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More precisely, it is shown that\n  $\\rate_{R^{(c)}}(M)\\leq \\lceil \\max\\{\\rate_{R}(M),\\rat(R)\\}/c\\rceil+\\max\\{0,\\lceil t^{R}_{0}(M)/c\\rceil\\},$ for all $c\\geq\n  1$. This extends a result of Herzog et al.\n  As a consequence of this, if $M$ is generated in degree zero, then $\\reg_{R^{(c)}}(M)=0$, for all\n  $c\\geq"},"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":"1410.7965","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-10-29T13:09:18Z","cross_cats_sorted":[],"title_canon_sha256":"0360df616114c641fd6d55b9c9fd35e8082bded73c3b2dc3719ded6b5705056d","abstract_canon_sha256":"b93cbb367e2d01e86d3fc7e7458bc1ea5e034e6b6964c46e83448bb42e90ba6f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:07.712571Z","signature_b64":"16syG0ttuIuPZxzWkWNevcUkzWwOniLkNfhblSaDz4RScFwd/lWOtv5shEFmiIgJ1l+VqePf3GVkrUd5Jb+yAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dbe3715c74fd4db1d95d36371f500a5d524d7854c89f18f334dc38e862c91c4b","last_reissued_at":"2026-05-18T02:39:07.711975Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:07.711975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rate and syzigies of modules over Veronese subrings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Rasoul Ahangari Maleki","submitted_at":"2014-10-29T13:09:18Z","abstract_excerpt":"Let $K$ be a field, $R$ be a standard graded $K$-algebra and $M$ be a finitely generated graded $R$-module. The rate of $M$, $\\rate_R(M)$, is a measure of the growth of the shifts in the minimal graded free resolution of $M$.\n  In this paper, we study the rate of Veronese modules of $M$. More precisely, it is shown that\n  $\\rate_{R^{(c)}}(M)\\leq \\lceil \\max\\{\\rate_{R}(M),\\rat(R)\\}/c\\rceil+\\max\\{0,\\lceil t^{R}_{0}(M)/c\\rceil\\},$ for all $c\\geq\n  1$. This extends a result of Herzog et al.\n  As a consequence of this, if $M$ is generated in degree zero, then $\\reg_{R^{(c)}}(M)=0$, for all\n  $c\\geq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7965","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":"1410.7965","created_at":"2026-05-18T02:39:07.712074+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.7965v1","created_at":"2026-05-18T02:39:07.712074+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7965","created_at":"2026-05-18T02:39:07.712074+00:00"},{"alias_kind":"pith_short_12","alias_value":"3PRXCXDU7VG3","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"3PRXCXDU7VG3DWK5","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"3PRXCXDU","created_at":"2026-05-18T12:28:11.866339+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/3PRXCXDU7VG3DWK5GY3R6UAKLV","json":"https://pith.science/pith/3PRXCXDU7VG3DWK5GY3R6UAKLV.json","graph_json":"https://pith.science/api/pith-number/3PRXCXDU7VG3DWK5GY3R6UAKLV/graph.json","events_json":"https://pith.science/api/pith-number/3PRXCXDU7VG3DWK5GY3R6UAKLV/events.json","paper":"https://pith.science/paper/3PRXCXDU"},"agent_actions":{"view_html":"https://pith.science/pith/3PRXCXDU7VG3DWK5GY3R6UAKLV","download_json":"https://pith.science/pith/3PRXCXDU7VG3DWK5GY3R6UAKLV.json","view_paper":"https://pith.science/paper/3PRXCXDU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.7965&json=true","fetch_graph":"https://pith.science/api/pith-number/3PRXCXDU7VG3DWK5GY3R6UAKLV/graph.json","fetch_events":"https://pith.science/api/pith-number/3PRXCXDU7VG3DWK5GY3R6UAKLV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3PRXCXDU7VG3DWK5GY3R6UAKLV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3PRXCXDU7VG3DWK5GY3R6UAKLV/action/storage_attestation","attest_author":"https://pith.science/pith/3PRXCXDU7VG3DWK5GY3R6UAKLV/action/author_attestation","sign_citation":"https://pith.science/pith/3PRXCXDU7VG3DWK5GY3R6UAKLV/action/citation_signature","submit_replication":"https://pith.science/pith/3PRXCXDU7VG3DWK5GY3R6UAKLV/action/replication_record"}},"created_at":"2026-05-18T02:39:07.712074+00:00","updated_at":"2026-05-18T02:39:07.712074+00:00"}