{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:3RK5SECB6HNRZZLEW45X4ZCWQ6","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":"c8ef150e56476d9b9dacd35fda7a8789c8f5baedb0d2cd57f5ff62bc8d1e5627","cross_cats_sorted":["math.FA","math.GR","math.RT"],"license":"","primary_cat":"math.OA","submitted_at":"2006-06-08T14:24:22Z","title_canon_sha256":"3b4995aa8bdd1b74b2eda69d6f1de5dce5253920e6e329255c29a598603108a8"},"schema_version":"1.0","source":{"id":"math/0606191","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0606191","created_at":"2026-05-18T01:05:22Z"},{"alias_kind":"arxiv_version","alias_value":"math/0606191v1","created_at":"2026-05-18T01:05:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0606191","created_at":"2026-05-18T01:05:22Z"},{"alias_kind":"pith_short_12","alias_value":"3RK5SECB6HNR","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"3RK5SECB6HNRZZLE","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"3RK5SECB","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:57bd8d3d08fc2471008cf727f6d0ad159dffa5d3f93a16b9ae26c6c8e34cbc78","target":"graph","created_at":"2026-05-18T01:05:22Z","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":"The present paper consists of two parts. In the first part, we prove a noncommutative analogue of the Riesz(-Markov-Kakutani) theorem on representation of functionals on an algebra of continuous functions by regular measures on the underlying space.\n In the second part, using this result, we prove a weak version of Burnside type theorem for twisted conjugacy for arbitrary discrete groups.","authors_text":"Evgenij Troitsky","cross_cats":["math.FA","math.GR","math.RT"],"headline":"","license":"","primary_cat":"math.OA","submitted_at":"2006-06-08T14:24:22Z","title":"Noncommutative Riesz theorem and weak Burnside type theorem on twisted conjugacy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0606191","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":"sha256:9cc033f7f085de4c31da881c372771ddc23a216ca8524c8dd90f405820e0827a","target":"record","created_at":"2026-05-18T01:05:22Z","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":"c8ef150e56476d9b9dacd35fda7a8789c8f5baedb0d2cd57f5ff62bc8d1e5627","cross_cats_sorted":["math.FA","math.GR","math.RT"],"license":"","primary_cat":"math.OA","submitted_at":"2006-06-08T14:24:22Z","title_canon_sha256":"3b4995aa8bdd1b74b2eda69d6f1de5dce5253920e6e329255c29a598603108a8"},"schema_version":"1.0","source":{"id":"math/0606191","kind":"arxiv","version":1}},"canonical_sha256":"dc55d91041f1db1ce564b73b7e645687a9d1423e2313fdcf68c4ad89b7d92df0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc55d91041f1db1ce564b73b7e645687a9d1423e2313fdcf68c4ad89b7d92df0","first_computed_at":"2026-05-18T01:05:22.650686Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:22.650686Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+zloQRFrmf0DC9EVZv4bvcxDFYeyCVNgFWaC+AVvS9gDSmW/eGAlsEDd/gSBq0WzwxR+2g9of+3j1G1lTR1PDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:22.651292Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0606191","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9cc033f7f085de4c31da881c372771ddc23a216ca8524c8dd90f405820e0827a","sha256:57bd8d3d08fc2471008cf727f6d0ad159dffa5d3f93a16b9ae26c6c8e34cbc78"],"state_sha256":"76437d4aa84ba0415e0d0b6721bc3efaf601ba058f6ee746ec4e32bc8fd2b0ac"}