{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:FGWULXI6FR25QWCBXADNX5CW7O","short_pith_number":"pith:FGWULXI6","canonical_record":{"source":{"id":"1612.06119","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-12-19T10:56:12Z","cross_cats_sorted":[],"title_canon_sha256":"aa67246051bcc13c2084d4bad031ba9b8610bb866c52b1c6bb9a36dca0a15f7c","abstract_canon_sha256":"e3c0f02b376bb0109d5ad8ebdde42b323ed3996f8b58d2c3937eaea29c828d38"},"schema_version":"1.0"},"canonical_sha256":"29ad45dd1e2c75d85841b806dbf456fb99144664dca409bd6bcad320bd011734","source":{"kind":"arxiv","id":"1612.06119","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.06119","created_at":"2026-05-18T00:54:45Z"},{"alias_kind":"arxiv_version","alias_value":"1612.06119v1","created_at":"2026-05-18T00:54:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.06119","created_at":"2026-05-18T00:54:45Z"},{"alias_kind":"pith_short_12","alias_value":"FGWULXI6FR25","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FGWULXI6FR25QWCB","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FGWULXI6","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:FGWULXI6FR25QWCBXADNX5CW7O","target":"record","payload":{"canonical_record":{"source":{"id":"1612.06119","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-12-19T10:56:12Z","cross_cats_sorted":[],"title_canon_sha256":"aa67246051bcc13c2084d4bad031ba9b8610bb866c52b1c6bb9a36dca0a15f7c","abstract_canon_sha256":"e3c0f02b376bb0109d5ad8ebdde42b323ed3996f8b58d2c3937eaea29c828d38"},"schema_version":"1.0"},"canonical_sha256":"29ad45dd1e2c75d85841b806dbf456fb99144664dca409bd6bcad320bd011734","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:45.891172Z","signature_b64":"gFK8zIJcO8bE+zLR05dJZn3rdfRDIYMGOmkjWQRCFG1iB950b4S3sxZURxJ97yTi6Pc6jDRx48WiuekxDHItDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29ad45dd1e2c75d85841b806dbf456fb99144664dca409bd6bcad320bd011734","last_reissued_at":"2026-05-18T00:54:45.890532Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:45.890532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.06119","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":"2026-05-18T00:54:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZXOjktYv5VE/p6MCDcspmU3Urfr2TUAWnWYjPDSPGHO1wBvbA6xCbgJaN7Afg2XK7Jro1OdHmKWppy1LxcPzAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T13:38:16.409507Z"},"content_sha256":"a199e156e538dbe51b7142d16f6c96731ccba07c63634239c3ea14fcfcd732f5","schema_version":"1.0","event_id":"sha256:a199e156e538dbe51b7142d16f6c96731ccba07c63634239c3ea14fcfcd732f5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:FGWULXI6FR25QWCBXADNX5CW7O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Remark on a theorem in Mumford's Red Book of Varieties and Schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Guanglian Zhang","submitted_at":"2016-12-19T10:56:12Z","abstract_excerpt":"In this paper, we firstly point out, by a counter example, that Proposition 6.4 of Section 6 in Bump's book (Algebraic Geometry) is error, and then give a correct statement with proof. We finally point out a gap in the proof of Theorem 3, in Chapter I Section 8, of Mumford's red book, and indicate a way to complete it."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06119","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":"2026-05-18T00:54:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/nE5Zx0rjqT01JqYAVDnpI7vcdQqO+TnNdBiyqf1ZSfTExaqIxO94uht8RnWXl2eRzxUZ51Jk06R7IjREtWTCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T13:38:16.410111Z"},"content_sha256":"37a98f1586493c8853acb37a0d830f392782e9df1dd5ce146e073f035de1c74a","schema_version":"1.0","event_id":"sha256:37a98f1586493c8853acb37a0d830f392782e9df1dd5ce146e073f035de1c74a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FGWULXI6FR25QWCBXADNX5CW7O/bundle.json","state_url":"https://pith