{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:OGDG77R3HFQFCJIMPSSZ3RPETD","short_pith_number":"pith:OGDG77R3","canonical_record":{"source":{"id":"2211.11237","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2022-11-21T08:02:37Z","cross_cats_sorted":[],"title_canon_sha256":"db92974ef598322e27c1c41c144a90623ddd7812563ec167456e987e44263d31","abstract_canon_sha256":"ec587d6af7c9f3b659bdee739a2c39866aadb6a7f15ba8bff11fb154e6a55c9e"},"schema_version":"1.0"},"canonical_sha256":"71866ffe3b396051250c7ca59dc5e498cfbf0609ea0165cd3e8287dce416235c","source":{"kind":"arxiv","id":"2211.11237","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.11237","created_at":"2026-07-05T05:17:51Z"},{"alias_kind":"arxiv_version","alias_value":"2211.11237v1","created_at":"2026-07-05T05:17:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.11237","created_at":"2026-07-05T05:17:51Z"},{"alias_kind":"pith_short_12","alias_value":"OGDG77R3HFQF","created_at":"2026-07-05T05:17:51Z"},{"alias_kind":"pith_short_16","alias_value":"OGDG77R3HFQFCJIM","created_at":"2026-07-05T05:17:51Z"},{"alias_kind":"pith_short_8","alias_value":"OGDG77R3","created_at":"2026-07-05T05:17:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:OGDG77R3HFQFCJIMPSSZ3RPETD","target":"record","payload":{"canonical_record":{"source":{"id":"2211.11237","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2022-11-21T08:02:37Z","cross_cats_sorted":[],"title_canon_sha256":"db92974ef598322e27c1c41c144a90623ddd7812563ec167456e987e44263d31","abstract_canon_sha256":"ec587d6af7c9f3b659bdee739a2c39866aadb6a7f15ba8bff11fb154e6a55c9e"},"schema_version":"1.0"},"canonical_sha256":"71866ffe3b396051250c7ca59dc5e498cfbf0609ea0165cd3e8287dce416235c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:17:51.573090Z","signature_b64":"t+5XOYVikn/nbW29SLjbfAR+P/EEQ32t+m1rBnmpgQQmAb/dVEWhff9W6XsX9Yfd/c4MmO8DHfJG4Qn7XU+LCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71866ffe3b396051250c7ca59dc5e498cfbf0609ea0165cd3e8287dce416235c","last_reissued_at":"2026-07-05T05:17:51.572685Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:17:51.572685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2211.11237","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":"2026-07-05T05:17:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K1I2oDibW3/feGB5enPC/zpku6n+2SW/8/foOjvqDnpY9aaKmJ1vtMqFv6qZe+R8ekqwH1SvjysWVUzNlMQ5AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T14:03:06.320274Z"},"content_sha256":"c1ba0958848c41dc315efce49b490bf68372c5a84874d764c9e9113dde95f91d","schema_version":"1.0","event_id":"sha256:c1ba0958848c41dc315efce49b490bf68372c5a84874d764c9e9113dde95f91d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:OGDG77R3HFQFCJIMPSSZ3RPETD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Moduli of algebraic varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Caucher Birkar","submitted_at":"2022-11-21T08:02:37Z","abstract_excerpt":"We develop a moduli theory of algebraic varieties and pairs of non-negative Kodaira dimension. We define stable minimal models and construct their projective coarse moduli spaces under certain natural conditions. This can be applied to a wide range of moduli problems in algebraic geometry."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.11237","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2211.11237/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T05:17:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NbgVYHl3EVur30AxOKrUSQ4KKm77cDu74ct3QWwJpNDIj3ijRG66PSjDjDW68MlzrWD2zs7JTprzR6dItxByDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T14:03:06.320973Z"},"content_sha256":"1a1c2cd0cff9f6877171ae1539b9bd2571754ba9f96ac7f196fc57f79b1e1945","schema_version":"1.0","event_id":"sha256:1a1c2cd0cff9f6877171ae1539b9bd2571754ba9f96ac7f196fc57f79b1e1945"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OGDG77R3HFQFCJIMPSSZ3RPETD/bundle.json","state_url":"https://pith