{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:J3VI37ZVZAORF3MHAJYFKNL7A2","short_pith_number":"pith:J3VI37ZV","canonical_record":{"source":{"id":"1804.06840","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-04-18T17:59:11Z","cross_cats_sorted":[],"title_canon_sha256":"8db4f313a137b92bcdc80fc9fd565a923e9f39b614c0f7e229a871b00fb20c89","abstract_canon_sha256":"c8ec3621108f2630e9092442d448b54ad7081fc17fd91d07ffa89fcfe47f5def"},"schema_version":"1.0"},"canonical_sha256":"4eea8dff35c81d12ed87027055357f069303ba3f9dfc137c0750dd1c2cff9c9f","source":{"kind":"arxiv","id":"1804.06840","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.06840","created_at":"2026-05-18T00:18:05Z"},{"alias_kind":"arxiv_version","alias_value":"1804.06840v1","created_at":"2026-05-18T00:18:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.06840","created_at":"2026-05-18T00:18:05Z"},{"alias_kind":"pith_short_12","alias_value":"J3VI37ZVZAOR","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"J3VI37ZVZAORF3MH","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"J3VI37ZV","created_at":"2026-05-18T12:32:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:J3VI37ZVZAORF3MHAJYFKNL7A2","target":"record","payload":{"canonical_record":{"source":{"id":"1804.06840","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-04-18T17:59:11Z","cross_cats_sorted":[],"title_canon_sha256":"8db4f313a137b92bcdc80fc9fd565a923e9f39b614c0f7e229a871b00fb20c89","abstract_canon_sha256":"c8ec3621108f2630e9092442d448b54ad7081fc17fd91d07ffa89fcfe47f5def"},"schema_version":"1.0"},"canonical_sha256":"4eea8dff35c81d12ed87027055357f069303ba3f9dfc137c0750dd1c2cff9c9f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:05.612628Z","signature_b64":"ej5IteGjdUt3+i1PMdqdVPT6uc/5oJEopeOLg5vGJqxZ1BClkmUmxY5X2cgYfU/5viPtGP42jLw/hcWjXyeVDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4eea8dff35c81d12ed87027055357f069303ba3f9dfc137c0750dd1c2cff9c9f","last_reissued_at":"2026-05-18T00:18:05.612093Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:05.612093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.06840","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":"2026-05-18T00:18:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F8ir2K0+4zc169jQXLqBtU9ynaMVnEYmTFnTvzmv/S6gf8/AiKp5rpbClfjZ61llE6t3o56MfIaajS17kx3eDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:24:20.300759Z"},"content_sha256":"423e303a9883df3104bf80bf7b0bfcd90288574b4d22f1be84e89ae039db8c27","schema_version":"1.0","event_id":"sha256:423e303a9883df3104bf80bf7b0bfcd90288574b4d22f1be84e89ae039db8c27"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:J3VI37ZVZAORF3MHAJYFKNL7A2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Mumford--Tate conjecture for products of abelian varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Johan Commelin","submitted_at":"2018-04-18T17:59:11Z","abstract_excerpt":"Let $X$ be a smooth projective variety over a finitely generated field $K$ of characteristic~$0$ and fix an embedding $K \\subset \\mathbb{C}$. The Mumford--Tate conjecture is a precise way of saying that certain extra structure on the $\\ell$-adic \\'etale cohomology groups of~$X$ (namely, a Galois representation) and certain extra structure on the singular cohomology groups of~$X$ (namely, a Hodge structure) convey the same information.\n  The main result of this paper says that if $A_1$ and~$A_2$ are abelian varieties (or abelian motives) over~$K$, and the Mumford--Tate conjecture holds for both"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06840","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":"2026-05-18T00:18:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eybD+Nj9QU7fYZwiKn4IFFfK90eQB5s8gjseo57bcpMSe3goA990ipRo8tUYc2pf+U5NiVLF9Bv5Hy2/C7KdBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:24:20.301114Z"},"content_sha256":"09524e802655c33af95e54cdf0dd16f170c4048f5081829c3e198d351fd8587a","schema_version":"1.0","event_id":"sha256:09524e802655c33af95e54cdf0dd16f170c4048f5081829c3e198d351fd8587a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J3VI37ZVZAORF3MHAJYFKNL7A2/bundle.json","state_url":"https://