{"as_of":"2026-08-12T03:26:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:40e28caad0275851ff6b8ce40c5f272f27d0c09a60b21d7baf2958b221d47a9b","coverage":[{"denominator":37,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":37,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-23T21:23:40.214843Z","state":"measured"},{"denominator":38,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":38,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-03T14:58:17.563054Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2409.02106","snapshot_observed_at":"2026-08-03T14:58:17.563054Z","title":"Chavez,An upper bound on the reciprocal zeta derivative at zeta zeros, preprint (2024); available asarXiv:2409.02106v1[math.NT], 3 Sep 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.18936","last_updated":"2026-06-05T00:03:04Z","snapshot_observed_at":"2026-08-03T14:58:15.966067Z","submitted_at":"2025-12-22T01:13:04Z","title":"Unimodular Fake Mobius Functions","version":3},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-03T14:58:17.563054Z"},"links":{"cited_paper":"/paper/2409.02106","citing_paper":"/paper/2512.18936"},"observation_digest":"sha256:18c311d22ab905ce18f753e67e01c15e4999e2e9a2b842c30c4ae002bda062a7","observation_id":"f359e548-981a-4a84-9024-d0fca0b107a2","resolution":{"observed_at":"2026-08-03T14:58:17.563054Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2409.02106/citation-record","integrity":"/paper/2409.02106/integrity","json":"/paper/2409.02106/citation-record.json","paper":"/paper/2409.02106"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"& Stark, H.M","venue":null,"work_id":"96be269a-0377-4987-816d-72584b23c4e0","year":1981},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:150586a64577c0af1cf675d6d1086553d5a5e8cd68e6e968173ee9afaa64f444","observation_id":"0adf47e9-3c6c-4bd8-8368-598cc980bb10","resolution":{"observed_at":"2026-05-23T21:25:52.325367Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"03d27bf1-2c20-4950-81ad-a65274833ac6","year":2008},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:45959393cabb92a2ee6637d5e41e1ace74a50641291e6f7f1e810285bb35a9c9","observation_id":"f666d7ca-9c03-46f7-9e29-65d98888f9e9","resolution":{"observed_at":"2026-05-23T21:25:52.393363Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"fc14c8d5-bd54-48e4-952e-440bfa4dbfe5","year":2012},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:5873346a2bf5e72af8a04852dbdfa018c921bc146db1f793f2642bf9d3c0c074","observation_id":"92b6fea0-f6db-487e-8faf-40c34f18648b","resolution":{"observed_at":"2026-05-23T21:25:52.395899Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"c6e21d87-02f9-4441-9137-aa6fc4524841","year":2013},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:426b3b09eeda10ac6bd04a22cef124fdee6ea826ab0707527fb6e6f8965b38a0","observation_id":"7d01a533-4b09-4aba-9feb-6b80997d67ef","resolution":{"observed_at":"2026-05-23T21:25:52.404326Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"bf73b5bf-7723-4cce-8d0e-9438c1527a5a","year":2015},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:55bf7380006175864c90d6b78d190dd870d5cd113e888e2c766a8199ba0be653","observation_id":"082b3a6d-c508-45e2-8dbc-eb031d45adb9","resolution":{"observed_at":"2026-05-23T21:25:52.399961Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"40b364fc-43ae-4599-9c2e-396ab0c653ca","year":1965},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:6e1f9adfdf4bfc4bcbef581b4ab570644518a28e0fb6dee1cba86f946a200302","observation_id":"cd9a4b06-6db7-4f0c-9130-bfc8ae4c2d27","resolution":{"observed_at":"2026-05-23T21:25:52.402109Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"cc5fad1c-02f1-496b-a3d3-1abdb6e4c064","year":null},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:199bf52da6d33e0aaa01079d89756e36eecd07fd61b303673b15