{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:YUAZTUNQEP5FJGARZ6L4R73MMS","short_pith_number":"pith:YUAZTUNQ","schema_version":"1.0","canonical_sha256":"c50199d1b023fa549811cf97c8ff6c64810b62fbf7d6314e6fdb2e84e5a8a268","source":{"kind":"arxiv","id":"1001.5216","version":2},"attestation_state":"computed","paper":{"title":"Degree bounds for separating invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Hanspeter Kraft, Martin Kohls","submitted_at":"2010-01-28T16:42:15Z","abstract_excerpt":"If V is a representation of a linear algebraic group G, a set S of G-invariant regular functions on V is called separating if the following holds: If two elements v,v' from V can be separated by an invariant function, then there is an f from S such that f(v) is different from f(v'). It is known that there always exist finite separating sets. Moreover, if the group G is finite, then the invariant functions of degree <= |G| form a separating set. We show that for a non-finite linear algebraic group G such an upper bound for the degrees of a separating set does not exist. If G is finite, we defin"},"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":"1001.5216","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-01-28T16:42:15Z","cross_cats_sorted":[],"title_canon_sha256":"259bcc5f39e3feca1b859eb0fd82da06bfd030153d35d98c42f3b62f0207f803","abstract_canon_sha256":"8ba01fcfa148513b99914798b1a2b18f40c42076174114317c341ca047a9a8dc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:10.229590Z","signature_b64":"O4f74bXhkdH4NlAQjm2RIsCWaNgAQd1ArEXCCO5lvJY+vIGSeam0y09ST9R2nguexvD3baQrx54IY5qTty16Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c50199d1b023fa549811cf97c8ff6c64810b62fbf7d6314e6fdb2e84e5a8a268","last_reissued_at":"2026-05-18T02:49:10.228969Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:10.228969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Degree bounds for separating invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Hanspeter Kraft, Martin Kohls","submitted_at":"2010-01-28T16:42:15Z","abstract_excerpt":"If V is a representation of a linear algebraic group G, a set S of G-invariant regular functions on V is called separating if the following holds: If two elements v,v' from V can be separated by an invariant function, then there is an f from S such that f(v) is different from f(v'). It is known that there always exist finite separating sets. Moreover, if the group G is finite, then the invariant functions of degree <= |G| form a separating set. We show that for a non-finite linear algebraic group G such an upper bound for the degrees of a separating set does not exist. If G is finite, we defin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.5216","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":"1001.5216","created_at":"2026-05-18T02:49:10.229065+00:00"},{"alias_kind":"arxiv_version","alias_value":"1001.5216v2","created_at":"2026-05-18T02:49:10.229065+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.5216","created_at":"2026-05-18T02:49:10.229065+00:00"},{"alias_kind":"pith_short_12","alias_value":"YUAZTUNQEP5F","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_16","alias_value":"YUAZTUNQEP5FJGAR","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_8","alias_value":"YUAZTUNQ","created_at":"2026-05-18T12:26:17.028572+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/YUAZTUNQEP5FJGARZ6L4R73MMS","json":"https://pith.science/pith/YUAZTUNQEP5FJGARZ6L4R73MMS.json","graph_json":"https://pith.science/api/pith-number/YUAZTUNQEP5FJGARZ6L4R73MMS/graph.json","events_json":"https://pith.science/api/pith-number/YUAZTUNQEP5FJGARZ6L4R73MMS/events.json","paper":"https://pith.science/paper/YUAZTUNQ"},"agent_actions":{"view_html":"https://pith.science/pith/YUAZTUNQEP5FJGARZ6L4R73MMS","download_json":"https://pith.science/pith/YUAZTUNQEP5FJGARZ6L4R73MMS.json","view_paper":"https://pith.science/paper/YUAZTUNQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1001.5216&json=true","fetch_graph":"https://pith.science/api/pith-number/YUAZTUNQEP5FJGARZ6L4R73MMS/graph.json","fetch_events":"https://pith.science/api/pith-number/YUAZTUNQEP5FJGARZ6L4R73MMS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YUAZTUNQEP5FJGARZ6L4R73MMS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YUAZTUNQEP5FJGARZ6L4R73MMS/action/storage_attestation","attest_author":"https://pith.science/pith/YUAZTUNQEP5FJGARZ6L4R73MMS/action/author_attestation","sign_citation":"https://pith.science/pith/YUAZTUNQEP5FJGARZ6L4R73MMS/action/citation_signature","submit_replication":"https://pith.science/pith/YUAZTUNQEP5FJGARZ6L4R73MMS/action/replication_record"}},"created_at":"2026-05-18T02:49:10.229065+00:00","updated_at":"2026-05-18T02:49:10.229065+00:00"}