{"as_of":"2026-08-08T20:05:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:934f1ad70b4d0ef4f945d6bc9906a3bdc5048de95c8c6758199989d9064d94fb","coverage":[{"denominator":26,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":26,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T05:24:43.133003Z","state":"measured"},{"denominator":26,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":26,"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/2506.08503/citation-record","integrity":"/paper/2506.08503/integrity","json":"/paper/2506.08503/citation-record.json","paper":"/paper/2506.08503"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:24:43.059677Z","title":"write newline","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2506.08503","last_updated":"2025-06-10T06:58:38Z","snapshot_observed_at":"2026-08-07T05:06:36.651486Z","submitted_at":"2025-06-10T06:58:38Z","title":"Transforming the Erd\\H{o}s-Kac theorem","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-07T05:24:43.059677Z"},"links":{"citing_paper":"/paper/2506.08503"},"observation_digest":"sha256:7505486c4d6b6dcf765fb2141dbe691e416b29922fbecc14ab4ba279977fd49f","observation_id":"597e6019-e4b6-42bc-8655-fa82cc62e9c1","resolution":{"observed_at":"2026-08-07T05:24:43.059677Z","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":"2026-08-07T05:24:43.063604Z","title":"write newline","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2506.08503","last_updated":"2025-06-10T06:58:38Z","snapshot_observed_at":"2026-08-07T05:06:36.651486Z","submitted_at":"2025-06-10T06:58:38Z","title":"Transforming the Erd\\H{o}s-Kac theorem","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-07T05:24:43.063604Z"},"links":{"citing_paper":"/paper/2506.08503"},"observation_digest":"sha256:8d6c3d24d4cc43c0fd0c9ee3c2e70d6255bb5b92ca800d37fec6946045b4825e","observation_id":"29b19e0b-cd5c-4ff7-acb3-66176736c0fc","resolution":{"observed_at":"2026-08-07T05:24:43.063604Z","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":"2026-08-07T05:24:43.067116Z","title":"write newline","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2506.08503","last_updated":"2025-06-10T06:58:38Z","snapshot_observed_at":"2026-08-07T05:06:36.651486Z","submitted_at":"2025-06-10T06:58:38Z","title":"Transforming the Erd\\H{o}s-Kac theorem","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-07T05:24:43.067116Z"},"links":{"citing_paper":"/paper/2506.08503"},"observation_digest":"sha256:ff8d53285e39f34bc71f1538f695c9254a95c0e10edb914618cb20dd91379682","observation_id":"d51db91b-77f8-4fe8-82f9-cf710a32c8ca","resolution":{"observed_at":"2026-08-07T05:24:43.067116Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:24:43.334906Z","title":null,"venue":null,"work_id":"f5820981-4071-4c3b-88f5-56768af60e9d","year":2023},"citing_paper":{"arxiv_id":"2506.08503","last_updated":"2025-06-10T06:58:38Z","snapshot_observed_at":"2026-08-07T05:06:36.651486Z","submitted_at":"2025-06-10T06:58:38Z","title":"Transforming the Erd\\H{o}s-Kac theorem","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-07T05:24:43.070432Z"},"links":{"citing_paper":"/paper/2506.08503"},"observation_digest":"sha256:28a90d74d2d1906b7f5388101b9f36c458e1ff00611ba5a3a1b182ff80b5a3e9","observation_id":"20fdc170-ad0c-43b0-9418-3b02b994e65f","resolution":{"observed_at":"2026-08-07T05:24:43.337864Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:24:43.327064Z","title":null,"venue":null,"work_id":"282c0875-7383-4d42-8ac9-15b0dc3ec182","year":1969},"citing_paper":{"arxiv_id":"2506.08503","last_updated":"2025-06-10T06:58:38Z","snapshot_observed_at":"2026-08-07T05:06:36.651486Z","submitted_at":"2025-06-10T06:58:38Z","title":"Transforming the Erd\\H{o}s-Kac