{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:U5AHMU3JRNUDAXJDWDZTPEAFGW","short_pith_number":"pith:U5AHMU3J","schema_version":"1.0","canonical_sha256":"a7407653698b68305d23b0f337900535a7388b4b5bca40fb1288156fd19df664","source":{"kind":"arxiv","id":"1410.8325","version":2},"attestation_state":"computed","paper":{"title":"On the rate of graded modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Maryam Jahangiri, Rasoul Ahangari Maleki","submitted_at":"2014-10-30T10:56:18Z","abstract_excerpt":"Let $K$ be a field, $R$ 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 $M$. In this paper, we find upper bounds for this invariant. More precisely, let $(A,\\mathfrak{n})$ be a regular local ring and $I\\subseteq \\mathfrak{n} ^t$ be an ideal of $A$, where $t\\geq 2$. We prove that if $(B=A/I, \\mathfrak{m} =\\mathfrak{n} /I)$ is a Cohen-Macaulay local ring with multiplicity $e(B)= \\binom{h+t-1}{h}$, where $h=embdim(B)-dim B$, then $rat(gr_{\\mathfrak{m}}(B"},"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":"1410.8325","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-10-30T10:56:18Z","cross_cats_sorted":[],"title_canon_sha256":"598309a2c3bad4c17212f3bc3f0dec065e8c0a47c3b3bfa556a711667b84e5c7","abstract_canon_sha256":"b74f07389f8f07f5f34b599d938992a3a2c2a6b9895c5096806460c411670884"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:24.179884Z","signature_b64":"HB4vpQMTipxe1FSyAwU3WKkXg+pgeEL89S0cuMyfmvYvF5fnxW4sOlu+9x3e0iJYqkqN3EuQZlyWvPud4xEWBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7407653698b68305d23b0f337900535a7388b4b5bca40fb1288156fd19df664","last_reissued_at":"2026-05-18T00:52:24.179238Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:24.179238Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the rate of graded modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Maryam Jahangiri, Rasoul Ahangari Maleki","submitted_at":"2014-10-30T10:56:18Z","abstract_excerpt":"Let $K$ be a field, $R$ 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 $M$. In this paper, we find upper bounds for this invariant. More precisely, let $(A,\\mathfrak{n})$ be a regular local ring and $I\\subseteq \\mathfrak{n} ^t$ be an ideal of $A$, where $t\\geq 2$. We prove that if $(B=A/I, \\mathfrak{m} =\\mathfrak{n} /I)$ is a Cohen-Macaulay local ring with multiplicity $e(B)= \\binom{h+t-1}{h}$, where $h=embdim(B)-dim B$, then $rat(gr_{\\mathfrak{m}}(B"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8325","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":"1410.8325","created_at":"2026-05-18T00:52:24.179351+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.8325v2","created_at":"2026-05-18T00:52:24.179351+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.8325","created_at":"2026-05-18T00:52:24.179351+00:00"},{"alias_kind":"pith_short_12","alias_value":"U5AHMU3JRNUD","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_16","alias_value":"U5AHMU3JRNUDAXJD","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_8","alias_value":"U5AHMU3J","created_at":"2026-05-18T12:28:52.271510+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/U5AHMU3JRNUDAXJDWDZTPEAFGW","json":"https://pith.science/pith/U5AHMU3JRNUDAXJDWDZTPEAFGW.json","graph_json":"https://pith.science/api/pith-number/U5AHMU3JRNUDAXJDWDZTPEAFGW/graph.json","events_json":"https://pith.science/api/pith-number/U5AHMU3JRNUDAXJDWDZTPEAFGW/events.json","paper":"https://pith.science/paper/U5AHMU3J"},"agent_actions":{"view_html":"https://pith.science/pith/U5AHMU3JRNUDAXJDWDZTPEAFGW","download_json":"https://pith.science/pith/U5AHMU3JRNUDAXJDWDZTPEAFGW.json","view_paper":"https://pith.science/paper/U5AHMU3J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.8325&json=true","fetch_graph":"https://pith.science/api/pith-number/U5AHMU3JRNUDAXJDWDZTPEAFGW/graph.json","fetch_events":"https://pith.science/api/pith-number/U5AHMU3JRNUDAXJDWDZTPEAFGW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U5AHMU3JRNUDAXJDWDZTPEAFGW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U5AHMU3JRNUDAXJDWDZTPEAFGW/action/storage_attestation","attest_author":"https://pith.science/pith/U5AHMU3JRNUDAXJDWDZTPEAFGW/action/author_attestation","sign_citation":"https://pith.science/pith/U5AHMU3JRNUDAXJDWDZTPEAFGW/action/citation_signature","submit_replication":"https://pith.science/pith/U5AHMU3JRNUDAXJDWDZTPEAFGW/action/replication_record"}},"created_at":"2026-05-18T00:52:24.179351+00:00","updated_at":"2026-05-18T00:52:24.179351+00:00"}