{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:ATFTZWTUFUOAVYIXMMZR4I5YXU","short_pith_number":"pith:ATFTZWTU","schema_version":"1.0","canonical_sha256":"04cb3cda742d1c0ae11763331e23b8bd0548c357103a49c1d5a43b84ae9ce4ce","source":{"kind":"arxiv","id":"0711.4740","version":3},"attestation_state":"computed","paper":{"title":"On the depth of invariant rings of infinite groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Martin Kohls","submitted_at":"2007-11-29T15:30:14Z","abstract_excerpt":"Let K be an algebraically closed field. For a finitely generated graded K algebra R, let cmdef R := dim R - depth R denote the Cohen-Macaulay-defect of R. Let G be a linear algebraic group over K that is reductive but not linearly reductive. We show that there exists a faithful rational representation V of G (which we will give explicitly) such that cmdef K[\\sum_i=1^k V]^G >= k-2 for all k. We give refinements in the case G = SL2."},"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":"0711.4740","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2007-11-29T15:30:14Z","cross_cats_sorted":[],"title_canon_sha256":"97bf978fc92cf50e3df12a53610c3018d060d275d76afd557ff747aa894831fa","abstract_canon_sha256":"6f94d0c6b2b7790fa9c5d311fa3a6dd602e7e51f93d9d4e5d307e0580c24cc2b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:10.244553Z","signature_b64":"UF+p26rUQH3Zq0fS0iTfA7TwJTTq+AzYCumFrDUVSAlUUPKH034+nV46Ajlg4x2R1d9gZm16HUDbHS0/vhFTDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04cb3cda742d1c0ae11763331e23b8bd0548c357103a49c1d5a43b84ae9ce4ce","last_reissued_at":"2026-05-18T02:49:10.243874Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:10.243874Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the depth of invariant rings of infinite groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Martin Kohls","submitted_at":"2007-11-29T15:30:14Z","abstract_excerpt":"Let K be an algebraically closed field. For a finitely generated graded K algebra R, let cmdef R := dim R - depth R denote the Cohen-Macaulay-defect of R. Let G be a linear algebraic group over K that is reductive but not linearly reductive. We show that there exists a faithful rational representation V of G (which we will give explicitly) such that cmdef K[\\sum_i=1^k V]^G >= k-2 for all k. We give refinements in the case G = SL2."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.4740","kind":"arxiv","version":3},"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":"0711.4740","created_at":"2026-05-18T02:49:10.243977+00:00"},{"alias_kind":"arxiv_version","alias_value":"0711.4740v3","created_at":"2026-05-18T02:49:10.243977+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0711.4740","created_at":"2026-05-18T02:49:10.243977+00:00"},{"alias_kind":"pith_short_12","alias_value":"ATFTZWTUFUOA","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"ATFTZWTUFUOAVYIX","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"ATFTZWTU","created_at":"2026-05-18T12:25:55.427421+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/ATFTZWTUFUOAVYIXMMZR4I5YXU","json":"https://pith.science/pith/ATFTZWTUFUOAVYIXMMZR4I5YXU.json","graph_json":"https://pith.science/api/pith-number/ATFTZWTUFUOAVYIXMMZR4I5YXU/graph.json","events_json":"https://pith.science/api/pith-number/ATFTZWTUFUOAVYIXMMZR4I5YXU/events.json","paper":"https://pith.science/paper/ATFTZWTU"},"agent_actions":{"view_html":"https://pith.science/pith/ATFTZWTUFUOAVYIXMMZR4I5YXU","download_json":"https://pith.science/pith/ATFTZWTUFUOAVYIXMMZR4I5YXU.json","view_paper":"https://pith.science/paper/ATFTZWTU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0711.4740&json=true","fetch_graph":"https://pith.science/api/pith-number/ATFTZWTUFUOAVYIXMMZR4I5YXU/graph.json","fetch_events":"https://pith.science/api/pith-number/ATFTZWTUFUOAVYIXMMZR4I5YXU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ATFTZWTUFUOAVYIXMMZR4I5YXU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ATFTZWTUFUOAVYIXMMZR4I5YXU/action/storage_attestation","attest_author":"https://pith.science/pith/ATFTZWTUFUOAVYIXMMZR4I5YXU/action/author_attestation","sign_citation":"https://pith.science/pith/ATFTZWTUFUOAVYIXMMZR4I5YXU/action/citation_signature","submit_replication":"https://pith.science/pith/ATFTZWTUFUOAVYIXMMZR4I5YXU/action/replication_record"}},"created_at":"2026-05-18T02:49:10.243977+00:00","updated_at":"2026-05-18T02:49:10.243977+00:00"}