a203a43eccb5","observation_id":"279fa83c-18c4-4af1-930b-191dfe1caef7","resolution":{"observed_at":"2026-05-23T21:25:52.408934Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"& Tenenbaum, G","venue":null,"work_id":"51725dd9-e02e-4320-940e-3edb0d252b70","year":2005},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:2055f8aa94eda33a786b8ebcb9017b647a4ee00982cdbca72c50f445151d66e8","observation_id":"8d7d4bc7-a880-458a-8d22-fc6e3171245e","resolution":{"observed_at":"2026-05-23T21:25:52.390924Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"4d2439b7-9d6b-4512-acf3-501a4e37bab0","year":1951},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:0490560d166e556063edcaf209d7b8388b80731ac3ce6904c7d752a6cd72c039","observation_id":"5a62318a-596f-448d-993f-931cf1686915","resolution":{"observed_at":"2026-05-23T21:25:52.384873Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"& Zhao, L","venue":null,"work_id":"3990aeb2-d0bd-430c-93bb-2dc4144dc844","year":2023},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:bdbaeea21733878cb2aad32878acbd09579c944d5d2b2f3279546fddc97eecc2","observation_id":"cc76c7fa-edab-49e3-ad3b-2cef945e3da1","resolution":{"observed_at":"2026-05-23T21:25:52.327720Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"283a5c3d-d969-4e68-a6f4-fc0ae3d46841","year":1989},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:8f00cfa0ff0937701422b0b0084435ef1c96120e6f06d74ae192013ce5ec6aca","observation_id":"0410c506-93f9-45d1-beeb-4a0989e33fc5","resolution":{"observed_at":"2026-05-23T21:25:52.330223Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"& Tao, T","venue":null,"work_id":"967fd6d6-d21e-4e7e-88fc-c15c8fdac768","year":2012},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:0ccc40a2c2b37eba76dfad9599aeddae81b31ba7b1e4e9fb0fbf7f1f7ffc6af2","observation_id":"9ff66480-ebd0-4b29-9b7e-09bf35b3fea9","resolution":{"observed_at":"2026-05-23T21:25:52.380261Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"f2ff19be-34b4-443f-b1ce-40b99554aaee","year":2012},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:4d5208880a591ad615ab5394dd7ebb9c53e96cfcf00c11c4e6f266351c8f1811","observation_id":"cceffb48-d9a9-4e6a-8b70-4203c789c764","resolution":{"observed_at":"2026-05-23T21:25:52.335291Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"& Wright, E.M","venue":null,"work_id":"f0fdde6c-b6d7-4d80-b4ad-f86818b84264","year":1979},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:0c5fad06dd83b6015beef7dc02a556c3784fe31bef647cdf2c5a2c37c4f971c6","observation_id":"73739382-2e6e-4086-83ad-da1f64897ad2","resolution":{"observed_at":"2026-05-23T21:25:52.332790Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"ccca6b66-2d06-4f83-ac1b-4a150cc98eb7","year":2022},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:e600b97d830708962bde89ac762ddba508e794a884d4e5331a23f27c3440a09f","observation_id":"70271534-28f2-445d-b07e-6c0478b931c8","resolution":{"observed_at":"2026-05-23T21:25:52.377979Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"f822151f-662e-493e-aa4f-0df2302e9955","year":1987},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:26c1499795c9937c2ea0fdbce93af559c5dd03b49b62b33d20855c3ea3fcd0a3","observation_id":"9171f8ed-4e38-49c8-a74d-a7a708639028","resolution":{"observed_at":"2026-05-23T21:25:52.382579Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"f249ced1-2bbb-48b4-87a1-6a6e7ddce935","year":2000},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:676375daa6d97118dd1bb267c226a72afaa2e907e2b0d02de7439fed7edefd3d","observation_id":"d522a110-6826-4f2e-9f4c-e4c6ac191858","resolution":{"observed_at":"2026-05-23T21:25:52.388482Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"09b89ced-44dc-4c30-9a9c-a92699a67d53","year":2024},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:890d1a48cce0073f06