{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:M3UIJCRAMYXT3DW2F7D6SUGPZB","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":"c254a0c482f4fb9c51cfe8e9f0bee0e481caabdac3058d9a0335063bb803a794","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-12-28T11:14:04Z","title_canon_sha256":"4ac934f7e822d253c8d0d8fe325b64f848b1394686a855a14996d62bcc76dacf"},"schema_version":"1.0","source":{"id":"1302.3519","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.3519","created_at":"2026-05-18T03:00:37Z"},{"alias_kind":"arxiv_version","alias_value":"1302.3519v1","created_at":"2026-05-18T03:00:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.3519","created_at":"2026-05-18T03:00:37Z"},{"alias_kind":"pith_short_12","alias_value":"M3UIJCRAMYXT","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"M3UIJCRAMYXT3DW2","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"M3UIJCRA","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:af0277aa64ce34be763240d78357ebf5635f25d7be32dfad328a35fd3c6d9ab7","target":"graph","created_at":"2026-05-18T03:00:37Z","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":"The class of skew lattices can be seen as an algebraic category. It models an algebraic theory in the category of Sets where the Green's relation D is a congruence describing an adjunction to the category of Lattices. In this paper we will discuss the relevance of this approach, revisit some known decompositions and relate the order structure of a skew lattice with its coset structure that describes the internal coset decomposition of the respective algebra.","authors_text":"Joao Pita Costa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-12-28T11:14:04Z","title":"On the coset structure of a skew lattice"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3519","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":"sha256:696a10e914c8de1319b8bc14b0cf6cdd3a2f85392898407864094c7352205a36","target":"record","created_at":"2026-05-18T03:00:37Z","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":"c254a0c482f4fb9c51cfe8e9f0bee0e481caabdac3058d9a0335063bb803a794","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-12-28T11:14:04Z","title_canon_sha256":"4ac934f7e822d253c8d0d8fe325b64f848b1394686a855a14996d62bcc76dacf"},"schema_version":"1.0","source":{"id":"1302.3519","kind":"arxiv","version":1}},"canonical_sha256":"66e8848a20662f3d8eda2fc7e950cfc8769eb9eafcddb5ed590a5292c97152ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66e8848a20662f3d8eda2fc7e950cfc8769eb9eafcddb5ed590a5292c97152ab","first_computed_at":"2026-05-18T03:00:37.405369Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:37.405369Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XRfXb8J+oK4w43VqTAW0MrpmNM9DWhTI8m06hI7gX1oXRImrrxafllA0liL8z2ZPLPU+hRVKBwOMbu7nyrdTAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:37.406119Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.3519","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:696a10e914c8de1319b8bc14b0cf6cdd3a2f85392898407864094c7352205a36","sha256:af0277aa64ce34be763240d78357ebf5635f25d7be32dfad328a35fd3c6d9ab7"],"state_sha256":"ab3c8addd42214e83f421d7397f1cb00f88dda3cdb49803dc9262a35ffe8fc64"}