{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:7B5DRYOPF6RE7V5BBGVSCDOQIV","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":"8ddd43083e5e9fcf463ec66631816c2e4c385799805484e2a40edd18919e0c03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-08-02T23:40:52Z","title_canon_sha256":"e0282fb7560a2b1ea47f565029d052da70911125b230d4bb52f3ab84b7a85ee0"},"schema_version":"1.0","source":{"id":"2308.01473","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.01473","created_at":"2026-07-05T06:52:25Z"},{"alias_kind":"arxiv_version","alias_value":"2308.01473v3","created_at":"2026-07-05T06:52:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.01473","created_at":"2026-07-05T06:52:25Z"},{"alias_kind":"pith_short_12","alias_value":"7B5DRYOPF6RE","created_at":"2026-07-05T06:52:25Z"},{"alias_kind":"pith_short_16","alias_value":"7B5DRYOPF6RE7V5B","created_at":"2026-07-05T06:52:25Z"},{"alias_kind":"pith_short_8","alias_value":"7B5DRYOP","created_at":"2026-07-05T06:52:25Z"}],"graph_snapshots":[{"event_id":"sha256:6a7270cbb340771aa0d40e02e634c54d78ac1823b12912bd853e4bbdc6c0d8f9","target":"graph","created_at":"2026-07-05T06:52:25Z","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/2308.01473/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we investigate the minimal and the next minimal volumes of normal KSBA stable surfaces with $p_g\\ge 2$. We show that in case of $|K_X|$ not composed with a pencil, the minimal and next minimal volumes are $2p_g-4$ and $2p_g-4+\\frac{1}{3}$. In case of $|K_X|$ composed with a pencil, the minimal and next minimal volumes are $\\frac{p_g-1}{p_g+1}(p_g-1)$ and $\\mathrm{min}\\{\\frac{2p_g-2}{2p_g+1}(p_g-1), \\frac{(3p_g-2)p_g-4}{3(p_g+2)}\\}$. We also characterize the surfaces achieving the minimal volumes.","authors_text":"Jinshan Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-08-02T23:40:52Z","title":"The minimal and next minimal volumes of normal KSBA stable surfaces with $p_g\\ge 2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.01473","kind":"arxiv","version":3},"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":"sha256:0f990b9e88d766bc242948ed0d0604172f19c9c353d986aa75ba53f1d4ccbf44","target":"record","created_at":"2026-07-05T06:52:25Z","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":"8ddd43083e5e9fcf463ec66631816c2e4c385799805484e2a40edd18919e0c03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-08-02T23:40:52Z","title_canon_sha256":"e0282fb7560a2b1ea47f565029d052da70911125b230d4bb52f3ab84b7a85ee0"},"schema_version":"1.0","source":{"id":"2308.01473","kind":"arxiv","version":3}},"canonical_sha256":"f87a38e1cf2fa24fd7a109ab210dd04569e046127a993044367552638e1548b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f87a38e1cf2fa24fd7a109ab210dd04569e046127a993044367552638e1548b8","first_computed_at":"2026-07-05T06:52:25.419916Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:52:25.419916Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ggvc2hEHDd+DRvXnjqO9sZmAiCCfofoCUcY2hE9Hif2Q4mDPLR73DdIvKi7kvVS4kSNKxJ0KlNmRdXn3thf1Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T06:52:25.420343Z","signed_message":"canonical_sha256_bytes"},"source_id":"2308.01473","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f990b9e88d766bc242948ed0d0604172f19c9c353d986aa75ba53f1d4ccbf44","sha256:6a7270cbb340771aa0d40e02e634c54d78ac1823b12912bd853e4bbdc6c0d8f9"],"state_sha256":"a5f494a50b6ee3399fab5f6cfef9ee97805bdefaaa97af1cd438f882fc044b71"}