{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:7HUF7WKBA64ERUTYCNEYP6NYEI","short_pith_number":"pith:7HUF7WKB","canonical_record":{"source":{"id":"0806.1243","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-06-06T22:21:02Z","cross_cats_sorted":[],"title_canon_sha256":"7563c1c10ed129748f2d6c77cfee722eb353855a3a143e3cf8f88239edee7bbe","abstract_canon_sha256":"7a33edbda8bdd382e304fb6823b5d49efce18d328c53e4e0ee163dd6c6fa459b"},"schema_version":"1.0"},"canonical_sha256":"f9e85fd94107b848d278134987f9b8220f67c199090babccdc6ee59fbfc50a0a","source":{"kind":"arxiv","id":"0806.1243","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0806.1243","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"arxiv_version","alias_value":"0806.1243v3","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.1243","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"pith_short_12","alias_value":"7HUF7WKBA64E","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"7HUF7WKBA64ERUTY","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"7HUF7WKB","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:7HUF7WKBA64ERUTYCNEYP6NYEI","target":"record","payload":{"canonical_record":{"source":{"id":"0806.1243","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-06-06T22:21:02Z","cross_cats_sorted":[],"title_canon_sha256":"7563c1c10ed129748f2d6c77cfee722eb353855a3a143e3cf8f88239edee7bbe","abstract_canon_sha256":"7a33edbda8bdd382e304fb6823b5d49efce18d328c53e4e0ee163dd6c6fa459b"},"schema_version":"1.0"},"canonical_sha256":"f9e85fd94107b848d278134987f9b8220f67c199090babccdc6ee59fbfc50a0a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:26.434999Z","signature_b64":"M0qD20uiPqcVtX26rqWpRb4Ldimv9n0g97Lmmrk67rjBCc8aLMSg+30wwjm/TdCLlJ2eFXc7jbjSCaraioxhDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9e85fd94107b848d278134987f9b8220f67c199090babccdc6ee59fbfc50a0a","last_reissued_at":"2026-05-18T03:40:26.434464Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:26.434464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0806.1243","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:40:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tI7mJaf2V3KOBKh5XjrwR94sPnT/HApEIInIT8WUcU6JqbAjwumajpoO3FNjHF4YteO6EGsmSYpvEbvXAGEEAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T09:32:08.199576Z"},"content_sha256":"baf1f36c0db11aa3c2f4f68bf5a8a9421fd186de746b534e29a2425f039cf805","schema_version":"1.0","event_id":"sha256:baf1f36c0db11aa3c2f4f68bf5a8a9421fd186de746b534e29a2425f039cf805"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:7HUF7WKBA64ERUTYCNEYP6NYEI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Noether-Lefschetz theorem with base locus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"John Brevik, Scott Nollet","submitted_at":"2008-06-06T22:21:02Z","abstract_excerpt":"We compute the class groups of very general normal surfaces in complex projective three-space containing an arbitrary base locus $Z$, thereby extending the classic Noether-Lefschetz theorem (the case when $Z$ is empty). Our method is an adaptation of Griffiths and Harris' degeneration proof, simplified by a cohomology and base change argument. We give applications to computing Picard groups, which generalize several known results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.1243","kind":"arxiv","version":3},"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":"2026-05-18T03:40:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DHfjlpTzVGUk5oEkW3TfK4wSoEHq9pRLqU8icr/45/FvSpANQzBC8bOuHXB7jY5/e77/uWnQF/a4CgHAbzBtAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T09:32:08.199922Z"},"content_sha256":"4a76f0f026b191ed0bc49dad509fd2ffb1439b80a1d5392d4f0c9831684cb530","schema_version":"1.0","event_id":"sha256:4a76f0f026b191ed0bc49dad509fd2ffb1439b80a1d5392d4f0c9831684cb530"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7HUF7WKBA64ERUTYCNEYP6NYEI/bundle.json","state_url":"https://pith.science/pith/