{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1998:UPTZVBFYSI4YYXPJUOAQH47OST","short_pith_number":"pith:UPTZVBFY","canonical_record":{"source":{"id":"math/9804050","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"1998-04-08T19:53:43Z","cross_cats_sorted":[],"title_canon_sha256":"3c0f53395c7a913a7e2bb40bfbf887d438b01ca9ec30edc67817de0b78d70601","abstract_canon_sha256":"db91630676fc1acd9151fbf3412dcf9ea4d40cdc51655a60d13944988c9c09d5"},"schema_version":"1.0"},"canonical_sha256":"a3e79a84b892398c5de9a38103f3ee94f746a870b5d34de64e8150164d67282e","source":{"kind":"arxiv","id":"math/9804050","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9804050","created_at":"2026-05-18T04:11:18Z"},{"alias_kind":"arxiv_version","alias_value":"math/9804050v1","created_at":"2026-05-18T04:11:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9804050","created_at":"2026-05-18T04:11:18Z"},{"alias_kind":"pith_short_12","alias_value":"UPTZVBFYSI4Y","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"UPTZVBFYSI4YYXPJ","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"UPTZVBFY","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1998:UPTZVBFYSI4YYXPJUOAQH47OST","target":"record","payload":{"canonical_record":{"source":{"id":"math/9804050","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"1998-04-08T19:53:43Z","cross_cats_sorted":[],"title_canon_sha256":"3c0f53395c7a913a7e2bb40bfbf887d438b01ca9ec30edc67817de0b78d70601","abstract_canon_sha256":"db91630676fc1acd9151fbf3412dcf9ea4d40cdc51655a60d13944988c9c09d5"},"schema_version":"1.0"},"canonical_sha256":"a3e79a84b892398c5de9a38103f3ee94f746a870b5d34de64e8150164d67282e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:18.295219Z","signature_b64":"dmiwRh75BTixzab+YH/w6RBKT+AREmcDXuN4agM9IkGUGurX2eiLJ6iMyI6MhbHwHKBW2mpf7mn6GgoTQSwFAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3e79a84b892398c5de9a38103f3ee94f746a870b5d34de64e8150164d67282e","last_reissued_at":"2026-05-18T04:11:18.294688Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:18.294688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9804050","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":"2026-05-18T04:11:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DKHQRPE4WzRPYv/18G4GKZMPrbG+47lQIx1IGVmU4n4SiNBbUrMdaelhmn65OJpxRSHEHCpmGK80jBC0nBIEDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T09:20:00.560857Z"},"content_sha256":"c46ea77e0cef114c2858fc9c709029df40e4b335eef5c4baba3e047589519db6","schema_version":"1.0","event_id":"sha256:c46ea77e0cef114c2858fc9c709029df40e4b335eef5c4baba3e047589519db6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1998:UPTZVBFYSI4YYXPJUOAQH47OST","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Topology of Birational Minimal Models","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Chin-Lung Wang","submitted_at":"1998-04-08T19:53:43Z","abstract_excerpt":"We show that birational smooth complex projective varieties with numerically effective canonical bundles along the exceptional loci have the same Betti numbers. In particular, birational smooth minimal models share the same Betti numbers. Our methods indicate a link between $p$-adic measure and the minimal model theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9804050","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":"2026-05-18T04:11:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3d60fl/2vXDAaBx+6Sd5rdIf13zTIIU0kj28+s14QVIgA5Ou/RfpZd1+tQg8JiYvFt5gfGFL3G1IVTZAsKu2BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T09:20:00.561581Z"},"content_sha256":"5c33097fabf84d66c9b88312e379ca84b1c5cee49456c51651ed6e79154cec1b","schema_version":"1.0","event_id":"sha256:5c33097fabf84d66c9b88312e379ca84b1c5cee49456c51651ed6e79154cec1b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UPTZVBFYSI4YYXPJUOAQH47OST/bundle.json","state_url":"https://pith.science