{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:W46INDZJQGONWXMK6YKXNCHY3B","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":"18e1633cc869213a9afa9487bcc7ee2fcc3c6b0f868fee5d0ea1945367c29082","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2016-10-03T12:58:13Z","title_canon_sha256":"a9b0bc308a82b5afc2446ec0d223cd3a4be962a369bba783b91815ae1c82703d"},"schema_version":"1.0","source":{"id":"1610.00525","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.00525","created_at":"2026-05-18T01:03:25Z"},{"alias_kind":"arxiv_version","alias_value":"1610.00525v1","created_at":"2026-05-18T01:03:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.00525","created_at":"2026-05-18T01:03:25Z"},{"alias_kind":"pith_short_12","alias_value":"W46INDZJQGON","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"W46INDZJQGONWXMK","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"W46INDZJ","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:322da09f5adfbb4a33b1f63c53603c8a9fbc39811d3f3a679f1ec56ef6832ef2","target":"graph","created_at":"2026-05-18T01:03:25Z","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 $(R,\\m,k)$ be a Noetherian local ring with maximal ideal $\\m$ and residue field $k$. The linearity defect of a finitely generated $R$-module $M$, which is denoted $\\ld_R(M)$, is a numerical measure of how far $M$ is from having linear resolution. We study the linearity defect of the residue field. We give a positive answer to the question raised by Herzog and Iyengar of whether $\\ld_R(k)<\\infty$ implies $\\ld_R(k)=0$, in the case when $\\m^4=0$.","authors_text":"Rasoul Ahangari Maleki","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2016-10-03T12:58:13Z","title":"Linearity defect of the residue field of short local rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00525","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":"sha256:2850bde1780014285472b06917d6ae9ebdb2871c6ac3c2ecd816fba1536bffbc","target":"record","created_at":"2026-05-18T01:03:25Z","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":"18e1633cc869213a9afa9487bcc7ee2fcc3c6b0f868fee5d0ea1945367c29082","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2016-10-03T12:58:13Z","title_canon_sha256":"a9b0bc308a82b5afc2446ec0d223cd3a4be962a369bba783b91815ae1c82703d"},"schema_version":"1.0","source":{"id":"1610.00525","kind":"arxiv","version":1}},"canonical_sha256":"b73c868f29819cdb5d8af6157688f8d87ceaca8e3c71eaca752b518636487c69","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b73c868f29819cdb5d8af6157688f8d87ceaca8e3c71eaca752b518636487c69","first_computed_at":"2026-05-18T01:03:25.318476Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:25.318476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/ePrvlAGVHKeDWUSYXxrYmkSBTYe8blyxgQc6GvucesCid58yBq5MEGC+u2kjPg7jmOuEnhLTjmM2o+x9Eg9Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:25.318992Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.00525","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2850bde1780014285472b06917d6ae9ebdb2871c6ac3c2ecd816fba1536bffbc","sha256:322da09f5adfbb4a33b1f63c53603c8a9fbc39811d3f3a679f1ec56ef6832ef2"],"state_sha256":"b89e7fecb0e4c5f5f895949a50f0f4645cc726545efa3a38c99b8b253e190428"}