{"as_of":"2026-08-08T22:25:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c1d05fa6c45b136d00b4f978195aae760ba842256ad4a199ad5c26be1ab69d12","coverage":[{"denominator":9,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":9,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T17:17:00.496502Z","state":"measured"},{"denominator":9,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":9,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+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/2607.17731/citation-record","integrity":"/paper/2607.17731/integrity","json":"/paper/2607.17731/citation-record.json","paper":"/paper/2607.17731"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T17:16:59.898803Z","title":"Hardy, J.E","venue":null,"work_id":null,"year":1918},"citing_paper":{"arxiv_id":"2607.17731","last_updated":"2026-07-20T09:21:11Z","snapshot_observed_at":"2026-08-07T21:05:58.442616Z","submitted_at":"2026-07-20T09:21:11Z","title":"Jacob's ladders and new $\\zeta$-functionals and corresponding $\\zeta$-equivalents of the Fermat-Wiles theory based on sums of elementary $\\zeta$-pulses","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-01T17:16:59.898803Z"},"links":{"citing_paper":"/paper/2607.17731"},"observation_digest":"sha256:a79e8409e23c6252016e0b3a48cee5096ba99df9ec5058677d8aa03c9da12140","observation_id":"4123b8fa-51eb-4677-8798-7fc95a5aa8d7","resolution":{"observed_at":"2026-08-01T17:16:59.898803Z","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":"2026-08-01T17:16:59.967201Z","title":"Moser, On some properties of Riemann zeta-function on the critical line, Acta Arith","venue":null,"work_id":null,"year":1974},"citing_paper":{"arxiv_id":"2607.17731","last_updated":"2026-07-20T09:21:11Z","snapshot_observed_at":"2026-08-07T21:05:58.442616Z","submitted_at":"2026-07-20T09:21:11Z","title":"Jacob's ladders and new $\\zeta$-functionals and corresponding $\\zeta$-equivalents of the Fermat-Wiles theory based on sums of elementary $\\zeta$-pulses","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-01T17:16:59.967201Z"},"links":{"citing_paper":"/paper/2607.17731"},"observation_digest":"sha256:1bf3c404782f57f06f37beca04e5206fd3d8e1976e8e6c5b9df3b558d97281fa","observation_id":"ce2ecf66-81a6-4080-af85-2696e8e700f7","resolution":{"observed_at":"2026-08-01T17:16:59.967201Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1307.1095","last_updated":"2013-07-28T17:24:42Z","snapshot_observed_at":"2026-07-06T03:17:21.560204Z","submitted_at":"2013-05-14T09:08:29Z","title":"Riemann's hypothesis and some infinite set of microscopic universes of the Einstein's type in the early period of the evolution of the Universe","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1307.1095","snapshot_observed_at":"2026-08-01T17:17:00.038125Z","title":"Moser, Riemann hypothesis and some infinite set of microscopic universes of the Einstein’s type in the early period of the evolution of the Universe, arXiv: 1307.1095v2","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.17731","last_updated":"2026-07-20T09:21:11Z","snapshot_observed_at":"2026-08-07T21:05:58.442616Z","submitted_at":"2026-07-20T09:21:11Z","title":"Jacob's ladders and new $\\zeta$-functionals and corresponding $\\zeta$-equivalents of the Fermat-Wiles theory based on sums of elementary $\\zeta$-pulses","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-01T17:17:00.038125Z"},"links":{"cited_paper":"/paper/1307.1095","citing_paper":"/paper/2607.17731"},"observation_digest":"sha256:d3548a3eb658e54a66c620f549f70cc50831330459dc5116c6142703060805dc","observation_id":"b2dcc2da-1640-4e3e-9cf5-3f80f5ea5523","resolution":{"observed_at":"2026-08-01T17:17:00.038125Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0901.3937","last_updated":"2009-01-26T02:01:56Z","snapshot_observed_at":"2026-07-06T01:50:45.963035Z","submitted_at":"2009-01-26T02:01:56Z","title":"Strange Quarks