{"as_of":"2026-08-19T13:40:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:d94a18c4eeba550ddfa506688f4a93a66107114700e2537a21a0354757e02e0b","coverage":[{"denominator":50,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":50,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-25T22:50:52.893106Z","state":"measured"},{"denominator":50,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":50,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-19T06:32:44.657259+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/2606.24536/citation-record","integrity":"/paper/2606.24536/integrity","json":"/paper/2606.24536/citation-record.json","paper":"/paper/2606.24536"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-25T22:50:52.893106Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:45b49cef28bc061d1b5a39e1145f4d8dc185ebc65b339b992a854fd80735b811","observation_id":"8b15f647-b6df-40ae-929b-8d1d10a2b900","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":null,"venue":null,"work_id":null,"year":1959},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:6830165d9eecef2bdbcdccd5fe9e88222f6e8c9bd9202429e4069b435876fe45","observation_id":"786506fb-1b0e-4b56-a700-4ac7eb165166","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":null,"venue":null,"work_id":null,"year":1974},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:23a0257e49589425e6981cd950dc72ce12ad6fa1619d96c1b7555a5cd8cf54f4","observation_id":"5f5e8b7d-0d85-4106-8501-b1e7d586178c","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":null,"venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:13b51f3c1b3bb3f64705219296667c524de8f55c3b0435a873226253268c7908","observation_id":"6bba1be3-6d7c-4914-9ede-142d014490ad","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":null,"venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:b01b274aa2347f024232d26045b951289330322169c27e550a7014fb289d7473","observation_id":"e5c0f959-b352-44fc-917f-7f6127ab9420","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":null,"venue":null,"work_id":null,"year":1970},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:e23dc3b014cd823a6319c48c9b1db06e24e09ef6ad8c1e62c81d00552afe5c83","observation_id":"c003e48f-741f-446d-87d7-2168dd44f90e","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":null,"venue":null,"work_id":null,"year":1971},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:04bf02e92e8d9eb7f284e40a58e443ec8d855bdaddeecb363acb72c7b45bdf02","observation_id":"6bb265d9-bb76-4ad2-81ba-588478e3aabe","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":null,"venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:83225aef6c25293ff74e9b75516600b506b241b371081603ab9039fabc07bad4","observation_id":"ace620af-f2d8-44c6-a656-c7dfde81c04f","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":null,"venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:d72cd83f7634e99f5ba87dfd264d3a085b257c37e536ada3ccbc5dc47d24c76e","observation_id":"6bbf1f2c-fe70-46c1-90eb-690bf81c08df","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":"Soul´ e, D","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:55bef42cee58396b7b97b63e52d843bfb0fddb1f4878fffcd890e199e13de1dc","observation_id":"92ee2af0-3f90-4b01-9b21-eb56578e0504","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":null,"venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:17458a4935dc981b10380725077ca18501e1e6320f481becf13c740326219276","observation_id":"709ee0d9-b4df-4dc6-a6ce-02421d3919dc","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":null,"venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:f40eb40e0f3b77d2e60c802226d2986dff18578ef55d50b7b83287de6443e3e3","observation_id":"fd21be13-2036-4032-bb94-6f78221046e9","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":"Kontsevich and S","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:2707826c912b80254bdbffc82b0411e307155eceeedd6a74079166e7928e0a2e","observation_id":"b177b05c-3388-41d7-b745-732718daa0df","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":null,"venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:f073123fc23e2916992d3d34e63b690e7c52dc80417ab474157bc8b7ab8f92f8","observation_id":"4ddd40bb-1281-4636-bfeb-d491db72215d","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:5ecbb4c31d3bf228508007b6902d0caafcbb17f2b6f9b2f183c28ffb5994fd8c","observation_id":"0283d8a9-829c-4710-b9b2-d9491723943d","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":"Elizalde","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:c215855467587ad9277bda5435c1c25266d6eb11f6105a35e72afd37c222f60b","observation_id":"7673c282-3ac4-45db-88e4-55fcad0e702b","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":"Elizalde, S","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:ed8c41633eb32ce425ca20325f3170120a5c120710a6ba8aee164a707675ac73","observation_id":"e79798f7-ed80-4bd4-8d2c-b6b4a0ea9712","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":null,"venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:8bdffebac3deeb7f0ba8308dfea1d46b4dd12252a6772fe4d42dc0ff4cbfc470","observation_id":"18d2ca72-969c-4a0f-ae00-90f24d30157f","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":"Mu˜ noz Garc ´ ıa and R","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:77fbecb9df7decdb89625bd4f7ec7b0242b8e85d97acea37fd6974af4700dcde","observation_id":"15725da9-501e-4d7f-b24b-2338079ee88c","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":"Mu˜ noz Garc ´ ıa and R","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:38655897111403ce807b936eeda12b5519181c638b3942a993bd89b965ac0a69","observation_id":"569a6b10-7be5-4396-b81f-5984664f4281","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":"Cognola, E","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:88f1ce07ad40a6fcf369ac3f8b7f23985f9b3d96ba6e742857a52f923ca42ecc","observation_id":"9e5ee830-8ceb-4242-b437-0cfef24fee34","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":"Fucci, M","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:021fcc019cbfcb743d886ea63a4270f9b08cae22ffb4f2172276bf3f8ce4aec2","observation_id":"07ee29e1-ffed-4e7b-a328-63b580c161c4","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":null,"venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:f7c3e1ce4f642d5d0a65ac07bcaa7e799fd26fab18730b5539f50f83a1543558","observation_id":"a2da7fe7-c4b7-437f-add8-1333a0000a7e","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":null,"venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:3a80cf639d4e584bd0fda3b61132d54ee8bfbc118ae6adae5f7a7a1aaaa1e32c","observation_id":"899d7c9e-81c6-4d3e-8513-2756180e31c6","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2310.12317","last_updated":"2023-10-18T20:41:22Z","snapshot_observed_at":"2026-08-16T14:50:55.233241Z","submitted_at":"2023-10-18T20:41:22Z","title":"Going to the Other Side via the Resurgent Bridge","version":1},"cited_work":{"arxiv_id":"2310.12317","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2310.12317","snapshot_observed_at":"2026-07-04T18:30:01.383879Z","title":"Dunne, Angus Gruen, and Sergei Gukov","venue":null,"work_id":"dbc1b880-4fa4-4645-87da-777cd5eccde9","year":2023},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"cited_paper":"/paper/2310.12317","citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:da751979338da5dce5f1617cd4d07fb99d7625eec38f3712f228c04a77ba4747","observation_id":"1b879618-636e-460a-95a1-54da9b41fb69","resolution":{"observed_at":"2026-07-04T18:30:01.385748Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-25T22:50:52.893106Z","title":"Caron-Huot, M","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:187b2990c06a788df4d0c73a0ebd96e682a789d550fbcd1bfd3801654d007fd1","observation_id":"2b370af9-934d-4e69-a917-e23b1ea233c0","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":"Adams, O","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:e8aa830819bb7786c27e7d4fd543f70335a08df31e2605fc1d92a30740edd33d","observation_id":"a4b320a2-40cd-406f-940c-b68d541f8640","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2603.04619","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-04T18:30:01.383003Z","title":"Adams and G","venue":null,"work_id":"04b8c03d-3d34-4573-825f-539571b1e9bf","year":2026},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:fb3ae971accf390fc7347202b0b25fff401ca5c627b1434c611a44a0fc044afb","observation_id":"e3d4e7c0-f9e2-4721-bc73-21af2b0da860","resolution":{"observed_at":"2026-07-04T18:30:01.384342Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-25T22:50:52.893106Z","title":null,"venue":null,"work_id":null,"year":1948},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:169ef648209da7c7d1f26bb303f189a03e95d2f7a4935a64ae17112c0931a8fd","observation_id":"64aadfeb-2a8f-43aa-a614-e85daecb2f3f","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:79ed82a8833e85829b40f7d82ceec11f8ab4d3653ce25c1d24104fa80cb18d3e","observation_id":"c0d82b8a-4f08-47c9-824b-22341f6f5162","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":"Bordag, U","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:61e6511de56f0ba5f882e8167940592ad4575c9eb3223d45c627ca05d5938845","observation_id":"c9098aea-87ff-4ac8-9601-cab8cb008900","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":"Goldfeld","venue":null,"work_id":null,"year":1985},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:f47099fb16b214a6bcbaf4746b64740e41bf45dce0fdbac32080b025cb253657","observation_id":"55488932-25d4-4177-bf00-8c7879d73055","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":"W