{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:GCI7SWXVR2CUQ5OAKFKNWZAXXG","short_pith_number":"pith:GCI7SWXV","schema_version":"1.0","canonical_sha256":"3091f95af58e854875c05154db6417b9a337d516e9fb8f1952e5a769d34209a4","source":{"kind":"arxiv","id":"1110.5067","version":2},"attestation_state":"computed","paper":{"title":"Resolutions of 2 and 3 dimensional rings of invariants for cyclic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"David L. Wehlau, John C. Harris","submitted_at":"2011-10-23T17:35:47Z","abstract_excerpt":"Let $G$ be the cyclic group of order $n$ and suppose ${\\bf F}$ is a field containing a primitive $n^\\text{th}$ root of unity. We consider the ring of invariants ${\\bf F}[W]^G$ of a three dimensional representation $W$ of $G$ where $G \\subset \\text{SL}(W)$. We describe minimal generators and relations for this ring and prove that the lead terms of the relations are quadratic. These minimal generators for the relations form a Gr\\\"obner basis with a surprisingly simple combinatorial structure. We describe the graded Betti numbers for a minimal free resolution of $F[W]^G$. The case where $W$ is an"},"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":"1110.5067","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-10-23T17:35:47Z","cross_cats_sorted":[],"title_canon_sha256":"ab18c0c56106cfc79ece22f4a1ccf5da00da2a9c62441b44ef4c6bc111fe63c1","abstract_canon_sha256":"196d2e8fba13efad51135790c016a5d80c99ede892b504ec89a90b54ee364fa9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:37.359001Z","signature_b64":"MsY9g34OcSOavVOaq91V+v2YZ8N6LevkuLz4VtW/kx+R3Xu4AGd16c0QuFWCY9T3STTgkn1ZlNVwxCwauX7RDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3091f95af58e854875c05154db6417b9a337d516e9fb8f1952e5a769d34209a4","last_reissued_at":"2026-05-18T03:55:37.358194Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:37.358194Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Resolutions of 2 and 3 dimensional rings of invariants for cyclic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"David L. Wehlau, John C. Harris","submitted_at":"2011-10-23T17:35:47Z","abstract_excerpt":"Let $G$ be the cyclic group of order $n$ and suppose ${\\bf F}$ is a field containing a primitive $n^\\text{th}$ root of unity. We consider the ring of invariants ${\\bf F}[W]^G$ of a three dimensional representation $W$ of $G$ where $G \\subset \\text{SL}(W)$. We describe minimal generators and relations for this ring and prove that the lead terms of the relations are quadratic. These minimal generators for the relations form a Gr\\\"obner basis with a surprisingly simple combinatorial structure. We describe the graded Betti numbers for a minimal free resolution of $F[W]^G$. The case where $W$ is an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5067","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":"1110.5067","created_at":"2026-05-18T03:55:37.358338+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.5067v2","created_at":"2026-05-18T03:55:37.358338+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.5067","created_at":"2026-05-18T03:55:37.358338+00:00"},{"alias_kind":"pith_short_12","alias_value":"GCI7SWXVR2CU","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_16","alias_value":"GCI7SWXVR2CUQ5OA","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_8","alias_value":"GCI7SWXV","created_at":"2026-05-18T12:26:28.662955+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/GCI7SWXVR2CUQ5OAKFKNWZAXXG","json":"https://pith.science/pith/GCI7SWXVR2CUQ5OAKFKNWZAXXG.json","graph_json":"https://pith.science/api/pith-number/GCI7SWXVR2CUQ5OAKFKNWZAXXG/graph.json","events_json":"https://pith.science/api/pith-number/GCI7SWXVR2CUQ5OAKFKNWZAXXG/events.json","paper":"https://pith.science/paper/GCI7SWXV"},"agent_actions":{"view_html":"https://pith.science/pith/GCI7SWXVR2CUQ5OAKFKNWZAXXG","download_json":"https://pith.science/pith/GCI7SWXVR2CUQ5OAKFKNWZAXXG.json","view_paper":"https://pith.science/paper/GCI7SWXV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.5067&json=true","fetch_graph":"https://pith.science/api/pith-number/GCI7SWXVR2CUQ5OAKFKNWZAXXG/graph.json","fetch_events":"https://pith.science/api/pith-number/GCI7SWXVR2CUQ5OAKFKNWZAXXG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GCI7SWXVR2CUQ5OAKFKNWZAXXG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GCI7SWXVR2CUQ5OAKFKNWZAXXG/action/storage_attestation","attest_author":"https://pith.science/pith/GCI7SWXVR2CUQ5OAKFKNWZAXXG/action/author_attestation","sign_citation":"https://pith.science/pith/GCI7SWXVR2CUQ5OAKFKNWZAXXG/action/citation_signature","submit_replication":"https://pith.science/pith/GCI7SWXVR2CUQ5OAKFKNWZAXXG/action/replication_record"}},"created_at":"2026-05-18T03:55:37.358338+00:00","updated_at":"2026-05-18T03:55:37.358338+00:00"}