Nuggets in Space: Charges in Seven Settings","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0901.3937","snapshot_observed_at":"2026-08-01T17:17:00.076751Z","title":"Moser,‘Jacob’s ladders and almost exact asymptotic representation of the Hardy- Littlewood integral‘, Math","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.17731","last_updated":"2026-07-20T09:21:11Z","snapshot_observed_at":"2026-08-07T21:05:58.442616Z","submitted_at":"2026-07-20T09:21:11Z","title":"Jacob's ladders and new $\\zeta$-functionals and corresponding $\\zeta$-equivalents of the Fermat-Wiles theory based on sums of elementary $\\zeta$-pulses","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-01T17:17:00.076751Z"},"links":{"cited_paper":"/paper/0901.3937","citing_paper":"/paper/2607.17731"},"observation_digest":"sha256:a6e6c44f053ac30b4aaf0a9148e825ba0e5728714811df8cebf617387188a7b5","observation_id":"c36b1b0c-ce6f-493e-a4a4-108e8ea5ac68","resolution":{"observed_at":"2026-08-01T17:17:00.076751Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1103.0359","last_updated":"2011-03-02T07:40:20Z","snapshot_observed_at":"2026-07-06T02:24:16.874339Z","submitted_at":"2011-03-02T07:40:20Z","title":"Jacob's ladders, the structure of the Hardy-Littlewood integral and some new class of nonlinear integral equations","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1103.0359","snapshot_observed_at":"2026-08-01T17:17:00.173499Z","title":"Moser, ‘Jacob’s ladders, the structure of the Hardy-Littlewood integral and some new class of nonlinear integral equations‘, Proc","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.17731","last_updated":"2026-07-20T09:21:11Z","snapshot_observed_at":"2026-08-07T21:05:58.442616Z","submitted_at":"2026-07-20T09:21:11Z","title":"Jacob's ladders and new $\\zeta$-functionals and corresponding $\\zeta$-equivalents of the Fermat-Wiles theory based on sums of elementary $\\zeta$-pulses","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-01T17:17:00.173499Z"},"links":{"cited_paper":"/paper/1103.0359","citing_paper":"/paper/2607.17731"},"observation_digest":"sha256:13fdc2bdbfc4ceb4f138bb721670206355e861b2597bd3415ac6848f854f4e08","observation_id":"11c747a9-56b7-4e71-96bf-48a1ca6d5791","resolution":{"observed_at":"2026-08-01T17:17:00.173499Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1402.2098","last_updated":"2014-02-10T10:55:44Z","snapshot_observed_at":"2026-07-06T03:35:33.967069Z","submitted_at":"2014-02-10T10:55:44Z","title":"Jacob's ladders, reverse iterations and new infinite set of $L_2$-orthogonal systems generated by the Riemann $\\zf$-function","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1402.2098","snapshot_observed_at":"2026-08-01T17:17:00.279030Z","title":"Moser, Jacob’s ladders, reverse iterations and new infinite set ofL 2-orthogonal systems generated by the Riemannζ 1 2 +it -function, arXiv: 1402.2098v1","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.17731","last_updated":"2026-07-20T09:21:11Z","snapshot_observed_at":"2026-08-07T21:05:58.442616Z","submitted_at":"2026-07-20T09:21:11Z","title":"Jacob's ladders and new $\\zeta$-functionals and corresponding $\\zeta$-equivalents of the Fermat-Wiles theory based on sums of elementary $\\zeta$-pulses","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-01T17:17:00.279030Z"},"links":{"cited_paper":"/paper/1402.2098","citing_paper":"/paper/2607.17731"},"observation_digest":"sha256:276a699786a27b4401054420f01232d7cf5cb7c61d398d52ebfa66a0d20bd57f","observation_id":"91177537-8c11-41db-84ed-5f5f8664b21a","resolution":{"observed_at":"2026-08-01T17:17:00.279030Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2304.09267","last_updated":"2023-04-18T20:16:17Z","snapshot_observed_at":"2026-07-06T15:17:13.786770Z","submitted_at":"2023-04-18T20:16:17Z","title":"Jacob's ladders, existence of almost linear increments of the Hardy-Littlewood integral