{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:O5NVYD6DKD7ZQVVXHIMBE6QPCQ","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":"00097a10b130b697e58ea25e3d3e6d4c32c4574754b6cd013d779a6e650cdbd5","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DB","submitted_at":"2019-04-08T10:26:35Z","title_canon_sha256":"536f45873944c25e5c27142bffe6903686da35f8c79838fdabc385647d29e2bc"},"schema_version":"1.0","source":{"id":"1904.03934","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.03934","created_at":"2026-05-17T23:49:07Z"},{"alias_kind":"arxiv_version","alias_value":"1904.03934v1","created_at":"2026-05-17T23:49:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.03934","created_at":"2026-05-17T23:49:07Z"},{"alias_kind":"pith_short_12","alias_value":"O5NVYD6DKD7Z","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"O5NVYD6DKD7ZQVVX","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"O5NVYD6D","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:d833c5c621134ecb8abf10a098f61c6e2bc7f75f65fdb723c607a45a396811bf","target":"graph","created_at":"2026-05-17T23:49:07Z","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 show that the matrix query language $\\mathsf{MATLANG}$ corresponds to a natural fragment of the positive relational algebra on $K$-relations. The fragment is defined by introducing a composition operator and restricting $K$-relation arities to two. We then proceed to show that $\\mathsf{MATLANG}$ can express all matrix queries expressible in the positive relational algebra on $K$-relations, when intermediate arities are restricted to three. Thus we offer an analogue, in a model with numerical data, to the situation in classical logic, where the algebra of binary relations is equivalent to fi","authors_text":"Jan Van den Bussche, Marc Gyssens, Robert Brijder","cross_cats":["cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DB","submitted_at":"2019-04-08T10:26:35Z","title":"On matrices and $K$-relations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.03934","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":"sha256:5471e6ad010d6e7f248e9bf67e78614edd5d8ec85dbfea2b602947088f8ed363","target":"record","created_at":"2026-05-17T23:49:07Z","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":"00097a10b130b697e58ea25e3d3e6d4c32c4574754b6cd013d779a6e650cdbd5","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DB","submitted_at":"2019-04-08T10:26:35Z","title_canon_sha256":"536f45873944c25e5c27142bffe6903686da35f8c79838fdabc385647d29e2bc"},"schema_version":"1.0","source":{"id":"1904.03934","kind":"arxiv","version":1}},"canonical_sha256":"775b5c0fc350ff9856b73a18127a0f140e6662fad53f0d80070460f11964b39f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"775b5c0fc350ff9856b73a18127a0f140e6662fad53f0d80070460f11964b39f","first_computed_at":"2026-05-17T23:49:07.640155Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:07.640155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Yp3MMgnvfxMb9K0v6YJ4zygGbc8st7bvD3rtbs8LbmHdOzIpsirBVLAgBdDpcKa+0O9VEChPI+8pL7pOcQBeAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:07.640619Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.03934","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5471e6ad010d6e7f248e9bf67e78614edd5d8ec85dbfea2b602947088f8ed363","sha256:d833c5c621134ecb8abf10a098f61c6e2bc7f75f65fdb723c607a45a396811bf"],"state_sha256":"c6fb63812a5cf7d4226cb84dfec50fe99fdc0d44d75232bf5ce734de9bd544f3"}