{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:LTZDTPTDHM5RLEZEWX5NYKA3IS","short_pith_number":"pith:LTZDTPTD","schema_version":"1.0","canonical_sha256":"5cf239be633b3b159324b5fadc281b44ace4440e70a43b50fe419c6276a66488","source":{"kind":"arxiv","id":"1402.2588","version":2},"attestation_state":"computed","paper":{"title":"Hilbert series of modules over positively graded polynomials rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Jan Uliczka, Julio Jos\\'e Moyano-Fern\\'andez, Lukas Katth\\\"an","submitted_at":"2014-02-11T18:14:10Z","abstract_excerpt":"In this note, we give examples of formal power series satisfying certain conditions that cannot be realized as Hilbert series of finitely generated modules. This answers to the negative a question raised in a recent article by the second and the third author. On the other hand, we show that the answer is positive after multiplication with a scalar."},"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":"1402.2588","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-02-11T18:14:10Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"6e2a4c444a9e82d42cea832725a1b1f5fa86f2810fc5c9bb0124e556ba7d7206","abstract_canon_sha256":"2b82548bb93b1a6bc047f368f392b277fcad9ae650632a624239e0dc494e39d8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:15.502330Z","signature_b64":"AZtfqFu+wcbzaqzXCQp98Qtbg+5zrD1J4MyiarBVZvTpD4ry4yWM5aDK1FhNL2zs6Myfq4RWEKfWSVsC4ljECw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5cf239be633b3b159324b5fadc281b44ace4440e70a43b50fe419c6276a66488","last_reissued_at":"2026-05-18T01:15:15.501622Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:15.501622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hilbert series of modules over positively graded polynomials rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Jan Uliczka, Julio Jos\\'e Moyano-Fern\\'andez, Lukas Katth\\\"an","submitted_at":"2014-02-11T18:14:10Z","abstract_excerpt":"In this note, we give examples of formal power series satisfying certain conditions that cannot be realized as Hilbert series of finitely generated modules. This answers to the negative a question raised in a recent article by the second and the third author. On the other hand, we show that the answer is positive after multiplication with a scalar."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2588","kind":"arxiv","version":2},"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":"1402.2588","created_at":"2026-05-18T01:15:15.501733+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.2588v2","created_at":"2026-05-18T01:15:15.501733+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.2588","created_at":"2026-05-18T01:15:15.501733+00:00"},{"alias_kind":"pith_short_12","alias_value":"LTZDTPTDHM5R","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_16","alias_value":"LTZDTPTDHM5RLEZE","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_8","alias_value":"LTZDTPTD","created_at":"2026-05-18T12:28:38.356838+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/LTZDTPTDHM5RLEZEWX5NYKA3IS","json":"https://pith.science/pith/LTZDTPTDHM5RLEZEWX5NYKA3IS.json","graph_json":"https://pith.science/api/pith-number/LTZDTPTDHM5RLEZEWX5NYKA3IS/graph.json","events_json":"https://pith.science/api/pith-number/LTZDTPTDHM5RLEZEWX5NYKA3IS/events.json","paper":"https://pith.science/paper/LTZDTPTD"},"agent_actions":{"view_html":"https://pith.science/pith/LTZDTPTDHM5RLEZEWX5NYKA3IS","download_json":"https://pith.science/pith/LTZDTPTDHM5RLEZEWX5NYKA3IS.json","view_paper":"https://pith.science/paper/LTZDTPTD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.2588&json=true","fetch_graph":"https://pith.science/api/pith-number/LTZDTPTDHM5RLEZEWX5NYKA3IS/graph.json","fetch_events":"https://pith.science/api/pith-number/LTZDTPTDHM5RLEZEWX5NYKA3IS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LTZDTPTDHM5RLEZEWX5NYKA3IS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LTZDTPTDHM5RLEZEWX5NYKA3IS/action/storage_attestation","attest_author":"https://pith.science/pith/LTZDTPTDHM5RLEZEWX5NYKA3IS/action/author_attestation","sign_citation":"https://pith.science/pith/LTZDTPTDHM5RLEZEWX5NYKA3IS/action/citation_signature","submit_replication":"https://pith.science/pith/LTZDTPTDHM5RLEZEWX5NYKA3IS/action/replication_record"}},"created_at":"2026-05-18T01:15:15.501733+00:00","updated_at":"2026-05-18T01:15:15.501733+00:00"}