{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:Z24WGA7BQ3D7LTP4OKWIPZKXAY","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":"05f3a0e3365aeb8ca88b090e17f2389083e59e4e28c26b21e8492235a35589c4","cross_cats_sorted":["nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-06-27T15:44:18Z","title_canon_sha256":"bb84e92efce14ca6e68063d669008459f5e87e3c26935dc8bc132bd6d922e1b9"},"schema_version":"1.0","source":{"id":"1006.5219","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.5219","created_at":"2026-05-18T04:38:39Z"},{"alias_kind":"arxiv_version","alias_value":"1006.5219v1","created_at":"2026-05-18T04:38:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.5219","created_at":"2026-05-18T04:38:39Z"},{"alias_kind":"pith_short_12","alias_value":"Z24WGA7BQ3D7","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"Z24WGA7BQ3D7LTP4","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"Z24WGA7B","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:d0cee937f31717e53f3ed829b4a65e48804f71e2a57cee90887975ea8f401ec5","target":"graph","created_at":"2026-05-18T04:38:39Z","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 compare and contrast three different methods for the construction of the differential relations satisfied by the fundamental Abelian functions associated with an algebraic curve. We realize these Abelian functions as logarithmic derivatives of the associated sigma function. In two of the methods, the use of the tau function, expressed in terms of the sigma function, is central to the construction of differential relations between the Abelian functions.","authors_text":"J. C. Eilbeck, J. Gibbons, V. Z. Enolski","cross_cats":["nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-06-27T15:44:18Z","title":"Sigma, tau and Abelian functions of algebraic curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.5219","kind":"arxiv","version":1},"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":"sha256:0ad5b85f87aeb0674ee772652ff8c8d3affe1def259d654c3b18718ddd2d5630","target":"record","created_at":"2026-05-18T04:38:39Z","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":"05f3a0e3365aeb8ca88b090e17f2389083e59e4e28c26b21e8492235a35589c4","cross_cats_sorted":["nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-06-27T15:44:18Z","title_canon_sha256":"bb84e92efce14ca6e68063d669008459f5e87e3c26935dc8bc132bd6d922e1b9"},"schema_version":"1.0","source":{"id":"1006.5219","kind":"arxiv","version":1}},"canonical_sha256":"ceb96303e186c7f5cdfc72ac87e557061f4ae6ff487754f5b62667509294bfbe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ceb96303e186c7f5cdfc72ac87e557061f4ae6ff487754f5b62667509294bfbe","first_computed_at":"2026-05-18T04:38:39.991371Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:38:39.991371Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oxLuo217ybK/pE+aok+eTPGNt+0fqfIg8wV3b0Z+KAk76FmQbWrqij5gU8+ELtxA8L83zDvhB49h3w7mk6xFCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:38:39.991931Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.5219","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ad5b85f87aeb0674ee772652ff8c8d3affe1def259d654c3b18718ddd2d5630","sha256:d0cee937f31717e53f3ed829b4a65e48804f71e2a57cee90887975ea8f401ec5"],"state_sha256":"6533141818bb7a108a2b1ab21c5ca2924c17eb0727c703935a5e506f751a3bed"}