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We also prove that the converse is true if ${\\rm char}(K)=0$. To show the latter statement, the radicalness of these ideals and a result of Etingof et al. are crucial. We also remark that $R/I^{\\rm Sp}_{(n-3,3)}$ is NOT Cohen--Macaulay if and only if ${\\rm char}(K)=2$."},"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":"1902.06577","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-02-18T14:06:59Z","cross_cats_sorted":[],"title_canon_sha256":"982364302174e0f9bdd35d36eae84db912470d9bb3562dccbae7a6ecadc2b6dc","abstract_canon_sha256":"43607471b06b091c030aa021b542977b2ef47751a4e31cdcea8837a826ac1852"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:45.083176Z","signature_b64":"KdfBxo/3vm1tucMYCLrNAetGAxCY+v7PcjrcXJOhc3J74zd7EgFAhJtcbt3K657+ghHvUCXUhWH8bKnqFDNiBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eea42b11dbe1f7a08bb44b754159b739e08c3c0b48fa30da24ea8258bc2c674f","last_reissued_at":"2026-05-17T23:53:45.082689Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:45.082689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"When is a Specht ideal Cohen-Macaulay?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Kohji Yanagawa","submitted_at":"2019-02-18T14:06:59Z","abstract_excerpt":"For a partition $\\lambda$ of $n$, let $I^{\\rm Sp}_\\lambda$ be the ideal of $R=K[x_1, \\ldots, x_n]$ generated by all Specht polynomials of shape $\\lambda$. We show that if $R/I^{\\rm Sp}_\\lambda$ is Cohen--Macaulay then $\\lambda$ is of the form either $(a, 1, \\ldots, 1)$, $(a,b)$, or $(a,a,1)$. We also prove that the converse is true if ${\\rm char}(K)=0$. To show the latter statement, the radicalness of these ideals and a result of Etingof et al. are crucial. We also remark that $R/I^{\\rm Sp}_{(n-3,3)}$ is NOT Cohen--Macaulay if and only if ${\\rm char}(K)=2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.06577","kind":"arxiv","version":1},"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":"1902.06577","created_at":"2026-05-17T23:53:45.082768+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.06577v1","created_at":"2026-05-17T23:53:45.082768+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.06577","created_at":"2026-05-17T23:53:45.082768+00:00"},{"alias_kind":"pith_short_12","alias_value":"52SCWEO34H32","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_16","alias_value":"52SCWEO34H32BC5U","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_8","alias_value":"52SCWEO3","created_at":"2026-05-18T12:33:10.108867+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/52SCWEO34H32BC5UJN2UCWNXHH","json":"https://pith.science/pith/52SCWEO34H32BC5UJN2UCWNXHH.json","graph_json":"https://pith.science/api/pith-number/52SCWEO34H32BC5UJN2UCWNXHH/graph.json","events_json":"https://pith.science/api/pith-number/52SCWEO34H32BC5UJN2UCWNXHH/events.json","paper":"https://pith.science/paper/52SCWEO3"},"agent_actions":{"view_html":"https://pith.science/pith/52SCWEO34H32BC5UJN2UCWNXHH","download_json":"https://pith.science/pith/52SCWEO34H32BC5UJN2UCWNXHH.json","view_paper":"https://pith.science/paper/52SCWEO3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.06577&json=true","fetch_graph":"https://pith.science/api/pith-number/52SCWEO34H32BC5UJN2UCWNXHH/graph.json","fetch_events":"https://pith.science/api/pith-number/52SCWEO34H32BC5UJN2UCWNXHH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/52SCWEO34H32BC5UJN2UCWNXHH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/52SCWEO34H32BC5UJN2UCWNXHH/action/storage_attestation","attest_author":"https://pith.science/pith/52SCWEO34H32BC5UJN2UCWNXHH/action/author_attestation","sign_citation":"https://pith.science/pith/52SCWEO34H32BC5UJN2UCWNXHH/action/citation_signature","submit_replication":"https://pith.science/pith/52SCWEO34H32BC5UJN2UCWNXHH/action/replication_record"}},"created_at":"2026-05-17T23:53:45.082768+00:00","updated_at":"2026-05-17T23:53:45.082768+00:00"}