{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2004:R5HYBKFRLQ2DKTTCKNYPXTFNRI","short_pith_number":"pith:R5HYBKFR","schema_version":"1.0","canonical_sha256":"8f4f80a8b15c34354e625370fbccad8a064ac16117b06eb4bd3451950a55cde4","source":{"kind":"arxiv","id":"math/0402434","version":1},"attestation_state":"computed","paper":{"title":"The essential ideal is a Cohen-Macaulay module","license":"","headline":"","cross_cats":["math.AC"],"primary_cat":"math.GR","authors_text":"David J. Green","submitted_at":"2004-02-26T15:55:19Z","abstract_excerpt":"Let G be a finite p-group which does not contain a rank two elementary abelian p-group as a direct factor. Then the ideal of essential classes in the mod-p cohomology ring of G is a Cohen-Macaulay module whose Krull dimension is the p-rank of the centre of G. This basically answers in the affirmative a question posed by J. F. Carlson."},"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":"math/0402434","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GR","submitted_at":"2004-02-26T15:55:19Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"dcf95ebc15360c17e3e36a05dd69784f6690b2be9fe3c23b35bb79e902fc0ff9","abstract_canon_sha256":"8c08abb6d8881c04d9ba5b084a29c4e1318213dd0e3039351b9dd38f150cb3a3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:39.796533Z","signature_b64":"RrMvC/9cNm3qyyhAMNgfAU+cfIQ6dVRO7a4pwWc4oxXUHq4UK3LV3kds4ZsMtbrxcavNetFdykDdU7qyC3aiAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f4f80a8b15c34354e625370fbccad8a064ac16117b06eb4bd3451950a55cde4","last_reissued_at":"2026-05-18T02:26:39.796022Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:39.796022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The essential ideal is a Cohen-Macaulay module","license":"","headline":"","cross_cats":["math.AC"],"primary_cat":"math.GR","authors_text":"David J. Green","submitted_at":"2004-02-26T15:55:19Z","abstract_excerpt":"Let G be a finite p-group which does not contain a rank two elementary abelian p-group as a direct factor. Then the ideal of essential classes in the mod-p cohomology ring of G is a Cohen-Macaulay module whose Krull dimension is the p-rank of the centre of G. This basically answers in the affirmative a question posed by J. F. Carlson."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0402434","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":"math/0402434","created_at":"2026-05-18T02:26:39.796109+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0402434v1","created_at":"2026-05-18T02:26:39.796109+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0402434","created_at":"2026-05-18T02:26:39.796109+00:00"},{"alias_kind":"pith_short_12","alias_value":"R5HYBKFRLQ2D","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_16","alias_value":"R5HYBKFRLQ2DKTTC","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_8","alias_value":"R5HYBKFR","created_at":"2026-05-18T12:25:52.687210+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/R5HYBKFRLQ2DKTTCKNYPXTFNRI","json":"https://pith.science/pith/R5HYBKFRLQ2DKTTCKNYPXTFNRI.json","graph_json":"https://pith.science/api/pith-number/R5HYBKFRLQ2DKTTCKNYPXTFNRI/graph.json","events_json":"https://pith.science/api/pith-number/R5HYBKFRLQ2DKTTCKNYPXTFNRI/events.json","paper":"https://pith.science/paper/R5HYBKFR"},"agent_actions":{"view_html":"https://pith.science/pith/R5HYBKFRLQ2DKTTCKNYPXTFNRI","download_json":"https://pith.science/pith/R5HYBKFRLQ2DKTTCKNYPXTFNRI.json","view_paper":"https://pith.science/paper/R5HYBKFR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0402434&json=true","fetch_graph":"https://pith.science/api/pith-number/R5HYBKFRLQ2DKTTCKNYPXTFNRI/graph.json","fetch_events":"https://pith.science/api/pith-number/R5HYBKFRLQ2DKTTCKNYPXTFNRI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R5HYBKFRLQ2DKTTCKNYPXTFNRI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R5HYBKFRLQ2DKTTCKNYPXTFNRI/action/storage_attestation","attest_author":"https://pith.science/pith/R5HYBKFRLQ2DKTTCKNYPXTFNRI/action/author_attestation","sign_citation":"https://pith.science/pith/R5HYBKFRLQ2DKTTCKNYPXTFNRI/action/citation_signature","submit_replication":"https://pith.science/pith/R5HYBKFRLQ2DKTTCKNYPXTFNRI/action/replication_record"}},"created_at":"2026-05-18T02:26:39.796109+00:00","updated_at":"2026-05-18T02:26:39.796109+00:00"}