{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:ZNU6JE3YJOSCUVNZJCKD3BV6KT","short_pith_number":"pith:ZNU6JE3Y","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"},"canonical_sha256":"cb69e493784ba42a55b948943d86be54fe5088ef2f3045332a66002a30fd2fbb","source":{"kind":"arxiv","id":"0805.1302","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0805.1302","created_at":"2026-05-18T02:15:52Z"},{"alias_kind":"arxiv_version","alias_value":"0805.1302v1","created_at":"2026-05-18T02:15:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0805.1302","created_at":"2026-05-18T02:15:52Z"},{"alias_kind":"pith_short_12","alias_value":"ZNU6JE3YJOSC","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"ZNU6JE3YJOSCUVNZ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"ZNU6JE3Y","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:ZNU6JE3YJOSCUVNZJCKD3BV6KT","target":"record","payload":{"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"},"canonical_sha256":"cb69e493784ba42a55b948943d86be54fe5088ef2f3045332a66002a30fd2fbb","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"},"source_kind":"arxiv","source_id":"0805.1302","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:15:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DTVyeTYi6GOLOnvImyPRlnIpAkksQ+eakcHRO7cT7/eZ1BHgRh9+gML/wRkhAQWMAxcyRjtVuc+cwPNhhkc/Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:02:37.429916Z"},"content_sha256":"50917ed9b3e4f7c0eebceede37acf01ecfa61ac6a6616749ef1eab93d4ca4724","schema_version":"1.0","event_id":"sha256:50917ed9b3e4f7c0eebceede37acf01ecfa61ac6a6616749ef1eab93d4ca4724"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:ZNU6JE3YJOSCUVNZJCKD3BV6KT","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:15:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hi8UcQdeFuaxSu9RVouo595xIH/kizkUPIsj1J5hmf5tjMd7KdO7KKl6CYnrpMuHdV/zeQhP87jk7VIdSjXDCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:02:37.430252Z"},"content_sha256":"dff9b6eb1fc5add08b680f617c997dd3b801d48eb9528834fa76ea88c5aad65d","schema_version":"1.0","event_id":"sha256:dff9b6eb1fc5add08b680f617c997dd3b801d48eb9528834fa76ea88c5aad65d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZNU6JE3YJOSCUVNZJCKD3BV6KT/bundle.json","state_url":"https://pith.science/pith/ZNU6JE3YJOSCUVNZJCKD3BV6KT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZNU6JE3YJOSCUVNZJCKD3BV6KT/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T06:02:37Z","links":{"resolver":"https://pith.science/pith/ZNU6JE3YJOSCUVNZJCKD3BV6KT","bundle":"https://pith.science/pith/ZNU6JE3YJOSCUVNZJCKD3BV6KT/bundle.json","state":"https://pith.science/pith/ZNU6JE3YJOSCUVNZJCKD3BV6KT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZNU6JE3YJOSCUVNZJCKD3BV6KT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:ZNU6JE3YJOSCUVNZJCKD3BV6KT","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":"2d92877ebfb65bffe3abf1ea8861caa6d0069a9ebd02160d9b8b552e69cd1f50","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-05-09T08:27:50Z","title_canon_sha256":"38503c5cf9a7859020d2100527fd558d8218699eb10c56ad66b1d0dba4ca376f"},"schema_version":"1.0","source":{"id":"0805.1302","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0805.1302","created_at":"2026-05-18T02:15:52Z"},{"alias_kind":"arxiv_version","alias_value":"0805.1302v1","created_at":"2026-05-18T02:15:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0805.1302","created_at":"2026-05-18T02:15:52Z"},{"alias_kind":"pith_short_12","alias_value":"ZNU6JE3YJOSC","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"ZNU6JE3YJOSCUVNZ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"ZNU6JE3Y","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:dff9b6eb1fc5add08b680f617c997dd3b801d48eb9528834fa76ea88c5aad65d","target":"graph","created_at":"2026-05-18T02:15:52Z","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 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 $A_f$.","authors_text":"Jordi Guardia, Josep Gonzalez","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-05-09T08:27:50Z","title":"Genus two curves with quaternionic multiplication and modular jacobian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.1302","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":"sha256:50917ed9b3e4f7c0eebceede37acf01ecfa61ac6a6616749ef1eab93d4ca4724","target":"record","created_at":"2026-05-18T02:15:52Z","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":"2d92877ebfb65bffe3abf1ea8861caa6d0069a9ebd02160d9b8b552e69cd1f50","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-05-09T08:27:50Z","title_canon_sha256":"38503c5cf9a7859020d2100527fd558d8218699eb10c56ad66b1d0dba4ca376f"},"schema_version":"1.0","source":{"id":"0805.1302","kind":"arxiv","version":1}},"canonical_sha256":"cb69e493784ba42a55b948943d86be54fe5088ef2f3045332a66002a30fd2fbb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb69e493784ba42a55b948943d86be54fe5088ef2f3045332a66002a30fd2fbb","first_computed_at":"2026-05-18T02:15:52.951025Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:15:52.951025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rqQ8BVoPybHMgpbTxywAvjwIv8mRTskAphfbqL0elk6DTMuQ7/EQBOUtghJ+zzBLDpzf75eHWWzY20as192CAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:15:52.951779Z","signed_message":"canonical_sha256_bytes"},"source_id":"0805.1302","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50917ed9b3e4f7c0eebceede37acf01ecfa61ac6a6616749ef1eab93d4ca4724","sha256:dff9b6eb1fc5add08b680f617c997dd3b801d48eb9528834fa76ea88c5aad65d"],"state_sha256":"90880ee6a1751d48dfd01b4e4482b1b36af446e8e253c4e47506284f28a9ff1c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8QBRq2sTA6eka9MX65KGzHBbd2ebDxkuoni2mX2IZMmpH60Y5dYRO267yBEnIwEvQrk+xjnuJUoqEdQ8DlPqDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T06:02:37.432288Z","bundle_sha256":"37838b124bf0c288e57d048164820b884db3482d0138a60ab4c4084726944806"}}