{"as_of":"2026-08-11T22:01:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:40b9537a4c6245bbec5e286781559a7fcda72e1520bc32e145872e768fd6c388","coverage":[{"denominator":22,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":22,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-15T12:30:43.755266Z","state":"measured"},{"denominator":23,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":23,"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":"2026-05-10T10:15:35.157086Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-10T10:24:22.164161Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2603.08587","last_updated":"2026-03-09T16:39:49Z","snapshot_observed_at":"2026-08-11T12:09:02.956543Z","submitted_at":"2026-03-09T16:39:49Z","title":"Informational Cardinality: A Unifying Framework for Set Theory, Fractal Geometry, and Analytic Number Theory","version":1},"cited_work":{"arxiv_id":"2603.08587","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2603.08587","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Li, Informational Cardinality: A Unifying Framework for Set Theory, Fractal Geometry, and Analytic Number Theory,arXiv preprint","venue":null,"work_id":"4c15b47e-c2f0-4d9b-83f3-d075529b09a7","year":2026},"citing_paper":{"arxiv_id":"2604.14596","last_updated":"2026-04-16T03:59:18Z","snapshot_observed_at":"2026-08-08T04:52:03.546047Z","submitted_at":"2026-04-16T03:59:18Z","title":"Prime--Zero Duality: Fractal Geometry, Renormalization-Group Flow, and an Information-Ontological Framework for Number Theory","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-05-10T10:15:35.157086Z"},"links":{"cited_paper":"/paper/2603.08587","citing_paper":"/paper/2604.14596"},"observation_digest":"sha256:aadc696eee6d03df1af47ac18a7a50a8847ca7327899530c084fc3b2c8cf2407","observation_id":"6555a8dc-d5c1-4d80-8a31-6545d7c1d718","resolution":{"observed_at":"2026-05-27T00:04:12.542062Z","resolver_source":"arxiv_id","status":"verified_exact"},"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"}}],"links":{"evidence":"/evidence","html":"/paper/2603.08587/citation-record","integrity":"/paper/2603.08587/integrity","json":"/paper/2603.08587/citation-record.json","paper":"/paper/2603.08587"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-15T12:30:43.755266Z","title":"Riemann,Über die Anzahl der Primzahlen unter einer gegebenen Größe, Monatsberichte der Berliner Akademie (1859)","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2603.08587","last_updated":"2026-03-09T16:39:49Z","snapshot_observed_at":"2026-08-11T12:09:02.956543Z","submitted_at":"2026-03-09T16:39:49Z","title":"Informational Cardinality: A Unifying Framework for Set Theory, Fractal Geometry, and Analytic Number Theory","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-07-15T12:30:43.755266Z"},"links":{"citing_paper":"/paper/2603.08587"},"observation_digest":"sha256:d0a2d93fe27b63fde44d070e73847c82ce235961317888e3fc1fdd6f24ba2191","observation_id":"6ab1f520-ca54-47ba-a5e9-f735b9cb43db","resolution":{"observed_at":"2026-07-15T12:30:43.755266Z","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":"2026-07-15T12:30:43.755266Z","title":"Cantor,Über eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen, Journal für die reine und angewandte Mathematik77(1874), 258–262","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2603.08587","last_updated":"2026-03-09T16:39:49Z","snapshot_observed_at":"2026-08-11T12:09:02.956543Z","submitted_at":"2026-03-09T16:39:49Z","title":"Informational Cardinality: A Unifying Framework for Set Theory, Fractal Geometry, and Analytic Number Theory","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-07-15T12:30:43.755266Z"},"links":{"citing_paper":"/paper/2603.08587"},"observation_digest":"sha256:d5b17562545f2af64aba8434ab24590d8f5968006ce6d78d73c5e5f77288174d","observation_id":"bfdaab30-39b3-4385-b05b-a01b70a8dd15","resolution":{"observed_at":"2026-07-15T12:30:43.755266Z","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":"2026-07-15T12:30:43.755266Z","title":"Mandelbrot,The