{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:IJYUVU4HMOFGJITXKA76AIHXDX","short_pith_number":"pith:IJYUVU4H","canonical_record":{"source":{"id":"1904.02731","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-04-04T18:11:00Z","cross_cats_sorted":[],"title_canon_sha256":"951f4a59f4a7ec93cdf9a3b564a22a86c1c7c055666c7becad741b53015ea902","abstract_canon_sha256":"127ffb35a83ba28f489d877d614e0cb683ae1d7704b0da7aa4a454d52805aaeb"},"schema_version":"1.0"},"canonical_sha256":"42714ad387638a64a277503fe020f71dce9708e2922163955a186b923c635df5","source":{"kind":"arxiv","id":"1904.02731","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.02731","created_at":"2026-05-17T23:49:19Z"},{"alias_kind":"arxiv_version","alias_value":"1904.02731v1","created_at":"2026-05-17T23:49:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.02731","created_at":"2026-05-17T23:49:19Z"},{"alias_kind":"pith_short_12","alias_value":"IJYUVU4HMOFG","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"IJYUVU4HMOFGJITX","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"IJYUVU4H","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:IJYUVU4HMOFGJITXKA76AIHXDX","target":"record","payload":{"canonical_record":{"source":{"id":"1904.02731","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-04-04T18:11:00Z","cross_cats_sorted":[],"title_canon_sha256":"951f4a59f4a7ec93cdf9a3b564a22a86c1c7c055666c7becad741b53015ea902","abstract_canon_sha256":"127ffb35a83ba28f489d877d614e0cb683ae1d7704b0da7aa4a454d52805aaeb"},"schema_version":"1.0"},"canonical_sha256":"42714ad387638a64a277503fe020f71dce9708e2922163955a186b923c635df5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:19.874836Z","signature_b64":"U4P/x+zsTE51tWh187/zdasgxlj6ohTV4bu7MTAqhcEr8PDbj4gdwuLK8DbpEsBGQc13tghSkAuJ6o0Us5AkCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"42714ad387638a64a277503fe020f71dce9708e2922163955a186b923c635df5","last_reissued_at":"2026-05-17T23:49:19.874168Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:19.874168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.02731","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":"2026-05-17T23:49:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xydrSzjWXOCeJizH224mVJPAakTcfNB+jmmpZKzxGBBRE6NTS2W22R8uLRzGVRyGq1bYU7ZIvtgk5rkEwCcUCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T22:34:21.790248Z"},"content_sha256":"b5a09348b86a3eeb85b5bd7cc9cf598053ea8ef7e0353937c5360072d64c58cc","schema_version":"1.0","event_id":"sha256:b5a09348b86a3eeb85b5bd7cc9cf598053ea8ef7e0353937c5360072d64c58cc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:IJYUVU4HMOFGJITXKA76AIHXDX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equations for abelian subvarieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Angel Carocca, Herbert Lange, Rub\\'i E. Rodr\\'iguez","submitted_at":"2019-04-04T18:11:00Z","abstract_excerpt":"Given a finite group $G$ and an abelian variety $A$ acted on by $G$, to any subgroup $H$ of $G$, we associate an abelian subvariety $A_H$ on which the associated Hecke algebra $\\mathcal{H}_H$ for $H$ in $G$ acts. Any irreducible rational representation $\\widetilde W$ of $\\mathcal{H}_H$ induces an abelian subvariety of $A_H$ in a natural way. In this paper we give equations for this abelian subvariety. In a special case these equations become much easier. We work out some examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.02731","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":"2026-05-17T23:49:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DUcF2xjtGOJvdzlqRQD7IMqrMfwHm4ePWSN35ynL7MpiZ1a0+dmn/P23rNRX3y0bNFYi/Ud1BQE82Fw9HHUZDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T22:34:21.790609Z"},"content_sha256":"3b2dbab168ff9207ec1d1b20f9af7bb77794e5a6bfeda736101ef782269f7e63","schema_version":"1.0","event_id":"sha256:3b2dbab168ff9207ec1d1b20f9af7bb77794e5a6bfeda736101ef782269f7e63"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IJYUVU4HMOFGJITXKA76AIHXDX/bundle.json","state_url":"https://pith.science