atkins","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:ee763efc34f461869300128c4cda501944939f3e75f29f5bb10f506d7e63e5c1","observation_id":"d8366c26-d546-4e05-a9c8-cc6218a1ae5a","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":null,"venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:025fd579ec4093d16c4a4116a97b97a6616233061745f660131abeb973d92db1","observation_id":"49eed943-9598-447b-be5f-9994b375e0e6","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":null,"venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:3d69fc0f7a4e9d082bd495d2827c2beb9233f7d137f435cf304e9056bee27952","observation_id":"470e5628-3206-454b-9c0a-f8a7d773182a","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":null,"venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:71dc908da701bb09793abfab9012bb1b0a917da824a683d7db2911dfd5edd859","observation_id":"8d9f0a96-8c76-414d-853f-7987dc82871b","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":"Itzykson and J","venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:286ffeabd079d3a3b2ec96783f127da5d43cbbb2dd6ddc2a703bf90877f4b280","observation_id":"77bad0ad-9081-4ef6-8c4c-adfd85ff8edc","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":"Itzykson","venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:bb87c302e0131247dc406f8e23c7d398b14af85091ca333971820bac28d18095","observation_id":"4716e842-5e01-40e7-8884-4f86050adaed","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":"De Clerck, S","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:a50160852d649f0b5cbec1b20bfa07fd8bc5f1632787639f8399d98b13879e0b","observation_id":"cd3b943e-e541-4eea-b363-bce321d7f8c3","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:5c0dfe370ddb3014a1e8da6884b893d90651a80d37a8b9b49cc0bfe9cda50822","observation_id":"49bde73a-5e48-442f-bdd9-404543539fab","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:3cb19da2e5193b3c10e1ded6232c61ea7e252801a0034bb6e401df765eb369b7","observation_id":"b4ef81dc-bd6a-4ecb-abbe-e124f2a4fb2b","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":"Landau and A","venue":null,"work_id":null,"year":1920},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:4c48de1b25d14b151d242aff834b379c349151c70b958e2d30aabe77f258ff31","observation_id":"36fa5778-fd4f-4546-9ea2-14eeb89733ba","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":"Dahlquist","venue":null,"work_id":null,"year":1951},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:4f8deb11a3a1842057fce4249f8752369785018caca7e39eb8646b2078137a46","observation_id":"6b4a31ab-9b41-4338-ba98-51d4b68a7e87","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":"Fr¨ oberg","venue":null,"work_id":null,"year":1968},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:18fdfff1eed5932f6f6e8fc0d204b8e3be3912b03e5d5ecd81e58417aeb14232","observation_id":"102db463-9d31-4ffd-b278-3cc5398386da","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:97cf4b535960c510b1506d20a46b21c0c1a324f3ae7488e12ad08ba1315a29e7","observation_id":"7c11450e-a7f9-4734-a696-a67c693e94bc","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":"Kurokawa and M","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:f62d694db3dfb07120ddbdf84499ad6de0538076c457e2b9a3b3a27d8c68a3e8","observation_id":"18a689da-c31f-45db-b9b3-857927d7ae5a","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":null,"venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:6d55d9e9420bcf61a66e7a774c30b4f944a3635c6b4f9f592cbcd2701bb70641","observation_id":"40051d71-bd8f-4f6d-b058-e4d3213ff121","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":null,"venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:559e8b24839e91a48d5d69a45f91520bed5b1c372dcffe52502bc2c1db6c1230","observation_id":"19f9dda5-dcd5-4807-b781-71b8c75cfcf3","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":"Kurokawa, M","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:a882ca36a3dd9157b83b1908de50183fe8a2a56a07d43f6cc44c7d355978beb2","observation_id":"2b4ddffe-7f74-47f9-a8f4-e7a76724af19","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","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":"2026-06-25T22:50:52.893106Z","title":null,"venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-06-25T22:50:52.893106Z"},"links":{"citing_paper":"/paper/2606.24536"},"observation_digest":"sha256:1a63bf4ad1a000afedc96b8f90098dfacc0a0bd235be4a7305026a96a275d54f","observation_id":"da77b6b6-2331-4a2a-a752-d77dc561914f","resolution":{"observed_at":"2026-06-25T22:50:52.893106Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2606.24536","last_updated":"2026-06-23T13:04:44Z","latest_version":1,"primary_category":"math.NT","snapshot_observed_at":"2026-08-09T03:24:27.301947Z","submitted_at":"2026-06-23T13:04:44Z","title":"Zeta-regularization and natural boundaries: Sums and products of integers and primes"},"reference_resolution":{"displayed":50,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":48,"verified_exact":2,"verified_fuzzy":0},"total_outbound_references":50},"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":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"thesis":"As of 19 August 2026, this Paper Citation Record lists 50 of 50 outbound references and 0 inbound Pith citation observations for arXiv:2606.24536."}