{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:4P5TXBV5C7UTGIOSFGAQWPJH5P","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":"9387b42ade76d8d7d9724bc6d2ca2b7aec2b954dce29b6134b3b66d2fe5824f0","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-12-16T19:58:29Z","title_canon_sha256":"d39353c7bcb4b4bdb4c7967c2ef88daf61bb9b8ae3c9aca1bcc0a97cad0265fc"},"schema_version":"1.0","source":{"id":"1012.3731","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.3731","created_at":"2026-05-18T04:33:05Z"},{"alias_kind":"arxiv_version","alias_value":"1012.3731v1","created_at":"2026-05-18T04:33:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.3731","created_at":"2026-05-18T04:33:05Z"},{"alias_kind":"pith_short_12","alias_value":"4P5TXBV5C7UT","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"4P5TXBV5C7UTGIOS","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"4P5TXBV5","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:d3ed248f7893f239dcc210f09c0a897da323360fd353353f6ca6b2d48a62b3dd","target":"graph","created_at":"2026-05-18T04:33:05Z","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":"Let $n=2g+2$ be a positive even integer, $f(x)$ a degree $n$ complex polynomial without multiple roots and $C_f: y^2=f(x)$ the corresponding genus $g$ hyperelliptic curve over the field $\\C$ of complex numbers. Let a $(g-1)$-dimensional complex abelian variety $P$ be a Prym variety of $C_f$ that corresponds to a unramified double cover of $C_f$. Suppose that there exists a subfield $K$ of $\\C$ such that $f(x)$ lies in $K[x]$, is irreducible over $K$ and its Galois group is the full symmetric group. Assuming that $g>2$, we prove that $End(P)$ is either the ring of integers $Z$ or the direct sum","authors_text":"Yuri G. Zarhin","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-12-16T19:58:29Z","title":"Hodge classes on certain hyperelliptic prymians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3731","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":"sha256:1697b863ecaa3a243a60ce593707a2203ec0f948e316752317d60ba0e1d7ef29","target":"record","created_at":"2026-05-18T04:33:05Z","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":"9387b42ade76d8d7d9724bc6d2ca2b7aec2b954dce29b6134b3b66d2fe5824f0","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-12-16T19:58:29Z","title_canon_sha256":"d39353c7bcb4b4bdb4c7967c2ef88daf61bb9b8ae3c9aca1bcc0a97cad0265fc"},"schema_version":"1.0","source":{"id":"1012.3731","kind":"arxiv","version":1}},"canonical_sha256":"e3fb3b86bd17e93321d229810b3d27ebde31a35b7e1bc727c436d91a836caed3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3fb3b86bd17e93321d229810b3d27ebde31a35b7e1bc727c436d91a836caed3","first_computed_at":"2026-05-18T04:33:05.741166Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:33:05.741166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pm2wPKqV/Kze6ljSWg30IbWlE/8Myc6TF9SdMPWQ79nv2bKDd0nvtGdl/0txDlpY/HjnZGLNKDVx9YeAY9u7Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:33:05.741958Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.3731","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1697b863ecaa3a243a60ce593707a2203ec0f948e316752317d60ba0e1d7ef29","sha256:d3ed248f7893f239dcc210f09c0a897da323360fd353353f6ca6b2d48a62b3dd"],"state_sha256":"06bdaaace4f50fbe41fe852da12de79ba89276b120ca3a3024a188008e6ddd5c"}