.science/pith/OGDG77R3HFQFCJIMPSSZ3RPETD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OGDG77R3HFQFCJIMPSSZ3RPETD/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":"2026-08-19T14:03:06Z","links":{"resolver":"https://pith.science/pith/OGDG77R3HFQFCJIMPSSZ3RPETD","bundle":"https://pith.science/pith/OGDG77R3HFQFCJIMPSSZ3RPETD/bundle.json","state":"https://pith.science/pith/OGDG77R3HFQFCJIMPSSZ3RPETD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OGDG77R3HFQFCJIMPSSZ3RPETD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:OGDG77R3HFQFCJIMPSSZ3RPETD","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":"ec587d6af7c9f3b659bdee739a2c39866aadb6a7f15ba8bff11fb154e6a55c9e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2022-11-21T08:02:37Z","title_canon_sha256":"db92974ef598322e27c1c41c144a90623ddd7812563ec167456e987e44263d31"},"schema_version":"1.0","source":{"id":"2211.11237","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.11237","created_at":"2026-07-05T05:17:51Z"},{"alias_kind":"arxiv_version","alias_value":"2211.11237v1","created_at":"2026-07-05T05:17:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.11237","created_at":"2026-07-05T05:17:51Z"},{"alias_kind":"pith_short_12","alias_value":"OGDG77R3HFQF","created_at":"2026-07-05T05:17:51Z"},{"alias_kind":"pith_short_16","alias_value":"OGDG77R3HFQFCJIM","created_at":"2026-07-05T05:17:51Z"},{"alias_kind":"pith_short_8","alias_value":"OGDG77R3","created_at":"2026-07-05T05:17:51Z"}],"graph_snapshots":[{"event_id":"sha256:1a1c2cd0cff9f6877171ae1539b9bd2571754ba9f96ac7f196fc57f79b1e1945","target":"graph","created_at":"2026-07-05T05:17:51Z","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/2211.11237/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop a moduli theory of algebraic varieties and pairs of non-negative Kodaira dimension. We define stable minimal models and construct their projective coarse moduli spaces under certain natural conditions. This can be applied to a wide range of moduli problems in algebraic geometry.","authors_text":"Caucher Birkar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2022-11-21T08:02:37Z","title":"Moduli of algebraic varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.11237","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:c1ba0958848c41dc315efce49b490bf68372c5a84874d764c9e9113dde95f91d","target":"record","created_at":"2026-07-05T05:17:51Z","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":"ec587d6af7c9f3b659bdee739a2c39866aadb6a7f15ba8bff11fb154e6a55c9e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2022-11-21T08:02:37Z","title_canon_sha256":"db92974ef598322e27c1c41c144a90623ddd7812563ec167456e987e44263d31"},"schema_version":"1.0","source":{"id":"2211.11237","kind":"arxiv","version":1}},"canonical_sha256":"71866ffe3b396051250c7ca59dc5e498cfbf0609ea0165cd3e8287dce416235c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71866ffe3b396051250c7ca59dc5e498cfbf0609ea0165cd3e8287dce416235c","first_computed_at":"2026-07-05T05:17:51.572685Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:17:51.572685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t+5XOYVikn/nbW29SLjbfAR+P/EEQ32t+m1rBnmpgQQmAb/dVEWhff9W6XsX9Yfd/c4MmO8DHfJG4Qn7XU+LCw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:17:51.573090Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.11237","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1ba0958848c41dc315efce49b490bf68372c5a84874d764c9e9113dde95f91d","sha256:1a1c2cd0cff9f6877171ae1539b9bd2571754ba9f96ac7f196fc57f79b1e1945"],"state_sha256":"09c68bb32c8ceddf6454c2aa5090e6f6c21adf1c3ec026fc57d5a249f3ded85e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9zFAws6IYYaiWCf/o+KPq2yUsMXR53ZQxJGOxAuOkjsLpwapOcSVjfYG67Tly68fcBaISPrcRY2UQlNa/1ZYBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T14:03:06.331155Z","bundle_sha256":"98f2ff5627bdfb47b429111807d0d1c162fca458cb2536098f7e057fa17ede2a"}}