{"as_of":"2026-08-13T19:55:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:dbb21a0f27b81299a4941af94da7671056a07067e3dab10d563a32718843a5d3","coverage":[{"denominator":34,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":34,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T22:48:08.768483Z","state":"measured"},{"denominator":37,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":37,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+00:00","state":"measured"},{"denominator":3,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":3,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T18:29:26.909653Z","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":"2026-06-30T16:54:58.627966Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.21642","snapshot_observed_at":"2026-08-06T18:29:26.909653Z","title":"Dartyge and J","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.08714","last_updated":"2025-07-11T16:15:38Z","snapshot_observed_at":"2026-08-10T08:35:13.625851Z","submitted_at":"2025-07-11T16:15:38Z","title":"The Zsiflaw--Legeis theorem for arbitrary bases","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T18:29:26.909653Z"},"links":{"cited_paper":"/paper/2506.21642","citing_paper":"/paper/2507.08714"},"observation_digest":"sha256:df055a403bfeaf5a416dfc1f79a0f9aeaf173f761aae21be65e13c7a1154c88a","observation_id":"8b986cfe-d0e6-4395-9b75-fe8c64274ef0","resolution":{"observed_at":"2026-08-06T18:29:26.909653Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"cited_work":{"arxiv_id":"2506.21642","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2506.21642","snapshot_observed_at":"2026-06-30T16:54:58.627966Z","title":"Prime numbers with an almost prime reverse","venue":null,"work_id":"68152795-1275-4f1e-8111-42239acc9905","year":2025},"citing_paper":{"arxiv_id":"2605.21876","last_updated":"2026-06-27T07:04:08Z","snapshot_observed_at":"2026-08-06T22:41:03.041861Z","submitted_at":"2026-05-21T01:38:50Z","title":"The reverse Goldbach problem and a refined Zsiflaw--Legeis theorem","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-05-22T06:18:13.298117Z"},"links":{"cited_paper":"/paper/2506.21642","citing_paper":"/paper/2605.21876"},"observation_digest":"sha256:df8b27ed08368d799a2d784a262064cd62025a585f08b40f53d15590e75876b5","observation_id":"f42f40ff-2a96-4f38-a344-e1e67123d24f","resolution":{"observed_at":"2026-05-22T06:21:10.684987Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"cited_work":{"arxiv_id":"2506.21642","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2506.21642","snapshot_observed_at":"2026-06-30T16:54:58.627966Z","title":"Prime numbers with an almost prime reverse","venue":null,"work_id":"68152795-1275-4f1e-8111-42239acc9905","year":2025},"citing_paper":{"arxiv_id":"2605.21876","last_updated":"2026-06-27T07:04:08Z","snapshot_observed_at":"2026-08-06T22:41:03.041861Z","submitted_at":"2026-05-21T01:38:50Z","title":"The reverse Goldbach problem and a refined Zsiflaw--Legeis theorem","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-06-30T16:51:01.422868Z"},"links":{"cited_paper":"/paper/2506.21642","citing_paper":"/paper/2605.21876"},"observation_digest":"sha256:ff564b0d3b4e7d3ed580861d4ffaa570acb27230a83cf693fe55e9837d767a53","observation_id":"0470fb5e-5a28-4cf4-aa2c-acd6f4c9ff74","resolution":{"observed_at":"2026-06-30T16:54:58.631818Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2506.21642/citation-record","integrity":"/paper/2506.21642/integrity","json":"/paper/2506.21642/citation-record.json","paper":"/paper/2506.21642"