{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:YW6O4YCVERABNWCXXEAVW35BXY","short_pith_number":"pith:YW6O4YCV","schema_version":"1.0","canonical_sha256":"c5bcee6055244016d857b9015b6fa1be3304769fc5c6740f8d46b8c0fa310291","source":{"kind":"arxiv","id":"1310.7608","version":1},"attestation_state":"computed","paper":{"title":"Symmetric polynomials and non-finitely generated $Sym (\\mathbb N)$-invariant ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Alexei Krasilnikov, Eudes Antonio da Costa","submitted_at":"2013-10-28T20:17:56Z","abstract_excerpt":"Let $K$ be a field and let $\\mathbb N = \\{1,2, \\dots \\}$. Let $R_n=K[x_{ij} \\mid 1\\le i\\le n, j\\in \\mathbb N]$ be the ring of polynomials in $x_{ij}$ $(1 \\le i \\le n, j \\in \\mathbb N)$ over $K$. Let $S_n = Sym (\\{1,2, \\ldots, n \\})$ and $Sym (\\mathbb N)$ be the groups of the permutations of the sets $\\{1,2,\\dots, n \\}$ and $\\mathbb N$, respectively. Then $S_n$ and $Sym (\\mathbb N)$ act on $R_n$ in a natural way: $\\tau (x_{ij})=x_{\\tau(i)j}$ and $\\sigma (x_{ij})=x_{i\\sigma (j)}$ for all $\\tau \\in S_n$ and $\\sigma \\in Sym(\\mathbb N)$. Let $\\overline{R}_n$ be the subalgebra of the symmetric polyn"},"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":"1310.7608","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-10-28T20:17:56Z","cross_cats_sorted":[],"title_canon_sha256":"37f539b30fd8989cd5723c234960c291be9aa92cd5c39ebf12066ecd7d22d24a","abstract_canon_sha256":"25fadb6e53f82469fda78cb62737ead66097de13598cd134230b1e8cb22440bd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:46.795485Z","signature_b64":"kDsc8Rr0NAqhHPIoCJmgkyG/1nr2EeghlSA1oJztTMtVchGY9hzbbjA+wchKg3NZ5YPYuYli0yjB7gmdbqHDBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5bcee6055244016d857b9015b6fa1be3304769fc5c6740f8d46b8c0fa310291","last_reissued_at":"2026-05-18T01:31:46.795011Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:46.795011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symmetric polynomials and non-finitely generated $Sym (\\mathbb N)$-invariant ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Alexei Krasilnikov, Eudes Antonio da Costa","submitted_at":"2013-10-28T20:17:56Z","abstract_excerpt":"Let $K$ be a field and let $\\mathbb N = \\{1,2, \\dots \\}$. Let $R_n=K[x_{ij} \\mid 1\\le i\\le n, j\\in \\mathbb N]$ be the ring of polynomials in $x_{ij}$ $(1 \\le i \\le n, j \\in \\mathbb N)$ over $K$. Let $S_n = Sym (\\{1,2, \\ldots, n \\})$ and $Sym (\\mathbb N)$ be the groups of the permutations of the sets $\\{1,2,\\dots, n \\}$ and $\\mathbb N$, respectively. Then $S_n$ and $Sym (\\mathbb N)$ act on $R_n$ in a natural way: $\\tau (x_{ij})=x_{\\tau(i)j}$ and $\\sigma (x_{ij})=x_{i\\sigma (j)}$ for all $\\tau \\in S_n$ and $\\sigma \\in Sym(\\mathbb N)$. Let $\\overline{R}_n$ be the subalgebra of the symmetric polyn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7608","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":"1310.7608","created_at":"2026-05-18T01:31:46.795097+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.7608v1","created_at":"2026-05-18T01:31:46.795097+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7608","created_at":"2026-05-18T01:31:46.795097+00:00"},{"alias_kind":"pith_short_12","alias_value":"YW6O4YCVERAB","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"YW6O4YCVERABNWCX","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"YW6O4YCV","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/YW6O4YCVERABNWCXXEAVW35BXY","json":"https://pith.science/pith/YW6O4YCVERABNWCXXEAVW35BXY.json","graph_json":"https://pith.science/api/pith-number/YW6O4YCVERABNWCXXEAVW35BXY/graph.json","events_json":"https://pith.science/api/pith-number/YW6O4YCVERABNWCXXEAVW35BXY/events.json","paper":"https://pith.science/paper/YW6O4YCV"},"agent_actions":{"view_html":"https://pith.science/pith/YW6O4YCVERABNWCXXEAVW35BXY","download_json":"https://pith.science/pith/YW6O4YCVERABNWCXXEAVW35BXY.json","view_paper":"https://pith.science/paper/YW6O4YCV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.7608&json=true","fetch_graph":"https://pith.science/api/pith-number/YW6O4YCVERABNWCXXEAVW35BXY/graph.json","fetch_events":"https://pith.science/api/pith-number/YW6O4YCVERABNWCXXEAVW35BXY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YW6O4YCVERABNWCXXEAVW35BXY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YW6O4YCVERABNWCXXEAVW35BXY/action/storage_attestation","attest_author":"https://pith.science/pith/YW6O4YCVERABNWCXXEAVW35BXY/action/author_attestation","sign_citation":"https://pith.science/pith/YW6O4YCVERABNWCXXEAVW35BXY/action/citation_signature","submit_replication":"https://pith.science/pith/YW6O4YCVERABNWCXXEAVW35BXY/action/replication_record"}},"created_at":"2026-05-18T01:31:46.795097+00:00","updated_at":"2026-05-18T01:31:46.795097+00:00"}