{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:DKVSOIDR4LP6UHZA57V55QC43H","short_pith_number":"pith:DKVSOIDR","schema_version":"1.0","canonical_sha256":"1aab272071e2dfea1f20efebdec05cd9f7fdab034bed820c318df69a9be5d518","source":{"kind":"arxiv","id":"2310.08357","version":1},"attestation_state":"computed","paper":{"title":"Difference of Hilbert series of homogeneous monoid algebras and their normalizations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Akihiro Higashitani","submitted_at":"2023-10-12T14:26:27Z","abstract_excerpt":"Let $Q$ be an affine monoid, $\\Bbbk[Q]$ the associated monoid $\\Bbbk$-algebra, and $\\Bbbk[\\overline{Q}]$ its normalization, where we let $\\Bbbk$ be a field. In this paper, in the case where $\\Bbbk[Q]$ is homogeneous (i.e., standard graded), a difference of the Hilbert series of $\\Bbbk[Q]$ and $\\Bbbk[\\overline{Q}]$ is discussed. More precisely, we prove that if $\\Bbbk[Q]$ satisfies Serre's condition $(S_2)$, then the degree of the $h$-polynomial of $\\Bbbk[Q]$ is always greater than or equal to that of $\\Bbbk[\\overline{Q}]$. Moreover, we also show counterexamples of this statement if we drop the"},"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":"2310.08357","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2023-10-12T14:26:27Z","cross_cats_sorted":[],"title_canon_sha256":"baa747cf0b2c41967ae8def76cc59a78f681502887af3029e2ded711b5c09ead","abstract_canon_sha256":"98bbcaf1b69e83908e2e039561b1678cc3cfb327ed392a5cb6cc9f7ed99cf595"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:00:14.466178Z","signature_b64":"slSdJ4tVBLuwLSnzkDAwuEtaBE/onpuBNLWOzthHpshZI3+G7KxjMHDYbD93uOKEIvacijJ6grhmx24vIsNfDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1aab272071e2dfea1f20efebdec05cd9f7fdab034bed820c318df69a9be5d518","last_reissued_at":"2026-07-05T07:00:14.465709Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:00:14.465709Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Difference of Hilbert series of homogeneous monoid algebras and their normalizations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Akihiro Higashitani","submitted_at":"2023-10-12T14:26:27Z","abstract_excerpt":"Let $Q$ be an affine monoid, $\\Bbbk[Q]$ the associated monoid $\\Bbbk$-algebra, and $\\Bbbk[\\overline{Q}]$ its normalization, where we let $\\Bbbk$ be a field. In this paper, in the case where $\\Bbbk[Q]$ is homogeneous (i.e., standard graded), a difference of the Hilbert series of $\\Bbbk[Q]$ and $\\Bbbk[\\overline{Q}]$ is discussed. More precisely, we prove that if $\\Bbbk[Q]$ satisfies Serre's condition $(S_2)$, then the degree of the $h$-polynomial of $\\Bbbk[Q]$ is always greater than or equal to that of $\\Bbbk[\\overline{Q}]$. Moreover, we also show counterexamples of this statement if we drop the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.08357","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2310.08357/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2310.08357","created_at":"2026-07-05T07:00:14.465765+00:00"},{"alias_kind":"arxiv_version","alias_value":"2310.08357v1","created_at":"2026-07-05T07:00:14.465765+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.08357","created_at":"2026-07-05T07:00:14.465765+00:00"},{"alias_kind":"pith_short_12","alias_value":"DKVSOIDR4LP6","created_at":"2026-07-05T07:00:14.465765+00:00"},{"alias_kind":"pith_short_16","alias_value":"DKVSOIDR4LP6UHZA","created_at":"2026-07-05T07:00:14.465765+00:00"},{"alias_kind":"pith_short_8","alias_value":"DKVSOIDR","created_at":"2026-07-05T07:00:14.465765+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/DKVSOIDR4LP6UHZA57V55QC43H","json":"https://pith.science/pith/DKVSOIDR4LP6UHZA57V55QC43H.json","graph_json":"https://pith.science/api/pith-number/DKVSOIDR4LP6UHZA57V55QC43H/graph.json","events_json":"https://pith.science/api/pith-number/DKVSOIDR4LP6UHZA57V55QC43H/events.json","paper":"https://pith.science/paper/DKVSOIDR"},"agent_actions":{"view_html":"https://pith.science/pith/DKVSOIDR4LP6UHZA57V55QC43H","download_json":"https://pith.science/pith/DKVSOIDR4LP6UHZA57V55QC43H.json","view_paper":"https://pith.science/paper/DKVSOIDR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2310.08357&json=true","fetch_graph":"https://pith.science/api/pith-number/DKVSOIDR4LP6UHZA57V55QC43H/graph.json","fetch_events":"https://pith.science/api/pith-number/DKVSOIDR4LP6UHZA57V55QC43H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DKVSOIDR4LP6UHZA57V55QC43H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DKVSOIDR4LP6UHZA57V55QC43H/action/storage_attestation","attest_author":"https://pith.science/pith/DKVSOIDR4LP6UHZA57V55QC43H/action/author_attestation","sign_citation":"https://pith.science/pith/DKVSOIDR4LP6UHZA57V55QC43H/action/citation_signature","submit_replication":"https://pith.science/pith/DKVSOIDR4LP6UHZA57V55QC43H/action/replication_record"}},"created_at":"2026-07-05T07:00:14.465765+00:00","updated_at":"2026-07-05T07:00:14.465765+00:00"}