{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:DL66W74QZKRBRIULVWAYCP6QTW","short_pith_number":"pith:DL66W74Q","canonical_record":{"source":{"id":"1201.5556","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-01-26T15:35:59Z","cross_cats_sorted":[],"title_canon_sha256":"f4c0b10c889b3e3dead2aae1b0a7fe3b73c30892e03698b5c2f54395db10747b","abstract_canon_sha256":"63ab0f05d0cf0715c2b8a99c9cc831a1b64564bdf5a4297006c172a9411c8a5c"},"schema_version":"1.0"},"canonical_sha256":"1afdeb7f90caa218a28bad81813fd09daa359019f99f960ae44ffd84b1b51694","source":{"kind":"arxiv","id":"1201.5556","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.5556","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"arxiv_version","alias_value":"1201.5556v1","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.5556","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"pith_short_12","alias_value":"DL66W74QZKRB","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DL66W74QZKRBRIUL","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DL66W74Q","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:DL66W74QZKRBRIULVWAYCP6QTW","target":"record","payload":{"canonical_record":{"source":{"id":"1201.5556","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-01-26T15:35:59Z","cross_cats_sorted":[],"title_canon_sha256":"f4c0b10c889b3e3dead2aae1b0a7fe3b73c30892e03698b5c2f54395db10747b","abstract_canon_sha256":"63ab0f05d0cf0715c2b8a99c9cc831a1b64564bdf5a4297006c172a9411c8a5c"},"schema_version":"1.0"},"canonical_sha256":"1afdeb7f90caa218a28bad81813fd09daa359019f99f960ae44ffd84b1b51694","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:18.987118Z","signature_b64":"BdSacvZ7lSUMrexnOAG286G682TWG1DIY84oe92HIMgc6JRmgbQtDJhVHhB7YnoDB/1lagXYx43tFkPMZn7PCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1afdeb7f90caa218a28bad81813fd09daa359019f99f960ae44ffd84b1b51694","last_reissued_at":"2026-05-17T23:53:18.986523Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:18.986523Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.5556","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":"2026-05-17T23:53:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PwxofHLNAKas4AHNK+V0JDIYyCGBL6IeF/1IqAagghY/Df7Aryi6WyHTvCPD1IXuRhjAxP2SrSNuVQ81GZdbBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:38:42.358528Z"},"content_sha256":"ca6ab9266fe0c1784301d057c3fae4192ff08335bdc1ddc6909cfb565f900800","schema_version":"1.0","event_id":"sha256:ca6ab9266fe0c1784301d057c3fae4192ff08335bdc1ddc6909cfb565f900800"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:DL66W74QZKRBRIULVWAYCP6QTW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Andr\\'e-Oort Conjecture for Drinfeld Modular Varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Patrik Hubschmid","submitted_at":"2012-01-26T15:35:59Z","abstract_excerpt":"We consider the analogue of the Andr\\'e-Oort conjecture for Drinfeld modular varieties which was formulated by Breuer. We prove this analogue for special points with separable reflex field over the base field by adapting methods which were used by Klingler and Yafaev to prove the Andr\\'e-Oort conjecture under the generalized Riemann hypothesis in the classical case. Our result extends results of Breuer showing the correctness of the analogue for special points lying in a curve and for special points having a certain behaviour at a fixed set of primes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5556","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":"2026-05-17T23:53:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xD8/jSfGRUU8RRLA1+ikDv/0rA44t6+mk6IFKCrf8rcWH4M1vPoQcN695ksnUjuN7el2SyxxgrmPgYWcgGZZCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:38:42.358862Z"},"content_sha256":"0a840af1b3611c90ed8a3f4292ab5f9151117aeffdda000b0c43e07b992d7077","schema_version":"1.0","event_id":"sha256:0a840af1b3611c90ed8a3f4292ab5f9151117aeffdda000b0c43e07b992d7077"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DL66W74QZKRBRIULVWAYCP6QTW/bundle.json","state_url":"https://pith.science