{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:4KHIRKZBSMYVYWH7DVFDZQDDNE","short_pith_number":"pith:4KHIRKZB","canonical_record":{"source":{"id":"1508.06426","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-08-26T09:48:05Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"ff82670905221d9e9c16a975a842ea35aa2a82aea192d28c9152322d8289e322","abstract_canon_sha256":"54eaa97f4bbc28f9a896db3ab4c52b436b5a5ae4ecfdbc90ae317335f0f666fc"},"schema_version":"1.0"},"canonical_sha256":"e28e88ab2193315c58ff1d4a3cc06369180893f28e5bcdecd58bbdb754bd3f41","source":{"kind":"arxiv","id":"1508.06426","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.06426","created_at":"2026-05-18T01:34:43Z"},{"alias_kind":"arxiv_version","alias_value":"1508.06426v1","created_at":"2026-05-18T01:34:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06426","created_at":"2026-05-18T01:34:43Z"},{"alias_kind":"pith_short_12","alias_value":"4KHIRKZBSMYV","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4KHIRKZBSMYVYWH7","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4KHIRKZB","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:4KHIRKZBSMYVYWH7DVFDZQDDNE","target":"record","payload":{"canonical_record":{"source":{"id":"1508.06426","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-08-26T09:48:05Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"ff82670905221d9e9c16a975a842ea35aa2a82aea192d28c9152322d8289e322","abstract_canon_sha256":"54eaa97f4bbc28f9a896db3ab4c52b436b5a5ae4ecfdbc90ae317335f0f666fc"},"schema_version":"1.0"},"canonical_sha256":"e28e88ab2193315c58ff1d4a3cc06369180893f28e5bcdecd58bbdb754bd3f41","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:43.034939Z","signature_b64":"f1iwTU0Itqz1bf6C4K+V4Z3Fivc3LepuH+LyVFpirC6V5hGQ5rIPmmMZidIm63ZBUIniGg6/OYoNdy+QLvRkCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e28e88ab2193315c58ff1d4a3cc06369180893f28e5bcdecd58bbdb754bd3f41","last_reissued_at":"2026-05-18T01:34:43.034269Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:43.034269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.06426","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":"2026-05-18T01:34:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EhruGvcJicUs1Q7Aj+wFCwbb9F2tQHOB2XcOTLw0kNufiLDWO3RIwaPIhz++azEwOExaB2jV9MOqEqT6dJZAAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:30:48.131951Z"},"content_sha256":"6fa3815bff030d1a440114e3ea2f24708e157ccd5959d3f8580974974ee37d19","schema_version":"1.0","event_id":"sha256:6fa3815bff030d1a440114e3ea2f24708e157ccd5959d3f8580974974ee37d19"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:4KHIRKZBSMYVYWH7DVFDZQDDNE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Integral and adelic aspects of the Mumford-Tate conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Anna Cadoret, Ben Moonen","submitted_at":"2015-08-26T09:48:05Z","abstract_excerpt":"Let $Y$ be an abelian variety over a subfield $k \\subset \\mathbb{C}$ that is of finite type over $\\mathbb{Q}$. We prove that if the Mumford-Tate conjecture for $Y$ is true, then also some refined integral and adelic conjectures due to Serre are true for $Y$. In particular, if a certain Hodge-maximality condition is satisfied, we obtain an adelic open image theorem for the Galois representation on the (full) Tate module of $Y$. Our second main result is an (unconditional) adelic open image theorem for K3 surfaces. The proofs of these results rely on the study of a natural representation of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06426","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":"2026-05-18T01:34:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B3HU1hAX5yvXY54h5kw45UuRJWVQiwhVCUlBTSQfVRK6j69CFvcWPP4YSuot7iwhoeFh6njCXCmk5vYLiISFDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:30:48.132552Z"},"content_sha256":"6cc9c23f9aa1c5d3b27fe29c647fdbe6ca3bfba3c61d286138f57e4a55b3c754","schema_version":"1.0","event_id":"sha256:6cc9c23f9aa1c5d3b27fe29c647fdbe6ca3bfba3c61d286138f57e4a55b3c754"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4KHIRKZBSMYVYWH7DVFDZQDDNE/bundle.json","state_url":"https://pith.science