006bdbb2e8bea9301bce03949b4772079212f061f8cd33","observation_id":"a6db098b-221c-4122-864c-3f5f9813eff4","resolution":{"observed_at":"2026-05-23T21:25:52.406621Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"84406058-f55b-424d-8645-359b16f5c75d","year":2013},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:6190a825b50943ba52728c391b8986abf4a69c51a47107cc5bfb0afb2bae12b8","observation_id":"e10a5168-5ea6-45cb-9286-c98eaaca5c47","resolution":{"observed_at":"2026-05-23T21:25:52.411189Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"b1273249-aac1-4786-ae56-dd7392dba3b2","year":1906},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:7e4473c02a720479c1550e8620e9016e6416899c145d4c80b4251164947eeb3d","observation_id":"ac8e10d7-fd1f-47f8-90f4-4e6f9b5acf6e","resolution":{"observed_at":"2026-05-23T21:25:52.413449Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"ae122ac7-d66b-4f19-8fef-2dbdb1faa28e","year":1924},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:4dd2e5493ee6bea11acd27fd7d212f1f1a7f23538d7f316e0da804c49d7a7053","observation_id":"fea5dffc-0650-4c09-8729-2a9f1e3862f7","resolution":{"observed_at":"2026-05-23T21:25:52.366469Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"edde42bf-fe2d-4eae-8b0c-6308afb77f5c","year":1912},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:b9daa5b15a432b37f6b707a68b780b8fca6ce891d38b252e2e8823c7670a88a3","observation_id":"cfea951e-5fed-41d9-aae5-3e11453fa2cb","resolution":{"observed_at":"2026-05-23T21:25:52.368868Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"f9cad260-7641-4fc3-a80c-b292f0aee94d","year":1923},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:0752d533a5b739da95804e1cbe127349d3dc28ff445d211a0ddd1af894cfd735","observation_id":"7ae107c9-e4a5-4aa4-b51f-ee7ad25bf95f","resolution":{"observed_at":"2026-05-23T21:25:52.364080Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"& Montgomery, H.L","venue":null,"work_id":"eae61e6b-e502-4765-baab-5f22ca0fd55d","year":2009},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:18b1ee9a862d78323fed53c84aba212f04de4b9f25ee7eac81cad596e2812ca0","observation_id":"526029b9-b621-4b51-8bed-e8cf4e46cae0","resolution":{"observed_at":"2026-05-23T21:25:52.342061Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"b1d9509d-0c34-4d7f-a159-3a3673519c84","year":2015},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:1e58e89bfaa02ebe029824fd4e8c871d129b8adcbaf6956f487624610dd5c25d","observation_id":"5a9ec3fe-39e0-4c46-ac64-051b06f2933e","resolution":{"observed_at":"2026-05-23T21:25:52.361850Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"& Radziwill, M","venue":null,"work_id":"02b1f205-66e7-4acd-aae1-41ff72022a51","year":2016},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:ff234332280752748871a4ca578fadec2bd3a67f2075614c20e8df92113edd8a","observation_id":"d3083c67-135c-4f1b-b724-cb258dd509c0","resolution":{"observed_at":"2026-05-23T21:25:52.371204Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"& Rivat, J","venue":null,"work_id":"5b201684-5c88-4611-8d5c-1b311582ca2b","year":2010},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:bf14f56a2a914a6bc0d40c8e9c2c9ab7abec0b33eeec00c55f322577c1e6686d","observation_id":"8dc5aa9d-413f-416f-a152-507f07ebe3e5","resolution":{"observed_at":"2026-05-23T21:25:52.359193Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"36cb87be-3288-42fc-9c98-1171fb04f0f4","year":2012},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:e1c803372d8689b55ee1b80458cf287febd51535a86e2fe24cd36ef3e68b6ab6","observation_id":"265f051d-ea83-4e9a-afab-591e2f6d928b","resolution":{"observed_at":"2026-05-23T21:25:52.375607Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"322c9716-ebb2-4409-986c-a7bf9357face","year":1973},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:5b408aef7cba