/pith/IJYUVU4HMOFGJITXKA76AIHXDX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IJYUVU4HMOFGJITXKA76AIHXDX/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":"2026-06-08T22:34:21Z","links":{"resolver":"https://pith.science/pith/IJYUVU4HMOFGJITXKA76AIHXDX","bundle":"https://pith.science/pith/IJYUVU4HMOFGJITXKA76AIHXDX/bundle.json","state":"https://pith.science/pith/IJYUVU4HMOFGJITXKA76AIHXDX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IJYUVU4HMOFGJITXKA76AIHXDX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:IJYUVU4HMOFGJITXKA76AIHXDX","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":"127ffb35a83ba28f489d877d614e0cb683ae1d7704b0da7aa4a454d52805aaeb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-04-04T18:11:00Z","title_canon_sha256":"951f4a59f4a7ec93cdf9a3b564a22a86c1c7c055666c7becad741b53015ea902"},"schema_version":"1.0","source":{"id":"1904.02731","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.02731","created_at":"2026-05-17T23:49:19Z"},{"alias_kind":"arxiv_version","alias_value":"1904.02731v1","created_at":"2026-05-17T23:49:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.02731","created_at":"2026-05-17T23:49:19Z"},{"alias_kind":"pith_short_12","alias_value":"IJYUVU4HMOFG","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"IJYUVU4HMOFGJITX","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"IJYUVU4H","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:3b2dbab168ff9207ec1d1b20f9af7bb77794e5a6bfeda736101ef782269f7e63","target":"graph","created_at":"2026-05-17T23:49:19Z","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":"Given a finite group $G$ and an abelian variety $A$ acted on by $G$, to any subgroup $H$ of $G$, we associate an abelian subvariety $A_H$ on which the associated Hecke algebra $\\mathcal{H}_H$ for $H$ in $G$ acts. Any irreducible rational representation $\\widetilde W$ of $\\mathcal{H}_H$ induces an abelian subvariety of $A_H$ in a natural way. In this paper we give equations for this abelian subvariety. In a special case these equations become much easier. We work out some examples.","authors_text":"Angel Carocca, Herbert Lange, Rub\\'i E. Rodr\\'iguez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-04-04T18:11:00Z","title":"Equations for abelian subvarieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.02731","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:b5a09348b86a3eeb85b5bd7cc9cf598053ea8ef7e0353937c5360072d64c58cc","target":"record","created_at":"2026-05-17T23:49:19Z","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":"127ffb35a83ba28f489d877d614e0cb683ae1d7704b0da7aa4a454d52805aaeb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-04-04T18:11:00Z","title_canon_sha256":"951f4a59f4a7ec93cdf9a3b564a22a86c1c7c055666c7becad741b53015ea902"},"schema_version":"1.0","source":{"id":"1904.02731","kind":"arxiv","version":1}},"canonical_sha256":"42714ad387638a64a277503fe020f71dce9708e2922163955a186b923c635df5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42714ad387638a64a277503fe020f71dce9708e2922163955a186b923c635df5","first_computed_at":"2026-05-17T23:49:19.874168Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:19.874168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U4P/x+zsTE51tWh187/zdasgxlj6ohTV4bu7MTAqhcEr8PDbj4gdwuLK8DbpEsBGQc13tghSkAuJ6o0Us5AkCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:19.874836Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.02731","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5a09348b86a3eeb85b5bd7cc9cf598053ea8ef7e0353937c5360072d64c58cc","sha256:3b2dbab168ff9207ec1d1b20f9af7bb77794e5a6bfeda736101ef782269f7e63"],"state_sha256":"8de8b4614f69dc8bd01676e6ec2bf7cb19650ef7ac13543995f9c6e517877880"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/FEzZZu6jirtRnoAjQIfLj+1uj9HHxo1JRX58Ubx0bv06VPfxTmSGpdUG47qP18HwNvTxtlhRUmL/ay097kxAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T22:34:21.792487Z","bundle_sha256":"636e0e04cea41313aff68926bc10a7dc3f54c3533cbfe89433071afe8f168870"}}