{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:7I4ZXYVYMTPXLB7AIMKYXEXKUP","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":"56d6476e457073ed6777801d8f5498d0c15e55ef085aae59ac4fdf16e847579b","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-06-13T15:46:41Z","title_canon_sha256":"877199e804452e85af38d48b543bb7e2540b1498895510848452674b404ed839"},"schema_version":"1.0","source":{"id":"2406.09243","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.09243","created_at":"2026-06-09T01:05:03Z"},{"alias_kind":"arxiv_version","alias_value":"2406.09243v2","created_at":"2026-06-09T01:05:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.09243","created_at":"2026-06-09T01:05:03Z"},{"alias_kind":"pith_short_12","alias_value":"7I4ZXYVYMTPX","created_at":"2026-06-09T01:05:03Z"},{"alias_kind":"pith_short_16","alias_value":"7I4ZXYVYMTPXLB7A","created_at":"2026-06-09T01:05:03Z"},{"alias_kind":"pith_short_8","alias_value":"7I4ZXYVY","created_at":"2026-06-09T01:05:03Z"}],"graph_snapshots":[{"event_id":"sha256:df43d55f3fafceef04f495135012f13f459e402961a1513203b9b27605ee3232","target":"graph","created_at":"2026-06-09T01:05:03Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2406.09243/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recently, Donoso, Le, Moreira and Sun studied the asymptotic behavior of the averages of completely multiplicative functions over the Gaussian integers. They derived Wirsing's theorem for Gaussian integers, answered a question of Frantzikinakis and Host for sum of two squares, and obtained a variant of a theorem of Bergelson and Richter on ergodic averages along the number of prime factors of integers. In this paper, we will show the analogue of these results for co-prime integer pairs. Moreover, building on Frantzikinakis and Host's results, we obtain some convergences on the multilinear aver","authors_text":"Biao Wang","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-06-13T15:46:41Z","title":"On averages of completely multiplicative functions over co-prime integer pairs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.09243","kind":"arxiv","version":2},"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:b24819fd96074422d21c9d2c2297577ba0ad4cecc4ae181a19396a9a06f922ca","target":"record","created_at":"2026-06-09T01:05:03Z","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":"56d6476e457073ed6777801d8f5498d0c15e55ef085aae59ac4fdf16e847579b","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-06-13T15:46:41Z","title_canon_sha256":"877199e804452e85af38d48b543bb7e2540b1498895510848452674b404ed839"},"schema_version":"1.0","source":{"id":"2406.09243","kind":"arxiv","version":2}},"canonical_sha256":"fa399be2b864df7587e043158b92eaa3d267f120f40ff3e790de551f428e2d54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa399be2b864df7587e043158b92eaa3d267f120f40ff3e790de551f428e2d54","first_computed_at":"2026-06-09T01:05:03.437700Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T01:05:03.437700Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+EZkOIohV8h1m7qsWvJR8ILWTFcppksPn+ezPD1wAjXBNsymtz0GuQ1L2MEenExvYBCCv3p1uwt1AX/zfqI0Bw==","signature_status":"signed_v1","signed_at":"2026-06-09T01:05:03.438243Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.09243","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b24819fd96074422d21c9d2c2297577ba0ad4cecc4ae181a19396a9a06f922ca","sha256:df43d55f3fafceef04f495135012f13f459e402961a1513203b9b27605ee3232"],"state_sha256":"55be0b0f77426f8b04ca89ff890aa2b06f72262c6e0c80718fa8c04be6a3038e"}