{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:6R5KISWTBY6P6ZMCHTNSPHZ7NF","short_pith_number":"pith:6R5KISWT","schema_version":"1.0","canonical_sha256":"f47aa44ad30e3cff65823cdb279f3f6952faf2e2bad99268718ef8e5b9dade27","source":{"kind":"arxiv","id":"1708.02815","version":2},"attestation_state":"computed","paper":{"title":"The Golod property of powers of the maximal ideal of a local ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Lars Winther Christensen, Oana Veliche","submitted_at":"2017-08-09T12:46:15Z","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."},"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":"1708.02815","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-08-09T12:46:15Z","cross_cats_sorted":[],"title_canon_sha256":"eae9a70ebd3344f969c26a7843df42789c0d040cc88550ff056b43e416ebb096","abstract_canon_sha256":"70c8cb82850e90e624f1cc1a7abd2badb2176fbb51606bd29421eca11e2569f4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:29.392644Z","signature_b64":"LG6VHYQXWrxzM2sXZ8O1if12vm8PioGEmpeHcXHO7dHKPVA1xArd2rMbDnH081Al7myP/Gk7pkVPWAPgpeTeAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f47aa44ad30e3cff65823cdb279f3f6952faf2e2bad99268718ef8e5b9dade27","last_reissued_at":"2026-05-18T00:26:29.391868Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:29.391868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Golod property of powers of the maximal ideal of a local ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Lars Winther Christensen, Oana Veliche","submitted_at":"2017-08-09T12:46:15Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02815","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":"1708.02815","created_at":"2026-05-18T00:26:29.391997+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.02815v2","created_at":"2026-05-18T00:26:29.391997+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.02815","created_at":"2026-05-18T00:26:29.391997+00:00"},{"alias_kind":"pith_short_12","alias_value":"6R5KISWTBY6P","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_16","alias_value":"6R5KISWTBY6P6ZMC","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_8","alias_value":"6R5KISWT","created_at":"2026-05-18T12:31:03.183658+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/6R5KISWTBY6P6ZMCHTNSPHZ7NF","json":"https://pith.science/pith/6R5KISWTBY6P6ZMCHTNSPHZ7NF.json","graph_json":"https://pith.science/api/pith-number/6R5KISWTBY6P6ZMCHTNSPHZ7NF/graph.json","events_json":"https://pith.science/api/pith-number/6R5KISWTBY6P6ZMCHTNSPHZ7NF/events.json","paper":"https://pith.science/paper/6R5KISWT"},"agent_actions":{"view_html":"https://pith.science/pith/6R5KISWTBY6P6ZMCHTNSPHZ7NF","download_json":"https://pith.science/pith/6R5KISWTBY6P6ZMCHTNSPHZ7NF.json","view_paper":"https://pith.science/paper/6R5KISWT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.02815&json=true","fetch_graph":"https://pith.science/api/pith-number/6R5KISWTBY6P6ZMCHTNSPHZ7NF/graph.json","fetch_events":"https://pith.science/api/pith-number/6R5KISWTBY6P6ZMCHTNSPHZ7NF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6R5KISWTBY6P6ZMCHTNSPHZ7NF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6R5KISWTBY6P6ZMCHTNSPHZ7NF/action/storage_attestation","attest_author":"https://pith.science/pith/6R5KISWTBY6P6ZMCHTNSPHZ7NF/action/author_attestation","sign_citation":"https://pith.science/pith/6R5KISWTBY6P6ZMCHTNSPHZ7NF/action/citation_signature","submit_replication":"https://pith.science/pith/6R5KISWTBY6P6ZMCHTNSPHZ7NF/action/replication_record"}},"created_at":"2026-05-18T00:26:29.391997+00:00","updated_at":"2026-05-18T00:26:29.391997+00:00"}