{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:QPBQCF26HCGTCVKZGBFRXUBEK4","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":"9a1d9a34b6ea7ed68cfc79c1192180ae675624b8fefcd8f7c68db5c14d9115a4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AG","submitted_at":"2010-02-16T01:04:29Z","title_canon_sha256":"940fb8f2c3bd65be1e41c0f00d562d5d59d9be040270faff781790c34dba0709"},"schema_version":"1.0","source":{"id":"1002.2984","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.2984","created_at":"2026-05-18T04:23:13Z"},{"alias_kind":"arxiv_version","alias_value":"1002.2984v2","created_at":"2026-05-18T04:23:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.2984","created_at":"2026-05-18T04:23:13Z"},{"alias_kind":"pith_short_12","alias_value":"QPBQCF26HCGT","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"QPBQCF26HCGTCVKZ","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"QPBQCF26","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:b6f7b340e98f7a376c023949854a0918dd841a8d3dec4221819e08108731c12c","target":"graph","created_at":"2026-05-18T04:23:13Z","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":"A point of an algebraic curve of genus g is subcanonical if some regular differential vanishes only at that point, with multiplicity 2g-2. Subcanonical points are Weierstrass points, and we compute the associated gap sequence at a general point of each component of the moduli space of curves with marked subcanonical point. We also construct subcanonical points with other gap sequences as ramification points of certain cyclic covers.","authors_text":"Evan M. Bullock","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AG","submitted_at":"2010-02-16T01:04:29Z","title":"Subcanonical points on algebraic curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.2984","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":"sha256:7178ce40153e80bac26ca50e1791afe8fdd17662465e73685d926521df1f25e1","target":"record","created_at":"2026-05-18T04:23:13Z","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":"9a1d9a34b6ea7ed68cfc79c1192180ae675624b8fefcd8f7c68db5c14d9115a4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AG","submitted_at":"2010-02-16T01:04:29Z","title_canon_sha256":"940fb8f2c3bd65be1e41c0f00d562d5d59d9be040270faff781790c34dba0709"},"schema_version":"1.0","source":{"id":"1002.2984","kind":"arxiv","version":2}},"canonical_sha256":"83c301175e388d315559304b1bd024570ebb8dab4c6b38de5ffc60c9bbd37b11","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83c301175e388d315559304b1bd024570ebb8dab4c6b38de5ffc60c9bbd37b11","first_computed_at":"2026-05-18T04:23:13.350029Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:13.350029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pTEuhJgGbFjRoQvr50qJ8+EiO+ZX1rw/l1mpxouzxW0UyukxxQMoje9twLDfd5f99xQmk1vInts2kFGZSjVtAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:13.350740Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.2984","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7178ce40153e80bac26ca50e1791afe8fdd17662465e73685d926521df1f25e1","sha256:b6f7b340e98f7a376c023949854a0918dd841a8d3dec4221819e08108731c12c"],"state_sha256":"ec88a5857aa21c3ec77ebe4c10dce82f601da985679ef3d04503244efb32446c"}