{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NC3B3YNWFOMU6OK4RG6Z4NM6RW","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":"62d02e9c6d0d3b360c31277d7e65e41d4ebecb8dd89e933d80971a09e3f8d81a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-06-25T18:31:03Z","title_canon_sha256":"48c851f9b0bc36489e7ea166a92244c8d1707694f92b8879e620f74936c66176"},"schema_version":"1.0","source":{"id":"1806.09654","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.09654","created_at":"2026-05-18T00:12:23Z"},{"alias_kind":"arxiv_version","alias_value":"1806.09654v1","created_at":"2026-05-18T00:12:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.09654","created_at":"2026-05-18T00:12:23Z"},{"alias_kind":"pith_short_12","alias_value":"NC3B3YNWFOMU","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NC3B3YNWFOMU6OK4","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NC3B3YNW","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:5b282a350d2c718f771188c6c38da923e33ac8ee0b21f05a45671af65b47df08","target":"graph","created_at":"2026-05-18T00:12:23Z","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 investigate the finite subgroups that occur in the Hamiltonian quaternion algebra over the real subfield of cyclotomic fields. When possible, we investigate their distribution among the maximal orders.","authors_text":"Mark Lewis, Murray Schacher","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-06-25T18:31:03Z","title":"Subgroups of Division Rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.09654","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":"sha256:033dfabdbf2c038b483f3bd3c776ec394815332c325a986777763918e947d0fa","target":"record","created_at":"2026-05-18T00:12:23Z","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":"62d02e9c6d0d3b360c31277d7e65e41d4ebecb8dd89e933d80971a09e3f8d81a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-06-25T18:31:03Z","title_canon_sha256":"48c851f9b0bc36489e7ea166a92244c8d1707694f92b8879e620f74936c66176"},"schema_version":"1.0","source":{"id":"1806.09654","kind":"arxiv","version":1}},"canonical_sha256":"68b61de1b62b994f395c89bd9e359e8da18775a1e926a98569dba4f7c32ca890","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68b61de1b62b994f395c89bd9e359e8da18775a1e926a98569dba4f7c32ca890","first_computed_at":"2026-05-18T00:12:23.828675Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:23.828675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GAc4qHitcDBe9CyLZYYt2iBdWc/IpbCWZyil+eb7NgXYx/9cLrOVhHSsYiSxKbI8w6OQMUJaw1SRJgMycgHpAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:23.829266Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.09654","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:033dfabdbf2c038b483f3bd3c776ec394815332c325a986777763918e947d0fa","sha256:5b282a350d2c718f771188c6c38da923e33ac8ee0b21f05a45671af65b47df08"],"state_sha256":"aa0682f0f9c013efba57d4735327bf1a622baa349a5bd96c01951e0d69607644"}