{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:HR7LUMBEELL6TXKLEFKOISOPEV","short_pith_number":"pith:HR7LUMBE","canonical_record":{"source":{"id":"1209.3653","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-09-17T13:55:51Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"bf2e5bb0ef7c066b0f2fe8610256fdec21c8f2583982d03028c818c5bcc79fcc","abstract_canon_sha256":"17cd3237c01fbf6391153a0ea36b64e85f63b6d22d269043b5a00aeea1cecac0"},"schema_version":"1.0"},"canonical_sha256":"3c7eba302422d7e9dd4b2154e449cf25568e5b5af9724620d95faaa6112b695b","source":{"kind":"arxiv","id":"1209.3653","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3653","created_at":"2026-05-18T01:04:46Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3653v4","created_at":"2026-05-18T01:04:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3653","created_at":"2026-05-18T01:04:46Z"},{"alias_kind":"pith_short_12","alias_value":"HR7LUMBEELL6","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HR7LUMBEELL6TXKL","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HR7LUMBE","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:HR7LUMBEELL6TXKLEFKOISOPEV","target":"record","payload":{"canonical_record":{"source":{"id":"1209.3653","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-09-17T13:55:51Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"bf2e5bb0ef7c066b0f2fe8610256fdec21c8f2583982d03028c818c5bcc79fcc","abstract_canon_sha256":"17cd3237c01fbf6391153a0ea36b64e85f63b6d22d269043b5a00aeea1cecac0"},"schema_version":"1.0"},"canonical_sha256":"3c7eba302422d7e9dd4b2154e449cf25568e5b5af9724620d95faaa6112b695b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:46.166524Z","signature_b64":"P2GoCJqXKXM2J78WlWEdR/NCVLPfBqHZuEzNgE2ehZwmXp8AIBNg5gvKrqxgh4PkDozdKT8hTuvyRuf0BKEXBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c7eba302422d7e9dd4b2154e449cf25568e5b5af9724620d95faaa6112b695b","last_reissued_at":"2026-05-18T01:04:46.166031Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:46.166031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.3653","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:04:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lD3wqIo2tXIOtleKzfM/xzPb77fREJjHjtECus6latMmof191Sy+qq0Aw0VCUQjO/m7g3VkPbliMxVoMp7VLCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:09:02.427657Z"},"content_sha256":"96d2d36cedb763a28a5a48ea0482993554a4facac9cb5b2cf6626cbb84cf6875","schema_version":"1.0","event_id":"sha256:96d2d36cedb763a28a5a48ea0482993554a4facac9cb5b2cf6626cbb84cf6875"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:HR7LUMBEELL6TXKLEFKOISOPEV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Families of abelian varieties with many isogenous fibres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Martin Orr","submitted_at":"2012-09-17T13:55:51Z","abstract_excerpt":"Let Z be a subvariety of the moduli space of principally polarised abelian varieties of dimension g over the complex numbers. Suppose that Z contains a Zariski dense set of points which correspond to abelian varieties from a single isogeny class. A generalisation of a conjecture of Andr\\'e and Pink predicts that Z is a weakly special subvariety. We prove this when dim Z = 1 using the Pila--Zannier method and the Masser--W\\\"ustholz isogeny theorem. This generalises results of Edixhoven and Yafaev when the Hecke orbit consists of CM points and of Pink when it consists of Galois generic points."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3653","kind":"arxiv","version":4},"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":"2026-05-18T01:04:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UiBTrndDwdebuYlBvJF75SWQyZRKAIYaXfgFzpPTDeQpN+OBkUrGuObZ4WV1vDxlOBCeT+KhdZzge8npDfW+CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:09:02.427985Z"},"content_sha256":"50dabafbfc244c699bf4f7216c48b11f8ece9f56d3759e194fae26540dc089e5","schema_version":"1.0","event_id":"sha256:50dabafbfc244c699bf4f7216c48b11f8ece9f56d3759e194fae26540dc089e5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HR7LUMBEELL6TXKLEFKOISOPEV/bundle.json","state_url":"https://pith.science/pith