{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MWXWSECULQF6R3574P5LIOJEML","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":"6969ae2fc89089db80632da61e59c900abcc91d571bdf07cd015acbb0c2dfc4d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-11-09T05:43:03Z","title_canon_sha256":"c90b1103a989b1af9745ca33da07d8506d568b1f03f4eba4cf964621d9ad995c"},"schema_version":"1.0","source":{"id":"1411.2200","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2200","created_at":"2026-05-18T00:12:01Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2200v2","created_at":"2026-05-18T00:12:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2200","created_at":"2026-05-18T00:12:01Z"},{"alias_kind":"pith_short_12","alias_value":"MWXWSECULQF6","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MWXWSECULQF6R357","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MWXWSECU","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:6f8d3117947df8abbc7a6aeeb0568ad8fdaf009db912fe7d31e6972fcc6321f6","target":"graph","created_at":"2026-05-18T00:12:01Z","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 study canonically polarized Gorenstein $3$-folds with at most terminal singularities and satisfying $K_X^3=\\frac 43p_g(X)-\\frac {10}3$ and $p_g(X) \\ge 7$. We characterize the canonical maps of such $3$-folds, describe a structure theorem for the locally factorial ones and completely classify the smooth ones. New examples of canonically polarized smooth $3$-folds with $K_X^3=\\frac 43p_g(X)-\\frac {10}3$ and $p_g(X) \\ge 7$ are constructed. These examples are natural extensions of those constructed by M.~Kobayashi.","authors_text":"Yifan Chen, Yong Hu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-11-09T05:43:03Z","title":"On canonically polarized Gorenstein 3-folds satisfying the Noether equality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2200","kind":"arxiv","version":2},"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":"sha256:9a9ed2e8d614de48d88a0753f2d3b44abcf10425d42db2a1a333e246a27ec9bc","target":"record","created_at":"2026-05-18T00:12:01Z","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":"6969ae2fc89089db80632da61e59c900abcc91d571bdf07cd015acbb0c2dfc4d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-11-09T05:43:03Z","title_canon_sha256":"c90b1103a989b1af9745ca33da07d8506d568b1f03f4eba4cf964621d9ad995c"},"schema_version":"1.0","source":{"id":"1411.2200","kind":"arxiv","version":2}},"canonical_sha256":"65af6910545c0be8efbfe3fab4392462c2aeb8a64ea5dbbce42362281385263e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65af6910545c0be8efbfe3fab4392462c2aeb8a64ea5dbbce42362281385263e","first_computed_at":"2026-05-18T00:12:01.224594Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:01.224594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HqBpgL/rAk4Cnry4FPrDGYwdJSU/RkeiFlAKFmF+hjBFrC5pZBt1lSMHp/pVgDJ7nz7gv+BV6hPktCdcpr+tBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:01.225155Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.2200","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9a9ed2e8d614de48d88a0753f2d3b44abcf10425d42db2a1a333e246a27ec9bc","sha256:6f8d3117947df8abbc7a6aeeb0568ad8fdaf009db912fe7d31e6972fcc6321f6"],"state_sha256":"970404cbcbe5ceba231a80bf11fcd2b33e0fb3f5204bb852b19224696b93f735"}