{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7H5RSDCLV4OBC6E4QQSFIF2G3B","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":"33bd5f0468bdbd4086e1b10eda6ae491ce0fbec76daee298c952ba7509bf3a23","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-29T13:22:31Z","title_canon_sha256":"d4a9bbafff565ab9aea2cde5eb11ae194e563dd355bf6aa687370fe764b1d824"},"schema_version":"1.0","source":{"id":"1509.08736","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.08736","created_at":"2026-05-18T00:49:34Z"},{"alias_kind":"arxiv_version","alias_value":"1509.08736v4","created_at":"2026-05-18T00:49:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.08736","created_at":"2026-05-18T00:49:34Z"},{"alias_kind":"pith_short_12","alias_value":"7H5RSDCLV4OB","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7H5RSDCLV4OBC6E4","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7H5RSDCL","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:27a97a3ae588d2915d7ab74564a43bebee483812df04c7b7bdff1d9591c275d7","target":"graph","created_at":"2026-05-18T00:49:34Z","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":"In this paper we consider the original and different generalizations of Postnikov-Shapiro algebra which enumerate forests and trees of graphs, see~\\cite{PSh}. Our main result is that the algebra counting forests depends only on graphical matroid and converse. Also we generalize algebras for a hypergraph. For this, we define spanning forests and trees of a hypergraph and the corresponding \"hypergraphical\" matroid. We present $3$ different equivalent definitions of spanning forests and trees, which can be read independently from other parts of the paper.","authors_text":"Gleb Nenashev","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-29T13:22:31Z","title":"Postnikov-Shapiro Algebras, Graphical Matroids and their generalizations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08736","kind":"arxiv","version":4},"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":"sha256:3012b4011e67170e0a5869cfcbd224b6bdfa8d1deb360cf4bb75ad4889509d5d","target":"record","created_at":"2026-05-18T00:49:34Z","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":"33bd5f0468bdbd4086e1b10eda6ae491ce0fbec76daee298c952ba7509bf3a23","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-29T13:22:31Z","title_canon_sha256":"d4a9bbafff565ab9aea2cde5eb11ae194e563dd355bf6aa687370fe764b1d824"},"schema_version":"1.0","source":{"id":"1509.08736","kind":"arxiv","version":4}},"canonical_sha256":"f9fb190c4baf1c11789c8424541746d856b1efc815ea29b957c503d45f3d5207","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9fb190c4baf1c11789c8424541746d856b1efc815ea29b957c503d45f3d5207","first_computed_at":"2026-05-18T00:49:34.876802Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:34.876802Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OqN4RWnFnT/cY8QOPg4hzuMfchI16Nq8F3ZrieDJu1BxeTL5oNnvFe6nByqch+E1JR0cCBwdonKPmopqEFlPBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:34.877514Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.08736","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3012b4011e67170e0a5869cfcbd224b6bdfa8d1deb360cf4bb75ad4889509d5d","sha256:27a97a3ae588d2915d7ab74564a43bebee483812df04c7b7bdff1d9591c275d7"],"state_sha256":"00696a5603a08aadcaf33177fb5a4bf4c2518c29883e0f045ac8d0ca83a29e06"}