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T22:48:14.584916Z","title":"Barat, B","venue":null,"work_id":"46ece3b7-6946-4c5c-8bef-a9d2c3e6ce4c","year":2025},"citing_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T22:48:06.281969Z"},"links":{"citing_paper":"/paper/2506.21642"},"observation_digest":"sha256:7475a041db0c9e16b603a80417127067c84f14fe0dc099084861c5dcb1aea9df","observation_id":"af86c899-2d6e-4ce4-b201-5d34355d7dcb","resolution":{"observed_at":"2026-08-06T22:48:14.675047Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2406.13334","last_updated":"2024-06-19T08:35:02Z","snapshot_observed_at":"2026-08-13T10:53:34.475140Z","submitted_at":"2024-06-19T08:35:02Z","title":"On Telhcirid's theorem on arithmetic progressions","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2406.13334","snapshot_observed_at":"2026-08-06T22:48:06.344429Z","title":"Bhowmik and Y","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T22:48:06.344429Z"},"links":{"cited_paper":"/paper/2406.13334","citing_paper":"/paper/2506.21642"},"observation_digest":"sha256:a0dcf753886d311328221f240250a8e64cbecda70ef3e93d7fbfb27bc2ce9fe4","observation_id":"d7383af3-48f3-4f16-af49-6c8b5bdf54d2","resolution":{"observed_at":"2026-08-06T22:48:06.344429Z","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":"2026-08-06T22:48:14.372767Z","title":null,"venue":null,"work_id":"109bb05a-dc29-445d-b693-fa1840be078d","year":1954},"citing_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T22:48:06.397192Z"},"links":{"citing_paper":"/paper/2506.21642"},"observation_digest":"sha256:90bd8905fc6ab08635c2308604fc11d89b981378855948b6eba1fa72111b5090","observation_id":"09caa0c5-7c2f-44f6-bbb1-e3cfc5eaf54a","resolution":{"observed_at":"2026-08-06T22:48:14.480187Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T22:48:14.144098Z","title":"Bourgain , Prescribing the binary digits of primes , Israel J","venue":null,"work_id":"01db2f2b-db22-4f6d-8db7-491582109b72","year":2013},"citing_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T22:48:06.459382Z"},"links":{"citing_paper":"/paper/2506.21642"},"observation_digest":"sha256:32bb853c28e7fd11caab451279f032fdf2400f3e601000dcea0268d81bf89e5b","observation_id":"e5137758-236e-4230-8ef0-9743deef58a9","resolution":{"observed_at":"2026-08-06T22:48:14.255833Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T22:48:13.948578Z","title":"Math., 206 (2015), pp","venue":null,"work_id":"a8a89f9e-a041-4cb2-9971-cf3c44454d4a","year":2015},"citing_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T22:48:06.510943Z"},"links":{"citing_paper":"/paper/2506.21642"},"observation_digest":"sha256:36ce55fb1b352f75f95a8428a7826b49aab992aac85c77a32a2af65a77b6a23c","observation_id":"b9d83ebc-c55f-4de0-8c2f-9429d4f0db64","resolution":{"observed_at":"2026-08-06T22:48:14.048853Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2504.08502","last_updated":"2025-08-07T11:56:30Z","snapshot_observed_at":"2026-08-07T16:06:31.624749Z","submitted_at":"2025-04-11T13:08:35Z","title":"Powerfree integers and Fourier bounds","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2504.08502","snapshot_observed_at":"2026-08-06T22:48:06.558367Z","title":"Carillo Santana , Powerfree integers and Fourier bounds , arXiv:2504.08502, (2025)","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T22:48:06.558367Z"},"links":{"cited_paper":"/paper/2504.08502","citing_paper":"/paper/2506.21642"},"observation_digest":"sha256:9715d00c276e25ef2b57a67678dcb1ae523a5e711ec10f8f632d48fc5c00ec52","observation_id":"092020fd-4fd5-4adf-a058-257bf4248cc0","resolution":{"observed_at":"2026-08-06T22:48:06.558367Z","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":"2026-08-06T22:48:13.741519Z","title":"Chen, On