{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3PRXCXDU7VG3DWK5GY3R6UAKLV","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b93cbb367e2d01e86d3fc7e7458bc1ea5e034e6b6964c46e83448bb42e90ba6f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-10-29T13:09:18Z","title_canon_sha256":"0360df616114c641fd6d55b9c9fd35e8082bded73c3b2dc3719ded6b5705056d"},"schema_version":"1.0","source":{"id":"1410.7965","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.7965","created_at":"2026-05-18T02:39:07Z"},{"alias_kind":"arxiv_version","alias_value":"1410.7965v1","created_at":"2026-05-18T02:39:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7965","created_at":"2026-05-18T02:39:07Z"},{"alias_kind":"pith_short_12","alias_value":"3PRXCXDU7VG3","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3PRXCXDU7VG3DWK5","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3PRXCXDU","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:a7f43cf269ed6c8754aeabe28bf25cd33d6fea059c2c5989a2700cff7f7efb20","target":"graph","created_at":"2026-05-18T02:39:07Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Rasoul Ahangari Maleki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-10-29T13:09:18Z","title":"Rate and syzigies of modules over Veronese subrings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7965","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7c1a35ebad44c829aece27398f99f3bfa51af5924000cf89bdfeaf00b8c31627","target":"record","created_at":"2026-05-18T02:39:07Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"b93cbb367e2d01e86d3fc7e7458bc1ea5e034e6b6964c46e83448bb42e90ba6f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-10-29T13:09:18Z","title_canon_sha256":"0360df616114c641fd6d55b9c9fd35e8082bded73c3b2dc3719ded6b5705056d"},"schema_version":"1.0","source":{"id":"1410.7965","kind":"arxiv","version":1}},"canonical_sha256":"dbe3715c74fd4db1d95d36371f500a5d524d7854c89f18f334dc38e862c91c4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dbe3715c74fd4db1d95d36371f500a5d524d7854c89f18f334dc38e862c91c4b","first_computed_at":"2026-05-18T02:39:07.711975Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:07.711975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"16syG0ttuIuPZxzWkWNevcUkzWwOniLkNfhblSaDz4RScFwd/lWOtv5shEFmiIgJ1l+VqePf3GVkrUd5Jb+yAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:07.712571Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.7965","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c1a35ebad44c829aece27398f99f3bfa51af5924000cf89bdfeaf00b8c31627","sha256:a7f43cf269ed6c8754aeabe28bf25cd33d6fea059c2c5989a2700cff7f7efb20"],"state_sha256":"67724c7bcf1818d8a3d72f0fad3094abacd3607c20e3d52706724f3882f0a307"}