7HUF7WKBA64ERUTYCNEYP6NYEI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7HUF7WKBA64ERUTYCNEYP6NYEI/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":"2026-06-25T09:32:08Z","links":{"resolver":"https://pith.science/pith/7HUF7WKBA64ERUTYCNEYP6NYEI","bundle":"https://pith.science/pith/7HUF7WKBA64ERUTYCNEYP6NYEI/bundle.json","state":"https://pith.science/pith/7HUF7WKBA64ERUTYCNEYP6NYEI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7HUF7WKBA64ERUTYCNEYP6NYEI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:7HUF7WKBA64ERUTYCNEYP6NYEI","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":"7a33edbda8bdd382e304fb6823b5d49efce18d328c53e4e0ee163dd6c6fa459b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-06-06T22:21:02Z","title_canon_sha256":"7563c1c10ed129748f2d6c77cfee722eb353855a3a143e3cf8f88239edee7bbe"},"schema_version":"1.0","source":{"id":"0806.1243","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0806.1243","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"arxiv_version","alias_value":"0806.1243v3","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.1243","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"pith_short_12","alias_value":"7HUF7WKBA64E","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"7HUF7WKBA64ERUTY","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"7HUF7WKB","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:4a76f0f026b191ed0bc49dad509fd2ffb1439b80a1d5392d4f0c9831684cb530","target":"graph","created_at":"2026-05-18T03:40:26Z","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":"We compute the class groups of very general normal surfaces in complex projective three-space containing an arbitrary base locus $Z$, thereby extending the classic Noether-Lefschetz theorem (the case when $Z$ is empty). Our method is an adaptation of Griffiths and Harris' degeneration proof, simplified by a cohomology and base change argument. We give applications to computing Picard groups, which generalize several known results.","authors_text":"John Brevik, Scott Nollet","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-06-06T22:21:02Z","title":"Noether-Lefschetz theorem with base locus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.1243","kind":"arxiv","version":3},"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:baf1f36c0db11aa3c2f4f68bf5a8a9421fd186de746b534e29a2425f039cf805","target":"record","created_at":"2026-05-18T03:40:26Z","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":"7a33edbda8bdd382e304fb6823b5d49efce18d328c53e4e0ee163dd6c6fa459b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-06-06T22:21:02Z","title_canon_sha256":"7563c1c10ed129748f2d6c77cfee722eb353855a3a143e3cf8f88239edee7bbe"},"schema_version":"1.0","source":{"id":"0806.1243","kind":"arxiv","version":3}},"canonical_sha256":"f9e85fd94107b848d278134987f9b8220f67c199090babccdc6ee59fbfc50a0a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9e85fd94107b848d278134987f9b8220f67c199090babccdc6ee59fbfc50a0a","first_computed_at":"2026-05-18T03:40:26.434464Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:26.434464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M0qD20uiPqcVtX26rqWpRb4Ldimv9n0g97Lmmrk67rjBCc8aLMSg+30wwjm/TdCLlJ2eFXc7jbjSCaraioxhDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:26.434999Z","signed_message":"canonical_sha256_bytes"},"source_id":"0806.1243","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:baf1f36c0db11aa3c2f4f68bf5a8a9421fd186de746b534e29a2425f039cf805","sha256:4a76f0f026b191ed0bc49dad509fd2ffb1439b80a1d5392d4f0c9831684cb530"],"state_sha256":"44723db36a69233303ad0896571962946bb7b19407136d8c68105ded80830581"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Okmizvs+Hs7gzDG0YPV0TYWQs3Lu+yFFqEpg+5+SCTXiNdqV3QZophiQ01WpLxw0nydTEQJpygp7tb5NypC0Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T09:32:08.201899Z","bundle_sha256":"302677dd9d6521b6690ef13dbcace53353077cf8f8cdaf28a0c250e29c7a8040"}}