/pith/4KHIRKZBSMYVYWH7DVFDZQDDNE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4KHIRKZBSMYVYWH7DVFDZQDDNE/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":"2026-05-30T05:30:48Z","links":{"resolver":"https://pith.science/pith/4KHIRKZBSMYVYWH7DVFDZQDDNE","bundle":"https://pith.science/pith/4KHIRKZBSMYVYWH7DVFDZQDDNE/bundle.json","state":"https://pith.science/pith/4KHIRKZBSMYVYWH7DVFDZQDDNE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4KHIRKZBSMYVYWH7DVFDZQDDNE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4KHIRKZBSMYVYWH7DVFDZQDDNE","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":"54eaa97f4bbc28f9a896db3ab4c52b436b5a5ae4ecfdbc90ae317335f0f666fc","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-08-26T09:48:05Z","title_canon_sha256":"ff82670905221d9e9c16a975a842ea35aa2a82aea192d28c9152322d8289e322"},"schema_version":"1.0","source":{"id":"1508.06426","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.06426","created_at":"2026-05-18T01:34:43Z"},{"alias_kind":"arxiv_version","alias_value":"1508.06426v1","created_at":"2026-05-18T01:34:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06426","created_at":"2026-05-18T01:34:43Z"},{"alias_kind":"pith_short_12","alias_value":"4KHIRKZBSMYV","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4KHIRKZBSMYVYWH7","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4KHIRKZB","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:6cc9c23f9aa1c5d3b27fe29c647fdbe6ca3bfba3c61d286138f57e4a55b3c754","target":"graph","created_at":"2026-05-18T01:34:43Z","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 $Y$ be an abelian variety over a subfield $k \\subset \\mathbb{C}$ that is of finite type over $\\mathbb{Q}$. We prove that if the Mumford-Tate conjecture for $Y$ is true, then also some refined integral and adelic conjectures due to Serre are true for $Y$. In particular, if a certain Hodge-maximality condition is satisfied, we obtain an adelic open image theorem for the Galois representation on the (full) Tate module of $Y$. Our second main result is an (unconditional) adelic open image theorem for K3 surfaces. The proofs of these results rely on the study of a natural representation of the ","authors_text":"Anna Cadoret, Ben Moonen","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-08-26T09:48:05Z","title":"Integral and adelic aspects of the Mumford-Tate conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06426","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":"sha256:6fa3815bff030d1a440114e3ea2f24708e157ccd5959d3f8580974974ee37d19","target":"record","created_at":"2026-05-18T01:34:43Z","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":"54eaa97f4bbc28f9a896db3ab4c52b436b5a5ae4ecfdbc90ae317335f0f666fc","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-08-26T09:48:05Z","title_canon_sha256":"ff82670905221d9e9c16a975a842ea35aa2a82aea192d28c9152322d8289e322"},"schema_version":"1.0","source":{"id":"1508.06426","kind":"arxiv","version":1}},"canonical_sha256":"e28e88ab2193315c58ff1d4a3cc06369180893f28e5bcdecd58bbdb754bd3f41","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e28e88ab2193315c58ff1d4a3cc06369180893f28e5bcdecd58bbdb754bd3f41","first_computed_at":"2026-05-18T01:34:43.034269Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:43.034269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f1iwTU0Itqz1bf6C4K+V4Z3Fivc3LepuH+LyVFpirC6V5hGQ5rIPmmMZidIm63ZBUIniGg6/OYoNdy+QLvRkCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:43.034939Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.06426","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6fa3815bff030d1a440114e3ea2f24708e157ccd5959d3f8580974974ee37d19","sha256:6cc9c23f9aa1c5d3b27fe29c647fdbe6ca3bfba3c61d286138f57e4a55b3c754"],"state_sha256":"fe0008e184b304bb9e1e0964534821aa49311d79482c3b5856d703f333aba601"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yo1fj3jeTzt89Jx2pPdTHvfhL3V+F394M+TfPk/DWaaZajQH6J04hTIh0Nz5bNR3tRgYAt666Mu7jjAx8afaDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T05:30:48.134860Z","bundle_sha256":"e23315d1df0b924bec16cf2613423abc754e56d4741ceea68c696e96e7b73336"}}