theorem","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-07T05:24:43.073836Z"},"links":{"citing_paper":"/paper/2506.08503"},"observation_digest":"sha256:751f6e6bf38f83a0f55ef82522331b667c41fc4f8b85619c6abfd2758674042c","observation_id":"0def4991-5554-4a7b-8754-d1423db65bc9","resolution":{"observed_at":"2026-08-07T05:24:43.330142Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:24:43.319129Z","title":null,"venue":null,"work_id":"9e8e6b2d-e26e-4e0c-a3dd-3e3f29cfc59a","year":1974},"citing_paper":{"arxiv_id":"2506.08503","last_updated":"2025-06-10T06:58:38Z","snapshot_observed_at":"2026-08-07T05:06:36.651486Z","submitted_at":"2025-06-10T06:58:38Z","title":"Transforming the Erd\\H{o}s-Kac theorem","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-07T05:24:43.076881Z"},"links":{"citing_paper":"/paper/2506.08503"},"observation_digest":"sha256:d54e491883066c7584a111d9fcaf0dc5c95be0709c5f79666b0d12c90d221af3","observation_id":"9f158fcc-5654-4c62-86db-f32742d65b1e","resolution":{"observed_at":"2026-08-07T05:24:43.322106Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:24:43.311361Z","title":null,"venue":null,"work_id":"b2f6fc5a-16a8-48b8-8316-cff4d74f8f7f","year":1964},"citing_paper":{"arxiv_id":"2506.08503","last_updated":"2025-06-10T06:58:38Z","snapshot_observed_at":"2026-08-07T05:06:36.651486Z","submitted_at":"2025-06-10T06:58:38Z","title":"Transforming the Erd\\H{o}s-Kac theorem","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-07T05:24:43.080074Z"},"links":{"citing_paper":"/paper/2506.08503"},"observation_digest":"sha256:20a18bd81127b4e59b04dde6f4b805fd77716fc8dce5ff532459a4bfe8871474","observation_id":"06f2a635-81bf-4d00-bdba-9c0a29171ae8","resolution":{"observed_at":"2026-08-07T05:24:43.314203Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:24:43.303531Z","title":null,"venue":null,"work_id":"8da00174-54cc-4ed5-8597-966bbaa34bcd","year":1978},"citing_paper":{"arxiv_id":"2506.08503","last_updated":"2025-06-10T06:58:38Z","snapshot_observed_at":"2026-08-07T05:06:36.651486Z","submitted_at":"2025-06-10T06:58:38Z","title":"Transforming the Erd\\H{o}s-Kac theorem","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-07T05:24:43.083151Z"},"links":{"citing_paper":"/paper/2506.08503"},"observation_digest":"sha256:805d6caca4c329dbd7c3afcaba6d3149158b6f7fae3921095e35dfd84486174b","observation_id":"5d569317-7abd-4be7-b6fc-ee58c963f214","resolution":{"observed_at":"2026-08-07T05:24:43.306434Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:24:43.295742Z","title":null,"venue":null,"work_id":"efb416cf-e73d-4fd2-ae91-9732a7151dcb","year":1980},"citing_paper":{"arxiv_id":"2506.08503","last_updated":"2025-06-10T06:58:38Z","snapshot_observed_at":"2026-08-07T05:06:36.651486Z","submitted_at":"2025-06-10T06:58:38Z","title":"Transforming the Erd\\H{o}s-Kac theorem","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-07T05:24:43.086074Z"},"links":{"citing_paper":"/paper/2506.08503"},"observation_digest":"sha256:b95ebe38268bf16a6849ef7bc33cdb22a2029f28276a6781be43a86e45606d77","observation_id":"578fecb6-3d06-4baf-9c44-1ecd86c66546","resolution":{"observed_at":"2026-08-07T05:24:43.298767Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:24:43.288065Z","title":"and Kac, M","venue":null,"work_id":"d5a83403-e9d7-4a11-bc61-8163b05626e0","year":1939},"citing_paper":{"arxiv_id":"2506.08503","last_updated":"2025-06-10T06:58:38Z","snapshot_observed_at":"2026-08-07T05:06:36.651486Z","submitted_at":"2025-06-10T06:58:38Z","title":"Transforming the Erd\\H{o}s-Kac theorem","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-07T05:24:43.089273Z"},"links":{"citing_paper":"/paper/2506.08503"},"observation_digest":"sha256:dd3b159f85dce14116bd0063747d61ad8d34036fe1e8eaee504be5cfb45f6c0c","observation_id":"f0f3d43e-c6ca-42cd-a1c4-96a8b7cee47f","resolution":{"observed_at":"2026-08-07T05:24:43.290872Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:24:43.279760Z","title":"and