{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:7KGPEH7HDMB7F3LKP73HT6JAXE","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":"8ef3da9eb1f26a0d8a033872a92819859c68238316f27d779650031728abf141","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-04-10T02:49:16Z","title_canon_sha256":"f0556010afb562ff8f0896e807b5f1a039a1fefaf64db7d0a90fefba6af8542e"},"schema_version":"1.0","source":{"id":"1904.04988","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.04988","created_at":"2026-05-17T23:48:54Z"},{"alias_kind":"arxiv_version","alias_value":"1904.04988v1","created_at":"2026-05-17T23:48:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.04988","created_at":"2026-05-17T23:48:54Z"},{"alias_kind":"pith_short_12","alias_value":"7KGPEH7HDMB7","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"7KGPEH7HDMB7F3LK","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"7KGPEH7H","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:f86e22818bed0d8992ac986ed27155a3b228f2e20ad868b923bd1a5f9e46022d","target":"graph","created_at":"2026-05-17T23:48:54Z","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 consider the fiber cone of monomial ideals. It is shown that for monomial ideals $I\\subset K[x,y]$ of height $2$, generated by $3$ elements, the fiber cone $F(I)$ of $I$ is a hypersurface ring, and that $F(I)$ has positive depth for interesting classes of height $2$ monomial ideals $I\\subset K[x,y]$, which are generated by $4$ elements. For these classes of ideals we also show that $F(I)$ is Cohen--Macaulay if and only if the defining ideal $J$ of $F(I)$ is generated by at most 3 elements. In all the cases a minimal set of generators of $J$ is determined.","authors_text":"Guangjun Zhu, J\\\"urgen Herzog","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-04-10T02:49:16Z","title":"On the fiber cone of monomial ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.04988","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":"sha256:7dd4a6ad3b84029c5a74d48c7ca3a48a4bdc28ac1f6c0532950cdaa6906237c9","target":"record","created_at":"2026-05-17T23:48:54Z","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":"8ef3da9eb1f26a0d8a033872a92819859c68238316f27d779650031728abf141","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-04-10T02:49:16Z","title_canon_sha256":"f0556010afb562ff8f0896e807b5f1a039a1fefaf64db7d0a90fefba6af8542e"},"schema_version":"1.0","source":{"id":"1904.04988","kind":"arxiv","version":1}},"canonical_sha256":"fa8cf21fe71b03f2ed6a7ff679f920b928e5133bc7942e6f0021d02c5721b50f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa8cf21fe71b03f2ed6a7ff679f920b928e5133bc7942e6f0021d02c5721b50f","first_computed_at":"2026-05-17T23:48:54.507618Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:54.507618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oDX86pAH2/VPOsbYzQW6Jq+1yy1dSNINnqeY6fvlhESWM2+egv8htbr+ySG/fCvK4T13IROL0OA+cz+14W/6CA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:54.508209Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.04988","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7dd4a6ad3b84029c5a74d48c7ca3a48a4bdc28ac1f6c0532950cdaa6906237c9","sha256:f86e22818bed0d8992ac986ed27155a3b228f2e20ad868b923bd1a5f9e46022d"],"state_sha256":"01a2f5d582fb2b8f2b61f69d369cbaf06cbe8386dd77281650c745404a34fda9"}