{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:ALG2E5JFUMA64KT5HNXVJ3WYUI","short_pith_number":"pith:ALG2E5JF","schema_version":"1.0","canonical_sha256":"02cda27525a301ee2a7d3b6f54eed8a213f57e118f824e6544c6d29c3b8c4204","source":{"kind":"arxiv","id":"1506.08549","version":2},"attestation_state":"computed","paper":{"title":"Bounded Normal Generation and Invariant Automatic Continuity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.GR"],"primary_cat":"math.OA","authors_text":"Andreas Thom, Philip A. Dowerk","submitted_at":"2015-06-29T08:57:20Z","abstract_excerpt":"We study the question how quickly products of a fixed conjugacy class in the projective unitary group of a II${}_1$-factor von Neumann algebra cover the entire group. Our result is that the number of factors that are needed is essentially as small as permitted by the $1$-norm - in analogy to a result of Liebeck-Shalev for non-abelian finite simple groups. As an application of the techniques, we prove that every homomorphism from the projective unitary group of a II${}_1$-factor to a polish SIN group is continuous. Moreover, we show that the projective unitary group of a II${}_1$-factor carries"},"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":"1506.08549","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-06-29T08:57:20Z","cross_cats_sorted":["math.FA","math.GR"],"title_canon_sha256":"10da501a228ca1dbe3c4c38d9a7f9316e29b8d503ee9294702efb086632972c1","abstract_canon_sha256":"651a167a6933cbab8550989853c3deabb1386616ccf1c6b83ee0e9a870abf722"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:26.507311Z","signature_b64":"F0PyDVOl9DK6qfO+TwHIiE2uXOxbWiypM+nTXnEnKIn7ajjJEK4Iyf0Rnsh1PksbrwVvRuEKvCJEyZSvo8v3CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02cda27525a301ee2a7d3b6f54eed8a213f57e118f824e6544c6d29c3b8c4204","last_reissued_at":"2026-05-18T01:35:26.506701Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:26.506701Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounded Normal Generation and Invariant Automatic Continuity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.GR"],"primary_cat":"math.OA","authors_text":"Andreas Thom, Philip A. Dowerk","submitted_at":"2015-06-29T08:57:20Z","abstract_excerpt":"We study the question how quickly products of a fixed conjugacy class in the projective unitary group of a II${}_1$-factor von Neumann algebra cover the entire group. Our result is that the number of factors that are needed is essentially as small as permitted by the $1$-norm - in analogy to a result of Liebeck-Shalev for non-abelian finite simple groups. As an application of the techniques, we prove that every homomorphism from the projective unitary group of a II${}_1$-factor to a polish SIN group is continuous. Moreover, we show that the projective unitary group of a II${}_1$-factor carries"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08549","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":"1506.08549","created_at":"2026-05-18T01:35:26.506775+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.08549v2","created_at":"2026-05-18T01:35:26.506775+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.08549","created_at":"2026-05-18T01:35:26.506775+00:00"},{"alias_kind":"pith_short_12","alias_value":"ALG2E5JFUMA6","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"ALG2E5JFUMA64KT5","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"ALG2E5JF","created_at":"2026-05-18T12:29:10.953037+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/ALG2E5JFUMA64KT5HNXVJ3WYUI","json":"https://pith.science/pith/ALG2E5JFUMA64KT5HNXVJ3WYUI.json","graph_json":"https://pith.science/api/pith-number/ALG2E5JFUMA64KT5HNXVJ3WYUI/graph.json","events_json":"https://pith.science/api/pith-number/ALG2E5JFUMA64KT5HNXVJ3WYUI/events.json","paper":"https://pith.science/paper/ALG2E5JF"},"agent_actions":{"view_html":"https://pith.science/pith/ALG2E5JFUMA64KT5HNXVJ3WYUI","download_json":"https://pith.science/pith/ALG2E5JFUMA64KT5HNXVJ3WYUI.json","view_paper":"https://pith.science/paper/ALG2E5JF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.08549&json=true","fetch_graph":"https://pith.science/api/pith-number/ALG2E5JFUMA64KT5HNXVJ3WYUI/graph.json","fetch_events":"https://pith.science/api/pith-number/ALG2E5JFUMA64KT5HNXVJ3WYUI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ALG2E5JFUMA64KT5HNXVJ3WYUI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ALG2E5JFUMA64KT5HNXVJ3WYUI/action/storage_attestation","attest_author":"https://pith.science/pith/ALG2E5JFUMA64KT5HNXVJ3WYUI/action/author_attestation","sign_citation":"https://pith.science/pith/ALG2E5JFUMA64KT5HNXVJ3WYUI/action/citation_signature","submit_replication":"https://pith.science/pith/ALG2E5JFUMA64KT5HNXVJ3WYUI/action/replication_record"}},"created_at":"2026-05-18T01:35:26.506775+00:00","updated_at":"2026-05-18T01:35:26.506775+00:00"}