{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:OAGFBCQDVSK2KEFWFYS4PHFVWW","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":"4e79ab7487c5017490312aec9c0d54d8fd559ed6daa2c08d7c6e406a0c476537","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-06T02:31:03Z","title_canon_sha256":"e8c117b1742b7abbd3c244dd29693ed243adb7b0fde66e19f33b7152d3c0ddc7"},"schema_version":"1.0","source":{"id":"1908.01933","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.01933","created_at":"2026-07-05T00:05:24Z"},{"alias_kind":"arxiv_version","alias_value":"1908.01933v2","created_at":"2026-07-05T00:05:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.01933","created_at":"2026-07-05T00:05:24Z"},{"alias_kind":"pith_short_12","alias_value":"OAGFBCQDVSK2","created_at":"2026-07-05T00:05:24Z"},{"alias_kind":"pith_short_16","alias_value":"OAGFBCQDVSK2KEFW","created_at":"2026-07-05T00:05:24Z"},{"alias_kind":"pith_short_8","alias_value":"OAGFBCQD","created_at":"2026-07-05T00:05:24Z"}],"graph_snapshots":[{"event_id":"sha256:575e6838ff33864bf47619a10b1be111aa5aeb082726540d8910c0e0e630db4e","target":"graph","created_at":"2026-07-05T00:05:24Z","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/1908.01933/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $X$ be a minimal surface of general type over an algebraically closed field $\\mathbf{k}$ of $\\mathrm{char}.(\\mathbf{k})=p\\ge 0$. If the Albanese morphism $a_X:X\\to \\mathrm{Alb}_X$ is generically finite onto its image, we formulate a constant $c(X,L)\\ge 0$ for a very ample line bundle $L$ on $\\mathrm{Alb}_X$ such that $c(X,L)=0$ if and only if $\\dim \\mathrm{Alb}_X=2$ and $a_X: X\\to \\mathrm{Alb}_X$ is a double cover. A refined Severi inequality $$K^2_X\\ge (4+{\\rm min}\\{\\,c(X,L),\\,\\frac{1}{3}\\,\\})\\chi(\\mathcal{O}_X)$$ is proved. Then we prove that $K^2_X=4\\chi(\\mathcal{O}_X)$ if and only if t","authors_text":"Mingshuo Zhou, Xiaotao Sun, Yi Gu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-06T02:31:03Z","title":"Surfaces on the Severi line in positive characteristics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.01933","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:c426c082d8820a04a36680ce2f563902216d921bb930ca99b13fce713a53f057","target":"record","created_at":"2026-07-05T00:05:24Z","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":"4e79ab7487c5017490312aec9c0d54d8fd559ed6daa2c08d7c6e406a0c476537","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-06T02:31:03Z","title_canon_sha256":"e8c117b1742b7abbd3c244dd29693ed243adb7b0fde66e19f33b7152d3c0ddc7"},"schema_version":"1.0","source":{"id":"1908.01933","kind":"arxiv","version":2}},"canonical_sha256":"700c508a03ac95a510b62e25c79cb5b59bbc1b7bf877108e8b36063ef66b7c05","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"700c508a03ac95a510b62e25c79cb5b59bbc1b7bf877108e8b36063ef66b7c05","first_computed_at":"2026-07-05T00:05:24.826289Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:05:24.826289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GeT+HeR+JqTPGJegrgLxs3EIF8ccnVoT3aGuXIC3BdqoQF1NPh3TnxSD1eO+qO4brykzV60omLfXD3u/gFgYBg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:05:24.826677Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.01933","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c426c082d8820a04a36680ce2f563902216d921bb930ca99b13fce713a53f057","sha256:575e6838ff33864bf47619a10b1be111aa5aeb082726540d8910c0e0e630db4e"],"state_sha256":"fbcdda124cb8cdd61618b01338fb68a67741c27a0b5a92d6954f37c225e319f7"}