{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:XCLQGMUHP7LBGUEZQ654OUQEYA","short_pith_number":"pith:XCLQGMUH","canonical_record":{"source":{"id":"1001.3662","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-01-20T20:16:28Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"1ac0007c4b084fef0b3610746aacbbc077dcedbb0bc07a427712f00dc189fe17","abstract_canon_sha256":"a98f52a8ed6277bf2dccadd84e06f8282ad74bd6c501149607c951e39f696dfd"},"schema_version":"1.0"},"canonical_sha256":"b8970332877fd613509987bbc75204c03f4fdf9cbd0380d91457741864286bc3","source":{"kind":"arxiv","id":"1001.3662","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.3662","created_at":"2026-05-18T04:16:42Z"},{"alias_kind":"arxiv_version","alias_value":"1001.3662v4","created_at":"2026-05-18T04:16:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.3662","created_at":"2026-05-18T04:16:42Z"},{"alias_kind":"pith_short_12","alias_value":"XCLQGMUHP7LB","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XCLQGMUHP7LBGUEZ","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XCLQGMUH","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:XCLQGMUHP7LBGUEZQ654OUQEYA","target":"record","payload":{"canonical_record":{"source":{"id":"1001.3662","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-01-20T20:16:28Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"1ac0007c4b084fef0b3610746aacbbc077dcedbb0bc07a427712f00dc189fe17","abstract_canon_sha256":"a98f52a8ed6277bf2dccadd84e06f8282ad74bd6c501149607c951e39f696dfd"},"schema_version":"1.0"},"canonical_sha256":"b8970332877fd613509987bbc75204c03f4fdf9cbd0380d91457741864286bc3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:42.364120Z","signature_b64":"QG5CEKda0iRiTw7VLjfdvtTiopvoZUXpUzUBAC5lCGMENmmvCG0RPEGPFXQ0vF5RuvsF594CF5N3JBtCY416CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b8970332877fd613509987bbc75204c03f4fdf9cbd0380d91457741864286bc3","last_reissued_at":"2026-05-18T04:16:42.363444Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:42.363444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1001.3662","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:16:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XWbc1rwcEGfta5/RsHra/mQy+dqJS2gybaL3tgFtMXQi1aEa/HQgvVbfq30wnYBcqTSoPZqgNOVRRPmKzhUMBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T19:48:01.493567Z"},"content_sha256":"7a6f6acc68603b9623e59babe0c41a1b6add982ba3db6e5275bd5172fdfd72c6","schema_version":"1.0","event_id":"sha256:7a6f6acc68603b9623e59babe0c41a1b6add982ba3db6e5275bd5172fdfd72c6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:XCLQGMUHP7LBGUEZQ654OUQEYA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lyubeznik numbers of projective schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Wenliang Zhang","submitted_at":"2010-01-20T20:16:28Z","abstract_excerpt":"Let $X$ be a projective scheme over a field $k$ and let $A$ be the local ring at the vertex of the affine cone of $X$ under some embedding $X\\hookrightarrow\\mathbb{P}^n_k$. We prove that, when $\\ch(k)>0$, the Lyubeznik numbers $\\lambda_{i,j}(A)$ are intrinsic numerical invariants of $X$, i.e., $\\lambda_{i,j}(A)$ depend only on $X$, but not on the embedding."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.3662","kind":"arxiv","version":4},"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":"2026-05-18T04:16:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iifrC4jK+I7oiY5mUK4zjgbRUq5qhRa/hn32A81qC7f3yFxkwCpewnwX75kWjsqniKL7dEx89/gb2jm3JoUnCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T19:48:01.493914Z"},"content_sha256":"ab9015f9d85ea79bcecff9143208ec7a1afaf4684397f19557e18181375b39f2","schema_version":"1.0","event_id":"sha256:ab9015f9d85ea79bcecff9143208ec7a1afaf4684397f19557e18181375b39f2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XCLQGMUHP7LBGUEZQ654OUQEYA/bundle.json","state_url":"https://pith.science/pith/XCLQGMUHP7LBGUEZQ654OUQEYA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XCLQGMUHP7LBGUEZQ654OUQEYA/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":"2026-06-03T19:48:01Z","links":{"resolver":"https://pith.science/pith/XCLQGMUHP7LBGUEZQ654OUQEYA","bundle":"https://pith.science/pith/XCLQGMUHP7LBGUEZQ654OUQEYA/bundle.json","state":"https://pith.science/pith/XCLQGMUHP7LBGUEZQ654OUQEYA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XCLQGMUHP7LBGUEZQ654OUQEYA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:XCLQGMUHP7LBGUEZQ654OUQEYA","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":"a98f52a8ed6277bf2dccadd84e06f8282ad74bd6c501149607c951e39f696dfd","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-01-20T20:16:28Z","title_canon_sha256":"1ac0007c4b084fef0b3610746aacbbc077dcedbb0bc07a427712f00dc189fe17"},"schema_version":"1.0","source":{"id":"1001.3662","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.3662","created_at":"2026-05-18T04:16:42Z"},{"alias_kind":"arxiv_version","alias_value":"1001.3662v4","created_at":"2026-05-18T04:16:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.3662","created_at":"2026-05-18T04:16:42Z"},{"alias_kind":"pith_short_12","alias_value":"XCLQGMUHP7LB","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XCLQGMUHP7LBGUEZ","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XCLQGMUH","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:ab9015f9d85ea79bcecff9143208ec7a1afaf4684397f19557e18181375b39f2","target":"graph","created_at":"2026-05-18T04:16:42Z","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":"Let $X$ be a projective scheme over a field $k$ and let $A$ be the local ring at the vertex of the affine cone of $X$ under some embedding $X\\hookrightarrow\\mathbb{P}^n_k$. We prove that, when $\\ch(k)>0$, the Lyubeznik numbers $\\lambda_{i,j}(A)$ are intrinsic numerical invariants of $X$, i.e., $\\lambda_{i,j}(A)$ depend only on $X$, but not on the embedding.","authors_text":"Wenliang Zhang","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-01-20T20:16:28Z","title":"Lyubeznik numbers of projective schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.3662","kind":"arxiv","version":4},"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":"sha256:7a6f6acc68603b9623e59babe0c41a1b6add982ba3db6e5275bd5172fdfd72c6","target":"record","created_at":"2026-05-18T04:16:42Z","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":"a98f52a8ed6277bf2dccadd84e06f8282ad74bd6c501149607c951e39f696dfd","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-01-20T20:16:28Z","title_canon_sha256":"1ac0007c4b084fef0b3610746aacbbc077dcedbb0bc07a427712f00dc189fe17"},"schema_version":"1.0","source":{"id":"1001.3662","kind":"arxiv","version":4}},"canonical_sha256":"b8970332877fd613509987bbc75204c03f4fdf9cbd0380d91457741864286bc3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8970332877fd613509987bbc75204c03f4fdf9cbd0380d91457741864286bc3","first_computed_at":"2026-05-18T04:16:42.363444Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:42.363444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QG5CEKda0iRiTw7VLjfdvtTiopvoZUXpUzUBAC5lCGMENmmvCG0RPEGPFXQ0vF5RuvsF594CF5N3JBtCY416CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:42.364120Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.3662","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a6f6acc68603b9623e59babe0c41a1b6add982ba3db6e5275bd5172fdfd72c6","sha256:ab9015f9d85ea79bcecff9143208ec7a1afaf4684397f19557e18181375b39f2"],"state_sha256":"9314ada7dd39cf7efbb29cad23517f64a5e2c0e2f882a56d392516f488cc4978"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FnLCBgKdtegv9QOxIZ5lw5MnI9UB5U2TdVDxO/0iKiOjzrs4UIJBXtQmys0Aea3LHZXaDoJxHl1WWwZk6WxjDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T19:48:01.496361Z","bundle_sha256":"97050efab3ea9cea502d79ffc4c274830a057cece218669723a50471601c0253"}}