012a67262","abstract_canon_sha256":"076190bfd85e7a5efd077598967d77768e1f4b859b8c2a99253473a31a13ad60"},"schema_version":"1.0"},"canonical_sha256":"f2c4645c1373097ef1c2eb3f8f78e7576b6cb113eb3f20800ccb6721b6b5415c","source":{"kind":"arxiv","id":"2011.09637","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.09637","created_at":"2026-07-05T01:52:50Z"},{"alias_kind":"arxiv_version","alias_value":"2011.09637v1","created_at":"2026-07-05T01:52:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.09637","created_at":"2026-07-05T01:52:50Z"},{"alias_kind":"pith_short_12","alias_value":"6LCGIXATOMEX","created_at":"2026-07-05T01:52:50Z"},{"alias_kind":"pith_short_16","alias_value":"6LCGIXATOMEX54OC","created_at":"2026-07-05T01:52:50Z"},{"alias_kind":"pith_short_8","alias_value":"6LCGIXAT","created_at":"2026-07-05T01:52:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:6LCGIXATOMEX54OC5M7Y66HHK5","target":"record","payload":{"canonical_record":{"source":{"id":"2011.09637","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2020-11-19T03:59:09Z","cross_cats_sorted":[],"title_canon_sha256":"1cd5cb738d187c443a3d221706ab3e0b5de309fa821bd7c841db8c9012a67262","abstract_canon_sha256":"076190bfd85e7a5efd077598967d77768e1f4b859b8c2a99253473a31a13ad60"},"schema_version":"1.0"},"canonical_sha256":"f2c4645c1373097ef1c2eb3f8f78e7576b6cb113eb3f20800ccb6721b6b5415c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:52:50.623345Z","signature_b64":"UbgqRxUMmXCZOQPuRKVoyg3UcqUq/IIvyM82oGlZP1NEgKPVlWtPj1X72AuJGvd83M9yqpDe4ICGuGE/bpPABQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2c4645c1373097ef1c2eb3f8f78e7576b6cb113eb3f20800ccb6721b6b5415c","last_reissued_at":"2026-07-05T01:52:50.622949Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:52:50.622949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2011.09637","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":"2026-07-05T01:52:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TosuLZEMiTLLpCXxXNVSUG9FnMQBALRwiASx+5vpyt035zM8tIjWleGygFFZcNFrVL45rOmJwjRYMu1OIXkgBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T22:05:50.613353Z"},"content_sha256":"4c3afe949e07eec89764f55f3e5dce4ecfddf99f236890a80be4d298f6de754f","schema_version":"1.0","event_id":"sha256:4c3afe949e07eec89764f55f3e5dce4ecfddf99f236890a80be4d298f6de754f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:6LCGIXATOMEX54OC5M7Y66HHK5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A generalization of Nadel vanishing theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Xiangyu Zhou, Xiankui Meng","submitted_at":"2020-11-19T03:59:09Z","abstract_excerpt":"In this paper we first prove a version of $L^{2}$ existence theorem for line bundles equipped a singular Hermitian metrics. Aa an application, we establish a vanishing theorem which generalizes the classical Nadel vanishing theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.09637","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2011.09637/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":"2026-07-05T01:52:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"upa1iADhzN7Pdl/L+jddo5J57BwIH2S9vmw63J7HVPfLRyFPGYDDWL/TCpu34xAVWYOoa80lz3RonbefY0K7AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T22:05:50.614216Z"},"content_sha256":"627e3e60c60b468f2e81db8cafdf86c6f10fcfdc8c58c2e6b8a17362d380e752","schema_version":"1.0","event_id":"sha256:627e3e60c60b468f2e81db8cafdf86c6f10fcfdc8c58c2e6b8a17362d380e752"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6LCGIXATOMEX54OC5M7Y66HHK5/bundle.json","state_url":"https://pith.science/pith/6LCGIXATOMEX54OC5M7Y66HHK5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6LCGIXATOMEX54OC5M7Y66HHK5/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":