{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:NPGRNEE3T2IGC6LLRXFQ6BB5NO","short_pith_number":"pith:NPGRNEE3","schema_version":"1.0","canonical_sha256":"6bcd16909b9e9061796b8dcb0f043d6b992f4a37eb1bf37b88f95dfb5fde499f","source":{"kind":"arxiv","id":"1105.4478","version":1},"attestation_state":"computed","paper":{"title":"On the invariants of the splitting algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Anders Thorup","submitted_at":"2011-05-23T12:24:21Z","abstract_excerpt":"For a given monic polynomial $p(t)$ of degree $n$ over a commutative ring $k$, the splitting algebra is the universal $k$-algebra in which $p(t)$ has $n$ roots, or, more precisely, over which $p(t)$ factors, $p(t)=(t-\\xi_1)...(t-\\xi_n)$. The symmetric group $S_r$ for $1\\le r\\le n$ acts on the splitting algebra by permuting the first $r$ roots $\\xi_1,...,\\xi_r$. We give a natural, simple condition on the polynomial $p(t)$ that holds if and only if there are only trivial invariants under the actions. In particular, if the condition on $p(t)$ holds then the elements of $k$ are the only invariants"},"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":"1105.4478","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-05-23T12:24:21Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"596f53c3c19d56eaa0ccec73ae3266ee9572b32791028dd73346e00fd2ba95ce","abstract_canon_sha256":"5fa8c3dfb4d5d6310c7f4446563885ea28d47622f24ccf44893ab4dcabc0cc29"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:29.214928Z","signature_b64":"HPMdyjIIRZj2fxd9lrlAwdjLM/sjq5ZjgSJA91jb09I6nyucpSetza5X7/9686fjajcG7yMVFUldaLxxLo0HBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6bcd16909b9e9061796b8dcb0f043d6b992f4a37eb1bf37b88f95dfb5fde499f","last_reissued_at":"2026-05-18T04:21:29.214584Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:29.214584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the invariants of the splitting algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Anders Thorup","submitted_at":"2011-05-23T12:24:21Z","abstract_excerpt":"For a given monic polynomial $p(t)$ of degree $n$ over a commutative ring $k$, the splitting algebra is the universal $k$-algebra in which $p(t)$ has $n$ roots, or, more precisely, over which $p(t)$ factors, $p(t)=(t-\\xi_1)...(t-\\xi_n)$. The symmetric group $S_r$ for $1\\le r\\le n$ acts on the splitting algebra by permuting the first $r$ roots $\\xi_1,...,\\xi_r$. We give a natural, simple condition on the polynomial $p(t)$ that holds if and only if there are only trivial invariants under the actions. In particular, if the condition on $p(t)$ holds then the elements of $k$ are the only invariants"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4478","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":"1105.4478","created_at":"2026-05-18T04:21:29.214640+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.4478v1","created_at":"2026-05-18T04:21:29.214640+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4478","created_at":"2026-05-18T04:21:29.214640+00:00"},{"alias_kind":"pith_short_12","alias_value":"NPGRNEE3T2IG","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_16","alias_value":"NPGRNEE3T2IGC6LL","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_8","alias_value":"NPGRNEE3","created_at":"2026-05-18T12:26:37.096874+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/NPGRNEE3T2IGC6LLRXFQ6BB5NO","json":"https://pith.science/pith/NPGRNEE3T2IGC6LLRXFQ6BB5NO.json","graph_json":"https://pith.science/api/pith-number/NPGRNEE3T2IGC6LLRXFQ6BB5NO/graph.json","events_json":"https://pith.science/api/pith-number/NPGRNEE3T2IGC6LLRXFQ6BB5NO/events.json","paper":"https://pith.science/paper/NPGRNEE3"},"agent_actions":{"view_html":"https://pith.science/pith/NPGRNEE3T2IGC6LLRXFQ6BB5NO","download_json":"https://pith.science/pith/NPGRNEE3T2IGC6LLRXFQ6BB5NO.json","view_paper":"https://pith.science/paper/NPGRNEE3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.4478&json=true","fetch_graph":"https://pith.science/api/pith-number/NPGRNEE3T2IGC6LLRXFQ6BB5NO/graph.json","fetch_events":"https://pith.science/api/pith-number/NPGRNEE3T2IGC6LLRXFQ6BB5NO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NPGRNEE3T2IGC6LLRXFQ6BB5NO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NPGRNEE3T2IGC6LLRXFQ6BB5NO/action/storage_attestation","attest_author":"https://pith.science/pith/NPGRNEE3T2IGC6LLRXFQ6BB5NO/action/author_attestation","sign_citation":"https://pith.science/pith/NPGRNEE3T2IGC6LLRXFQ6BB5NO/action/citation_signature","submit_replication":"https://pith.science/pith/NPGRNEE3T2IGC6LLRXFQ6BB5NO/action/replication_record"}},"created_at":"2026-05-18T04:21:29.214640+00:00","updated_at":"2026-05-18T04:21:29.214640+00:00"}