{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ZXTOZL4VXNU3REXGTCG2XOJK64","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":"d09bf484764445209f0125d4ccab19521edf019638a37613ecbacf427a8d79b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-05-11T17:07:25Z","title_canon_sha256":"000c62f12c88659545d5aa11adbcf2bd8d931667cce837425b9773ff3cec29c8"},"schema_version":"1.0","source":{"id":"1105.2253","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.2253","created_at":"2026-05-18T02:58:00Z"},{"alias_kind":"arxiv_version","alias_value":"1105.2253v2","created_at":"2026-05-18T02:58:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.2253","created_at":"2026-05-18T02:58:00Z"},{"alias_kind":"pith_short_12","alias_value":"ZXTOZL4VXNU3","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"ZXTOZL4VXNU3REXG","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"ZXTOZL4V","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:13be32f7c081f647694b57dbe50263a2c2347a74179c8773420222bda20b2ca3","target":"graph","created_at":"2026-05-18T02:58:00Z","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":"Let C be a 2-connected Gorenstein curve either reduced or contained in a smooth algebraic surface and let S be a subcanonical cluster (i.e. a 0-dim scheme such that the space H^0(C, I_S K_C) contains a generically invertible section). Under some general assumptions on S or C we show that h^0(C, I_S K_C) <= p_a(C) - deg (S)/2 and if equality holds then either S is trivial, or C is honestly hyperelliptic or 3-disconnected. As a corollary we give a generalization of Clifford's theorem for reduced curves.","authors_text":"Elisa Tenni, Marco Franciosi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-05-11T17:07:25Z","title":"On Clifford's theorem for singular curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2253","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:d42f1af6364de6e3c6449fccc846ece70542f03de234a5791b44441e84cf0424","target":"record","created_at":"2026-05-18T02:58:00Z","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":"d09bf484764445209f0125d4ccab19521edf019638a37613ecbacf427a8d79b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-05-11T17:07:25Z","title_canon_sha256":"000c62f12c88659545d5aa11adbcf2bd8d931667cce837425b9773ff3cec29c8"},"schema_version":"1.0","source":{"id":"1105.2253","kind":"arxiv","version":2}},"canonical_sha256":"cde6ecaf95bb69b892e6988dabb92af71aa07536484ef63d24bb33388792db0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cde6ecaf95bb69b892e6988dabb92af71aa07536484ef63d24bb33388792db0d","first_computed_at":"2026-05-18T02:58:00.926458Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:00.926458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K31yZ7lS1FWdaQmWc3plgy9iLl/nFfyroy3UdzGRqb2XrfHz05vWLDE2PNvK2g2rAK3uh8ljdNi7JiaJuHAjDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:00.927135Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.2253","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d42f1af6364de6e3c6449fccc846ece70542f03de234a5791b44441e84cf0424","sha256:13be32f7c081f647694b57dbe50263a2c2347a74179c8773420222bda20b2ca3"],"state_sha256":"e3d9701ddcc8ca0bd9af4f97e467cf6aaea3ed77160fa9b7a3776060dcd5f6bc"}