the representation of a large even integer as the sum of a prime and the product of at most two primes , Scientia Sinica, 16 (1973), pp","venue":null,"work_id":"8ea7fb9e-e485-4a39-a11a-31780182975d","year":1973},"citing_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T22:48:06.628163Z"},"links":{"citing_paper":"/paper/2506.21642"},"observation_digest":"sha256:d71e38577c1d91fc6a746364cd699e89ebba12237a2e3e18a51bc08ee5e93997","observation_id":"69093189-32fe-4a16-b0f5-1a1117502e4d","resolution":{"observed_at":"2026-08-06T22:48:13.824697Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T22:48:06.677200Z","title":"Chourasiya and D","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T22:48:06.677200Z"},"links":{"citing_paper":"/paper/2506.21642"},"observation_digest":"sha256:a58f1ce51c5fa881cc4a9c064fc21a92255d958ac407762ff2ff4f99ab0dcad7","observation_id":"bab669a2-9352-4dd9-9059-ce8e121dcd68","resolution":{"observed_at":"2026-08-06T22:48:06.677200Z","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":"2026-08-06T22:48:13.574890Z","title":"Cohen, Number theory","venue":null,"work_id":"a8fd4da3-4362-44e3-afbf-eb19ebaa005c","year":2007},"citing_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T22:48:06.747760Z"},"links":{"citing_paper":"/paper/2506.21642"},"observation_digest":"sha256:10092ce6ee40275d5cec5d91c74a46ad2916194449b257f0beceabbf4801faa2","observation_id":"a6079b95-11a7-4489-b041-48540b5db316","resolution":{"observed_at":"2026-08-06T22:48:13.626293Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T22:48:13.438239Z","title":"Col , Palindromes dans les progressions arithm´ etiques, Acta Arith., 137 (2009), pp","venue":null,"work_id":"e1cd1ce0-fc44-4174-9602-6ecbdf9e684d","year":2009},"citing_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T22:48:06.810455Z"},"links":{"citing_paper":"/paper/2506.21642"},"observation_digest":"sha256:ad15cf023c31c9a767bf8b1bd8985fd3e55629298fd694a156a92881f822b376","observation_id":"891649ac-8876-43fe-8136-9fb690514696","resolution":{"observed_at":"2026-08-06T22:48:13.493179Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T22:48:13.327567Z","title":"Dartyge, B","venue":null,"work_id":"964ef9c3-0999-4831-a523-cc23b81b5e75","year":2024},"citing_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T22:48:06.863055Z"},"links":{"citing_paper":"/paper/2506.21642"},"observation_digest":"sha256:5ca1ccdec691ade1a2f864a134fb626c749ab4e524a3739cd8844a85d5d2a77f","observation_id":"3d750b3c-d598-454b-a149-3d14a7db5d5e","resolution":{"observed_at":"2026-08-06T22:48:13.382682Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T22:48:13.180304Z","title":"Dartyge and C","venue":null,"work_id":"ee2163fe-c255-4b9e-98cd-51974d682557","year":2000},"citing_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T22:48:06.957799Z"},"links":{"citing_paper":"/paper/2506.21642"},"observation_digest":"sha256:f2e9dd04dd32e8a64cf4abd98fe130577f5ce7c12f1684d6ae190cd09d2787e7","observation_id":"fcfdce2b-5584-45ea-990e-46a30e824618","resolution":{"observed_at":"2026-08-06T22:48:13.233042Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T22:48:13.060996Z","title":"Number Theory, 91 (2001), pp","venue":null,"work_id":"44f7a282-417f-45f0-a396-396b0ce0ccad","year":2001},"citing_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T22:48:07.024330Z"},"links":{"citing_paper":"/paper/2506.21642"},"observation_digest":"sha256:d8f0a79821472d41864ff49cb02d0ce7e3a6d22c7846cf3dcf55a696ef96c908","observation_id":"421f23ba-c544-435c-a831-5395f655f292","resolution":{"observed_at":"2026-08-06T22:48:13.097828Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T22:48:12.894973Z","title":"Dartyge and G","venue":null,"work_id":"1a5c6fc2-8b8e-44e3-ad47-1d60ef1cd4cf","year":2005},"citing_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T22:48:07.087940Z"},"links":{"citing_paper":"/paper/2506.21642"},"observation_digest":"sha256:0095ce315d9ca354164b58f3ab063232c9e4c623099dc14a19e7e98170df334b","observation_id":"1d33e555-ea42-45ba-b037-33aa68199aeb","resolution":{"observed_at":"2026-08-06T22:48:12.937096Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T22:48:12.748985Z","title":"London Math","venue":null,"work_id":"d2ab0f5a-729b-49ed-a097-91ae756848b6","year":2006},"citing_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T22:48:07.149785Z"},"links":{"citing_paper":"/paper/2506.21642"},"observation_digest":"sha256:2edfabcf9eab585894171ef6e6b070411b65a3974d9b81846532ecf37335530b","observation_id":"be347cc9-e4b0-4378-a2b2-20f41d677c68","resolution":{"observed_at":"2026-08-06T22:48:12.803491Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T22:48:12.596869Z","title":"Fouvry and C","venue":null,"work_id":"26bcfb2d-0d8f-4d27-925b-08025343e0cc","year":1996},"citing_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T22:48:07.229803Z"},"links":{"citing_paper":"/paper/2506.21642"},"observation_digest":"sha256:99dcf1e1047b981dd15bdc79c15b5eec9af6ddc3955b1765bbafa7206d5a2bca","observation_id":"835ab93c-5390-48b3-beb5-4f1616377c06","resolution":{"observed_at":"2026-08-06T22:48:12.657309Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T22:48:12.252108Z","title":null,"venue":null,"work_id":"6dc585a1-c5de-4d87-bf45-6373756f1dd1","year":1996},"citing_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T22:48:07.275800Z"},"links":{"citing_paper":"/paper/2506.21642"},"observation_digest":"sha256:0ffd760b39ceffc0448d5e9d894a0fe28a76993547114bde052a0a26b9b289b1","observation_id":"550ec2b0-ceb5-4354-8b6a-86e7ec99a9a8","resolution":{"observed_at":"2026-08-06T22:48:12.492969Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T22:48:12.000157Z","title":"Friedlander and H","venue":null,"work_id":"ca2aa60e-1143-49ad-8198-5569d571aaff","year":2010},"citing_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T22:48:07.368049Z"},"links":{"citing_paper":"/paper/2506.21642"},"observation_digest":"sha256:a4f93ffaad4b1701685aa3ca7bf5bebafbee07a4c913d3af792f6cba57a5eb3d","observation_id":"95567554-feb9-4b47-8fb1-5d14fdf7cbae","resolution":{"observed_at":"2026-08-06T22:48:12.129393Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T22:48:11.864283Z","title":null,"venue":null,"work_id":"844db11d-370a-482d-85dd-6188ea7fa2ca","year":1967},"citing_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T22:48:07.387291Z"},"links":{"citing_paper":"/paper/2506.21642"},"observation_digest":"sha256:6d14c55660c4dec5f596335d75cca6592db80f456e2f21ce2590e13461703611","observation_id":"7bd31387-c6d0-498d-959e-4397ef7f5c74","resolution":{"observed_at":"2026-08-06T22:48:11.923997Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T22:48:11.659549Z","title":"Greaves, Sieves in number theory , vol","venue":null,"work_id":"e04b5789-cfb2-44f3-9286-266c05f0aecc","year":2001},"citing_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T22:48:07.430972Z"},"links":{"citing_paper":"/paper/2506.21642"},"observation_digest":"sha256:5078b0531d7357000f6068ed0ba674b4266913f63c78f56a96f6150334e2bbe8","observation_id":"daa8eb24-c2f5-486c-9d43-0d9f37761a5f","resolution":{"observed_at":"2026-08-06T22:48:11.725657Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T22:48:11.533338Z","title":"Halberstam and H.