Fractal Geometry of Nature, W","venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"2603.08587","last_updated":"2026-03-09T16:39:49Z","snapshot_observed_at":"2026-08-11T12:09:02.956543Z","submitted_at":"2026-03-09T16:39:49Z","title":"Informational Cardinality: A Unifying Framework for Set Theory, Fractal Geometry, and Analytic Number Theory","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-07-15T12:30:43.755266Z"},"links":{"citing_paper":"/paper/2603.08587"},"observation_digest":"sha256:78c794dfc01504b948ca2484fa8a2fa0b50f7e94bb954cae9c4d8d27b6910162","observation_id":"c52a9623-37d5-49ee-a5f8-0c184f97eb70","resolution":{"observed_at":"2026-07-15T12:30:43.755266Z","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":"2026-07-15T12:30:43.755266Z","title":null,"venue":null,"work_id":null,"year":1981},"citing_paper":{"arxiv_id":"2603.08587","last_updated":"2026-03-09T16:39:49Z","snapshot_observed_at":"2026-08-11T12:09:02.956543Z","submitted_at":"2026-03-09T16:39:49Z","title":"Informational Cardinality: A Unifying Framework for Set Theory, Fractal Geometry, and Analytic Number Theory","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-07-15T12:30:43.755266Z"},"links":{"citing_paper":"/paper/2603.08587"},"observation_digest":"sha256:c9780955456259712750b9f678d45ec95c18ebf335870fdddd69161a9031b83b","observation_id":"9cf20408-b36d-4bfa-a440-fc6c0e6d33a1","resolution":{"observed_at":"2026-07-15T12:30:43.755266Z","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":"2026-07-15T12:30:43.755266Z","title":"Falconer,Fractal Geometry: Mathematical Foundations and Applications, 2nd ed., Wiley, 2003","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2603.08587","last_updated":"2026-03-09T16:39:49Z","snapshot_observed_at":"2026-08-11T12:09:02.956543Z","submitted_at":"2026-03-09T16:39:49Z","title":"Informational Cardinality: A Unifying Framework for Set Theory, Fractal Geometry, and Analytic Number Theory","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-07-15T12:30:43.755266Z"},"links":{"citing_paper":"/paper/2603.08587"},"observation_digest":"sha256:9898ffb0cc0afdb9f7ff682d0592b0c72e3314ac261a2f0afd6fd7f3eaba5c9b","observation_id":"103d6766-8cff-4949-8373-ce3687767023","resolution":{"observed_at":"2026-07-15T12:30:43.755266Z","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":"2026-07-15T12:30:43.755266Z","title":"Connes,Trace formula in noncommutative geometry and the zeros of the Riemann zeta function, Selecta Mathematica5(1999), 29–106","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2603.08587","last_updated":"2026-03-09T16:39:49Z","snapshot_observed_at":"2026-08-11T12:09:02.956543Z","submitted_at":"2026-03-09T16:39:49Z","title":"Informational Cardinality: A Unifying Framework for Set Theory, Fractal Geometry, and Analytic Number Theory","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-07-15T12:30:43.755266Z"},"links":{"citing_paper":"/paper/2603.08587"},"observation_digest":"sha256:e8361e6a4df62200751d3689c7eb8250a6fa71a8fcf69f6653a81b8ffdc62611","observation_id":"70547fb6-faf1-4637-9080-c728672feb90","resolution":{"observed_at":"2026-07-15T12:30:43.755266Z","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":"2026-07-15T12:30:43.755266Z","title":null,"venue":null,"work_id":null,"year":1965},"citing_paper":{"arxiv_id":"2603.08587","last_updated":"2026-03-09T16:39:49Z","snapshot_observed_at":"2026-08-11T12:09:02.956543Z","submitted_at":"2026-03-09T16:39:49Z","title":"Informational Cardinality: A Unifying Framework for Set Theory, Fractal Geometry, and Analytic Number Theory","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-07-15T12:30:43.755266Z"},"links":{"citing_paper":"/paper/2603.08587"},"observation_digest":"sha256:97ecb363b727d8f38659ff6f6a70ada4ccf228d489038824279fb45604cafa90","observation_id":"3f414850-67b8-45b4-9ad6-f864ad4eb727","resolution":{"observed_at":"2026-07-15T12:30:43.755266Z","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":"2026-07-15T12:30:43.755266Z","title":"Davenport,Multiplicative