{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HUCGCDYWMICK2KHMWNGLBO6K5W","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":"8104b06952166c2a5a4b9239b8dc26bb18a2f241e8c2011dc5514116722504fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-07-31T21:43:52Z","title_canon_sha256":"48b0951ed8919d4935aeadc0d0b12d23ee4b2223355febbc837d2b255e4bb172"},"schema_version":"1.0","source":{"id":"1508.00041","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.00041","created_at":"2026-05-18T01:35:59Z"},{"alias_kind":"arxiv_version","alias_value":"1508.00041v1","created_at":"2026-05-18T01:35:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.00041","created_at":"2026-05-18T01:35:59Z"},{"alias_kind":"pith_short_12","alias_value":"HUCGCDYWMICK","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HUCGCDYWMICK2KHM","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HUCGCDYW","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:5243b024242e09291f0fd54e05ce29a963bb940092164006912e99e0069416af","target":"graph","created_at":"2026-05-18T01:35:59Z","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":"Let $ m , n \\in \\mathbb{N}$, $D$ be a division ring, and $M_{m \\times n}(D)$ denote the bimodule of all $m \\times n$ matrices with entries from $D$. First, we characterize one-sided submodules of $M_{m \\times n}(D)$ in terms of left row reduced echelon or right column reduced echelon matrices with entries from $D$. Next, we introduce the notion of a nest module of matrices with entries from $D$. We then characterize submodules of nest modules of matrices over $D$ in terms of certain finite sequences of left row reduced echelon or right column reduced echelon matrices with entries from $D$. We ","authors_text":"Bamdad R. Yahaghi, M. Rahimi-Alangi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-07-31T21:43:52Z","title":"On nest modules of matrices over division rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00041","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":"sha256:2530a22368e8f6276529b5506fdd16a7f8081b0c737d1158e819857fa2e024a5","target":"record","created_at":"2026-05-18T01:35:59Z","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":"8104b06952166c2a5a4b9239b8dc26bb18a2f241e8c2011dc5514116722504fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-07-31T21:43:52Z","title_canon_sha256":"48b0951ed8919d4935aeadc0d0b12d23ee4b2223355febbc837d2b255e4bb172"},"schema_version":"1.0","source":{"id":"1508.00041","kind":"arxiv","version":1}},"canonical_sha256":"3d04610f166204ad28ecb34cb0bbcaed8f5a51a2c2b8d172536370c70fdc2247","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d04610f166204ad28ecb34cb0bbcaed8f5a51a2c2b8d172536370c70fdc2247","first_computed_at":"2026-05-18T01:35:59.270612Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:59.270612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YXq9IdyaOkkWbPkaQd0jJvG1kmRKpHJqtxf251P/BYSrEYylf+ceK+ZRxqRbHJjoOztO0550kQKmeqOAe96iCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:59.271070Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.00041","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2530a22368e8f6276529b5506fdd16a7f8081b0c737d1158e819857fa2e024a5","sha256:5243b024242e09291f0fd54e05ce29a963bb940092164006912e99e0069416af"],"state_sha256":"02a3d7374d4db388dda74d28529a2f00685819a5b9941661fadadca5426b1679"}