{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:EVGQUT24FFIR6LGWOZEOKZUCQF","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":"f944b89e2a17e4a01c8785d0a40c0814855b779102c21f6095fbd178dc361889","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2005-06-10T11:18:32Z","title_canon_sha256":"00bda0d0da87a714e4e5a04f9252f624d8cdb25020782557578728dc0d8cf628"},"schema_version":"1.0","source":{"id":"math/0506194","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0506194","created_at":"2026-05-18T01:08:51Z"},{"alias_kind":"arxiv_version","alias_value":"math/0506194v1","created_at":"2026-05-18T01:08:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0506194","created_at":"2026-05-18T01:08:51Z"},{"alias_kind":"pith_short_12","alias_value":"EVGQUT24FFIR","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"EVGQUT24FFIR6LGW","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"EVGQUT24","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:7a6968023f3b4a3597de63cd8e500d821836115255f4dedd1a97eb3b7c43cf3a","target":"graph","created_at":"2026-05-18T01:08:51Z","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":"In this paper, an explicit hierarchy of differential equations for the $\\tau$-functions defining the moduli space of curves with automorphisms as a subscheme of the Sato Grassmannian is obtained. The Schottky problem for Riemann surfaces with automorphisms consists of characterizing those p.p.a.v. that are Jacobian varieties of a curve with a non-trivial automorphism. A characterization in terms of hierarchies of p.d.e. for theta functions is also given.","authors_text":"E. G\\'omez, F. J. Plaza, J. M. Mu\\~noz, R. E. Rodr\\'iguez, S. Recillas","cross_cats":[],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2005-06-10T11:18:32Z","title":"A solution of the Schottky-Type problem for curves with automorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0506194","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:cfef7e71195073756033f1a81fec6b1d181b3e90f78f7e5553edce8622de93dc","target":"record","created_at":"2026-05-18T01:08:51Z","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":"f944b89e2a17e4a01c8785d0a40c0814855b779102c21f6095fbd178dc361889","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2005-06-10T11:18:32Z","title_canon_sha256":"00bda0d0da87a714e4e5a04f9252f624d8cdb25020782557578728dc0d8cf628"},"schema_version":"1.0","source":{"id":"math/0506194","kind":"arxiv","version":1}},"canonical_sha256":"254d0a4f5c29511f2cd67648e56682817ac962e2dc0e651b5ec73035f3d8e37a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"254d0a4f5c29511f2cd67648e56682817ac962e2dc0e651b5ec73035f3d8e37a","first_computed_at":"2026-05-18T01:08:51.043137Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:51.043137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h0uxF5OeBzXDAhD6icliGYSOJJqV3F8r0jjapSqlp4atBm4C7gFAIsQ2MkVIiEQB1t8slIaQ1TDQpZO7YecfDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:51.043666Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0506194","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfef7e71195073756033f1a81fec6b1d181b3e90f78f7e5553edce8622de93dc","sha256:7a6968023f3b4a3597de63cd8e500d821836115255f4dedd1a97eb3b7c43cf3a"],"state_sha256":"57b3cbf7206d4ea8e2eac297a06812876682fe01cfdf4e3364d608506caf1d9d"}