{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:7KGPEH7HDMB7F3LKP73HT6JAXE","short_pith_number":"pith:7KGPEH7H","canonical_record":{"source":{"id":"1904.04988","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-04-10T02:49:16Z","cross_cats_sorted":[],"title_canon_sha256":"f0556010afb562ff8f0896e807b5f1a039a1fefaf64db7d0a90fefba6af8542e","abstract_canon_sha256":"8ef3da9eb1f26a0d8a033872a92819859c68238316f27d779650031728abf141"},"schema_version":"1.0"},"canonical_sha256":"fa8cf21fe71b03f2ed6a7ff679f920b928e5133bc7942e6f0021d02c5721b50f","source":{"kind":"arxiv","id":"1904.04988","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:7KGPEH7HDMB7F3LKP73HT6JAXE","target":"record","payload":{"canonical_record":{"source":{"id":"1904.04988","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-04-10T02:49:16Z","cross_cats_sorted":[],"title_canon_sha256":"f0556010afb562ff8f0896e807b5f1a039a1fefaf64db7d0a90fefba6af8542e","abstract_canon_sha256":"8ef3da9eb1f26a0d8a033872a92819859c68238316f27d779650031728abf141"},"schema_version":"1.0"},"canonical_sha256":"fa8cf21fe71b03f2ed6a7ff679f920b928e5133bc7942e6f0021d02c5721b50f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:54.508209Z","signature_b64":"oDX86pAH2/VPOsbYzQW6Jq+1yy1dSNINnqeY6fvlhESWM2+egv8htbr+ySG/fCvK4T13IROL0OA+cz+14W/6CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa8cf21fe71b03f2ed6a7ff679f920b928e5133bc7942e6f0021d02c5721b50f","last_reissued_at":"2026-05-17T23:48:54.507618Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:54.507618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.04988","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:48:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EeOGTWxIh6PXBYyV4UV8cILY4pN6LMdqEmro8gbHEWHXyrHWf4iZKly3gPvcDy+iM05PHVFYN8rPORXz4llNCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T02:51:28.668365Z"},"content_sha256":"7dd4a6ad3b84029c5a74d48c7ca3a48a4bdc28ac1f6c0532950cdaa6906237c9","schema_version":"1.0","event_id":"sha256:7dd4a6ad3b84029c5a74d48c7ca3a48a4bdc28ac1f6c0532950cdaa6906237c9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:7KGPEH7HDMB7F3LKP73HT6JAXE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the fiber cone of monomial ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Guangjun Zhu, J\\\"urgen Herzog","submitted_at":"2019-04-10T02:49:16Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.04988","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:48:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sYCQkFI9XGFaoGtd7AvTlwIXBxisA77qlqYAt1hmC8+5PkKov+pMza0dN7icx+KNmHR/QEyjhH3s5Yx4hBUCBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T02:51:28.668839Z"},"content_sha256":"f86e22818bed0d8992ac986ed27155a3b228f2e20ad868b923bd1a5f9e46022d","schema_version":"1.0","event_id":"sha256:f86e22818bed0d8992ac986ed27155a3b228f2e20ad868b923bd1a5f9e46022d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7KGPEH7HDMB7F3LKP73HT6JAXE/bundle.json","state_url":"https://pith.science/pith/7KGPEH7HDMB7F3LKP73HT6JAXE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7KGPEH7HDMB7F3LKP73HT6JAXE/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-07T02:51:28Z","links":{"resolver":"https://pith.science/pith/7KGPEH7HDMB7F3LKP73HT6JAXE","bundle":"https://pith.science/pith/7KGPEH7HDMB7F3LKP73HT6JAXE/bundle.json","state":"https://pith.science/pith/7KGPEH7HDMB7F3LKP73HT6JAXE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7KGPEH7HDMB7F3LKP73HT6JAXE/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WiqSAIBvQu5beoaAbFi0fPzmnG+aQPuYGwOR/zs2a8GByRF/SdTkUOBpi2n6WSzw4AvMgEmwSkbZLagZ8884CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T02:51:28.672246Z","bundle_sha256":"5804a671cfd20e56507a93f15d8fbc0a4ad210b04dfc2f52c25022e8e2f4a64a"}}