{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:O7EWIFIMQKSTDKZV66FJY5CCZR","short_pith_number":"pith:O7EWIFIM","canonical_record":{"source":{"id":"1511.00406","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-11-02T08:10:36Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"5ec9840e322e5717060f0458b2155ae625a9e62ef66d3db3af93c8ea9badefce","abstract_canon_sha256":"2f3598a0ebfa37f9ee5df84d3e73f074d82a22758e03b18f4088818f4df79793"},"schema_version":"1.0"},"canonical_sha256":"77c964150c82a531ab35f78a9c7442cc63f185abbe07bc951ec472405907dc4f","source":{"kind":"arxiv","id":"1511.00406","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.00406","created_at":"2026-05-18T00:02:13Z"},{"alias_kind":"arxiv_version","alias_value":"1511.00406v3","created_at":"2026-05-18T00:02:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.00406","created_at":"2026-05-18T00:02:13Z"},{"alias_kind":"pith_short_12","alias_value":"O7EWIFIMQKST","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"O7EWIFIMQKSTDKZV","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"O7EWIFIM","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:O7EWIFIMQKSTDKZV66FJY5CCZR","target":"record","payload":{"canonical_record":{"source":{"id":"1511.00406","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-11-02T08:10:36Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"5ec9840e322e5717060f0458b2155ae625a9e62ef66d3db3af93c8ea9badefce","abstract_canon_sha256":"2f3598a0ebfa37f9ee5df84d3e73f074d82a22758e03b18f4088818f4df79793"},"schema_version":"1.0"},"canonical_sha256":"77c964150c82a531ab35f78a9c7442cc63f185abbe07bc951ec472405907dc4f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:13.898064Z","signature_b64":"xzNNdYrQ4QK5JLErR2J8cq3AbDn/7KFDjFQ6CXkCZpP1sS/OVh5utUNPn3LcePpGhisii929ytHmmlvl3J+gDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77c964150c82a531ab35f78a9c7442cc63f185abbe07bc951ec472405907dc4f","last_reissued_at":"2026-05-18T00:02:13.897573Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:13.897573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.00406","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":"2026-05-18T00:02:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YA3pt8IIiQ1MI88ZQDv7D54tB+HpRZFfxCz4wONwLpT8iKarOWZeEGBFSekADMRZNGRnUdmYkwnjetknTDD+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:59:37.325945Z"},"content_sha256":"f1bbbf742394d9d60d9225c5b88472747dc6a3df9c09c834e52e6b482e557ebf","schema_version":"1.0","event_id":"sha256:f1bbbf742394d9d60d9225c5b88472747dc6a3df9c09c834e52e6b482e557ebf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:O7EWIFIMQKSTDKZV66FJY5CCZR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Contractions and deformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Michael Wemyss, Will Donovan","submitted_at":"2015-11-02T08:10:36Z","abstract_excerpt":"Suppose that f is a projective birational morphism with at most one-dimensional fibres between d-dimensional varieties X and Y, satisfying ${\\bf R}f_* \\mathcal{O}_X = \\mathcal{O}_Y$. Consider the locus L in Y over which f is not an isomorphism. Taking the scheme-theoretic fibre C over any closed point of L, we construct algebras $A_{fib}$ and $A_{con}$ which prorepresent the functors of commutative deformations of C, and noncommutative deformations of the reduced fibre, respectively. Our main theorem is that the algebras $A_{con}$ recover L, and in general the commutative deformations of neith"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00406","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":"2026-05-18T00:02:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/nvhGKnb+szfvpDwZ5Hw894plOc4TpJXBOOJS2o8EMMwrpMaY+oyRv/fc6SGJYn3iZgIL9N/RPnzS/oIbrusDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:59:37.326300Z"},"content_sha256":"e7f9e4b79455b5149b2391edba197b26b0bc632ddd20601849d2339bb21c6171","schema_version":"1.0","event_id":"sha256:e7f9e4b79455b5149b2391edba197b26b0bc632ddd20601849d2339bb21c6171"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O7EWIFIMQKSTDKZV66FJY5CCZR/bundle.json","state_url":"https://pith.science