{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:IFVLLHCE7OHID2XDRTYHPCSVMH","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":"a97e712d89da3ae8a6397e597ade8ff0b3eb830c7bee7ba948cba45080565a71","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-10-15T08:07:26Z","title_canon_sha256":"73d62da4b35b8360ed83b979ae541493def3f453ac3a2e1582c2fc1c3c8e7f86"},"schema_version":"1.0","source":{"id":"1510.04435","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.04435","created_at":"2026-05-18T00:19:14Z"},{"alias_kind":"arxiv_version","alias_value":"1510.04435v2","created_at":"2026-05-18T00:19:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04435","created_at":"2026-05-18T00:19:14Z"},{"alias_kind":"pith_short_12","alias_value":"IFVLLHCE7OHI","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IFVLLHCE7OHID2XD","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IFVLLHCE","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:1919fe2861116465e8d962cd4f05b0e79e15ac796688877962a09225c25dd4f2","target":"graph","created_at":"2026-05-18T00:19:14Z","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 $S$ be a regular local ring or a polynomial ring over a field and $I$ be an ideal of $S$. Motivated by a recent result of Herzog and Huneke, we study the natural question of whether $I^m$ is a Golod ideal for all $m\\geq 2$. We observe that the Golod property of an ideal can be detected through the vanishing of certain maps induced in homology. This observation leads us to generalize some known results from the graded case to local rings and obtain new classes of Golod ideals.","authors_text":"Rasoul Ahangari Maleki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-10-15T08:07:26Z","title":"The Golod property for powers of ideals and Koszul ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04435","kind":"arxiv","version":2},"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":"sha256:1ec922cc942ea52af5a2e5299b86fce25056fa7ce21edccc794be8d03d885383","target":"record","created_at":"2026-05-18T00:19:14Z","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":"a97e712d89da3ae8a6397e597ade8ff0b3eb830c7bee7ba948cba45080565a71","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-10-15T08:07:26Z","title_canon_sha256":"73d62da4b35b8360ed83b979ae541493def3f453ac3a2e1582c2fc1c3c8e7f86"},"schema_version":"1.0","source":{"id":"1510.04435","kind":"arxiv","version":2}},"canonical_sha256":"416ab59c44fb8e81eae38cf0778a5561cfd2d2acdb17008c65385c30aa4b822d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"416ab59c44fb8e81eae38cf0778a5561cfd2d2acdb17008c65385c30aa4b822d","first_computed_at":"2026-05-18T00:19:14.439004Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:14.439004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kJXbyNA8GDWMzEyPuQ+4hYcfGjWQCZxtnrm2dwVdjYZE9P+6IgFPMeF+sbasI14GPa2rshUYlJnuqVbjViNxBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:14.439723Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.04435","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ec922cc942ea52af5a2e5299b86fce25056fa7ce21edccc794be8d03d885383","sha256:1919fe2861116465e8d962cd4f05b0e79e15ac796688877962a09225c25dd4f2"],"state_sha256":"30190515251b3f4710b7417d330fb7c423131c96d2a4d43a0a85f8b8accfd416"}