{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:SSX3VIMOJ7P44HP24IJL3GUNGE","short_pith_number":"pith:SSX3VIMO","canonical_record":{"source":{"id":"1601.07671","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-28T07:19:26Z","cross_cats_sorted":[],"title_canon_sha256":"5999da24acd98d38ecf691e35594e6f1e4835cd85364284c54fc6c991051df8d","abstract_canon_sha256":"a6dd2032e849ab0273868ae56582e75b7037f68c662cd137a08b23b906faa837"},"schema_version":"1.0"},"canonical_sha256":"94afbaa18e4fdfce1dfae212bd9a8d313627403c56b4e1d8779a78db88576e90","source":{"kind":"arxiv","id":"1601.07671","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.07671","created_at":"2026-05-18T00:38:04Z"},{"alias_kind":"arxiv_version","alias_value":"1601.07671v2","created_at":"2026-05-18T00:38:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.07671","created_at":"2026-05-18T00:38:04Z"},{"alias_kind":"pith_short_12","alias_value":"SSX3VIMOJ7P4","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SSX3VIMOJ7P44HP2","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SSX3VIMO","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:SSX3VIMOJ7P44HP24IJL3GUNGE","target":"record","payload":{"canonical_record":{"source":{"id":"1601.07671","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-28T07:19:26Z","cross_cats_sorted":[],"title_canon_sha256":"5999da24acd98d38ecf691e35594e6f1e4835cd85364284c54fc6c991051df8d","abstract_canon_sha256":"a6dd2032e849ab0273868ae56582e75b7037f68c662cd137a08b23b906faa837"},"schema_version":"1.0"},"canonical_sha256":"94afbaa18e4fdfce1dfae212bd9a8d313627403c56b4e1d8779a78db88576e90","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:04.553744Z","signature_b64":"n4thHyWq2xz1hgP1wDSsFdlw43VShb+V8NkGDcAyNx+ZtXq0cjYwLCPxumhitu5BUyw7XS9rgd7V+atVl8uPCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94afbaa18e4fdfce1dfae212bd9a8d313627403c56b4e1d8779a78db88576e90","last_reissued_at":"2026-05-18T00:38:04.553086Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:04.553086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.07671","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:38:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+qcE2Oyr4jV/Q/SVHnHvTW2Qv08Wv1scOu2B87wiU8yCVYrAX6hmqYgln3cV+ZTehXBQiF+93+4s7PSntpHuBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T18:05:18.655501Z"},"content_sha256":"31246bfd208fd922a21ee094e4a5784c8bb6ffbfab824c65fdb9655fb8ab4542","schema_version":"1.0","event_id":"sha256:31246bfd208fd922a21ee094e4a5784c8bb6ffbfab824c65fdb9655fb8ab4542"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:SSX3VIMOJ7P44HP24IJL3GUNGE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Threefold extremal contractions of type (IIA), I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Shigefumi Mori, Yuri Prokhorov","submitted_at":"2016-01-28T07:19:26Z","abstract_excerpt":"Let $(X, C)$ be a germ of a threefold $X$ with terminal singularities along an irreducible reduced complete curve $C$ with a contraction $f: (X, C)\\to (Z, o)$ such that $C=f^{-1}(o)_{red}$ and $-K_X$ is ample. Assume that $(X, C)$ contains a point of type (IIA) and that a general member $H\\in |O_X|$ containing $C$ is normal. We classify such germs in terms of $H$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07671","kind":"arxiv","version":2},"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":"2026-05-18T00:38:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TaVDJs1RmHN7/sGAbL4dNc9MpJ6R+8v9wj29+igDEadGM5Olr8mRdypFOyEXPvQIKGChJQ27mgnemPRZJyWuCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T18:05:18.656170Z"},"content_sha256":"044b455df5af8e9e786381a881555b900e4111da5571c5be40a7c9605b8eb111","schema_version":"1.0","event_id":"sha256:044b455df5af8e9e786381a881555b900e4111da5571c5be40a7c9605b8eb111"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SSX3VIMOJ7P44HP24IJL3GUNGE/bundle.json","state_url":"https://pith.science/pith