{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6R5KISWTBY6P6ZMCHTNSPHZ7NF","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":"70c8cb82850e90e624f1cc1a7abd2badb2176fbb51606bd29421eca11e2569f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-08-09T12:46:15Z","title_canon_sha256":"eae9a70ebd3344f969c26a7843df42789c0d040cc88550ff056b43e416ebb096"},"schema_version":"1.0","source":{"id":"1708.02815","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.02815","created_at":"2026-05-18T00:26:29Z"},{"alias_kind":"arxiv_version","alias_value":"1708.02815v2","created_at":"2026-05-18T00:26:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.02815","created_at":"2026-05-18T00:26:29Z"},{"alias_kind":"pith_short_12","alias_value":"6R5KISWTBY6P","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6R5KISWTBY6P6ZMC","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6R5KISWT","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:53681e43f247141173eca1776890496b0eb1acf9201e026dc17e30e9a482444b","target":"graph","created_at":"2026-05-18T00:26:29Z","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":"We identify minimal cases in which a power $m^i\\not=0$ of the maximal ideal of a local ring $R$ is not Golod, i.e.\\ the quotient ring $R/m^i$ is not Golod. Complementary to a 2014 result by Rossi and \\c{S}ega, we prove that for a generic artinian Gorenstein local ring with $m^4=0\\not= m^3$, the quotient $R/m^3$ is not Golod. This is provided that $m$ is minimally generated by at least $3$ elements. Indeed, we show that if $m$ is $2$-generated, then every power $m^i\\not= 0$ is Golod.","authors_text":"Lars Winther Christensen, Oana Veliche","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-08-09T12:46:15Z","title":"The Golod property of powers of the maximal ideal of a local ring"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02815","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:ba61a96e9f5c10a82afde74a070e3b74ba0d62af69d48b4672859aa327770df7","target":"record","created_at":"2026-05-18T00:26:29Z","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":"70c8cb82850e90e624f1cc1a7abd2badb2176fbb51606bd29421eca11e2569f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-08-09T12:46:15Z","title_canon_sha256":"eae9a70ebd3344f969c26a7843df42789c0d040cc88550ff056b43e416ebb096"},"schema_version":"1.0","source":{"id":"1708.02815","kind":"arxiv","version":2}},"canonical_sha256":"f47aa44ad30e3cff65823cdb279f3f6952faf2e2bad99268718ef8e5b9dade27","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f47aa44ad30e3cff65823cdb279f3f6952faf2e2bad99268718ef8e5b9dade27","first_computed_at":"2026-05-18T00:26:29.391868Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:29.391868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LG6VHYQXWrxzM2sXZ8O1if12vm8PioGEmpeHcXHO7dHKPVA1xArd2rMbDnH081Al7myP/Gk7pkVPWAPgpeTeAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:29.392644Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.02815","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba61a96e9f5c10a82afde74a070e3b74ba0d62af69d48b4672859aa327770df7","sha256:53681e43f247141173eca1776890496b0eb1acf9201e026dc17e30e9a482444b"],"state_sha256":"bcbb0a2e3f27ee18967e017239a415b3e42f52bbeb8d5427fbd27bf9f35f0d8f"}