{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GZ26YVPT7ULFSO447QHPMJ4QGH","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":"de48dcd65520143db659523c034ce2b50531152dd4ee5a4764269b8caa2bef79","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-02-05T22:34:17Z","title_canon_sha256":"878d404cbdb1cee35bd82c3f0c3cf6f53e877f09bd2c0351843a2b233c202032"},"schema_version":"1.0","source":{"id":"1402.1210","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.1210","created_at":"2026-05-18T02:59:59Z"},{"alias_kind":"arxiv_version","alias_value":"1402.1210v1","created_at":"2026-05-18T02:59:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.1210","created_at":"2026-05-18T02:59:59Z"},{"alias_kind":"pith_short_12","alias_value":"GZ26YVPT7ULF","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GZ26YVPT7ULFSO44","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GZ26YVPT","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:f9483be31fc023ecd385a77d2aeaf25c409a8a8d0621bcf4c1e67242c952d7ae","target":"graph","created_at":"2026-05-18T02:59:59Z","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":"For many finite groups, the Inverse Galois Problem can be approached through modular/automorphic Galois representations. This is a report explaining the basic strategy, ideas and methods behind some recent results. It focusses mostly on the 2-dimensional case and underlines in particular the importance of understanding coefficient fields.","authors_text":"Gabor Wiese","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-02-05T22:34:17Z","title":"Applying modular Galois representations to the Inverse Galois Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.1210","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":"sha256:63b0e9695559ac9d5e0f64373738a9b54c77e419482871a5f9b10c692aec364d","target":"record","created_at":"2026-05-18T02:59:59Z","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":"de48dcd65520143db659523c034ce2b50531152dd4ee5a4764269b8caa2bef79","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-02-05T22:34:17Z","title_canon_sha256":"878d404cbdb1cee35bd82c3f0c3cf6f53e877f09bd2c0351843a2b233c202032"},"schema_version":"1.0","source":{"id":"1402.1210","kind":"arxiv","version":1}},"canonical_sha256":"3675ec55f3fd16593b9cfc0ef6279031d40c43a6ea7729f5e11de0e66717dde4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3675ec55f3fd16593b9cfc0ef6279031d40c43a6ea7729f5e11de0e66717dde4","first_computed_at":"2026-05-18T02:59:59.901943Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:59:59.901943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PJVc7ss53W6IBW9pCUI3SJzskl1R227o46dfqgLAE57u2qCN5KklPW/EMXgEH/Ttc8v1664+opNO6k3ZBG1GAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:59:59.902725Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.1210","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63b0e9695559ac9d5e0f64373738a9b54c77e419482871a5f9b10c692aec364d","sha256:f9483be31fc023ecd385a77d2aeaf25c409a8a8d0621bcf4c1e67242c952d7ae"],"state_sha256":"93c3674449e48fd383027a0158cff690a4865c3804c382e686f06f91b2aaf084"}