Kac, M","venue":null,"work_id":"ece17056-3d9e-44fc-91a7-0ffc8352dbd0","year":1940},"citing_paper":{"arxiv_id":"2506.08503","last_updated":"2025-06-10T06:58:38Z","snapshot_observed_at":"2026-08-07T05:06:36.651486Z","submitted_at":"2025-06-10T06:58:38Z","title":"Transforming the Erd\\H{o}s-Kac theorem","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-07T05:24:43.092142Z"},"links":{"citing_paper":"/paper/2506.08503"},"observation_digest":"sha256:4cb5cce0ad55d52b6061f02c8132e874738a9701ba4efb336dffef187ad5b179","observation_id":"d50ad751-718d-4b10-8a14-2b5c57d71e2b","resolution":{"observed_at":"2026-08-07T05:24:43.282685Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:24:43.272053Z","title":"and Pomerance, C","venue":null,"work_id":"ebb5b3c7-beb0-4f98-9ac6-7b452bedad4c","year":1985},"citing_paper":{"arxiv_id":"2506.08503","last_updated":"2025-06-10T06:58:38Z","snapshot_observed_at":"2026-08-07T05:06:36.651486Z","submitted_at":"2025-06-10T06:58:38Z","title":"Transforming the Erd\\H{o}s-Kac theorem","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-07T05:24:43.094998Z"},"links":{"citing_paper":"/paper/2506.08503"},"observation_digest":"sha256:5ae32f3b1e10132263ea413b6a8f80961725b25acd78059e1b4995e45c432728","observation_id":"0c69a9c4-dae4-4bd0-8662-7827814062c6","resolution":{"observed_at":"2026-08-07T05:24:43.274944Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:24:43.264156Z","title":null,"venue":null,"work_id":"fbaece67-3c4e-4590-b859-ae5053c1f196","year":2005},"citing_paper":{"arxiv_id":"2506.08503","last_updated":"2025-06-10T06:58:38Z","snapshot_observed_at":"2026-08-07T05:06:36.651486Z","submitted_at":"2025-06-10T06:58:38Z","title":"Transforming the Erd\\H{o}s-Kac theorem","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-07T05:24:43.097853Z"},"links":{"citing_paper":"/paper/2506.08503"},"observation_digest":"sha256:d519532a91856c85afc1aa0702692a943b8ba24a33ec3ac3d3854427a666f044","observation_id":"859d3ea5-6612-48ef-bcee-2093e7ea019e","resolution":{"observed_at":"2026-08-07T05:24:43.267174Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:24:43.256458Z","title":null,"venue":null,"work_id":"f094014a-ac0f-411c-9ad4-07a90ec0fd61","year":1917},"citing_paper":{"arxiv_id":"2506.08503","last_updated":"2025-06-10T06:58:38Z","snapshot_observed_at":"2026-08-07T05:06:36.651486Z","submitted_at":"2025-06-10T06:58:38Z","title":"Transforming the Erd\\H{o}s-Kac theorem","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-07T05:24:43.100625Z"},"links":{"citing_paper":"/paper/2506.08503"},"observation_digest":"sha256:54340ba6bc74fb1f7e9c6fbd38aa06a5721175185f5318a6c0c0ebd9c2d1e441","observation_id":"e74ce1c2-a839-4a39-885d-75ef04789dec","resolution":{"observed_at":"2026-08-07T05:24:43.259299Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:24:43.248441Z","title":null,"venue":null,"work_id":"8b72f0cd-9e58-452f-bf22-7e7aa5b39a10","year":2009},"citing_paper":{"arxiv_id":"2506.08503","last_updated":"2025-06-10T06:58:38Z","snapshot_observed_at":"2026-08-07T05:06:36.651486Z","submitted_at":"2025-06-10T06:58:38Z","title":"Transforming the Erd\\H{o}s-Kac theorem","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-07T05:24:43.103391Z"},"links":{"citing_paper":"/paper/2506.08503"},"observation_digest":"sha256:4039c53ebbfc3e929e42e65ec3b02b988a57c6ddd6084b455d788485badc3baa","observation_id":"fea754d1-67af-496e-b318-3ef1fab52f9d","resolution":{"observed_at":"2026-08-07T05:24:43.251459Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:24:43.240421Z","title":null,"venue":null,"work_id":"1522d63f-3c0a-4dfd-9e41-00ecbfbe758f","year":2021},"citing_paper":{"arxiv_id":"2506.08503","last_updated":"2025-06-10T06:58:38Z","snapshot_observed_at":"2026-08-07T05:06:36.651486Z","submitted_at":"2025-06-10T06:58:38Z","title":"Transforming the Erd\\H{o}s-Kac