{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:ZNU6JE3YJOSCUVNZJCKD3BV6KT","short_pith_number":"pith:ZNU6JE3Y","schema_version":"1.0","canonical_sha256":"cb69e493784ba42a55b948943d86be54fe5088ef2f3045332a66002a30fd2fbb","source":{"kind":"arxiv","id":"0805.1302","version":1},"attestation_state":"computed","paper":{"title":"Genus two curves with quaternionic multiplication and modular jacobian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Jordi Guardia, Josep Gonzalez","submitted_at":"2008-05-09T08:27:50Z","abstract_excerpt":"We describe a method to determine all the isomorphism classes of principal polarizations of the modular abelian surfaces $A_f$ with quaternionic multiplication attached to a normalized newform $f$ without complex multiplication. We include an example of $A_f$ with quaternionic multiplication for which we find numerically a curve $C$ whose Jacobian is $A_f$ up to numerical approximation, and we prove that it has quaternionic multiplication and is isogenous to $A_f$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0805.1302","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-05-09T08:27:50Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"38503c5cf9a7859020d2100527fd558d8218699eb10c56ad66b1d0dba4ca376f","abstract_canon_sha256":"2d92877ebfb65bffe3abf1ea8861caa6d0069a9ebd02160d9b8b552e69cd1f50"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:15:52.951779Z","signature_b64":"rqQ8BVoPybHMgpbTxywAvjwIv8mRTskAphfbqL0elk6DTMuQ7/EQBOUtghJ+zzBLDpzf75eHWWzY20as192CAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb69e493784ba42a55b948943d86be54fe5088ef2f3045332a66002a30fd2fbb","last_reissued_at":"2026-05-18T02:15:52.951025Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:15:52.951025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Genus two curves with quaternionic multiplication and modular jacobian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Jordi Guardia, Josep Gonzalez","submitted_at":"2008-05-09T08:27:50Z","abstract_excerpt":"We describe a method to determine all the isomorphism classes of principal polarizations of the modular abelian surfaces $A_f$ with quaternionic multiplication attached to a normalized newform $f$ without complex multiplication. We include an example of $A_f$ with quaternionic multiplication for which we find numerically a curve $C$ whose Jacobian is $A_f$ up to numerical approximation, and we prove that it has quaternionic multiplication and is isogenous to $A_f$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.1302","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"0805.1302","created_at":"2026-05-18T02:15:52.951136+00:00"},{"alias_kind":"arxiv_version","alias_value":"0805.1302v1","created_at":"2026-05-18T02:15:52.951136+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0805.1302","created_at":"2026-05-18T02:15:52.951136+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZNU6JE3YJOSC","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZNU6JE3YJOSCUVNZ","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZNU6JE3Y","created_at":"2026-05-18T12:25:58.018023+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZNU6JE3YJOSCUVNZJCKD3BV6KT","json":"https://pith.science/pith/ZNU6JE3YJOSCUVNZJCKD3BV6KT.json","graph_json":"https://pith.science/api/pith-number/ZNU6JE3YJOSCUVNZJCKD3BV6KT/graph.json","events_json":"https://pith.science/api/pith-number/ZNU6JE3YJOSCUVNZJCKD3BV6KT/events.json","paper":"https://pith.science/paper/ZNU6JE3Y"},"agent_actions":{"view_html":"https://pith.science/pith/ZNU6JE3YJOSCUVNZJCKD3BV6KT","download_json":"https://pith.science/pith/ZNU6JE3YJOSCUVNZJCKD3BV6KT.json","view_paper":"https://pith.science/paper/ZNU6JE3Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0805.1302&json=true","fetch_graph":"https://pith.science/api/pith-number/ZNU6JE3YJOSCUVNZJCKD3BV6KT/graph.json","fetch_events":"https://pith.science/api/pith-number/ZNU6JE3YJOSCUVNZJCKD3BV6KT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZNU6JE3YJOSCUVNZJCKD3BV6KT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZNU6JE3YJOSCUVNZJCKD3BV6KT/action/storage_attestation","attest_author":"https://pith.science/pith/ZNU6JE3YJOSCUVNZJCKD3BV6KT/action/author_attestation","sign_citation":"https://pith.science/pith/ZNU6JE3YJOSCUVNZJCKD3BV6KT/action/citation_signature","submit_replication":"https://pith.science/pith/ZNU6JE3YJOSCUVNZJCKD3BV6KT/action/replication_record"}},"created_at":"2026-05-18T02:15:52.951136+00:00","updated_at":"2026-05-18T02:15:52.951136+00:00"}