{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HLS5PQ36L66SRVM6VMV2F3GD7U","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":"69d45115e2de09be9e2c69d092242caa4bfe81b4ff19a8e96c7e7dc096ec56e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-06-30T11:31:28Z","title_canon_sha256":"3a97a2a83fd03b642c4742a5dd8011496edd6161ef09f86674ed661e5b052dbc"},"schema_version":"1.0","source":{"id":"1106.6192","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.6192","created_at":"2026-05-18T04:19:03Z"},{"alias_kind":"arxiv_version","alias_value":"1106.6192v1","created_at":"2026-05-18T04:19:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.6192","created_at":"2026-05-18T04:19:03Z"},{"alias_kind":"pith_short_12","alias_value":"HLS5PQ36L66S","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HLS5PQ36L66SRVM6","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HLS5PQ36","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:f2ecfc3f50e7af1ca88a9a787afcff336ef6903788e5fc07d1cac24356fc3697","target":"graph","created_at":"2026-05-18T04:19:03Z","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 $(R, S,_R\\negthinspace M_S,_S\\negthinspace N_R, f, g)$ be a general Morita context, and let $T=[{cc} R &_RM_S_SN_R & S]$ be the ring associated with this context. Similarly, let $T'=[{cc} R' & M' N' & S']$ be another Morita context ring. We study the set ${Iso}(T,T')$ of ring isomorphisms from $T$ to $T'$. Our interest in this problem is motivated by: (i) the problem to determine the automorphism group of the ring $T$, and (ii) the recovery of the non-diagonal tiles problem for this type of generalized matrix rings.\n  We introduce two classes of isomorphisms from $T$ to $T'$, the disjoint ","authors_text":"C. Boboc, L. van Wyk, S. Dascalescu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-06-30T11:31:28Z","title":"Isomorphisms between Morita context rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.6192","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:d1a7918116e3f17758be835dae5336ca0b92395feb90039d2f28c9b96a39e6e7","target":"record","created_at":"2026-05-18T04:19:03Z","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":"69d45115e2de09be9e2c69d092242caa4bfe81b4ff19a8e96c7e7dc096ec56e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-06-30T11:31:28Z","title_canon_sha256":"3a97a2a83fd03b642c4742a5dd8011496edd6161ef09f86674ed661e5b052dbc"},"schema_version":"1.0","source":{"id":"1106.6192","kind":"arxiv","version":1}},"canonical_sha256":"3ae5d7c37e5fbd28d59eab2ba2ecc3fd310e4761af02cdde0cdd9c79d38f6660","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ae5d7c37e5fbd28d59eab2ba2ecc3fd310e4761af02cdde0cdd9c79d38f6660","first_computed_at":"2026-05-18T04:19:03.787333Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:19:03.787333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lvr22Kmp+ILoMyoZ0YS66MYWTfGVdae8VhK4G7SyQ07zqn/nRZ4qbmESd/AJrll9Q/7xmFHgDvgB4OCZK6jbCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:19:03.787931Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.6192","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1a7918116e3f17758be835dae5336ca0b92395feb90039d2f28c9b96a39e6e7","sha256:f2ecfc3f50e7af1ca88a9a787afcff336ef6903788e5fc07d1cac24356fc3697"],"state_sha256":"b9936bfd824f242c51b5c9ae14119f5872cc7a6feb789a4f4cd770704caf1384"}