{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:WUKP7DSABSZVCD37IKPD3YUQHR","short_pith_number":"pith:WUKP7DSA","canonical_record":{"source":{"id":"1812.10905","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-12-28T06:28:30Z","cross_cats_sorted":[],"title_canon_sha256":"dc4e446a1af35680e16c269943f0ea606edc86e61505ca858931a05390af980e","abstract_canon_sha256":"7cf0e79f3ff7f6eb4a6987ceb9ceddee9610309923734864fa5d287d7b666f78"},"schema_version":"1.0"},"canonical_sha256":"b514ff8e400cb3510f7f429e3de2903c5e8177ff915b7907ff78556d34f9ea6d","source":{"kind":"arxiv","id":"1812.10905","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.10905","created_at":"2026-05-17T23:57:16Z"},{"alias_kind":"arxiv_version","alias_value":"1812.10905v1","created_at":"2026-05-17T23:57:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.10905","created_at":"2026-05-17T23:57:16Z"},{"alias_kind":"pith_short_12","alias_value":"WUKP7DSABSZV","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"WUKP7DSABSZVCD37","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"WUKP7DSA","created_at":"2026-05-18T12:33:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:WUKP7DSABSZVCD37IKPD3YUQHR","target":"record","payload":{"canonical_record":{"source":{"id":"1812.10905","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-12-28T06:28:30Z","cross_cats_sorted":[],"title_canon_sha256":"dc4e446a1af35680e16c269943f0ea606edc86e61505ca858931a05390af980e","abstract_canon_sha256":"7cf0e79f3ff7f6eb4a6987ceb9ceddee9610309923734864fa5d287d7b666f78"},"schema_version":"1.0"},"canonical_sha256":"b514ff8e400cb3510f7f429e3de2903c5e8177ff915b7907ff78556d34f9ea6d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:16.800944Z","signature_b64":"JmwmXQcchrHTElA972l7D/KP3LS+dZIi5scL678WQHAexBTIww1EUhvdxifzjjoVVWt66P67Dj6hzjr7knNSBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b514ff8e400cb3510f7f429e3de2903c5e8177ff915b7907ff78556d34f9ea6d","last_reissued_at":"2026-05-17T23:57:16.800548Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:16.800548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.10905","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":"2026-05-17T23:57:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kwx6uYMMLCtyoXqUwPZtKpGAtvTKQRqzyrJGzp9dHDCcb+himlblY/fG/MrOANyBctA2I+PeridknfVCVUBFCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:14:01.670153Z"},"content_sha256":"144a6659a85527d5e595521d77947f41456e6d1249d23a93af136806a5bf0a45","schema_version":"1.0","event_id":"sha256:144a6659a85527d5e595521d77947f41456e6d1249d23a93af136806a5bf0a45"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:WUKP7DSABSZVCD37IKPD3YUQHR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Normal bundles on the exceptional sets of simple small resolutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Rong Du, Xinyi Fang","submitted_at":"2018-12-28T06:28:30Z","abstract_excerpt":"We study the normal bundles of the exceptional sets of isolated simple small singularities in the higher dimension when the Picard group of the exceptional set is $\\mathbb{Z}$ and the normal bundle of it has some good filtration. In particular, for the exceptional set is a projective space with the split normal bundle, we generalized Nakayama and Ando's results to higher dimension. Moreover, we also generalize Laufer's results of rationality and embedding dimension to higher dimension."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.10905","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":"2026-05-17T23:57:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dTubW97qlJTjnweyCpJhp/3y4K4kd/kAzjwhZZYyPxsTmvuIY89+SSLnqjo3YxiFxKSVI1sHnxELKmwm5MnCBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:14:01.670811Z"},"content_sha256":"f1aa820d6820873ecdb8070a00a7e7943d759982d07342765ab91648fbabd09f","schema_version":"1.0","event_id":"sha256:f1aa820d6820873ecdb8070a00a7e7943d759982d07342765ab91648fbabd09f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WUKP7DSABSZVCD37IKPD3YUQHR/bundle.json","state_url":"https://