{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:B3HHFXLFPHHRFNUQUWTWN2HLCL","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":"a42cdc95f65e84208f7b4ca664d52b2f68ce7167aed8c25e33b0ce83185e8b4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-03-08T02:55:12Z","title_canon_sha256":"b839fd24de047813d56ceaa8850239e90469b920fc6b4bd2af335514f1103afc"},"schema_version":"1.0","source":{"id":"2103.04522","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2103.04522","created_at":"2026-07-05T02:21:06Z"},{"alias_kind":"arxiv_version","alias_value":"2103.04522v1","created_at":"2026-07-05T02:21:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.04522","created_at":"2026-07-05T02:21:06Z"},{"alias_kind":"pith_short_12","alias_value":"B3HHFXLFPHHR","created_at":"2026-07-05T02:21:06Z"},{"alias_kind":"pith_short_16","alias_value":"B3HHFXLFPHHRFNUQ","created_at":"2026-07-05T02:21:06Z"},{"alias_kind":"pith_short_8","alias_value":"B3HHFXLF","created_at":"2026-07-05T02:21:06Z"}],"graph_snapshots":[{"event_id":"sha256:4a2d51a4ff0633de51d1495a885de8c699ec4b29dbdeccbd48990e58042b8f78","target":"graph","created_at":"2026-07-05T02:21:06Z","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/2103.04522/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The number of singular points on a klt Fano surface $X$ is $\\leq 2\\rho(X)+2$.","authors_text":"Jihao Liu, Lingyao Xie","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-03-08T02:55:12Z","title":"Number of singular points on projective surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.04522","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":"sha256:641bab81c938cd9b92f7ddf5059e42bb772ac9d025ced04b6910c79df61d27e9","target":"record","created_at":"2026-07-05T02:21:06Z","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":"a42cdc95f65e84208f7b4ca664d52b2f68ce7167aed8c25e33b0ce83185e8b4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-03-08T02:55:12Z","title_canon_sha256":"b839fd24de047813d56ceaa8850239e90469b920fc6b4bd2af335514f1103afc"},"schema_version":"1.0","source":{"id":"2103.04522","kind":"arxiv","version":1}},"canonical_sha256":"0ece72dd6579cf12b690a5a766e8eb12c811a924dfb3ef7b166cd0cda2171a6d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ece72dd6579cf12b690a5a766e8eb12c811a924dfb3ef7b166cd0cda2171a6d","first_computed_at":"2026-07-05T02:21:06.581327Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:21:06.581327Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1MVho5dQngguYEtTBMw/d+nj6rjlpxBnB7hxsOHw1OorXeEyqGvdM6KcB7Ayjo3vmjiFsBDp4Ddg3J/qYOW5AA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:21:06.581857Z","signed_message":"canonical_sha256_bytes"},"source_id":"2103.04522","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:641bab81c938cd9b92f7ddf5059e42bb772ac9d025ced04b6910c79df61d27e9","sha256:4a2d51a4ff0633de51d1495a885de8c699ec4b29dbdeccbd48990e58042b8f78"],"state_sha256":"2e969599bdedc186d069aa98e178af7872ca6ed98ccc86b5e168b73d6c808d29"}