{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:J56RVNP4EYDYLPMUUUQLPRZN5Y","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":"849498497b0ece9c1d02dd4b2dfe57c66baccf3c3d728877113297b54125149b","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-09-30T16:32:43Z","title_canon_sha256":"6bc8195db0e8faa0d7abba7deaa527a41ad8ff04c2979afd19ed6a4226505bc7"},"schema_version":"1.0","source":{"id":"1609.09802","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.09802","created_at":"2026-05-18T01:03:33Z"},{"alias_kind":"arxiv_version","alias_value":"1609.09802v1","created_at":"2026-05-18T01:03:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.09802","created_at":"2026-05-18T01:03:33Z"},{"alias_kind":"pith_short_12","alias_value":"J56RVNP4EYDY","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"J56RVNP4EYDYLPMU","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"J56RVNP4","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:c48403e73093b0fef36bc18fd0d1b66a7ce5eaf306f6c66baece578d7cc99aa0","target":"graph","created_at":"2026-05-18T01:03:33Z","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":"In this paper we investigate the structure of groups elementarily equivalent to the group $T_n(R)$ of all invertible upper triangular $n\\times n$ matrices, where $n\\geq 3$ and $R$ is a characteristic zero integral domain. In particular we give both necessary and sufficient conditions for a group being elementarily equivalent to $T_n(R)$ where $R$ is a characteristic zero algebraically closed field, a real closed field, a number field, or the ring of integers of a number field.","authors_text":"Alexei Miasnikov, Mahmood Sohrabi","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-09-30T16:32:43Z","title":"On groups elementarily equivalent to a group of triangular matrices $T_n(R)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.09802","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:af619db939622f5882317e0ca4005e24b186711ff7935c402347cd952c8f84b8","target":"record","created_at":"2026-05-18T01:03:33Z","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":"849498497b0ece9c1d02dd4b2dfe57c66baccf3c3d728877113297b54125149b","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-09-30T16:32:43Z","title_canon_sha256":"6bc8195db0e8faa0d7abba7deaa527a41ad8ff04c2979afd19ed6a4226505bc7"},"schema_version":"1.0","source":{"id":"1609.09802","kind":"arxiv","version":1}},"canonical_sha256":"4f7d1ab5fc260785bd94a520b7c72dee3706625f59238520a10aa7d93346fb38","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f7d1ab5fc260785bd94a520b7c72dee3706625f59238520a10aa7d93346fb38","first_computed_at":"2026-05-18T01:03:33.347669Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:33.347669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dET7JwZF3MoabpShCKsS+YH1rI91nE/bDT8C3HYl9yuuz59VwwoCoTyu92qAck+YV6s3qFxqtFCjcq1fWdtYDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:33.348245Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.09802","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af619db939622f5882317e0ca4005e24b186711ff7935c402347cd952c8f84b8","sha256:c48403e73093b0fef36bc18fd0d1b66a7ce5eaf306f6c66baece578d7cc99aa0"],"state_sha256":"e37e4a5e3adc8befb8e455aeed85610fd524273c74ec37714ba7024f25c43dc6"}