{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:Y5O2ESHJKJ7GPU2CV72QEFOJDV","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":"02bda79e05f97a498fc8e9478d4b13d0f086094ee6ebe7fd8402c9a4e008c9a7","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"2005-09-16T12:38:35Z","title_canon_sha256":"1cabade5a0287c88ebc3583f1b097dac2e676a45415127cb7cb2ba2f53ace7c6"},"schema_version":"1.0","source":{"id":"math/0509375","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0509375","created_at":"2026-05-18T00:12:02Z"},{"alias_kind":"arxiv_version","alias_value":"math/0509375v1","created_at":"2026-05-18T00:12:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0509375","created_at":"2026-05-18T00:12:02Z"},{"alias_kind":"pith_short_12","alias_value":"Y5O2ESHJKJ7G","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"Y5O2ESHJKJ7GPU2C","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"Y5O2ESHJ","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:b7db127232dbb67856238b858628b24ef711d85baa77d7ce72dcf22afd4dbeb1","target":"graph","created_at":"2026-05-18T00:12:02Z","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":"We extend previous results on noncommutative recurrence in unital *-algebras over the integers, to the case where one works over locally compact Hausdorff groups. We derive a generalization of Khintchine's recurrence theorem, as well as a form of multiple recurrence. This is done using the mean ergodic theorem in Hilbert space, via the GNS construction.","authors_text":"Anton Stroh, Richard de Beer, Rocco Duvenhage","cross_cats":[],"headline":"","license":"","primary_cat":"math.DS","submitted_at":"2005-09-16T12:38:35Z","title":"Noncommutative recurrence over locally compact Hausdorff groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0509375","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":"sha256:44cb3ce2da3d1c9f48c186b117c796154269e95c3f52953a2c500660d66614e3","target":"record","created_at":"2026-05-18T00:12:02Z","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":"02bda79e05f97a498fc8e9478d4b13d0f086094ee6ebe7fd8402c9a4e008c9a7","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"2005-09-16T12:38:35Z","title_canon_sha256":"1cabade5a0287c88ebc3583f1b097dac2e676a45415127cb7cb2ba2f53ace7c6"},"schema_version":"1.0","source":{"id":"math/0509375","kind":"arxiv","version":1}},"canonical_sha256":"c75da248e9527e67d342aff50215c91d65b8ddcbe64f62196863a4a2c0691327","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c75da248e9527e67d342aff50215c91d65b8ddcbe64f62196863a4a2c0691327","first_computed_at":"2026-05-18T00:12:02.779439Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:02.779439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gUl3KmYTZ/HQuYwG1qb4Yzg1tzosDypeY3hsuac/1SMfRWyXHlYVzKJtUb1FM/mLkDu3nHZPn5wBzOCUe4pABA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:02.780142Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0509375","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:44cb3ce2da3d1c9f48c186b117c796154269e95c3f52953a2c500660d66614e3","sha256:b7db127232dbb67856238b858628b24ef711d85baa77d7ce72dcf22afd4dbeb1"],"state_sha256":"b9abd7dec34f429bd21d6a8f46e050eaa062003088ed1d0ded49a63a90bdc141"}