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To our knowledge, this ring (for any prime $p$) was first studied by David Richman in 1990. 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He gave a first main theorem for $(V_2, C_2)$, that is, he proved that the ring of invariants when $p=2$ is generated by $\\{x_i, N_i = y_i^2 + x_iy_i, tr(A) | 2 \\le |A| \\le m\\}$ where $A \\subset \\{0,1\\}^m$, $y^A = y_1^{a_1} y_2^{a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3710","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":"1308.3710","created_at":"2026-05-18T03:15:42.799774+00:00"},{"alias_kind":"arxiv_version","alias_value":"1308.3710v1","created_at":"2026-05-18T03:15:42.799774+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.3710","created_at":"2026-05-18T03:15:42.799774+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z65COJ3MB4HN","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z65COJ3MB4HNUQ5H","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z65COJ3M","created_at":"2026-05-18T12:28:09.283467+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/Z65COJ3MB4HNUQ5HEMYBCKKU4K","json":"https://pith.science/pith/Z65COJ3MB4HNUQ5HEMYBCKKU4K.json","graph_json":"https://pith.science/api/pith-number/Z65COJ3MB4HNUQ5HEMYBCKKU4K/graph.json","events_json":"https://pith.science/api/pith-number/Z65COJ3MB4HNUQ5HEMYBCKKU4K/events.json","paper":"https://pith.science/paper/Z65COJ3M"},"agent_actions":{"view_html":"https://pith.science/pith/Z65COJ3MB4HNUQ5HEMYBCKKU4K","download_json":"https://pith.science/pith/Z65COJ3MB4HNUQ5HEMYBCKKU4K.json","view_paper":"https://pith.science/paper/Z65COJ3M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1308.3710&json=true","fetch_graph":"https://pith.science/api/pith-number/Z65COJ3MB4HNUQ5HEMYBCKKU4K/graph.json","fetch_events":"https://pith.science/api/pith-number/Z65COJ3MB4HNUQ5HEMYBCKKU4K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z65COJ3MB4HNUQ5HEMYBCKKU4K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z65COJ3MB4HNUQ5HEMYBCKKU4K/action/storage_attestation","attest_author":"https://pith.science/pith/Z65COJ3MB4HNUQ5HEMYBCKKU4K/action/author_attestation","sign_citation":"https://pith.science/pith/Z65COJ3MB4HNUQ5HEMYBCKKU4K/action/citation_signature","submit_replication":"https://pith.science/pith/Z65COJ3MB4HNUQ5HEMYBCKKU4K/action/replication_record"}},"created_at":"2026-05-18T03:15:42.799774+00:00","updated_at":"2026-05-18T03:15:42.799774+00:00"}