Number Theory, 3rd ed., Springer, 2000","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2603.08587","last_updated":"2026-03-09T16:39:49Z","snapshot_observed_at":"2026-08-11T12:09:02.956543Z","submitted_at":"2026-03-09T16:39:49Z","title":"Informational Cardinality: A Unifying Framework for Set Theory, Fractal Geometry, and Analytic Number Theory","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-07-15T12:30:43.755266Z"},"links":{"citing_paper":"/paper/2603.08587"},"observation_digest":"sha256:bd76a54345768cf83b8f03dd0d6c0b0246f9c7bcd31403a1c7d4c43381e14993","observation_id":"9aa0e5b4-2f23-4b87-9fc4-7b2bd225e5ac","resolution":{"observed_at":"2026-07-15T12:30:43.755266Z","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":"2026-07-15T12:30:43.755266Z","title":null,"venue":null,"work_id":null,"year":1974},"citing_paper":{"arxiv_id":"2603.08587","last_updated":"2026-03-09T16:39:49Z","snapshot_observed_at":"2026-08-11T12:09:02.956543Z","submitted_at":"2026-03-09T16:39:49Z","title":"Informational Cardinality: A Unifying Framework for Set Theory, Fractal Geometry, and Analytic Number Theory","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-07-15T12:30:43.755266Z"},"links":{"citing_paper":"/paper/2603.08587"},"observation_digest":"sha256:53c1e09f7c46bd97db0e1eec4c26c75a68bf7fd8cbaef3940dbeeba256214ed3","observation_id":"0b94646a-2570-40f2-bc12-4280c1bc353f","resolution":{"observed_at":"2026-07-15T12:30:43.755266Z","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":"2026-07-15T12:30:43.755266Z","title":null,"venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2603.08587","last_updated":"2026-03-09T16:39:49Z","snapshot_observed_at":"2026-08-11T12:09:02.956543Z","submitted_at":"2026-03-09T16:39:49Z","title":"Informational Cardinality: A Unifying Framework for Set Theory, Fractal Geometry, and Analytic Number Theory","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-07-15T12:30:43.755266Z"},"links":{"citing_paper":"/paper/2603.08587"},"observation_digest":"sha256:d11f0c9283fba3b72ee9cb36b48e458ea40376503e186a8bd11aab488a754536","observation_id":"1377edbf-7fba-4456-8df8-2cda8e97e4ae","resolution":{"observed_at":"2026-07-15T12:30:43.755266Z","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":"2026-07-15T12:30:43.755266Z","title":null,"venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2603.08587","last_updated":"2026-03-09T16:39:49Z","snapshot_observed_at":"2026-08-11T12:09:02.956543Z","submitted_at":"2026-03-09T16:39:49Z","title":"Informational Cardinality: A Unifying Framework for Set Theory, Fractal Geometry, and Analytic Number Theory","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-07-15T12:30:43.755266Z"},"links":{"citing_paper":"/paper/2603.08587"},"observation_digest":"sha256:79ddea81012cab5f3dcb4eefad0fef7f2f3e2ef0d9b28ac715261ef271facdff","observation_id":"5704fd88-c73e-4c71-899f-a5ed535262a1","resolution":{"observed_at":"2026-07-15T12:30:43.755266Z","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":"2026-07-15T12:30:43.755266Z","title":"Sarnak,Problems of the Millennium: The Riemann Hypothesis, Clay Mathematics Institute, 2004","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2603.08587","last_updated":"2026-03-09T16:39:49Z","snapshot_observed_at":"2026-08-11T12:09:02.956543Z","submitted_at":"2026-03-09T16:39:49Z","title":"Informational Cardinality: A Unifying Framework for Set Theory, Fractal Geometry, and Analytic Number Theory","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-07-15T12:30:43.755266Z"},"links":{"citing_paper":"/paper/2603.08587"},"observation_digest":"sha256:ecda0f73ca1638a170cb3aa0a9a7ca5b3299f760d4909d131f7ad2feb2d57db4","observation_id":"08f8a3dd-3f5d-49cf-9691-ea04493c4f56","resolution":{"observed_at":"2026-07-15T12:30:43.755266Z","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":"2026-07-15T12:30:43.755266Z","title":null,"venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2603.08587","last_updated":"2026-03-09T16:39:49Z","snapshot_observed_at":"2026-08-11T12:09:02.956543Z","submitted_at":"2026-03-09T16:39:49Z","title":"Informational