{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:DDXL3BOGWLLLQMQAR5CMBKBXKB","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":"6f7723486e8426050021a910484ba7c10e67d56c88596ad2242bab0a676ff2e6","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"1999-04-26T15:16:43Z","title_canon_sha256":"6d9fe122a9751278413edce85b09881bf01f0083c9122fe8922f4b24425bbc7d"},"schema_version":"1.0","source":{"id":"math/9904146","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9904146","created_at":"2026-07-04T14:41:07Z"},{"alias_kind":"arxiv_version","alias_value":"math/9904146v1","created_at":"2026-07-04T14:41:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9904146","created_at":"2026-07-04T14:41:07Z"},{"alias_kind":"pith_short_12","alias_value":"DDXL3BOGWLLL","created_at":"2026-07-04T14:41:07Z"},{"alias_kind":"pith_short_16","alias_value":"DDXL3BOGWLLLQMQA","created_at":"2026-07-04T14:41:07Z"},{"alias_kind":"pith_short_8","alias_value":"DDXL3BOG","created_at":"2026-07-04T14:41:07Z"}],"graph_snapshots":[{"event_id":"sha256:d3ff38a2da0a19dc3d830f67f5e9bd68bbd5c6df2f855e3f36b69ce149587174","target":"graph","created_at":"2026-07-04T14:41:07Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/9904146/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a short proof of W{\\lodarczyk's theorem that any birational map between smooth projective varieties in characteristic zero is a composition of weighted blowups and blowdowns.","authors_text":"Sean Keel, Yi Hu","cross_cats":[],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"1999-04-26T15:16:43Z","title":"A GIT proof of W{\\l}odarczyk's weighted factorization theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9904146","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":"sha256:4d45ab76826f5738040c8a58cbc200a7058d6c41c56684880d0c4e1de48148bf","target":"record","created_at":"2026-07-04T14:41:07Z","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":"6f7723486e8426050021a910484ba7c10e67d56c88596ad2242bab0a676ff2e6","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"1999-04-26T15:16:43Z","title_canon_sha256":"6d9fe122a9751278413edce85b09881bf01f0083c9122fe8922f4b24425bbc7d"},"schema_version":"1.0","source":{"id":"math/9904146","kind":"arxiv","version":1}},"canonical_sha256":"18eebd85c6b2d6b832008f44c0a837507ae4914b922753d2209ff0f273aae2bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18eebd85c6b2d6b832008f44c0a837507ae4914b922753d2209ff0f273aae2bf","first_computed_at":"2026-07-04T14:41:07.873529Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:41:07.873529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o5gfoOhnEb1eYfTg8lfuHpti/yp2jsYXUuJ3o60lXr8rpS98tAGWg2bbfbmqlKJArvQgFsvyP+tqhSzuAzMwCQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:41:07.873889Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9904146","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d45ab76826f5738040c8a58cbc200a7058d6c41c56684880d0c4e1de48148bf","sha256:d3ff38a2da0a19dc3d830f67f5e9bd68bbd5c6df2f855e3f36b69ce149587174"],"state_sha256":"101232342b652b46961c45774c278acca1499a1e40d81ba85b6922dc7366abe2"}