{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:GQ3PL7WF745VIBLVVDG5UOSH3T","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":"59c532d39b3ed6f790fcee2a6187ab4d52c6d4539129f0b0652b0b468a95ba12","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2000-08-01T10:32:36Z","title_canon_sha256":"607b42b4bd44da5eb5cce487d55cfd07821fdd8320a9ce20a3cdf51f84ff0db3"},"schema_version":"1.0","source":{"id":"math/0008005","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0008005","created_at":"2026-05-18T01:09:07Z"},{"alias_kind":"arxiv_version","alias_value":"math/0008005v2","created_at":"2026-05-18T01:09:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0008005","created_at":"2026-05-18T01:09:07Z"},{"alias_kind":"pith_short_12","alias_value":"GQ3PL7WF745V","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"GQ3PL7WF745VIBLV","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"GQ3PL7WF","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:f568ecb3adf5c1a6085f4356e05c14e64c894871bd75a19c54d04ea007c940b6","target":"graph","created_at":"2026-05-18T01:09:07Z","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":"This paper generalizes for non-abelian theta functions a number of formulae valid for theta functions of Jacobian varieties. The addition formula, the relation with the Szego kernel and with the multicomponent KP hierarchy and the behavior under cyclic coverings are given.","authors_text":"E. G\\'omez Gonz\\'alez, F. J. Plaza Mart\\'in","cross_cats":[],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2000-08-01T10:32:36Z","title":"Addition Formulae for Non-Abelian Theta Functions and Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0008005","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":"sha256:9762605115aa9f085e90d6258b3669d9ac0987e8b33b21b444742ec8392bba89","target":"record","created_at":"2026-05-18T01:09:07Z","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":"59c532d39b3ed6f790fcee2a6187ab4d52c6d4539129f0b0652b0b468a95ba12","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2000-08-01T10:32:36Z","title_canon_sha256":"607b42b4bd44da5eb5cce487d55cfd07821fdd8320a9ce20a3cdf51f84ff0db3"},"schema_version":"1.0","source":{"id":"math/0008005","kind":"arxiv","version":2}},"canonical_sha256":"3436f5fec5ff3b540575a8cdda3a47dcdafe6739b0ccd2477e50a674e1f1ac50","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3436f5fec5ff3b540575a8cdda3a47dcdafe6739b0ccd2477e50a674e1f1ac50","first_computed_at":"2026-05-18T01:09:07.896091Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:07.896091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QCMnAULvJ4TBnU4fwfE8sIjLwczQfSdajkfYByT56BxpuDPUwSvGc4x7dbrZd1sGHWFc+c8n2Gv9ZaVncXCzCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:07.896582Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0008005","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9762605115aa9f085e90d6258b3669d9ac0987e8b33b21b444742ec8392bba89","sha256:f568ecb3adf5c1a6085f4356e05c14e64c894871bd75a19c54d04ea007c940b6"],"state_sha256":"00209b571ba183822c6978159cfd76a8c869b6552bd32444dee5cdc33f577485"}