Cardinality: A Unifying Framework for Set Theory, Fractal Geometry, and Analytic Number Theory","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-07-15T12:30:43.755266Z"},"links":{"citing_paper":"/paper/2603.08587"},"observation_digest":"sha256:0612c377d4094df1b004d4fe36d57c265e04299201c508fd5e07a506a66592f0","observation_id":"db90470c-73dc-4938-89ce-7b0819a58534","resolution":{"observed_at":"2026-07-15T12:30:43.755266Z","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":"2026-07-15T12:30:43.755266Z","title":null,"venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2603.08587","last_updated":"2026-03-09T16:39:49Z","snapshot_observed_at":"2026-08-11T12:09:02.956543Z","submitted_at":"2026-03-09T16:39:49Z","title":"Informational Cardinality: A Unifying Framework for Set Theory, Fractal Geometry, and Analytic Number Theory","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-07-15T12:30:43.755266Z"},"links":{"citing_paper":"/paper/2603.08587"},"observation_digest":"sha256:13bd2e575dba29a3462ae2bf3f153c7dabba550c1953e941a4e597ba6ac651ef","observation_id":"901cf178-fffc-41c2-abc8-b75e3f56bba0","resolution":{"observed_at":"2026-07-15T12:30:43.755266Z","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":"2026-07-15T12:30:43.755266Z","title":"information content","venue":null,"work_id":null,"year":1973},"citing_paper":{"arxiv_id":"2603.08587","last_updated":"2026-03-09T16:39:49Z","snapshot_observed_at":"2026-08-11T12:09:02.956543Z","submitted_at":"2026-03-09T16:39:49Z","title":"Informational Cardinality: A Unifying Framework for Set Theory, Fractal Geometry, and Analytic Number Theory","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-07-15T12:30:43.755266Z"},"links":{"citing_paper":"/paper/2603.08587"},"observation_digest":"sha256:5666847e45ae84a0e2d546aaa6c2d3ef2f3a3f15141a52aeb6258175cea17d34","observation_id":"d697bc32-6055-496f-be96-06d521112797","resolution":{"observed_at":"2026-07-15T12:30:43.755266Z","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":"2026-07-15T12:30:43.755266Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2603.08587","last_updated":"2026-03-09T16:39:49Z","snapshot_observed_at":"2026-08-11T12:09:02.956543Z","submitted_at":"2026-03-09T16:39:49Z","title":"Informational Cardinality: A Unifying Framework for Set Theory, Fractal Geometry, and Analytic Number Theory","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-07-15T12:30:43.755266Z"},"links":{"citing_paper":"/paper/2603.08587"},"observation_digest":"sha256:487fa3afc21c1234411378b5292825bcc6e3bc5a81310256137e7f0c9714cbbc","observation_id":"f5af25ba-2bf8-48fa-8a6d-b711e4d6f457","resolution":{"observed_at":"2026-07-15T12:30:43.755266Z","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":"2026-07-15T12:30:43.755266Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2603.08587","last_updated":"2026-03-09T16:39:49Z","snapshot_observed_at":"2026-08-11T12:09:02.956543Z","submitted_at":"2026-03-09T16:39:49Z","title":"Informational Cardinality: A Unifying Framework for Set Theory, Fractal Geometry, and Analytic Number Theory","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-07-15T12:30:43.755266Z"},"links":{"citing_paper":"/paper/2603.08587"},"observation_digest":"sha256:af745e269ba764bdd7aa548a472ac659222bb5267ffc9526b0c32c3d8b058e08","observation_id":"414025a6-83a9-4db6-9ceb-0d7528ba5b4b","resolution":{"observed_at":"2026-07-15T12:30:43.755266Z","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":"2026-07-15T12:30:43.755266Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2603.08587","last_updated":"2026-03-09T16:39:49Z","snapshot_observed_at":"2026-08-11T12:09:02.956543Z","submitted_at":"2026-03-09T16:39:49Z","title":"Informational Cardinality: A Unifying Framework for Set Theory, Fractal Geometry, and Analytic Number