{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:IERQFAYASF2RRTO6TY3IUM4XLQ","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":"c1b5b63d23c5fcca56fc3dbb5a8048dde3948b5f36e918b46ae2f94b589b2b34","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-07-01T17:46:06Z","title_canon_sha256":"b02d5169fe91e6ad10060351c9bda607e4a727c3bd129567155237fb3b34249d"},"schema_version":"1.0","source":{"id":"0907.0212","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.0212","created_at":"2026-05-18T02:24:58Z"},{"alias_kind":"arxiv_version","alias_value":"0907.0212v2","created_at":"2026-05-18T02:24:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.0212","created_at":"2026-05-18T02:24:58Z"},{"alias_kind":"pith_short_12","alias_value":"IERQFAYASF2R","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"IERQFAYASF2RRTO6","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"IERQFAYA","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:d7a44cf4d7698097a39343e94a2328b727ef4b86f442ba3a10ecc2b2660f1dbe","target":"graph","created_at":"2026-05-18T02:24:58Z","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 prove results generalizing the classical Riemann Singularity Theorem to the case of integral, singular curves. The main result is a computation of the multiplicity of the theta divisor of an integral, nodal curve at an arbitrary point. We also conjecture a general formula for the multiplicity of points on the theta divisor of a singular integral curve and present some evidence for this conjecture. Our results give a partial answer to a question posed by Lucia Caporaso in a recent paper.","authors_text":"Jesse Leo Kass, Sebastian Casalaina-Martin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-07-01T17:46:06Z","title":"A Riemann singularity theorem for integral curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.0212","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:f9bd8dbe18e65da202679f4f01c0912ff1ce98ed51663aec8209770f6c603b25","target":"record","created_at":"2026-05-18T02:24:58Z","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":"c1b5b63d23c5fcca56fc3dbb5a8048dde3948b5f36e918b46ae2f94b589b2b34","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-07-01T17:46:06Z","title_canon_sha256":"b02d5169fe91e6ad10060351c9bda607e4a727c3bd129567155237fb3b34249d"},"schema_version":"1.0","source":{"id":"0907.0212","kind":"arxiv","version":2}},"canonical_sha256":"4123028300917518cdde9e368a33975c2af646693296a2e76101c81ea4aa0575","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4123028300917518cdde9e368a33975c2af646693296a2e76101c81ea4aa0575","first_computed_at":"2026-05-18T02:24:58.758685Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:58.758685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XhUEqNfQzYd0Q+mo2110l62UFaWsY5nAZgyGkjZS8OKYxqqxaUG9esHY5gF+IxadvHATwLE+25vXvAu2wVs/CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:58.759206Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.0212","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9bd8dbe18e65da202679f4f01c0912ff1ce98ed51663aec8209770f6c603b25","sha256:d7a44cf4d7698097a39343e94a2328b727ef4b86f442ba3a10ecc2b2660f1dbe"],"state_sha256":"247f0f7fb98fcfc19f30b7fe626d41e456070f6ba1ebd6f5f27ada8db4f09a89"}