"2026-08-11T22:05:50Z","links":{"resolver":"https://pith.science/pith/6LCGIXATOMEX54OC5M7Y66HHK5","bundle":"https://pith.science/pith/6LCGIXATOMEX54OC5M7Y66HHK5/bundle.json","state":"https://pith.science/pith/6LCGIXATOMEX54OC5M7Y66HHK5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6LCGIXATOMEX54OC5M7Y66HHK5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:6LCGIXATOMEX54OC5M7Y66HHK5","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":"076190bfd85e7a5efd077598967d77768e1f4b859b8c2a99253473a31a13ad60","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2020-11-19T03:59:09Z","title_canon_sha256":"1cd5cb738d187c443a3d221706ab3e0b5de309fa821bd7c841db8c9012a67262"},"schema_version":"1.0","source":{"id":"2011.09637","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.09637","created_at":"2026-07-05T01:52:50Z"},{"alias_kind":"arxiv_version","alias_value":"2011.09637v1","created_at":"2026-07-05T01:52:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.09637","created_at":"2026-07-05T01:52:50Z"},{"alias_kind":"pith_short_12","alias_value":"6LCGIXATOMEX","created_at":"2026-07-05T01:52:50Z"},{"alias_kind":"pith_short_16","alias_value":"6LCGIXATOMEX54OC","created_at":"2026-07-05T01:52:50Z"},{"alias_kind":"pith_short_8","alias_value":"6LCGIXAT","created_at":"2026-07-05T01:52:50Z"}],"graph_snapshots":[{"event_id":"sha256:627e3e60c60b468f2e81db8cafdf86c6f10fcfdc8c58c2e6b8a17362d380e752","target":"graph","created_at":"2026-07-05T01:52:50Z","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/2011.09637/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we first prove a version of $L^{2}$ existence theorem for line bundles equipped a singular Hermitian metrics. Aa an application, we establish a vanishing theorem which generalizes the classical Nadel vanishing theorem.","authors_text":"Xiangyu Zhou, Xiankui Meng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2020-11-19T03:59:09Z","title":"A generalization of Nadel vanishing theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.09637","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":"sha256:4c3afe949e07eec89764f55f3e5dce4ecfddf99f236890a80be4d298f6de754f","target":"record","created_at":"2026-07-05T01:52:50Z","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":"076190bfd85e7a5efd077598967d77768e1f4b859b8c2a99253473a31a13ad60","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2020-11-19T03:59:09Z","title_canon_sha256":"1cd5cb738d187c443a3d221706ab3e0b5de309fa821bd7c841db8c9012a67262"},"schema_version":"1.0","source":{"id":"2011.09637","kind":"arxiv","version":1}},"canonical_sha256":"f2c4645c1373097ef1c2eb3f8f78e7576b6cb113eb3f20800ccb6721b6b5415c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2c4645c1373097ef1c2eb3f8f78e7576b6cb113eb3f20800ccb6721b6b5415c","first_computed_at":"2026-07-05T01:52:50.622949Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:52:50.622949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UbgqRxUMmXCZOQPuRKVoyg3UcqUq/IIvyM82oGlZP1NEgKPVlWtPj1X72AuJGvd83M9yqpDe4ICGuGE/bpPABQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:52:50.623345Z","signed_message":"canonical_sha256_bytes"},"source_id":"2011.09637","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c3afe949e07eec89764f55f3e5dce4ecfddf99f236890a80be4d298f6de754f","sha256:627e3e60c60b468f2e81db8cafdf86c6f10fcfdc8c58c2e6b8a17362d380e752"],"state_sha256":"1ba21e89b4bc4f8e45e32b9e567ec0b1e988f2434b5e495bd73590a4e85b1831"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3/QBxrZk6ulIxSUgK+bbDouRL2ZgRyUIH7CHX/1DCt0/7nL63VOqI+VH2orgyonif8nhS9unjVpAQqFhaAdgAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T22:05:50.618563Z","bundle_sha256":"29c9003360c5e183e829c66f379f69d87f4c1813dbd807206b43fa7284fef5cf"}}