{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:YBO3MP4NKL2JU2QERV7RF2CPHY","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":"21b95906f126c564a6b9a162575827a1a0159da632ba6f6f8bdd2bf297a09715","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-03-26T16:27:55Z","title_canon_sha256":"2a3f550035b785d55c5b425b3342ea626c99e5777ae6f08efc231a76a771a570"},"schema_version":"1.0","source":{"id":"1203.5718","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.5718","created_at":"2026-05-18T03:06:52Z"},{"alias_kind":"arxiv_version","alias_value":"1203.5718v3","created_at":"2026-05-18T03:06:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.5718","created_at":"2026-05-18T03:06:52Z"},{"alias_kind":"pith_short_12","alias_value":"YBO3MP4NKL2J","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"YBO3MP4NKL2JU2QE","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"YBO3MP4N","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:1155123639cf2fd5f9a696c489bbd11ecbecddde09eb4315040931e7db9e9a47","target":"graph","created_at":"2026-05-18T03:06:52Z","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 prove the finiteness and compatibility with base change of the (phi,Gamma)-cohomology and the Iwasawa cohomology of arithmetic families of (phi,Gamma)-modules. Using this finiteness theorem, we show that a family of Galois representations that is densely pointwise refined in the sense of Mazur is actually trianguline as a family over a large subspace. In the case of the Coleman-Mazur eigencurve, we determine the behavior at all points.","authors_text":"Jonathan Pottharst, Kiran S. Kedlaya, Liang Xiao","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-03-26T16:27:55Z","title":"Cohomology of arithmetic families of (phi,Gamma)-modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.5718","kind":"arxiv","version":3},"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:b84dfcc85366c2fdbc6502aeb77f6d2f94310f5d9c6a62a9fd1f8586ff0e86b8","target":"record","created_at":"2026-05-18T03:06:52Z","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":"21b95906f126c564a6b9a162575827a1a0159da632ba6f6f8bdd2bf297a09715","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-03-26T16:27:55Z","title_canon_sha256":"2a3f550035b785d55c5b425b3342ea626c99e5777ae6f08efc231a76a771a570"},"schema_version":"1.0","source":{"id":"1203.5718","kind":"arxiv","version":3}},"canonical_sha256":"c05db63f8d52f49a6a048d7f12e84f3e1c07cab377554a5501494349fc0a31bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c05db63f8d52f49a6a048d7f12e84f3e1c07cab377554a5501494349fc0a31bb","first_computed_at":"2026-05-18T03:06:52.009287Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:52.009287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U48NzknIDatQlPcYXYVbwiB8pBIQvdNJakR55FppRzgT5ga8KUH+yVE9HpCemRtQmv44i4e8dfDE8rCk0hjRAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:52.010093Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.5718","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b84dfcc85366c2fdbc6502aeb77f6d2f94310f5d9c6a62a9fd1f8586ff0e86b8","sha256:1155123639cf2fd5f9a696c489bbd11ecbecddde09eb4315040931e7db9e9a47"],"state_sha256":"c290c6c57e57d55b3c81f5b8748547f7dbd24b6324984e0709629b87a238b335"}