9dd1e877b86f2593da5a49539b7def5dc15166a5f415b16f7507","observation_id":"8695c073-56ca-469d-b883-eec58829ca98","resolution":{"observed_at":"2026-05-23T21:25:52.339822Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"& Soundararajan, K","venue":null,"work_id":"f4727d3d-d394-4784-99d4-7b03434aadf6","year":2005},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:283c275b1498ed2e9aff9f3237ef0062b039ef16562e8b6aef39f6d406bca67f","observation_id":"1381051c-5fb9-4d64-baef-963a625d709a","resolution":{"observed_at":"2026-05-23T21:25:52.356538Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"658d72f1-3091-46d2-9be8-0b319b57725a","year":2010},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:56e3c59c87e5ccc084b2cf0517a0b24537143b776ed825f947edd70ede3d540a","observation_id":"9b929665-eae6-48c1-af42-829a66d187b3","resolution":{"observed_at":"2026-05-23T21:25:52.351961Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"& Shusterman, M","venue":null,"work_id":"b6ea4ebf-25c1-4c43-8e25-79e97bb58782","year":2022},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:32b880369653c3776943f5191ad01b5a8c954d38b5e6a0e5e4f0f73d505fe8cd","observation_id":"82a61363-9c5f-4b13-b043-58abb47eacb6","resolution":{"observed_at":"2026-05-23T21:25:52.346814Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"e8fe3ffe-2941-46f6-ab38-e5655222940b","year":2009},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:3f128f0b5bb97ec698f0b5a580eb18f33562e3ed56b275f86c9244bb7f8af4f7","observation_id":"53d12d40-dbf0-4e19-93b3-41df4f297d29","resolution":{"observed_at":"2026-05-23T21:25:52.354143Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"81b3e941-a7c4-4aec-94f1-407d4c818f31","year":2016},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:15cd5facb806765cb4f24e358009793db210d9295a918cc8e37a240b57a01514","observation_id":"c2057c70-e4be-4e76-ac5a-f705b5f8a93c","resolution":{"observed_at":"2026-05-23T21:25:52.373482Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"& Ter¨ av¨ ainen, J","venue":null,"work_id":"aa49baa8-cd79-47a4-b0f9-126b483de003","year":2019},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:8e8b02a108612ab4a09e4bb19926536940dfdac413ceb233d61ceec44185a95f","observation_id":"c43eb35a-7986-40cc-97d4-8ecde8e12e5a","resolution":{"observed_at":"2026-05-23T21:25:52.344421Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"0060772d-db45-4e35-b7e1-431caf7894e4","year":1927},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:6233f99f1fe7f82eaea559116cefdcc8d77aa486b89201ffa26f2feb11c68938","observation_id":"6b0b211a-39f4-484e-a8f0-c8d0d3e017f6","resolution":{"observed_at":"2026-05-23T21:25:52.349688Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"& Heath-Brown, D.R","venue":null,"work_id":"a9940a29-f1f0-48f4-9360-776f6c12bd5b","year":1986},"citing_paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums","version":10},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-05-23T21:23:40.214843Z"},"links":{"citing_paper":"/paper/2409.02106"},"observation_digest":"sha256:72094cb792b20183226c2181cf99e1e51af10f7611d113132a340dc3ae354d47","observation_id":"ec32047e-624f-4d40-ada4-193000017ba0","resolution":{"observed_at":"2026-05-23T21:25:52.337564Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2409.02106","last_updated":"2026-05-14T11:52:50Z","latest_version":10,"primary_category":"math.NT","snapshot_observed_at":"2026-07-06T19:09:55.393720Z","submitted_at":"2024-09-03T17:58:50Z","title":"Correlations of multiplicative functions with their partial sums"},"reference_resolution":{"displayed":37,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":25,"verified_exact":0,"verified_fuzzy":12},"total_outbound_references":37},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 1 inbound Pith citation observation for arXiv:2409.02106."}