theorem","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-07T05:24:43.106211Z"},"links":{"citing_paper":"/paper/2506.08503"},"observation_digest":"sha256:27c3e0f6e58806c9a7b5b9a35fea82c2a7f9e3669d0ac392102feb943718f28d","observation_id":"0567d6cc-82d4-4dae-94fa-3b248a579acb","resolution":{"observed_at":"2026-08-07T05:24:43.243456Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:24:43.232399Z","title":null,"venue":null,"work_id":"ace1d5e2-c1f3-4756-b461-0b46bc39b377","year":1900},"citing_paper":{"arxiv_id":"2506.08503","last_updated":"2025-06-10T06:58:38Z","snapshot_observed_at":"2026-08-07T05:06:36.651486Z","submitted_at":"2025-06-10T06:58:38Z","title":"Transforming the Erd\\H{o}s-Kac theorem","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-07T05:24:43.109135Z"},"links":{"citing_paper":"/paper/2506.08503"},"observation_digest":"sha256:4425116a2a9f0563701d686e573be1aaca499fc7af3608db7d8d9b1655ffd7d5","observation_id":"297595a7-6095-4567-8c2c-1cff886212f4","resolution":{"observed_at":"2026-08-07T05:24:43.235317Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:24:43.223715Z","title":null,"venue":null,"work_id":"4b015075-b522-4e31-910e-2af2d7e6e343","year":2023},"citing_paper":{"arxiv_id":"2506.08503","last_updated":"2025-06-10T06:58:38Z","snapshot_observed_at":"2026-08-07T05:06:36.651486Z","submitted_at":"2025-06-10T06:58:38Z","title":"Transforming the Erd\\H{o}s-Kac theorem","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-07T05:24:43.111885Z"},"links":{"citing_paper":"/paper/2506.08503"},"observation_digest":"sha256:e3b8f4e3aca88b4aedf9095235cbc5f4149e7b35da30ac1686f9a0460bbd7b76","observation_id":"611ec553-f223-4642-986d-af238dd7367b","resolution":{"observed_at":"2026-08-07T05:24:43.227246Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:24:43.214819Z","title":"and Ward, M","venue":null,"work_id":"0725313d-f27f-4ea2-904c-1262bbfdc10b","year":2024},"citing_paper":{"arxiv_id":"2506.08503","last_updated":"2025-06-10T06:58:38Z","snapshot_observed_at":"2026-08-07T05:06:36.651486Z","submitted_at":"2025-06-10T06:58:38Z","title":"Transforming the Erd\\H{o}s-Kac theorem","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-07T05:24:43.114569Z"},"links":{"citing_paper":"/paper/2506.08503"},"observation_digest":"sha256:5f00056de74dbb22f88306cddbfa84d28104d35298e58c4c1b18b2170b89614b","observation_id":"a6baf91d-1e90-449a-8aa3-cf1b53a310f2","resolution":{"observed_at":"2026-08-07T05:24:43.217748Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:24:43.206974Z","title":null,"venue":null,"work_id":"105d59ba-ed61-4eef-acfb-a05d932bd6a5","year":2024},"citing_paper":{"arxiv_id":"2506.08503","last_updated":"2025-06-10T06:58:38Z","snapshot_observed_at":"2026-08-07T05:06:36.651486Z","submitted_at":"2025-06-10T06:58:38Z","title":"Transforming the Erd\\H{o}s-Kac theorem","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-07T05:24:43.117317Z"},"links":{"citing_paper":"/paper/2506.08503"},"observation_digest":"sha256:7965cc33f3a7b3c03d4e15f718e6fbf95eb7d02b7073ef8e8fbced054eeb3bc3","observation_id":"e124868d-f741-4a71-a5da-f38754e4aa20","resolution":{"observed_at":"2026-08-07T05:24:43.209806Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:24:43.197335Z","title":null,"venue":null,"work_id":"c54e7162-ab8f-487f-b7aa-085d4d8a9132","year":1980},"citing_paper":{"arxiv_id":"2506.08503","last_updated":"2025-06-10T06:58:38Z","snapshot_observed_at":"2026-08-07T05:06:36.651486Z","submitted_at":"2025-06-10T06:58:38Z","title":"Transforming the Erd\\H{o}s-Kac theorem","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-07T05:24:43.119942Z"},"links":{"citing_paper":"/paper/2506.08503"},"observation_digest":"sha256:b0bbb9174813455f55d30a58f92c4482fbc534217155d36794cc7e028afab69a","observation_id":"d47b30db-6b6a-40d3-9f9c-5ce5203fbb22","resolution":{"observed_at":"2026-08-07T05:24:43.201372Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:24:43.188411Z","title":null,"venue":null,"work_id":"67c66796-e78e-4a04-b29c-4691ee397fc0","year":1976},"citing_paper":{"arxiv_id":"2506.08503","last_updated":"2025-06-10T06:58:38Z","snapshot_observed_at":"2026-08-07T05:06:36.651486Z","submitted_at":"2025-06-10T06:58:38Z","title":"Transforming