{"as_of":"2026-08-12T05:43:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:96c7e3a4ce00d0b55abf0e81046880d11a56fe24fe34ca282650819d7d8d42ac","coverage":[{"denominator":10,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":10,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-13T06:59:55.445988Z","state":"measured"},{"denominator":10,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":10,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"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":[],"links":{"evidence":"/evidence","html":"/paper/2607.04366/citation-record","integrity":"/paper/2607.04366/integrity","json":"/paper/2607.04366/citation-record.json","paper":"/paper/2607.04366"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T06:59:55.445988Z","title":"Popa, A double Mertens type evaluation , J","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.04366","last_updated":"2026-07-10T16:33:46Z","snapshot_observed_at":"2026-08-11T15:28:14.825832Z","submitted_at":"2026-07-05T15:50:33Z","title":"Complete Asymptotic Expansion of the Additive Mertens Sum $S_k(x)$","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-07-13T06:59:55.445988Z"},"links":{"citing_paper":"/paper/2607.04366"},"observation_digest":"sha256:76ef7519bfc43aa83649085de6b5537138dbfea95035b9bc7f688b1a3b66a266","observation_id":"e0773b8c-a66a-4179-b1ef-0fbbca1bf6cb","resolution":{"observed_at":"2026-07-13T06:59:55.445988Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T06:59:55.445988Z","title":"Popa, A triple Mertens evaluation , J","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.04366","last_updated":"2026-07-10T16:33:46Z","snapshot_observed_at":"2026-08-11T15:28:14.825832Z","submitted_at":"2026-07-05T15:50:33Z","title":"Complete Asymptotic Expansion of the Additive Mertens Sum $S_k(x)$","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-07-13T06:59:55.445988Z"},"links":{"citing_paper":"/paper/2607.04366"},"observation_digest":"sha256:bd37292490d5ff1665c3c0fbe22772fd1f1e42241ca11d31b05565c3c48670f8","observation_id":"96a87448-a412-4f8c-8e49-2ea52b521f0b","resolution":{"observed_at":"2026-07-13T06:59:55.445988Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T06:59:55.445988Z","title":"Tenenbaum, Generalized Mertens sums , in: Analytic Number Theory, Modular Forms and q-Hypergeometric Series, Springer Proc","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.04366","last_updated":"2026-07-10T16:33:46Z","snapshot_observed_at":"2026-08-11T15:28:14.825832Z","submitted_at":"2026-07-05T15:50:33Z","title":"Complete Asymptotic Expansion of the Additive Mertens Sum $S_k(x)$","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-07-13T06:59:55.445988Z"},"links":{"citing_paper":"/paper/2607.04366"},"observation_digest":"sha256:480229a2fb3707b55b2823fab322637e2ae77910a261e76f1da67292623b3212","observation_id":"121c6a62-6913-42ad-8222-88b838122763","resolution":{"observed_at":"2026-07-13T06:59:55.445988Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T06:59:55.445988Z","title":"Tenenbaum, Introduction to Analytic and Probabilistic Number Theory , 3rd ed., Grad","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.04366","last_updated":"2026-07-10T16:33:46Z","snapshot_observed_at":"2026-08-11T15:28:14.825832Z","submitted_at":"2026-07-05T15:50:33Z","title":"Complete Asymptotic Expansion of the Additive Mertens Sum $S_k(x)$","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-07-13T06:59:55.445988Z"},"links":{"citing_paper":"/paper/2607.04366"},"observation_digest":"sha256:30e74b19a4a70daad354aef32adbdf9d101504354c28b42e1db86ca12e5cda2f","observation_id":"38b1f3dc-b114-439c-b0cd-7a050d7ed9df","resolution":{"observed_at":"2026-07-13T06:59:55.445988Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1909.10930","last_updated":"2021-06-13T01:12:35Z","snapshot_observed_at":"2026-07-06T08:24:11.778237Z","submitted_at":"2019-09-24T13:55:12Z","title":"Multiple Mertens evaluations","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1909.10930","snapshot_observed_at":"2026-07-13T06:59:55.445988Z","title":null,"venue":null,"work_id":null,"year":1909},"citing_paper":{"arxiv_id":"2607.04366","last_updated":"2026-07-10T16:33:46Z","snapshot_observed_at":"2026-08-11T15:28:14.825832Z","submitted_at":"2026-07-05T15:50:33Z","title":"Complete Asymptotic Expansion of the Additive Mertens Sum $S_k(x)$","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-07-13T06:59:55.445988Z"},"links":{"cited_paper":"/paper/1909.10930","citing_paper":"/paper/2607.04366"},"observation_digest":"sha256:0c4ce20cade409e51ca7fe0bf42cf142c47fb07f108731dec0564010f1b22bbe","observation_id":"3b15e2ae-bedb-4a9a-8fde-3b95df22355c","resolution":{"observed_at":"2026-07-13T06:59:55.445988Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T06:59:55.445988Z","title":null,"venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2607.04366","last_updated":"2026-07-10T16:33:46Z","snapshot_observed_at":"2026-08-11T15:28:14.825832Z","submitted_at":"2026-07-05T15:50:33Z","title":"Complete Asymptotic Expansion of the Additive Mertens Sum $S_k(x)$","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-07-13T06:59:55.445988Z"},"links":{"citing_paper":"/paper/2607.04366"},"observation_digest":"sha256:05d0312e008dd5ac40fa363ede1a6fe1d3127239a327a72fd9add1a81809d3dc","observation_id":"7e49f397-8a24-4895-b204-b63b0909ad02","resolution":{"observed_at":"2026-07-13T06:59:55.445988Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T06:59:55.445988Z","title":"Arias-de-Reyna, On the Theorem of Frullani , Proc","venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2607.04366","last_updated":"2026-07-10T16:33:46Z","snapshot_observed_at":"2026-08-11T15:28:14.825832Z","submitted_at":"2026-07-05T15:50:33Z","title":"Complete Asymptotic Expansion of the Additive Mertens Sum $S_k(x)$","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-07-13T06:59:55.445988Z"},"links":{"citing_paper":"/paper/2607.04366"},"observation_digest":"sha256:8b2e6b15369655a57d2db6dca0d493240cfbb213990c704324770c47d89b3d11","observation_id":"7a49b260-7f1e-45ec-9adc-ebb27e09bf2a","resolution":{"observed_at":"2026-07-13T06:59:55.445988Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T06:59:55.445988Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.04366","last_updated":"2026-07-10T16:33:46Z","snapshot_observed_at":"2026-08-11T15:28:14.825832Z","submitted_at":"2026-07-05T15:50:33Z","title":"Complete Asymptotic Expansion of the Additive Mertens Sum $S_k(x)$","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-07-13T06:59:55.445988Z"},"links":{"citing_paper":"/paper/2607.04366"},"observation_digest":"sha256:2301b5c70cd24916b63189857284a44232612bf5d9ad48b95c12cefa44d76e21","observation_id":"fdfbe479-bb3a-464e-a8de-8f8294cfdbbe","resolution":{"observed_at":"2026-07-13T06:59:55.445988Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T06:59:55.445988Z","title":"Zagier, Values of zeta functions and their applications , in: First European Congress of Math- ematics, Vol","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2607.04366","last_updated":"2026-07-10T16:33:46Z","snapshot_observed_at":"2026-08-11T15:28:14.825832Z","submitted_at":"2026-07-05T15:50:33Z","title":"Complete Asymptotic Expansion of the Additive Mertens Sum $S_k(x)$","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-07-13T06:59:55.445988Z"},"links":{"citing_paper":"/paper/2607.04366"},"observation_digest":"sha256:863d735447733926ffad5217f68c732e8492d31e52db709e3c700fcf36824688","observation_id":"36e07c62-35a8-4e79-8a94-94f03d2a723a","resolution":{"observed_at":"2026-07-13T06:59:55.445988Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T06:59:55.445988Z","title":"Waldschmidt, Multiple polylogarithms: an introduction , in: Number Theory and Discrete Mathematics (A","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.04366","last_updated":"2026-07-10T16:33:46Z","snapshot_observed_at":"2026-08-11T15:28:14.825832Z","submitted_at":"2026-07-05T15:50:33Z","title":"Complete Asymptotic Expansion of the Additive Mertens Sum $S_k(x)$","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-07-13T06:59:55.445988Z"},"links":{"citing_paper":"/paper/2607.04366"},"observation_digest":"sha256:b844f940f8722051826700fd1e3e238fdfaaf2311cd3dfc70ad50d4cc5f31f7e","observation_id":"a4a60e69-5bed-426e-9d4d-8c5bcd345750","resolution":{"observed_at":"2026-07-13T06:59:55.445988Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.04366","last_updated":"2026-07-10T16:33:46Z","latest_version":2,"primary_category":"math.NT","snapshot_observed_at":"2026-08-11T15:28:14.825832Z","submitted_at":"2026-07-05T15:50:33Z","title":"Complete Asymptotic Expansion of the Additive Mertens Sum $S_k(x)$"},"reference_resolution":{"displayed":10,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":10,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":10},"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 10 of 10 outbound references and 0 inbound Pith citation observations for arXiv:2607.04366."}