{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:ECB5J6ZTNAHGH3UZQLPGCVC57B","short_pith_number":"pith:ECB5J6ZT","schema_version":"1.0","canonical_sha256":"2083d4fb33680e63ee9982de61545df86620f952f5c8cc5e23a4b0f3568b2078","source":{"kind":"arxiv","id":"1107.4503","version":3},"attestation_state":"computed","paper":{"title":"On the Koszul property of toric face rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Dang Hop Nguyen","submitted_at":"2011-07-22T12:49:21Z","abstract_excerpt":"Toric face rings is a generalization of the concepts of affine monoid rings and Stanley-Reisner rings. We consider several properties which imply Koszulness for toric face rings over a field $k$. Generalizing works of Laudal, Sletsj\\o{}e and Herzog et al., graded Betti numbers of $k$ over the toric face rings are computed, and a characterization of Koszul toric face rings is provided. We investigate a conjecture suggested by R\\\"{o}mer about the sufficient condition for the Koszul property. The conjecture is inspired by Fr\\\"{o}berg's theorem on the Koszulness of quadratic squarefree monomial id"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1107.4503","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-07-22T12:49:21Z","cross_cats_sorted":[],"title_canon_sha256":"b414b1fd83763b96aa686890c30588a81ed8318ddb6f1f662444b0045180ac89","abstract_canon_sha256":"b2370fe3453575a59235aba359d6d70ec9ab33a77b6755fbc5926843a3c962cc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:23.911817Z","signature_b64":"Pd9bodeQwEPJ/M7ohNuG+NTQDbFrhUODWqfmpPyXKmquHQUPvTTd0fSP3rmynermvVVwk5LUtnyPF8IrrBaWDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2083d4fb33680e63ee9982de61545df86620f952f5c8cc5e23a4b0f3568b2078","last_reissued_at":"2026-05-18T03:38:23.911132Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:23.911132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Koszul property of toric face rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Dang Hop Nguyen","submitted_at":"2011-07-22T12:49:21Z","abstract_excerpt":"Toric face rings is a generalization of the concepts of affine monoid rings and Stanley-Reisner rings. We consider several properties which imply Koszulness for toric face rings over a field $k$. Generalizing works of Laudal, Sletsj\\o{}e and Herzog et al., graded Betti numbers of $k$ over the toric face rings are computed, and a characterization of Koszul toric face rings is provided. We investigate a conjecture suggested by R\\\"{o}mer about the sufficient condition for the Koszul property. The conjecture is inspired by Fr\\\"{o}berg's theorem on the Koszulness of quadratic squarefree monomial id"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4503","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1107.4503","created_at":"2026-05-18T03:38:23.911234+00:00"},{"alias_kind":"arxiv_version","alias_value":"1107.4503v3","created_at":"2026-05-18T03:38:23.911234+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4503","created_at":"2026-05-18T03:38:23.911234+00:00"},{"alias_kind":"pith_short_12","alias_value":"ECB5J6ZTNAHG","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_16","alias_value":"ECB5J6ZTNAHGH3UZ","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_8","alias_value":"ECB5J6ZT","created_at":"2026-05-18T12:26:26.731475+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ECB5J6ZTNAHGH3UZQLPGCVC57B","json":"https://pith.science/pith/ECB5J6ZTNAHGH3UZQLPGCVC57B.json","graph_json":"https://pith.science/api/pith-number/ECB5J6ZTNAHGH3UZQLPGCVC57B/graph.json","events_json":"https://pith.science/api/pith-number/ECB5J6ZTNAHGH3UZQLPGCVC57B/events.json","paper":"https://pith.science/paper/ECB5J6ZT"},"agent_actions":{"view_html":"https://pith.science/pith/ECB5J6ZTNAHGH3UZQLPGCVC57B","download_json":"https://pith.science/pith/ECB5J6ZTNAHGH3UZQLPGCVC57B.json","view_paper":"https://pith.science/paper/ECB5J6ZT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1107.4503&json=true","fetch_graph":"https://pith.science/api/pith-number/ECB5J6ZTNAHGH3UZQLPGCVC57B/graph.json","fetch_events":"https://pith.science/api/pith-number/ECB5J6ZTNAHGH3UZQLPGCVC57B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ECB5J6ZTNAHGH3UZQLPGCVC57B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ECB5J6ZTNAHGH3UZQLPGCVC57B/action/storage_attestation","attest_author":"https://pith.science/pith/ECB5J6ZTNAHGH3UZQLPGCVC57B/action/author_attestation","sign_citation":"https://pith.science/pith/ECB5J6ZTNAHGH3UZQLPGCVC57B/action/citation_signature","submit_replication":"https://pith.science/pith/ECB5J6ZTNAHGH3UZQLPGCVC57B/action/replication_record"}},"created_at":"2026-05-18T03:38:23.911234+00:00","updated_at":"2026-05-18T03:38:23.911234+00:00"}