{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:KB7MQQD3FBBQDKRDUTRMUARN7X","short_pith_number":"pith:KB7MQQD3","canonical_record":{"source":{"id":"1901.07166","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-01-22T04:21:29Z","cross_cats_sorted":[],"title_canon_sha256":"fe7499cd942b0ae02a149b909f0843f990a886956caaa7e37083c8908351767c","abstract_canon_sha256":"f033101b35521d1bc4b8e06267cbc4b91446662a0d6f9f119bfaf61d88b3ae10"},"schema_version":"1.0"},"canonical_sha256":"507ec8407b284301aa23a4e2ca022dfdd2a3751973f8153b5b5ac25e0b31dc3d","source":{"kind":"arxiv","id":"1901.07166","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.07166","created_at":"2026-07-05T03:11:08Z"},{"alias_kind":"arxiv_version","alias_value":"1901.07166v2","created_at":"2026-07-05T03:11:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.07166","created_at":"2026-07-05T03:11:08Z"},{"alias_kind":"pith_short_12","alias_value":"KB7MQQD3FBBQ","created_at":"2026-07-05T03:11:08Z"},{"alias_kind":"pith_short_16","alias_value":"KB7MQQD3FBBQDKRD","created_at":"2026-07-05T03:11:08Z"},{"alias_kind":"pith_short_8","alias_value":"KB7MQQD3","created_at":"2026-07-05T03:11:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:KB7MQQD3FBBQDKRDUTRMUARN7X","target":"record","payload":{"canonical_record":{"source":{"id":"1901.07166","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-01-22T04:21:29Z","cross_cats_sorted":[],"title_canon_sha256":"fe7499cd942b0ae02a149b909f0843f990a886956caaa7e37083c8908351767c","abstract_canon_sha256":"f033101b35521d1bc4b8e06267cbc4b91446662a0d6f9f119bfaf61d88b3ae10"},"schema_version":"1.0"},"canonical_sha256":"507ec8407b284301aa23a4e2ca022dfdd2a3751973f8153b5b5ac25e0b31dc3d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:11:08.645212Z","signature_b64":"Ck2ujK4D5Z+HLHP5QGKw7i3e5CUmjJxEzRlfIzspIzk4xPwdHPqmPZOWLG2OSixHcmcd4CL9i7C8gQVM38ppBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"507ec8407b284301aa23a4e2ca022dfdd2a3751973f8153b5b5ac25e0b31dc3d","last_reissued_at":"2026-07-05T03:11:08.644842Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:11:08.644842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1901.07166","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:11:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8TtbcL4fQ6J6Hafj8BehMTtbdOIwBV3jUUKcmBxIG7fEo+aRofpSiVS9zzSIw7haAUjVgTXpzR291TIfLD7PCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T16:01:46.249667Z"},"content_sha256":"5f2423e726988d046db544e93fa462f9b7430ea9b2892e9dae68ce1a52df60e7","schema_version":"1.0","event_id":"sha256:5f2423e726988d046db544e93fa462f9b7430ea9b2892e9dae68ce1a52df60e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:KB7MQQD3FBBQDKRDUTRMUARN7X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Fontaine-Mazur conjecture in the residually reducible case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Lue Pan","submitted_at":"2019-01-22T04:21:29Z","abstract_excerpt":"We prove new cases of Fontaine-Mazur conjecture on two-dimensional Galois representations over Q when the residual representation is reducible. Our approach is via a semi-simple local-global compatibility of the completed cohomology and a Taylor-Wiles patching argument for the completed homology in this case. As a key input, we generalize the work of Skinner-Wiles in the ordinary case. In addition, we also treat the residually irreducible case at the end of the paper. Combining with people's earlier work, we can prove the Fontaine-Mazur conjecture completely in the regular case when p is at le"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.07166","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1901.07166/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T03:11:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f3cHHYScDNU5pSyOe9LoBGGXRsp+Hdn5AjrxNbBUIFGQo2s2x9xgJyDeG01rmulMLYaVJJp+Ro9u2Dgu9gM9AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T16:01:46.249999Z"},"content_sha256":"0421ec2a549b6e2cf0805f814619431fa4701879f131f1eb56df8652ac083919","schema_version":"1.0","event_id":"sha256:0421ec2a549b6e2cf0805f814619431fa4701879f131f1eb56df8652ac083919"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KB7MQQD3FBBQDKRDUTRMUARN7X/bundle.json","state_url":"https://pith.science/pith/KB7MQQD3FBBQDKRDUTRMUARN7X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KB7MQQD3FBBQDKRDUTRMUARN7X/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":"2026-08-17T16:01:46Z","links":{"resolver":"https://pith.science/pith/KB7MQQD3FBBQDKRDUTRMUARN7X","bundle":"https://pith.science/pith/KB7MQQD3FBBQDKRDUTRMUARN7X/bundle.json","state":"https://pith.science/pith/KB7MQQD3FBBQDKRDUTRMUARN7X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KB7MQQD3FBBQDKRDUTRMUARN7X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:KB7MQQD3FBBQDKRDUTRMUARN7X","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":"f033101b35521d1bc4b8e06267cbc4b91446662a0d6f9f119bfaf61d88b3ae10","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-01-22T04:21:29Z","title_canon_sha256":"fe7499cd942b0ae02a149b909f0843f990a886956caaa7e37083c8908351767c"},"schema_version":"1.0","source":{"id":"1901.07166","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.07166","created_at":"2026-07-05T03:11:08Z"},{"alias_kind":"arxiv_version","alias_value":"1901.07166v2","created_at":"2026-07-05T03:11:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.07166","created_at":"2026-07-05T03:11:08Z"},{"alias_kind":"pith_short_12","alias_value":"KB7MQQD3FBBQ","created_at":"2026-07-05T03:11:08Z"},{"alias_kind":"pith_short_16","alias_value":"KB7MQQD3FBBQDKRD","created_at":"2026-07-05T03:11:08Z"},{"alias_kind":"pith_short_8","alias_value":"KB7MQQD3","created_at":"2026-07-05T03:11:08Z"}],"graph_snapshots":[{"event_id":"sha256:0421ec2a549b6e2cf0805f814619431fa4701879f131f1eb56df8652ac083919","target":"graph","created_at":"2026-07-05T03:11:08Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1901.07166/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove new cases of Fontaine-Mazur conjecture on two-dimensional Galois representations over Q when the residual representation is reducible. Our approach is via a semi-simple local-global compatibility of the completed cohomology and a Taylor-Wiles patching argument for the completed homology in this case. As a key input, we generalize the work of Skinner-Wiles in the ordinary case. In addition, we also treat the residually irreducible case at the end of the paper. Combining with people's earlier work, we can prove the Fontaine-Mazur conjecture completely in the regular case when p is at le","authors_text":"Lue Pan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-01-22T04:21:29Z","title":"The Fontaine-Mazur conjecture in the residually reducible case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.07166","kind":"arxiv","version":2},"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":"sha256:5f2423e726988d046db544e93fa462f9b7430ea9b2892e9dae68ce1a52df60e7","target":"record","created_at":"2026-07-05T03:11:08Z","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":"f033101b35521d1bc4b8e06267cbc4b91446662a0d6f9f119bfaf61d88b3ae10","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-01-22T04:21:29Z","title_canon_sha256":"fe7499cd942b0ae02a149b909f0843f990a886956caaa7e37083c8908351767c"},"schema_version":"1.0","source":{"id":"1901.07166","kind":"arxiv","version":2}},"canonical_sha256":"507ec8407b284301aa23a4e2ca022dfdd2a3751973f8153b5b5ac25e0b31dc3d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"507ec8407b284301aa23a4e2ca022dfdd2a3751973f8153b5b5ac25e0b31dc3d","first_computed_at":"2026-07-05T03:11:08.644842Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:11:08.644842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ck2ujK4D5Z+HLHP5QGKw7i3e5CUmjJxEzRlfIzspIzk4xPwdHPqmPZOWLG2OSixHcmcd4CL9i7C8gQVM38ppBA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:11:08.645212Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.07166","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f2423e726988d046db544e93fa462f9b7430ea9b2892e9dae68ce1a52df60e7","sha256:0421ec2a549b6e2cf0805f814619431fa4701879f131f1eb56df8652ac083919"],"state_sha256":"3af90aedab0268352029c87653508d7247044b54d427b63e677bb83811552d36"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tTs31x/nKgdXnKlLWNslXBByPtqlLqIbT7olVIvZMowIDwWfSz4AFQHxzjvaJA6HISjzB5XWQ+w4SNnredQ/Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T16:01:46.252590Z","bundle_sha256":"93c69e234532719fab1d17f18561383ce415c653eb1c4354b90abe22ad29520a"}}