{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:V2QS3Y47ALSBYSPDWSHSVEX5PK","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":"589bbef966658e1e5591a2861a2676f3a657e9e1d97d99023d977a4902e6a292","cross_cats_sorted":["math.GN","math.PR","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-02-21T21:38:56Z","title_canon_sha256":"6dd41dd5995f26ee235097b6222da70ba636a17063c58707eaefced96741fc63"},"schema_version":"1.0","source":{"id":"1102.4353","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4353","created_at":"2026-05-18T04:28:09Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4353v1","created_at":"2026-05-18T04:28:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4353","created_at":"2026-05-18T04:28:09Z"},{"alias_kind":"pith_short_12","alias_value":"V2QS3Y47ALSB","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"V2QS3Y47ALSBYSPD","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"V2QS3Y47","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:8a4b6c4711c051bbe040fbc06a289d422df476335b3acd6abd9b731883ed1412","target":"graph","created_at":"2026-05-18T04:28:09Z","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":"Consider a group word w in n letters. For a compact group G, w induces a map G^n \\rightarrow G$ and thus a pushforward measure {\\mu}_w on G from the Haar measure on G^n. We associate to each word w a 2-dimensional cell complex X(w) and prove in Theorem 2.5 that {\\mu}_w is determined by the topology of X(w). The proof makes use of non-abelian cohomology and Nielsen's classification of automorphisms of free groups [Nie24]. Focusing on the case when X(w) is a surface, we rediscover representation-theoretic formulas for {\\mu}_w that were derived by Witten in the context of quantum gauge theory [Wi","authors_text":"Gene S. Kopp, John D. Wiltshire-Gordon","cross_cats":["math.GN","math.PR","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-02-21T21:38:56Z","title":"Word-Induced Measures on Compact Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4353","kind":"arxiv","version":1},"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:c1cbbf07cf7e44b302b00d90e70ddd6e0882b749e97064b62e0bd7b2df172412","target":"record","created_at":"2026-05-18T04:28:09Z","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":"589bbef966658e1e5591a2861a2676f3a657e9e1d97d99023d977a4902e6a292","cross_cats_sorted":["math.GN","math.PR","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-02-21T21:38:56Z","title_canon_sha256":"6dd41dd5995f26ee235097b6222da70ba636a17063c58707eaefced96741fc63"},"schema_version":"1.0","source":{"id":"1102.4353","kind":"arxiv","version":1}},"canonical_sha256":"aea12de39f02e41c49e3b48f2a92fd7ab3784b9082525c3af0cd889c15d42ed2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aea12de39f02e41c49e3b48f2a92fd7ab3784b9082525c3af0cd889c15d42ed2","first_computed_at":"2026-05-18T04:28:09.161424Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:28:09.161424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5ypynbuD9hmjiCp9d7Hx6yGzFfrTy0aAkJlblmV/ZZSLx1OloSQ/OC3OyhYq3DYi5l4HMkMJ+HYG1GD0wJbfAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:28:09.161915Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.4353","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1cbbf07cf7e44b302b00d90e70ddd6e0882b749e97064b62e0bd7b2df172412","sha256:8a4b6c4711c051bbe040fbc06a289d422df476335b3acd6abd9b731883ed1412"],"state_sha256":"e0e812580d6617a84ec5aa4434488bf404672fc5ff231f2e172ef66fdb325f1c"}