and new types of multiplicative laws","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2304.09267","snapshot_observed_at":"2026-08-01T17:17:00.349766Z","title":"Moser, Jacob’s ladders, existence of almost linear increments of the Hardy-Littlewood integral and new types of multiplicative laws, arXiv: 2304.09267","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.17731","last_updated":"2026-07-20T09:21:11Z","snapshot_observed_at":"2026-08-07T21:05:58.442616Z","submitted_at":"2026-07-20T09:21:11Z","title":"Jacob's ladders and new $\\zeta$-functionals and corresponding $\\zeta$-equivalents of the Fermat-Wiles theory based on sums of elementary $\\zeta$-pulses","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-01T17:17:00.349766Z"},"links":{"cited_paper":"/paper/2304.09267","citing_paper":"/paper/2607.17731"},"observation_digest":"sha256:2a1909d93aa9658685c506359316b7836d704699d83c2207a9530b4356d65600","observation_id":"e73bcc4a-6992-4ca2-bed9-ea85b6908582","resolution":{"observed_at":"2026-08-01T17:17:00.349766Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2312.12085","last_updated":"2023-12-19T12:04:57Z","snapshot_observed_at":"2026-07-06T17:05:14.915707Z","submitted_at":"2023-12-19T12:04:57Z","title":"Jacob's ladders, almost linear increments of the Hardy-Littlewood integral (1918), the classical Dirichet's sum of divisors (1849) and their relationship with the Fermat-Wiles theorem","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2312.12085","snapshot_observed_at":"2026-08-01T17:17:00.428663Z","title":null,"venue":null,"work_id":null,"year":1918},"citing_paper":{"arxiv_id":"2607.17731","last_updated":"2026-07-20T09:21:11Z","snapshot_observed_at":"2026-08-07T21:05:58.442616Z","submitted_at":"2026-07-20T09:21:11Z","title":"Jacob's ladders and new $\\zeta$-functionals and corresponding $\\zeta$-equivalents of the Fermat-Wiles theory based on sums of elementary $\\zeta$-pulses","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-01T17:17:00.428663Z"},"links":{"cited_paper":"/paper/2312.12085","citing_paper":"/paper/2607.17731"},"observation_digest":"sha256:267351a0b75dfdc12030eac6e1c4e9a70ee6fd3fd4708bcd5a05729f974c7313","observation_id":"b1445fa2-8b9f-42bf-aea2-9cfbdd685b2b","resolution":{"observed_at":"2026-08-01T17:17:00.428663Z","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":"2026-08-01T17:17:00.496502Z","title":"Kano (edit.),Georg Friedrich Bernhard Riemann, 1991, ISBN4-535-78181-8 C3041 P3800E, (in Japanese, our results are situated on pp","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2607.17731","last_updated":"2026-07-20T09:21:11Z","snapshot_observed_at":"2026-08-07T21:05:58.442616Z","submitted_at":"2026-07-20T09:21:11Z","title":"Jacob's ladders and new $\\zeta$-functionals and corresponding $\\zeta$-equivalents of the Fermat-Wiles theory based on sums of elementary $\\zeta$-pulses","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-01T17:17:00.496502Z"},"links":{"citing_paper":"/paper/2607.17731"},"observation_digest":"sha256:f7ad87c9722d0bb67d4c9428c039cdf40d8bf243296bdcb9187f19ff10a151f9","observation_id":"4682f972-42e7-4d81-803f-891f44a3c9d2","resolution":{"observed_at":"2026-08-01T17:17:00.496502Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.17731","last_updated":"2026-07-20T09:21:11Z","latest_version":1,"primary_category":"math.NT","snapshot_observed_at":"2026-08-07T21:05:58.442616Z","submitted_at":"2026-07-20T09:21:11Z","title":"Jacob's ladders and new $\\zeta$-functionals and corresponding $\\zeta$-equivalents of the Fermat-Wiles theory based on sums of elementary $\\zeta$-pulses"},"reference_resolution":{"displayed":9,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":9,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":9},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 9 of 9 outbound references and 0 inbound Pith citation observations for arXiv:2607.17731."}