{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7VY27CKE4V742UR6GLOQGD3SPT","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":"7189bacfa25f8cbbe20125e33a788d577498ea2ad9fc7cf4310819662104a4af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-12-26T04:13:26Z","title_canon_sha256":"b74e5efcc45150671db84e20a1f21bd74b85ef47dc103f3a4c315acfa896eec2"},"schema_version":"1.0","source":{"id":"1612.08322","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.08322","created_at":"2026-05-18T00:20:56Z"},{"alias_kind":"arxiv_version","alias_value":"1612.08322v1","created_at":"2026-05-18T00:20:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.08322","created_at":"2026-05-18T00:20:56Z"},{"alias_kind":"pith_short_12","alias_value":"7VY27CKE4V74","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7VY27CKE4V742UR6","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7VY27CKE","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:019f2782937224c6aad0c9d81945708219229a68c3015dbc738d296b228266a4","target":"graph","created_at":"2026-05-18T00:20:56Z","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 $G$ be a non-elementary discrete subgroup of $\\mathrm{Sp}(2,1)$. We show that if the sum of diagonal entries of each element of $G$ is a complex number, then $G$ is conjugate to a subgroup of $\\mathrm{U}(2,1)$.","authors_text":"Joonhyung Kim, Sungwoon Kim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-12-26T04:13:26Z","title":"A characterization of quaternionic Kleinian groups in dimension 2 with complex trace fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08322","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":"sha256:12b691e621ae42e3850a50d94affd754cb1e7e1554b3204266bae2e5f4d8b81f","target":"record","created_at":"2026-05-18T00:20:56Z","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":"7189bacfa25f8cbbe20125e33a788d577498ea2ad9fc7cf4310819662104a4af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-12-26T04:13:26Z","title_canon_sha256":"b74e5efcc45150671db84e20a1f21bd74b85ef47dc103f3a4c315acfa896eec2"},"schema_version":"1.0","source":{"id":"1612.08322","kind":"arxiv","version":1}},"canonical_sha256":"fd71af8944e57fcd523e32dd030f727cd2e5f54071f1120fedefcd2c8a5a0990","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd71af8944e57fcd523e32dd030f727cd2e5f54071f1120fedefcd2c8a5a0990","first_computed_at":"2026-05-18T00:20:56.866507Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:56.866507Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ww89QyG/5O5z5UGAWEi/uaYWzUal2LSZAYVr7A5n7hC9Qyn578k4mG8FLJ0FQ+eHST81pofE5S37u1qJ53yMCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:56.867049Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.08322","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12b691e621ae42e3850a50d94affd754cb1e7e1554b3204266bae2e5f4d8b81f","sha256:019f2782937224c6aad0c9d81945708219229a68c3015dbc738d296b228266a4"],"state_sha256":"304222ceab496576a90534304f4d332bd01a58b5ec52c18b44c755be428cbae2"}