Theory","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-07-15T12:30:43.755266Z"},"links":{"citing_paper":"/paper/2603.08587"},"observation_digest":"sha256:1eee894ee2d229091e020229e216e62001722911ced73eeca452c5338ba94520","observation_id":"04512ff2-10fc-4cde-83b7-e392854c2ce5","resolution":{"observed_at":"2026-07-15T12:30:43.755266Z","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":"2026-07-15T12:30:43.755266Z","title":"The first10 10 zeros are known, allowing computation ofJn forn≤10 10","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2603.08587","last_updated":"2026-03-09T16:39:49Z","snapshot_observed_at":"2026-08-11T12:09:02.956543Z","submitted_at":"2026-03-09T16:39:49Z","title":"Informational Cardinality: A Unifying Framework for Set Theory, Fractal Geometry, and Analytic Number Theory","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-07-15T12:30:43.755266Z"},"links":{"citing_paper":"/paper/2603.08587"},"observation_digest":"sha256:8f45b3f350fc5823873ea4f1ca95c8b7d2800d0ac831d7358530047889664e45","observation_id":"a616598f-5939-449f-9004-14536225354e","resolution":{"observed_at":"2026-07-15T12:30:43.755266Z","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":"2026-07-15T12:30:43.755266Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2603.08587","last_updated":"2026-03-09T16:39:49Z","snapshot_observed_at":"2026-08-11T12:09:02.956543Z","submitted_at":"2026-03-09T16:39:49Z","title":"Informational Cardinality: A Unifying Framework for Set Theory, Fractal Geometry, and Analytic Number Theory","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-07-15T12:30:43.755266Z"},"links":{"citing_paper":"/paper/2603.08587"},"observation_digest":"sha256:5db84baa91b579007d1676afeaf5be8661c5c086ba7ef844c3520a5b40d85a54","observation_id":"046a2b56-7fc4-4bf0-9c52-8bae40eeb6cc","resolution":{"observed_at":"2026-07-15T12:30:43.755266Z","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":"2026-07-15T12:30:43.755266Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2603.08587","last_updated":"2026-03-09T16:39:49Z","snapshot_observed_at":"2026-08-11T12:09:02.956543Z","submitted_at":"2026-03-09T16:39:49Z","title":"Informational Cardinality: A Unifying Framework for Set Theory, Fractal Geometry, and Analytic Number Theory","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-07-15T12:30:43.755266Z"},"links":{"citing_paper":"/paper/2603.08587"},"observation_digest":"sha256:5de835200e8affb5ef75d05c9805b549453783e29a17adab0a1c3a88f971e66d","observation_id":"d46d7d9e-55e0-4b45-a82a-625bb2ad2c91","resolution":{"observed_at":"2026-07-15T12:30:43.755266Z","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":"2026-07-15T12:30:43.755266Z","title":"This remains an open computational challenge","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2603.08587","last_updated":"2026-03-09T16:39:49Z","snapshot_observed_at":"2026-08-11T12:09:02.956543Z","submitted_at":"2026-03-09T16:39:49Z","title":"Informational Cardinality: A Unifying Framework for Set Theory, Fractal Geometry, and Analytic Number Theory","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-07-15T12:30:43.755266Z"},"links":{"citing_paper":"/paper/2603.08587"},"observation_digest":"sha256:d2141ab72a2bb36bbb0ccf2dceddacddd35bacfe9674bf3bbae34a1de068e351","observation_id":"db87a586-598b-437b-ab2d-7e79074e997c","resolution":{"observed_at":"2026-07-15T12:30:43.755266Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2603.08587","last_updated":"2026-03-09T16:39:49Z","latest_version":1,"primary_category":"math.GM","snapshot_observed_at":"2026-08-11T12:09:02.956543Z","submitted_at":"2026-03-09T16:39:49Z","title":"Informational Cardinality: A Unifying Framework for Set Theory, Fractal Geometry, and Analytic Number Theory"},"reference_resolution":{"displayed":22,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":22,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":22},"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 11 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 1 inbound Pith citation observation for arXiv:2603.08587."}