/pith/O7EWIFIMQKSTDKZV66FJY5CCZR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O7EWIFIMQKSTDKZV66FJY5CCZR/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":"2026-06-02T14:59:37Z","links":{"resolver":"https://pith.science/pith/O7EWIFIMQKSTDKZV66FJY5CCZR","bundle":"https://pith.science/pith/O7EWIFIMQKSTDKZV66FJY5CCZR/bundle.json","state":"https://pith.science/pith/O7EWIFIMQKSTDKZV66FJY5CCZR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O7EWIFIMQKSTDKZV66FJY5CCZR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:O7EWIFIMQKSTDKZV66FJY5CCZR","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":"2f3598a0ebfa37f9ee5df84d3e73f074d82a22758e03b18f4088818f4df79793","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-11-02T08:10:36Z","title_canon_sha256":"5ec9840e322e5717060f0458b2155ae625a9e62ef66d3db3af93c8ea9badefce"},"schema_version":"1.0","source":{"id":"1511.00406","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.00406","created_at":"2026-05-18T00:02:13Z"},{"alias_kind":"arxiv_version","alias_value":"1511.00406v3","created_at":"2026-05-18T00:02:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.00406","created_at":"2026-05-18T00:02:13Z"},{"alias_kind":"pith_short_12","alias_value":"O7EWIFIMQKST","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"O7EWIFIMQKSTDKZV","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"O7EWIFIM","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:e7f9e4b79455b5149b2391edba197b26b0bc632ddd20601849d2339bb21c6171","target":"graph","created_at":"2026-05-18T00:02:13Z","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":"Suppose that f is a projective birational morphism with at most one-dimensional fibres between d-dimensional varieties X and Y, satisfying ${\\bf R}f_* \\mathcal{O}_X = \\mathcal{O}_Y$. Consider the locus L in Y over which f is not an isomorphism. Taking the scheme-theoretic fibre C over any closed point of L, we construct algebras $A_{fib}$ and $A_{con}$ which prorepresent the functors of commutative deformations of C, and noncommutative deformations of the reduced fibre, respectively. Our main theorem is that the algebras $A_{con}$ recover L, and in general the commutative deformations of neith","authors_text":"Michael Wemyss, Will Donovan","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-11-02T08:10:36Z","title":"Contractions and deformations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00406","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:f1bbbf742394d9d60d9225c5b88472747dc6a3df9c09c834e52e6b482e557ebf","target":"record","created_at":"2026-05-18T00:02:13Z","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":"2f3598a0ebfa37f9ee5df84d3e73f074d82a22758e03b18f4088818f4df79793","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-11-02T08:10:36Z","title_canon_sha256":"5ec9840e322e5717060f0458b2155ae625a9e62ef66d3db3af93c8ea9badefce"},"schema_version":"1.0","source":{"id":"1511.00406","kind":"arxiv","version":3}},"canonical_sha256":"77c964150c82a531ab35f78a9c7442cc63f185abbe07bc951ec472405907dc4f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77c964150c82a531ab35f78a9c7442cc63f185abbe07bc951ec472405907dc4f","first_computed_at":"2026-05-18T00:02:13.897573Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:13.897573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xzNNdYrQ4QK5JLErR2J8cq3AbDn/7KFDjFQ6CXkCZpP1sS/OVh5utUNPn3LcePpGhisii929ytHmmlvl3J+gDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:13.898064Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.00406","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1bbbf742394d9d60d9225c5b88472747dc6a3df9c09c834e52e6b482e557ebf","sha256:e7f9e4b79455b5149b2391edba197b26b0bc632ddd20601849d2339bb21c6171"],"state_sha256":"8ecd5c248f140df1b7747ade82b4a85f33f68450b89d549bc0295b1542ba1bd2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cA6CTfpthJ+fr6HD47RNKTQr53/SPORJcGh0UuT+g+QIyPKCsj8ziUk9C0b+45C8kVGpRnhvBNR6MDIUsAWrAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T14:59:37.328165Z","bundle_sha256":"70e1e37af98aaf33bbbf5bbfd827330e94237d1578798a410bbd51832b3c90b2"}}