.science/pith/FGWULXI6FR25QWCBXADNX5CW7O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FGWULXI6FR25QWCBXADNX5CW7O/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":"2026-06-04T13:38:16Z","links":{"resolver":"https://pith.science/pith/FGWULXI6FR25QWCBXADNX5CW7O","bundle":"https://pith.science/pith/FGWULXI6FR25QWCBXADNX5CW7O/bundle.json","state":"https://pith.science/pith/FGWULXI6FR25QWCBXADNX5CW7O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FGWULXI6FR25QWCBXADNX5CW7O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FGWULXI6FR25QWCBXADNX5CW7O","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":"e3c0f02b376bb0109d5ad8ebdde42b323ed3996f8b58d2c3937eaea29c828d38","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-12-19T10:56:12Z","title_canon_sha256":"aa67246051bcc13c2084d4bad031ba9b8610bb866c52b1c6bb9a36dca0a15f7c"},"schema_version":"1.0","source":{"id":"1612.06119","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.06119","created_at":"2026-05-18T00:54:45Z"},{"alias_kind":"arxiv_version","alias_value":"1612.06119v1","created_at":"2026-05-18T00:54:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.06119","created_at":"2026-05-18T00:54:45Z"},{"alias_kind":"pith_short_12","alias_value":"FGWULXI6FR25","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FGWULXI6FR25QWCB","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FGWULXI6","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:37a98f1586493c8853acb37a0d830f392782e9df1dd5ce146e073f035de1c74a","target":"graph","created_at":"2026-05-18T00:54:45Z","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":"In this paper, we firstly point out, by a counter example, that Proposition 6.4 of Section 6 in Bump's book (Algebraic Geometry) is error, and then give a correct statement with proof. We finally point out a gap in the proof of Theorem 3, in Chapter I Section 8, of Mumford's red book, and indicate a way to complete it.","authors_text":"Guanglian Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-12-19T10:56:12Z","title":"Remark on a theorem in Mumford's Red Book of Varieties and Schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06119","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:a199e156e538dbe51b7142d16f6c96731ccba07c63634239c3ea14fcfcd732f5","target":"record","created_at":"2026-05-18T00:54:45Z","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":"e3c0f02b376bb0109d5ad8ebdde42b323ed3996f8b58d2c3937eaea29c828d38","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-12-19T10:56:12Z","title_canon_sha256":"aa67246051bcc13c2084d4bad031ba9b8610bb866c52b1c6bb9a36dca0a15f7c"},"schema_version":"1.0","source":{"id":"1612.06119","kind":"arxiv","version":1}},"canonical_sha256":"29ad45dd1e2c75d85841b806dbf456fb99144664dca409bd6bcad320bd011734","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29ad45dd1e2c75d85841b806dbf456fb99144664dca409bd6bcad320bd011734","first_computed_at":"2026-05-18T00:54:45.890532Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:45.890532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gFK8zIJcO8bE+zLR05dJZn3rdfRDIYMGOmkjWQRCFG1iB950b4S3sxZURxJ97yTi6Pc6jDRx48WiuekxDHItDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:45.891172Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.06119","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a199e156e538dbe51b7142d16f6c96731ccba07c63634239c3ea14fcfcd732f5","sha256:37a98f1586493c8853acb37a0d830f392782e9df1dd5ce146e073f035de1c74a"],"state_sha256":"dd9e4abf7cb6fdca23770eb30d04273780f76885f4d410a4494427a9f18a0cf9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0Q4cggXHproLT+ch3ux2eMbGJMJgGNvvr3kVMH1LcibUTwO9Da3vaFmAKMEKAx/S+snHDbLRZ2z2hLwHvvpvCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T13:38:16.413544Z","bundle_sha256":"f0d6bb657e8918556722c231746883996337880b765e08d40938e8174a2999ea"}}