{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:35UCFMZQFAOYBRMWXI3AWCSTMY","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0284d08399ba45e60f55206ac455f514183760a0cc4c14bdcc65750306dfa534","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-01-19T18:53:22Z","title_canon_sha256":"0574b8b3a98ee81c88841ba1a15b4ebdab1ebcc3cd5c48c6cb4988b7b1f9187c"},"schema_version":"1.0","source":{"id":"1401.4717","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.4717","created_at":"2026-05-18T00:41:08Z"},{"alias_kind":"arxiv_version","alias_value":"1401.4717v3","created_at":"2026-05-18T00:41:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.4717","created_at":"2026-05-18T00:41:08Z"},{"alias_kind":"pith_short_12","alias_value":"35UCFMZQFAOY","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"35UCFMZQFAOYBRMW","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"35UCFMZQ","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:9b08f224ce3b28ccd4b5a0f49cd5e7f48a76149cda812b34040086a4c8d71f72","target":"graph","created_at":"2026-05-18T00:41:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let G be a finite group and let F be a field of characteristic zero. In this paper we construct a generic G-crossed product over F using generic graded matrices. The center of this generic G-crossed product, denoted by F(G), is then the invariant field of a suitable G action on a field of rational functions in several indeterminates. The main goal of this paper is to study the extensions F(G)/F given that F contains enough roots of unity and determine how close they are to being purely transcendental.\n  In particular we show that F(G)/F is a stably rational extension for $G = C_2 \\times C_{2n}","authors_text":"Ofir David","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-01-19T18:53:22Z","title":"The center of the generic G-crossed product"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4717","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8ada9059e651722113060e25183e27fa66e8e8b51b526e67257b106c40c63a73","target":"record","created_at":"2026-05-18T00:41:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0284d08399ba45e60f55206ac455f514183760a0cc4c14bdcc65750306dfa534","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-01-19T18:53:22Z","title_canon_sha256":"0574b8b3a98ee81c88841ba1a15b4ebdab1ebcc3cd5c48c6cb4988b7b1f9187c"},"schema_version":"1.0","source":{"id":"1401.4717","kind":"arxiv","version":3}},"canonical_sha256":"df6822b330281d80c596ba360b0a53660798f102e69730abca11a5290c6bb3fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df6822b330281d80c596ba360b0a53660798f102e69730abca11a5290c6bb3fd","first_computed_at":"2026-05-18T00:41:08.642969Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:08.642969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CECIADYmRB0akI5pP+pP37883IAOLoftzBA06lAWEoS+njRRU1b3i9JLgWO4G9FLfbnZGKtPoAvDf0Hy+DVXCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:08.643445Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.4717","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ada9059e651722113060e25183e27fa66e8e8b51b526e67257b106c40c63a73","sha256:9b08f224ce3b28ccd4b5a0f49cd5e7f48a76149cda812b34040086a4c8d71f72"],"state_sha256":"a523881a4a553306813631f9b0c4c52e498cc7222db20c0dfe5866aabffa3b69"}