{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:V3WORXA22XX4BURQRA544GW2TP","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":"519afceb42a83f3aada3ea928fb564d3a831d99cdf5a7958d4d4d6fef9424b5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-06T07:46:33Z","title_canon_sha256":"cae8cf187032cb61403b0799dc3bf49118d20e26ecde1cfa4e96a51156b752ca"},"schema_version":"1.0","source":{"id":"1809.01860","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.01860","created_at":"2026-05-17T23:52:33Z"},{"alias_kind":"arxiv_version","alias_value":"1809.01860v2","created_at":"2026-05-17T23:52:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.01860","created_at":"2026-05-17T23:52:33Z"},{"alias_kind":"pith_short_12","alias_value":"V3WORXA22XX4","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"V3WORXA22XX4BURQ","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"V3WORXA2","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:b9d2f2b97ee6e3ed69b358844da00b882a68df3aedf2c118d07ad0f6c51ce5f9","target":"graph","created_at":"2026-05-17T23:52:33Z","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":"We develop a version of cluster algebra extending the ring of Laurent polynomials by adding Grassmann variables. These algebras can be described in terms of `extended quivers' which are oriented hypergraphs. We describe mutations of such objects and define a corresponding commutative superalgebra. Our construction includes the notion of weighted quivers that has already appeared in different contexts. This paper is a step of understanding the notion of cluster superalgebra","authors_text":"Michael Shapiro, Valentin Ovsienko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-06T07:46:33Z","title":"Cluster algebras with Grassmann variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.01860","kind":"arxiv","version":2},"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":"sha256:6f4ffa63ded8e642514de4d8da6c493bdbf45cf9661e9b3946695b46e1d98c46","target":"record","created_at":"2026-05-17T23:52:33Z","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":"519afceb42a83f3aada3ea928fb564d3a831d99cdf5a7958d4d4d6fef9424b5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-06T07:46:33Z","title_canon_sha256":"cae8cf187032cb61403b0799dc3bf49118d20e26ecde1cfa4e96a51156b752ca"},"schema_version":"1.0","source":{"id":"1809.01860","kind":"arxiv","version":2}},"canonical_sha256":"aeece8dc1ad5efc0d230883bce1ada9bc54e26a5026f7a3dba79e0838ac18260","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aeece8dc1ad5efc0d230883bce1ada9bc54e26a5026f7a3dba79e0838ac18260","first_computed_at":"2026-05-17T23:52:33.836606Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:33.836606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HKjPLknU+pq2Ws9Mo+cLciPH1qFLB6CC9+s71FACko/tYNkCZYPqkiXmbAsT5qE0Oa2rMHYii3Cy5kIvPBeHDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:33.837029Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.01860","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f4ffa63ded8e642514de4d8da6c493bdbf45cf9661e9b3946695b46e1d98c46","sha256:b9d2f2b97ee6e3ed69b358844da00b882a68df3aedf2c118d07ad0f6c51ce5f9"],"state_sha256":"f6f017c4fb80b07f07d35b864772e4b9e57551ae501b26df41a8ffd1b6715756"}