/SSX3VIMOJ7P44HP24IJL3GUNGE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SSX3VIMOJ7P44HP24IJL3GUNGE/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":"2026-05-24T18:05:18Z","links":{"resolver":"https://pith.science/pith/SSX3VIMOJ7P44HP24IJL3GUNGE","bundle":"https://pith.science/pith/SSX3VIMOJ7P44HP24IJL3GUNGE/bundle.json","state":"https://pith.science/pith/SSX3VIMOJ7P44HP24IJL3GUNGE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SSX3VIMOJ7P44HP24IJL3GUNGE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SSX3VIMOJ7P44HP24IJL3GUNGE","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":"a6dd2032e849ab0273868ae56582e75b7037f68c662cd137a08b23b906faa837","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-28T07:19:26Z","title_canon_sha256":"5999da24acd98d38ecf691e35594e6f1e4835cd85364284c54fc6c991051df8d"},"schema_version":"1.0","source":{"id":"1601.07671","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.07671","created_at":"2026-05-18T00:38:04Z"},{"alias_kind":"arxiv_version","alias_value":"1601.07671v2","created_at":"2026-05-18T00:38:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.07671","created_at":"2026-05-18T00:38:04Z"},{"alias_kind":"pith_short_12","alias_value":"SSX3VIMOJ7P4","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SSX3VIMOJ7P44HP2","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SSX3VIMO","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:044b455df5af8e9e786381a881555b900e4111da5571c5be40a7c9605b8eb111","target":"graph","created_at":"2026-05-18T00:38:04Z","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 $(X, C)$ be a germ of a threefold $X$ with terminal singularities along an irreducible reduced complete curve $C$ with a contraction $f: (X, C)\\to (Z, o)$ such that $C=f^{-1}(o)_{red}$ and $-K_X$ is ample. Assume that $(X, C)$ contains a point of type (IIA) and that a general member $H\\in |O_X|$ containing $C$ is normal. We classify such germs in terms of $H$.","authors_text":"Shigefumi Mori, Yuri Prokhorov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-28T07:19:26Z","title":"Threefold extremal contractions of type (IIA), I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07671","kind":"arxiv","version":2},"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":"sha256:31246bfd208fd922a21ee094e4a5784c8bb6ffbfab824c65fdb9655fb8ab4542","target":"record","created_at":"2026-05-18T00:38:04Z","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":"a6dd2032e849ab0273868ae56582e75b7037f68c662cd137a08b23b906faa837","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-28T07:19:26Z","title_canon_sha256":"5999da24acd98d38ecf691e35594e6f1e4835cd85364284c54fc6c991051df8d"},"schema_version":"1.0","source":{"id":"1601.07671","kind":"arxiv","version":2}},"canonical_sha256":"94afbaa18e4fdfce1dfae212bd9a8d313627403c56b4e1d8779a78db88576e90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94afbaa18e4fdfce1dfae212bd9a8d313627403c56b4e1d8779a78db88576e90","first_computed_at":"2026-05-18T00:38:04.553086Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:04.553086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n4thHyWq2xz1hgP1wDSsFdlw43VShb+V8NkGDcAyNx+ZtXq0cjYwLCPxumhitu5BUyw7XS9rgd7V+atVl8uPCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:04.553744Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.07671","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31246bfd208fd922a21ee094e4a5784c8bb6ffbfab824c65fdb9655fb8ab4542","sha256:044b455df5af8e9e786381a881555b900e4111da5571c5be40a7c9605b8eb111"],"state_sha256":"910fd2cd198a6aa30e29f2d54d6b33caeef66e9a2807e7f9839ee97b9194a940"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wjsYV9IHPnwC1tTe4M7/1dXrPFQjii2O7wOoW3by3rvDOqJw0ZU8cXl7lEIisxf5IZ99oz3IyQqMJWGDHORJDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T18:05:18.659797Z","bundle_sha256":"9c032b6a757a954c03270d712dd684500a098bcf45d1f8200217faf49498c3f4"}}