pith.science/pith/J3VI37ZVZAORF3MHAJYFKNL7A2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J3VI37ZVZAORF3MHAJYFKNL7A2/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":"2026-05-28T06:24:20Z","links":{"resolver":"https://pith.science/pith/J3VI37ZVZAORF3MHAJYFKNL7A2","bundle":"https://pith.science/pith/J3VI37ZVZAORF3MHAJYFKNL7A2/bundle.json","state":"https://pith.science/pith/J3VI37ZVZAORF3MHAJYFKNL7A2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J3VI37ZVZAORF3MHAJYFKNL7A2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:J3VI37ZVZAORF3MHAJYFKNL7A2","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":"c8ec3621108f2630e9092442d448b54ad7081fc17fd91d07ffa89fcfe47f5def","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-04-18T17:59:11Z","title_canon_sha256":"8db4f313a137b92bcdc80fc9fd565a923e9f39b614c0f7e229a871b00fb20c89"},"schema_version":"1.0","source":{"id":"1804.06840","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.06840","created_at":"2026-05-18T00:18:05Z"},{"alias_kind":"arxiv_version","alias_value":"1804.06840v1","created_at":"2026-05-18T00:18:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.06840","created_at":"2026-05-18T00:18:05Z"},{"alias_kind":"pith_short_12","alias_value":"J3VI37ZVZAOR","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"J3VI37ZVZAORF3MH","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"J3VI37ZV","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:09524e802655c33af95e54cdf0dd16f170c4048f5081829c3e198d351fd8587a","target":"graph","created_at":"2026-05-18T00:18:05Z","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 $X$ be a smooth projective variety over a finitely generated field $K$ of characteristic~$0$ and fix an embedding $K \\subset \\mathbb{C}$. The Mumford--Tate conjecture is a precise way of saying that certain extra structure on the $\\ell$-adic \\'etale cohomology groups of~$X$ (namely, a Galois representation) and certain extra structure on the singular cohomology groups of~$X$ (namely, a Hodge structure) convey the same information.\n  The main result of this paper says that if $A_1$ and~$A_2$ are abelian varieties (or abelian motives) over~$K$, and the Mumford--Tate conjecture holds for both","authors_text":"Johan Commelin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-04-18T17:59:11Z","title":"The Mumford--Tate conjecture for products of abelian varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06840","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":"sha256:423e303a9883df3104bf80bf7b0bfcd90288574b4d22f1be84e89ae039db8c27","target":"record","created_at":"2026-05-18T00:18:05Z","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":"c8ec3621108f2630e9092442d448b54ad7081fc17fd91d07ffa89fcfe47f5def","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-04-18T17:59:11Z","title_canon_sha256":"8db4f313a137b92bcdc80fc9fd565a923e9f39b614c0f7e229a871b00fb20c89"},"schema_version":"1.0","source":{"id":"1804.06840","kind":"arxiv","version":1}},"canonical_sha256":"4eea8dff35c81d12ed87027055357f069303ba3f9dfc137c0750dd1c2cff9c9f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4eea8dff35c81d12ed87027055357f069303ba3f9dfc137c0750dd1c2cff9c9f","first_computed_at":"2026-05-18T00:18:05.612093Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:05.612093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ej5IteGjdUt3+i1PMdqdVPT6uc/5oJEopeOLg5vGJqxZ1BClkmUmxY5X2cgYfU/5viPtGP42jLw/hcWjXyeVDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:05.612628Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.06840","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:423e303a9883df3104bf80bf7b0bfcd90288574b4d22f1be84e89ae039db8c27","sha256:09524e802655c33af95e54cdf0dd16f170c4048f5081829c3e198d351fd8587a"],"state_sha256":"36d4bb3c8453543cd62dd155177e9cc4e43af8bea0488a9fca711724e7df81a5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q/s1se7ULhfHlb4CVhiTtwR0aiA3AI+cmbU9YL9MIQMaV0YjqD4hAPPcQYPGhwPscxvYiurXfBolYpkrzatOAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T06:24:20.303186Z","bundle_sha256":"92573e6b44cadfe9cd9ffa39f7a1f1db4c49dd7d82daf0fc5f0753a10a48d16c"}}