/pith/UPTZVBFYSI4YYXPJUOAQH47OST/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UPTZVBFYSI4YYXPJUOAQH47OST/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":"2026-06-10T09:20:00Z","links":{"resolver":"https://pith.science/pith/UPTZVBFYSI4YYXPJUOAQH47OST","bundle":"https://pith.science/pith/UPTZVBFYSI4YYXPJUOAQH47OST/bundle.json","state":"https://pith.science/pith/UPTZVBFYSI4YYXPJUOAQH47OST/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UPTZVBFYSI4YYXPJUOAQH47OST/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:UPTZVBFYSI4YYXPJUOAQH47OST","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":"db91630676fc1acd9151fbf3412dcf9ea4d40cdc51655a60d13944988c9c09d5","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"1998-04-08T19:53:43Z","title_canon_sha256":"3c0f53395c7a913a7e2bb40bfbf887d438b01ca9ec30edc67817de0b78d70601"},"schema_version":"1.0","source":{"id":"math/9804050","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9804050","created_at":"2026-05-18T04:11:18Z"},{"alias_kind":"arxiv_version","alias_value":"math/9804050v1","created_at":"2026-05-18T04:11:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9804050","created_at":"2026-05-18T04:11:18Z"},{"alias_kind":"pith_short_12","alias_value":"UPTZVBFYSI4Y","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"UPTZVBFYSI4YYXPJ","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"UPTZVBFY","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:5c33097fabf84d66c9b88312e379ca84b1c5cee49456c51651ed6e79154cec1b","target":"graph","created_at":"2026-05-18T04:11:18Z","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 birational smooth complex projective varieties with numerically effective canonical bundles along the exceptional loci have the same Betti numbers. In particular, birational smooth minimal models share the same Betti numbers. Our methods indicate a link between $p$-adic measure and the minimal model theory.","authors_text":"Chin-Lung Wang","cross_cats":[],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"1998-04-08T19:53:43Z","title":"On the Topology of Birational Minimal Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9804050","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:c46ea77e0cef114c2858fc9c709029df40e4b335eef5c4baba3e047589519db6","target":"record","created_at":"2026-05-18T04:11:18Z","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":"db91630676fc1acd9151fbf3412dcf9ea4d40cdc51655a60d13944988c9c09d5","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"1998-04-08T19:53:43Z","title_canon_sha256":"3c0f53395c7a913a7e2bb40bfbf887d438b01ca9ec30edc67817de0b78d70601"},"schema_version":"1.0","source":{"id":"math/9804050","kind":"arxiv","version":1}},"canonical_sha256":"a3e79a84b892398c5de9a38103f3ee94f746a870b5d34de64e8150164d67282e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3e79a84b892398c5de9a38103f3ee94f746a870b5d34de64e8150164d67282e","first_computed_at":"2026-05-18T04:11:18.294688Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:18.294688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dmiwRh75BTixzab+YH/w6RBKT+AREmcDXuN4agM9IkGUGurX2eiLJ6iMyI6MhbHwHKBW2mpf7mn6GgoTQSwFAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:18.295219Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9804050","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c46ea77e0cef114c2858fc9c709029df40e4b335eef5c4baba3e047589519db6","sha256:5c33097fabf84d66c9b88312e379ca84b1c5cee49456c51651ed6e79154cec1b"],"state_sha256":"c7c711c97a8857a17973a01d78565c50096d9e760bf5e2452e63aff23c559fc7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OcQiFRHDH1W1JQeGmc2ZXTEr1erZVL7MeQW+OpiO4oirOKhF47R4YAjTnAYmkigFGwi6N4eR+njybVYFWM/xCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T09:20:00.565612Z","bundle_sha256":"859cfa03a6ef63f4dd6256cdd995bccd62dbf890a654ccf4d29c61dd6d61cca6"}}