{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:53MYTIVUJBU3XQ62FFPYSYAVFI","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":"0144b8a7f94a58ee2efb5fee8d3f2de4a3ffefbd5467424099c23cda7242dec9","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-04-21T14:27:14Z","title_canon_sha256":"1580ea865f6cea86a14be12d6a78bf3e08d92231b24a32a627a130dd4de45b56"},"schema_version":"1.0","source":{"id":"1804.07971","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.07971","created_at":"2026-05-18T00:01:19Z"},{"alias_kind":"arxiv_version","alias_value":"1804.07971v2","created_at":"2026-05-18T00:01:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.07971","created_at":"2026-05-18T00:01:19Z"},{"alias_kind":"pith_short_12","alias_value":"53MYTIVUJBU3","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"53MYTIVUJBU3XQ62","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"53MYTIVU","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:ab5aef1ab526c430c3bd01c461e5549ac7f1db210a1e92b3290807d86d581b64","target":"graph","created_at":"2026-05-18T00:01:19Z","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 $A$ be a $K$-subalgebra of the polynomial ring $S=K[x_1,\\ldots,x_d]$ of dimension $d$, generated by finitely many monomials of degree $r$. Then the Gauss algebra $\\GG(A)$ of $A$ is generated by monomials of degree $(r-1)d$ in $S$. We describe the generators and the structure of $\\GG(A)$, when $A$ is a Borel fixed algebra, a squarefree Veronese algebra, generated in degree $2$, or the edge ring of a bipartite graph with at least one loop. For a bipartite graph $G$ with one loop, the embedding dimension of $\\GG(A)$ is bounded by the complexity of the graph $G$.","authors_text":"Abbas Nasrollah Nejad, J\\\"urgen Herzog, Raheleh Jafari","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-04-21T14:27:14Z","title":"On the Gauss algebra of toric algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07971","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":"sha256:8a1fa65f808a01435dab1f26b3b9b9c3d28abbe0d00c12ee77a6d90e0fba1c3f","target":"record","created_at":"2026-05-18T00:01:19Z","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":"0144b8a7f94a58ee2efb5fee8d3f2de4a3ffefbd5467424099c23cda7242dec9","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-04-21T14:27:14Z","title_canon_sha256":"1580ea865f6cea86a14be12d6a78bf3e08d92231b24a32a627a130dd4de45b56"},"schema_version":"1.0","source":{"id":"1804.07971","kind":"arxiv","version":2}},"canonical_sha256":"eed989a2b44869bbc3da295f8960152a20748f4021bc3fdeb4c90ac8d84b38f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eed989a2b44869bbc3da295f8960152a20748f4021bc3fdeb4c90ac8d84b38f3","first_computed_at":"2026-05-18T00:01:19.537004Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:19.537004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9JE05DSQSxMmZYqXELGhKpPV8piy683yqxXTUMsCMmgRuJVm5AXNxqzghC8Gr3OHgV7MrTZuW8OO7Lg7rByNCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:19.537506Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.07971","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a1fa65f808a01435dab1f26b3b9b9c3d28abbe0d00c12ee77a6d90e0fba1c3f","sha256:ab5aef1ab526c430c3bd01c461e5549ac7f1db210a1e92b3290807d86d581b64"],"state_sha256":"db23a4963ef1e5367d0c85e1b0c9bc9d51ccacedf62db968fb762ba42165bd35"}