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Besicovitch,Almost periodic functions, Dover Publications, 1954","work_id":"2ef6821e-fd05-41a8-bf49-535866815f48","year":1954},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"Billingsley,Convergence of probability measures, John Wiley & Sons, New York, 1999","work_id":"1256185e-1049-4bfc-a36a-5abad6a3a0aa","year":1999}],"snapshot_sha256":"1e788abc6472bef46ba45c0939864a7232b6c6049300b22b78ec8012ab26b451"},"source":{"id":"2605.15580","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T19:55:00.275916Z","id":"74e245a9-ec46-4e2a-9c14-a10b481102aa","model_set":{"reader":"grok-4.3"},"one_line_summary":"Establishes a decomposition of LCA group actions on the torus into uniquely ergodic subsystems, with applications to Bohr orthogonality and Wiener-type theorems on LCA groups.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Every action of a locally compact Abelian group on the torus decomposes into uniquely ergodic subsystems.","strongest_claim":"Every action of a locally compact Abelian group on the torus admits a decomposition into uniquely ergodic subsystems, yielding a Weyl-type equidistribution theorem.","weakest_assumption":"The proof relies on a pre-existing characterization of unique ergodicity for amenable group actions on compact metric spaces; if this characterization fails to apply to the specific LCA actions considered here, the decomposition result does not follow."}},"verdict_id":"74e245a9-ec46-4e2a-9c14-a10b481102aa"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c42206bac33dda383549eab9133e2eeeac7b558e6d95c8825a72c7b8f45f4755","target":"record","created_at":"2026-05-20T00:01:06Z","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":"41759a7dd32aad1b2ddb3832d9ceb7b0dd10172810b98a8c8f3164519054eb99","cross_cats_sorted":["math.CA","math.NT"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DS","submitted_at":"2026-05-15T03:44:30Z","title_canon_sha256":"f8d87aed3c0b0990724867a589d7f9c2deb975e62d5f37e7102d95a2af4e6ffd"},"schema_version":"1.0","source":{"id":"2605.15580","kind":"arxiv","version":1}},"canonical_sha256":"b8db74ca2068f5f85fd5e3908879e18a5fa48f70e9ecfcf93f7a0a0fc6c40240","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8db74ca2068f5f85fd5e3908879e18a5fa48f70e9ecfcf93f7a0a0fc6c40240","first_computed_at":"2026-05-20T00:01:06.465726Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:01:06.465726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gSMwIS8jwIvScVAD5tjdGPOQr1nWibQzDueJ4i+/968tje7YfeHKZuMy0u6upu4O6gDkMYegyl3R4su0yiQeBA==","signature_status":"signed_v1","signed_at":"2026-05-20T00:01:06.466550Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.15580","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c42206bac33dda383549eab9133e2eeeac7b558e6d95c8825a72c7b8f45f4755","sha256:394f3e0f871172967f7418eeb84df6374156ddb1a0327d26e0dec6a8c4547655"],"state_sha256":"d85df854439150a8c57255c31180d492b55cb456e27ed35f267458be8591f20b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j0BG4Dn0NcImwl2eXEP+G3Pq3ic7YzL3VhPXr4tcqJEzY4BwP7u4XlXOSIpfBM9pLBYIaAwuHE3xPXitbW0RBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T10:06:50.625948Z","bundle_sha256":"9f8a05818680a75f215ec39fab468751fd012df13fc93d03c0a28e1a2b1f2bd3"}}