/pith/DL66W74QZKRBRIULVWAYCP6QTW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DL66W74QZKRBRIULVWAYCP6QTW/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":"2026-06-24T22:38:42Z","links":{"resolver":"https://pith.science/pith/DL66W74QZKRBRIULVWAYCP6QTW","bundle":"https://pith.science/pith/DL66W74QZKRBRIULVWAYCP6QTW/bundle.json","state":"https://pith.science/pith/DL66W74QZKRBRIULVWAYCP6QTW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DL66W74QZKRBRIULVWAYCP6QTW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DL66W74QZKRBRIULVWAYCP6QTW","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":"63ab0f05d0cf0715c2b8a99c9cc831a1b64564bdf5a4297006c172a9411c8a5c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-01-26T15:35:59Z","title_canon_sha256":"f4c0b10c889b3e3dead2aae1b0a7fe3b73c30892e03698b5c2f54395db10747b"},"schema_version":"1.0","source":{"id":"1201.5556","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.5556","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"arxiv_version","alias_value":"1201.5556v1","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.5556","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"pith_short_12","alias_value":"DL66W74QZKRB","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DL66W74QZKRBRIUL","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DL66W74Q","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:0a840af1b3611c90ed8a3f4292ab5f9151117aeffdda000b0c43e07b992d7077","target":"graph","created_at":"2026-05-17T23:53:18Z","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 consider the analogue of the Andr\\'e-Oort conjecture for Drinfeld modular varieties which was formulated by Breuer. We prove this analogue for special points with separable reflex field over the base field by adapting methods which were used by Klingler and Yafaev to prove the Andr\\'e-Oort conjecture under the generalized Riemann hypothesis in the classical case. Our result extends results of Breuer showing the correctness of the analogue for special points lying in a curve and for special points having a certain behaviour at a fixed set of primes.","authors_text":"Patrik Hubschmid","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-01-26T15:35:59Z","title":"The Andr\\'e-Oort Conjecture for Drinfeld Modular Varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5556","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:ca6ab9266fe0c1784301d057c3fae4192ff08335bdc1ddc6909cfb565f900800","target":"record","created_at":"2026-05-17T23:53:18Z","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":"63ab0f05d0cf0715c2b8a99c9cc831a1b64564bdf5a4297006c172a9411c8a5c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-01-26T15:35:59Z","title_canon_sha256":"f4c0b10c889b3e3dead2aae1b0a7fe3b73c30892e03698b5c2f54395db10747b"},"schema_version":"1.0","source":{"id":"1201.5556","kind":"arxiv","version":1}},"canonical_sha256":"1afdeb7f90caa218a28bad81813fd09daa359019f99f960ae44ffd84b1b51694","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1afdeb7f90caa218a28bad81813fd09daa359019f99f960ae44ffd84b1b51694","first_computed_at":"2026-05-17T23:53:18.986523Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:18.986523Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BdSacvZ7lSUMrexnOAG286G682TWG1DIY84oe92HIMgc6JRmgbQtDJhVHhB7YnoDB/1lagXYx43tFkPMZn7PCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:18.987118Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.5556","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca6ab9266fe0c1784301d057c3fae4192ff08335bdc1ddc6909cfb565f900800","sha256:0a840af1b3611c90ed8a3f4292ab5f9151117aeffdda000b0c43e07b992d7077"],"state_sha256":"364675f4d98b17a85a1638c366cd2dec3c04e9532fb107128ce93ff605a31ab0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nxsHEvEi1gRMgumC40pUm5Bkq4KKsWwEFZtHjgrLi01SsjWro4SfxMYDEBnN90bR48uWk1XPJFyf35cUt8fcDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T22:38:42.360747Z","bundle_sha256":"284ab58371879edb4730563cee43b7125c8eb854d73f80a1df650b23b6b8708a"}}