the Erd\\H{o}s-Kac theorem","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-07T05:24:43.122599Z"},"links":{"citing_paper":"/paper/2506.08503"},"observation_digest":"sha256:e4e184b1263da08123f460df67fc5a10f6b3a4afe1c15c08bd6a81ceae2dfd48","observation_id":"be9838b4-6d5a-4672-8be6-9b8561841f1b","resolution":{"observed_at":"2026-08-07T05:24:43.191523Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:24:43.179947Z","title":null,"venue":null,"work_id":"20678287-79fb-4ff4-b278-06bd120ffdba","year":2009},"citing_paper":{"arxiv_id":"2506.08503","last_updated":"2025-06-10T06:58:38Z","snapshot_observed_at":"2026-08-07T05:06:36.651486Z","submitted_at":"2025-06-10T06:58:38Z","title":"Transforming the Erd\\H{o}s-Kac theorem","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-07T05:24:43.125316Z"},"links":{"citing_paper":"/paper/2506.08503"},"observation_digest":"sha256:1928f9c994c4ab11723292920c8960de8ee82ceff1a8779160d87933b7699977","observation_id":"19a82c94-24eb-4e04-8b6e-848b0f44e1cf","resolution":{"observed_at":"2026-08-07T05:24:43.183065Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:24:43.171429Z","title":null,"venue":null,"work_id":"d805450d-b03a-4ef8-81f3-33c0f68ccfc5","year":2015},"citing_paper":{"arxiv_id":"2506.08503","last_updated":"2025-06-10T06:58:38Z","snapshot_observed_at":"2026-08-07T05:06:36.651486Z","submitted_at":"2025-06-10T06:58:38Z","title":"Transforming the Erd\\H{o}s-Kac theorem","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-07T05:24:43.127833Z"},"links":{"citing_paper":"/paper/2506.08503"},"observation_digest":"sha256:9a455f42c45f0a3651818c2341a2cef94bb73dc95c0b3a6233e56605d7175f9d","observation_id":"54694b20-68f2-4763-b6a3-2c48beadcbb1","resolution":{"observed_at":"2026-08-07T05:24:43.174359Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:24:43.162773Z","title":null,"venue":null,"work_id":"9312db4e-016f-4426-8f02-a36ade1310f7","year":1927},"citing_paper":{"arxiv_id":"2506.08503","last_updated":"2025-06-10T06:58:38Z","snapshot_observed_at":"2026-08-07T05:06:36.651486Z","submitted_at":"2025-06-10T06:58:38Z","title":"Transforming the Erd\\H{o}s-Kac theorem","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-07T05:24:43.130453Z"},"links":{"citing_paper":"/paper/2506.08503"},"observation_digest":"sha256:18d89d66d2bafc2ec47944558a8ab945ad6f48a748f890f8faa60269487c7a28","observation_id":"3efd5f84-ff4e-4f73-ab9b-5b5cb4a9ee35","resolution":{"observed_at":"2026-08-07T05:24:43.165853Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:24:43.152130Z","title":null,"venue":null,"work_id":"bd105a47-2c2a-4ba3-a830-72e6d9c3905b","year":2009},"citing_paper":{"arxiv_id":"2506.08503","last_updated":"2025-06-10T06:58:38Z","snapshot_observed_at":"2026-08-07T05:06:36.651486Z","submitted_at":"2025-06-10T06:58:38Z","title":"Transforming the Erd\\H{o}s-Kac theorem","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-07T05:24:43.133003Z"},"links":{"citing_paper":"/paper/2506.08503"},"observation_digest":"sha256:13c86248c0c3a89b60173df85b9b1e3977f1e20c660f98c48a283b2224225f67","observation_id":"4fefd2ab-9322-48fe-aef3-908c21f1394f","resolution":{"observed_at":"2026-08-07T05:24:43.156762Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.08503","last_updated":"2025-06-10T06:58:38Z","latest_version":1,"primary_category":"math.NT","snapshot_observed_at":"2026-08-07T05:06:36.651486Z","submitted_at":"2025-06-10T06:58:38Z","title":"Transforming the Erd\\H{o}s-Kac theorem"},"reference_resolution":{"displayed":26,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":22,"verified_exact":0,"verified_fuzzy":4},"total_outbound_references":26},"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 26 of 26 outbound references and 0 inbound Pith citation observations for arXiv:2506.08503."}