pith.science/pith/WUKP7DSABSZVCD37IKPD3YUQHR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WUKP7DSABSZVCD37IKPD3YUQHR/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":"2026-05-27T20:14:01Z","links":{"resolver":"https://pith.science/pith/WUKP7DSABSZVCD37IKPD3YUQHR","bundle":"https://pith.science/pith/WUKP7DSABSZVCD37IKPD3YUQHR/bundle.json","state":"https://pith.science/pith/WUKP7DSABSZVCD37IKPD3YUQHR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WUKP7DSABSZVCD37IKPD3YUQHR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WUKP7DSABSZVCD37IKPD3YUQHR","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":"7cf0e79f3ff7f6eb4a6987ceb9ceddee9610309923734864fa5d287d7b666f78","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-12-28T06:28:30Z","title_canon_sha256":"dc4e446a1af35680e16c269943f0ea606edc86e61505ca858931a05390af980e"},"schema_version":"1.0","source":{"id":"1812.10905","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.10905","created_at":"2026-05-17T23:57:16Z"},{"alias_kind":"arxiv_version","alias_value":"1812.10905v1","created_at":"2026-05-17T23:57:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.10905","created_at":"2026-05-17T23:57:16Z"},{"alias_kind":"pith_short_12","alias_value":"WUKP7DSABSZV","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"WUKP7DSABSZVCD37","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"WUKP7DSA","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:f1aa820d6820873ecdb8070a00a7e7943d759982d07342765ab91648fbabd09f","target":"graph","created_at":"2026-05-17T23:57:16Z","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 study the normal bundles of the exceptional sets of isolated simple small singularities in the higher dimension when the Picard group of the exceptional set is $\\mathbb{Z}$ and the normal bundle of it has some good filtration. In particular, for the exceptional set is a projective space with the split normal bundle, we generalized Nakayama and Ando's results to higher dimension. Moreover, we also generalize Laufer's results of rationality and embedding dimension to higher dimension.","authors_text":"Rong Du, Xinyi Fang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-12-28T06:28:30Z","title":"Normal bundles on the exceptional sets of simple small resolutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.10905","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":"sha256:144a6659a85527d5e595521d77947f41456e6d1249d23a93af136806a5bf0a45","target":"record","created_at":"2026-05-17T23:57:16Z","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":"7cf0e79f3ff7f6eb4a6987ceb9ceddee9610309923734864fa5d287d7b666f78","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-12-28T06:28:30Z","title_canon_sha256":"dc4e446a1af35680e16c269943f0ea606edc86e61505ca858931a05390af980e"},"schema_version":"1.0","source":{"id":"1812.10905","kind":"arxiv","version":1}},"canonical_sha256":"b514ff8e400cb3510f7f429e3de2903c5e8177ff915b7907ff78556d34f9ea6d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b514ff8e400cb3510f7f429e3de2903c5e8177ff915b7907ff78556d34f9ea6d","first_computed_at":"2026-05-17T23:57:16.800548Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:16.800548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JmwmXQcchrHTElA972l7D/KP3LS+dZIi5scL678WQHAexBTIww1EUhvdxifzjjoVVWt66P67Dj6hzjr7knNSBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:16.800944Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.10905","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:144a6659a85527d5e595521d77947f41456e6d1249d23a93af136806a5bf0a45","sha256:f1aa820d6820873ecdb8070a00a7e7943d759982d07342765ab91648fbabd09f"],"state_sha256":"a0acf9b308e881439956dfe9848990db4f96782b68064d6183b007c93dcef7ab"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m442CmpkiDC5pED825tN/sQxWd9TNBWRkHnSkUNQZr0AxGTV7GLfpeTmshGXR80E3igC/5qq8wmJiai/FCO3BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T20:14:01.673825Z","bundle_sha256":"eef99b4db21d3a64b8cb81ae42461dd8207939f7f13dd848dd54721116282bcc"}}