{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:ZE7DL46FIX6FYF6DT3B3MGWOPB","short_pith_number":"pith:ZE7DL46F","schema_version":"1.0","canonical_sha256":"c93e35f3c545fc5c17c39ec3b61ace7849f118bc7f7994cb94b9c1fd5ec5abf2","source":{"kind":"arxiv","id":"1112.5015","version":1},"attestation_state":"computed","paper":{"title":"Lefschetz properties and the Veronese construction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CO","authors_text":"Martina Kubitzke, Satoshi Murai","submitted_at":"2011-12-21T13:17:51Z","abstract_excerpt":"In this paper, we investigate Lefschetz properties of Veronese subalgebras. We show that, for a sufficiently large $r$, the $r$\\textsuperscript{th} Veronese subalgebra of a Cohen-Macaulay standard graded $K$-algebra has properties similar to the weak and strong Lefschetz properties, which we call the `almost weak' and `almost strong' Lefschetz properties. By using this result, we obtain new results on $h$- and $g$-polynomials of Veronese subalgebras."},"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":"1112.5015","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-12-21T13:17:51Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"71dec347ba3ae0f085c9552a4c536c3efd261757ca957de22fb556876e6fd0b5","abstract_canon_sha256":"5307992e4c87ff6982c37b338b9d595ae5ead695a67dc30228ce6a4aa5887fc4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:56.461905Z","signature_b64":"MkqKufIlBRH9iH5Y7sTk2Lad16H7Vq5scsedbOuIeq0RV5c2Ig2HNS0hphW/SRQSckdIZMXZMLOKkC+z2523Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c93e35f3c545fc5c17c39ec3b61ace7849f118bc7f7994cb94b9c1fd5ec5abf2","last_reissued_at":"2026-05-18T04:05:56.461067Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:56.461067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lefschetz properties and the Veronese construction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CO","authors_text":"Martina Kubitzke, Satoshi Murai","submitted_at":"2011-12-21T13:17:51Z","abstract_excerpt":"In this paper, we investigate Lefschetz properties of Veronese subalgebras. We show that, for a sufficiently large $r$, the $r$\\textsuperscript{th} Veronese subalgebra of a Cohen-Macaulay standard graded $K$-algebra has properties similar to the weak and strong Lefschetz properties, which we call the `almost weak' and `almost strong' Lefschetz properties. By using this result, we obtain new results on $h$- and $g$-polynomials of Veronese subalgebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.5015","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1112.5015","created_at":"2026-05-18T04:05:56.461213+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.5015v1","created_at":"2026-05-18T04:05:56.461213+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.5015","created_at":"2026-05-18T04:05:56.461213+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZE7DL46FIX6F","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZE7DL46FIX6FYF6D","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZE7DL46F","created_at":"2026-05-18T12:26:47.523578+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/ZE7DL46FIX6FYF6DT3B3MGWOPB","json":"https://pith.science/pith/ZE7DL46FIX6FYF6DT3B3MGWOPB.json","graph_json":"https://pith.science/api/pith-number/ZE7DL46FIX6FYF6DT3B3MGWOPB/graph.json","events_json":"https://pith.science/api/pith-number/ZE7DL46FIX6FYF6DT3B3MGWOPB/events.json","paper":"https://pith.science/paper/ZE7DL46F"},"agent_actions":{"view_html":"https://pith.science/pith/ZE7DL46FIX6FYF6DT3B3MGWOPB","download_json":"https://pith.science/pith/ZE7DL46FIX6FYF6DT3B3MGWOPB.json","view_paper":"https://pith.science/paper/ZE7DL46F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.5015&json=true","fetch_graph":"https://pith.science/api/pith-number/ZE7DL46FIX6FYF6DT3B3MGWOPB/graph.json","fetch_events":"https://pith.science/api/pith-number/ZE7DL46FIX6FYF6DT3B3MGWOPB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZE7DL46FIX6FYF6DT3B3MGWOPB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZE7DL46FIX6FYF6DT3B3MGWOPB/action/storage_attestation","attest_author":"https://pith.science/pith/ZE7DL46FIX6FYF6DT3B3MGWOPB/action/author_attestation","sign_citation":"https://pith.science/pith/ZE7DL46FIX6FYF6DT3B3MGWOPB/action/citation_signature","submit_replication":"https://pith.science/pith/ZE7DL46FIX6FYF6DT3B3MGWOPB/action/replication_record"}},"created_at":"2026-05-18T04:05:56.461213+00:00","updated_at":"2026-05-18T04:05:56.461213+00:00"}