/HR7LUMBEELL6TXKLEFKOISOPEV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HR7LUMBEELL6TXKLEFKOISOPEV/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":"2026-06-20T07:09:02Z","links":{"resolver":"https://pith.science/pith/HR7LUMBEELL6TXKLEFKOISOPEV","bundle":"https://pith.science/pith/HR7LUMBEELL6TXKLEFKOISOPEV/bundle.json","state":"https://pith.science/pith/HR7LUMBEELL6TXKLEFKOISOPEV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HR7LUMBEELL6TXKLEFKOISOPEV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HR7LUMBEELL6TXKLEFKOISOPEV","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":"17cd3237c01fbf6391153a0ea36b64e85f63b6d22d269043b5a00aeea1cecac0","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-09-17T13:55:51Z","title_canon_sha256":"bf2e5bb0ef7c066b0f2fe8610256fdec21c8f2583982d03028c818c5bcc79fcc"},"schema_version":"1.0","source":{"id":"1209.3653","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3653","created_at":"2026-05-18T01:04:46Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3653v4","created_at":"2026-05-18T01:04:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3653","created_at":"2026-05-18T01:04:46Z"},{"alias_kind":"pith_short_12","alias_value":"HR7LUMBEELL6","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HR7LUMBEELL6TXKL","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HR7LUMBE","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:50dabafbfc244c699bf4f7216c48b11f8ece9f56d3759e194fae26540dc089e5","target":"graph","created_at":"2026-05-18T01:04:46Z","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 Z be a subvariety of the moduli space of principally polarised abelian varieties of dimension g over the complex numbers. Suppose that Z contains a Zariski dense set of points which correspond to abelian varieties from a single isogeny class. A generalisation of a conjecture of Andr\\'e and Pink predicts that Z is a weakly special subvariety. We prove this when dim Z = 1 using the Pila--Zannier method and the Masser--W\\\"ustholz isogeny theorem. This generalises results of Edixhoven and Yafaev when the Hecke orbit consists of CM points and of Pink when it consists of Galois generic points.","authors_text":"Martin Orr","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-09-17T13:55:51Z","title":"Families of abelian varieties with many isogenous fibres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3653","kind":"arxiv","version":4},"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":"sha256:96d2d36cedb763a28a5a48ea0482993554a4facac9cb5b2cf6626cbb84cf6875","target":"record","created_at":"2026-05-18T01:04:46Z","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":"17cd3237c01fbf6391153a0ea36b64e85f63b6d22d269043b5a00aeea1cecac0","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-09-17T13:55:51Z","title_canon_sha256":"bf2e5bb0ef7c066b0f2fe8610256fdec21c8f2583982d03028c818c5bcc79fcc"},"schema_version":"1.0","source":{"id":"1209.3653","kind":"arxiv","version":4}},"canonical_sha256":"3c7eba302422d7e9dd4b2154e449cf25568e5b5af9724620d95faaa6112b695b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c7eba302422d7e9dd4b2154e449cf25568e5b5af9724620d95faaa6112b695b","first_computed_at":"2026-05-18T01:04:46.166031Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:46.166031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P2GoCJqXKXM2J78WlWEdR/NCVLPfBqHZuEzNgE2ehZwmXp8AIBNg5gvKrqxgh4PkDozdKT8hTuvyRuf0BKEXBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:46.166524Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.3653","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96d2d36cedb763a28a5a48ea0482993554a4facac9cb5b2cf6626cbb84cf6875","sha256:50dabafbfc244c699bf4f7216c48b11f8ece9f56d3759e194fae26540dc089e5"],"state_sha256":"7b0fb97663374ba80b2e28a9a5440936b53eb3a765d1e00de037681516e1ef8d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7/Kmwjp4eohmS6jU6J5fOd8hy4Aiifj9MTUReRufoupV9nKmNWoU0IxxWyU6KXdZvl+E+fpP6/CAlAYoiO85Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T07:09:02.429783Z","bundle_sha256":"c5fb67da87bac95ba18f679fc252f5dd9dcc772e8f2f8b31ba00eb6f912a83f7"}}