{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:4NO7GHFHMQDVSWSI2H3J7BFJJX","short_pith_number":"pith:4NO7GHFH","canonical_record":{"source":{"id":"1106.1705","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-06-09T05:29:04Z","cross_cats_sorted":[],"title_canon_sha256":"b7fd5b0f9c6d2485e03fd50341a0d4fb2d2defda66ab1b7145a6d061149cd0df","abstract_canon_sha256":"b764fcf132808a55b205ee492916b57658fa4f03ce05f9af5dc28f280ad359af"},"schema_version":"1.0"},"canonical_sha256":"e35df31ca76407595a48d1f69f84a94de757ab82f566c4340372d8f0eef8b5e7","source":{"kind":"arxiv","id":"1106.1705","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.1705","created_at":"2026-05-18T04:20:15Z"},{"alias_kind":"arxiv_version","alias_value":"1106.1705v1","created_at":"2026-05-18T04:20:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.1705","created_at":"2026-05-18T04:20:15Z"},{"alias_kind":"pith_short_12","alias_value":"4NO7GHFHMQDV","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4NO7GHFHMQDVSWSI","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4NO7GHFH","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:4NO7GHFHMQDVSWSI2H3J7BFJJX","target":"record","payload":{"canonical_record":{"source":{"id":"1106.1705","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-06-09T05:29:04Z","cross_cats_sorted":[],"title_canon_sha256":"b7fd5b0f9c6d2485e03fd50341a0d4fb2d2defda66ab1b7145a6d061149cd0df","abstract_canon_sha256":"b764fcf132808a55b205ee492916b57658fa4f03ce05f9af5dc28f280ad359af"},"schema_version":"1.0"},"canonical_sha256":"e35df31ca76407595a48d1f69f84a94de757ab82f566c4340372d8f0eef8b5e7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:15.293689Z","signature_b64":"pCJFptLQgc8mKpFMjTYvT87l80W5+iMMWeFCbR9HRXgFM3qWgYLuJ4j0xMou64BzUNcMOkbDVQ8egWZlV76dDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e35df31ca76407595a48d1f69f84a94de757ab82f566c4340372d8f0eef8b5e7","last_reissued_at":"2026-05-18T04:20:15.293226Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:15.293226Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.1705","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":"2026-05-18T04:20:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fzMPzGdHpYbZSgcjjor1uCHQS2b9b9CqVOMpKUP8GthN/pTYZFnXLKn3H648nsGOeaz2WNpEWvQc78UYzuUvDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T16:47:38.227491Z"},"content_sha256":"b989319061ce4c365c32bce9f1392b45ad1b9771077a1a78157bac8cbc31b4bb","schema_version":"1.0","event_id":"sha256:b989319061ce4c365c32bce9f1392b45ad1b9771077a1a78157bac8cbc31b4bb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:4NO7GHFHMQDVSWSI2H3J7BFJJX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Factoring threefold divisorial contractions to points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jungkai Alfred Chen","submitted_at":"2011-06-09T05:29:04Z","abstract_excerpt":"We show that terminal 3-fold divisorial contraction to a point of index $>1$ with non-minimal discrepancy may be factored into a sequence of flips, flops and divisorial contractions to a point with minimal discrepancies."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1705","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":"2026-05-18T04:20:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v7E7VWV5W46oxqZYxeSLXXB2mbJUT1jr2I+WJilpPfQIIfoMpPXBWplaCfLKzMV1RzsXaytvnTpKUeFUXv+KAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T16:47:38.227835Z"},"content_sha256":"75140a1f54f2304b209600037ca290b8d4fcc1a46f2c351c72b248f39b4ad472","schema_version":"1.0","event_id":"sha256:75140a1f54f2304b209600037ca290b8d4fcc1a46f2c351c72b248f39b4ad472"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4NO7GHFHMQDVSWSI2H3J7BFJJX/bundle.json","state_url":"https://pith.science/pith/4NO7GHFHMQDVSWSI2H3J7BFJJX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4NO7GHFHMQDVSWSI2H3J7BFJJX/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":"2026-06-26T16:47:38Z","links":{"resolver":"https://pith.science/pith/4NO7GHFHMQDVSWSI2H3J7BFJJX","bundle":"https://pith.science/pith/4NO7GHFHMQDVSWSI2H3J7BFJJX/bundle.json","state":"https://pith.science/pith/4NO7GHFHMQDVSWSI2H3J7BFJJX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4NO7GHFHMQDVSWSI2H3J7BFJJX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:4NO7GHFHMQDVSWSI2H3J7BFJJX","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":"b764fcf132808a55b205ee492916b57658fa4f03ce05f9af5dc28f280ad359af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-06-09T05:29:04Z","title_canon_sha256":"b7fd5b0f9c6d2485e03fd50341a0d4fb2d2defda66ab1b7145a6d061149cd0df"},"schema_version":"1.0","source":{"id":"1106.1705","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.1705","created_at":"2026-05-18T04:20:15Z"},{"alias_kind":"arxiv_version","alias_value":"1106.1705v1","created_at":"2026-05-18T04:20:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.1705","created_at":"2026-05-18T04:20:15Z"},{"alias_kind":"pith_short_12","alias_value":"4NO7GHFHMQDV","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4NO7GHFHMQDVSWSI","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4NO7GHFH","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:75140a1f54f2304b209600037ca290b8d4fcc1a46f2c351c72b248f39b4ad472","target":"graph","created_at":"2026-05-18T04:20:15Z","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 show that terminal 3-fold divisorial contraction to a point of index $>1$ with non-minimal discrepancy may be factored into a sequence of flips, flops and divisorial contractions to a point with minimal discrepancies.","authors_text":"Jungkai Alfred Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-06-09T05:29:04Z","title":"Factoring threefold divisorial contractions to points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1705","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:b989319061ce4c365c32bce9f1392b45ad1b9771077a1a78157bac8cbc31b4bb","target":"record","created_at":"2026-05-18T04:20:15Z","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":"b764fcf132808a55b205ee492916b57658fa4f03ce05f9af5dc28f280ad359af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-06-09T05:29:04Z","title_canon_sha256":"b7fd5b0f9c6d2485e03fd50341a0d4fb2d2defda66ab1b7145a6d061149cd0df"},"schema_version":"1.0","source":{"id":"1106.1705","kind":"arxiv","version":1}},"canonical_sha256":"e35df31ca76407595a48d1f69f84a94de757ab82f566c4340372d8f0eef8b5e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e35df31ca76407595a48d1f69f84a94de757ab82f566c4340372d8f0eef8b5e7","first_computed_at":"2026-05-18T04:20:15.293226Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:15.293226Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pCJFptLQgc8mKpFMjTYvT87l80W5+iMMWeFCbR9HRXgFM3qWgYLuJ4j0xMou64BzUNcMOkbDVQ8egWZlV76dDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:15.293689Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.1705","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b989319061ce4c365c32bce9f1392b45ad1b9771077a1a78157bac8cbc31b4bb","sha256:75140a1f54f2304b209600037ca290b8d4fcc1a46f2c351c72b248f39b4ad472"],"state_sha256":"8aa1e3271a2aa93a6bd1a09434252d4038a0ca9318f40a12f01f2aecf838b08e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0el7LBj+D4+FKojdql7zEiNZP/XxrIPZuBddigtcFCHHkha1O9zXNOlgtuGiNtrzRCcmAkDy12wBU3O1Xtg0Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T16:47:38.229860Z","bundle_sha256":"ba5525a3cde14da6169e7031590e0b766bd5c6b37835b2170a9fdd1151cfbe9d"}}