-R","venue":null,"work_id":"370d302b-303b-4784-8c01-589c3404338c","year":1974},"citing_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T22:48:07.547303Z"},"links":{"citing_paper":"/paper/2506.21642"},"observation_digest":"sha256:6b786f0b2c736531628cbfc0a56db4cb597aea58a8c3343891d4f2313eb74c21","observation_id":"8f0be984-3bac-4505-8324-3f7de412ac56","resolution":{"observed_at":"2026-08-06T22:48:11.610897Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T22:48:11.367328Z","title":"Iwaniec, Rosser’s sieve, Acta Arith., 36 (1980), pp","venue":null,"work_id":"d1c7d7bb-2c46-4e04-8eb1-b49414cabcfb","year":1980},"citing_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T22:48:07.666180Z"},"links":{"citing_paper":"/paper/2506.21642"},"observation_digest":"sha256:2c84cf4da8e07a4fd48d678253c258b6da33124e0d4cfec7d5ef81a5538572d4","observation_id":"f18eaf47-f297-4b3c-a26c-671830df1fea","resolution":{"observed_at":"2026-08-06T22:48:11.495218Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T22:48:11.151910Z","title":"Iwaniec and E","venue":null,"work_id":"4f22e898-80ff-4db6-867b-d99297260c77","year":2004},"citing_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T22:48:07.783210Z"},"links":{"citing_paper":"/paper/2506.21642"},"observation_digest":"sha256:978f834d7806a1cb46ee63c380cc726346bb4d73c920be50a653b1e8de6881f7","observation_id":"0417835b-816f-4b24-9d64-bdc47e133fa0","resolution":{"observed_at":"2026-08-06T22:48:11.216161Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T22:48:10.980239Z","title":"Mauduit and J","venue":null,"work_id":"c2b843d3-f797-4610-acb2-522f0e6bfb79","year":2009},"citing_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T22:48:07.879067Z"},"links":{"citing_paper":"/paper/2506.21642"},"observation_digest":"sha256:128c422bf7cc68055803dd830f2d14e3c79c5f9e5b6b35eeb0b943267e736033","observation_id":"4639d01c-7539-40f3-b6ae-7c7c56f90b45","resolution":{"observed_at":"2026-08-06T22:48:11.075847Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T22:48:10.833516Z","title":null,"venue":null,"work_id":"17080aaa-f996-4f49-92dc-7e66364076ff","year":2010},"citing_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T22:48:08.019657Z"},"links":{"citing_paper":"/paper/2506.21642"},"observation_digest":"sha256:ab9e2c6ed5e12dc44ffd73b47fa17b7acbcb347df4513ec0a497f80efef63105","observation_id":"0ac9a3be-e4dc-4740-a818-d93fbb74d238","resolution":{"observed_at":"2026-08-06T22:48:10.888128Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T22:48:10.611899Z","title":null,"venue":null,"work_id":"6383c36c-4a2a-41bb-a8c1-53c1abe637f9","year":2015},"citing_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T22:48:08.113492Z"},"links":{"citing_paper":"/paper/2506.21642"},"observation_digest":"sha256:7caacf66a56b02292c875cbc4a15cd2a14f8a1062ee08bbeeea6dd102e03ce64","observation_id":"97b8199a-03f2-4fff-a685-bb638663c477","resolution":{"observed_at":"2026-08-06T22:48:10.747361Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T22:48:10.353638Z","title":"Maynard, Primes with restricted digits , Invent","venue":null,"work_id":"43299067-3ad8-4451-bae1-8eab380a41b9","year":2019},"citing_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T22:48:08.191752Z"},"links":{"citing_paper":"/paper/2506.21642"},"observation_digest":"sha256:f10276ab0aa1a815dba6bf61d082d39006f5efa1adbbc6c9e5b5bf64aad69e9d","observation_id":"aaba1fc9-db7e-4e0b-abbb-84e68147d10a","resolution":{"observed_at":"2026-08-06T22:48:10.471394Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T22:48:10.138527Z","title":null,"venue":null,"work_id":"8f2a40df-d635-4947-b3bb-624aaa14d77e","year":2021},"citing_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T22:48:08.272250Z"},"links":{"citing_paper":"/paper/2506.21642"},"observation_digest":"sha256:923a0a88f5cb3dde4013c1026f832e8aca6666e877ce6961ec6440beef2d1adc","observation_id":"a9e31691-202a-42cb-af21-c1bad1581277","resolution":{"observed_at":"2026-08-06T22:48:10.247447Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T22:48:09.972511Z","title":null,"venue":null,"work_id":"b41630fc-b805-4033-ad51-5a2b2f61013d","year":1978},"citing_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T22:48:08.344731Z"},"links":{"citing_paper":"/paper/2506.21642"},"observation_digest":"sha256:def3a82c6c85b1a1e47ad367da9e2fcdc20bfc0bb05550393241b01d6d0329ab","observation_id":"4f1c1994-45a3-4179-a7d5-845ff0eab3d2","resolution":{"observed_at":"2026-08-06T22:48:10.047135Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T22:48:09.828930Z","title":"R´enyi, On the representation of an even number as the sum of a single prime and single almost-prime number , Izv","venue":null,"work_id":"a04f853e-9975-44d5-971f-5a47d842f5e8","year":1948},"citing_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T22:48:08.441034Z"},"links":{"citing_paper":"/paper/2506.21642"},"observation_digest":"sha256:7542aa9e07c546cfe5cb52467d96d14fc3996760238260d349e741ca2cc7164c","observation_id":"e987d900-7ebb-4286-a268-137b6059c37c","resolution":{"observed_at":"2026-08-06T22:48:09.875998Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T22:48:09.701371Z","title":"Swaenepoel , Prime numbers with a positive proportion of preassigned digits , Proc","venue":null,"work_id":"780280b1-f9d4-4727-9c21-778f5fc21ad9","year":2020},"citing_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T22:48:08.529458Z"},"links":{"citing_paper":"/paper/2506.21642"},"observation_digest":"sha256:712286fe6f7e8c99e8b7124c8b0e637f2ffaa3263f098e2fac8a312b17607d7e","observation_id":"dc5c27aa-d92f-4278-bbab-dd7d007a91b8","resolution":{"observed_at":"2026-08-06T22:48:09.756245Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T22:48:09.490997Z","title":"Tenenbaum , Introduction ` a la th´ eorie analytique et probabiliste des nombres , Dunod, cinqui` eme ed., 2022","venue":null,"work_id":"73d20cb7-ceee-4b11-b5c1-a0221eac7415","year":2022},"citing_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T22:48:08.588543Z"},"links":{"citing_paper":"/paper/2506.21642"},"observation_digest":"sha256:026b633b5311dbe787802330878546f611d29a3159700b4ace5e1eace970385c","observation_id":"fd7a364f-a2c3-4754-8b49-c8ec521cdd39","resolution":{"observed_at":"2026-08-06T22:48:09.562494Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T22:48:09.244722Z","title":"Tuxanidy and D","venue":null,"work_id":"df622aca-8216-42ca-9d82-71b17493aa38","year":2024},"citing_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T22:48:08.687965Z"},"links":{"citing_paper":"/paper/2506.21642"},"observation_digest":"sha256:e4aabf06c509e6fb98a703e0916bb23430bb7aadf417fcc47b5e9c18dd36c8ad","observation_id":"1403a2d8-878b-4cc1-98e7-073815578c26","resolution":{"observed_at":"2026-08-06T22:48:09.356535Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T22:48:09.064472Z","title":"Zygmund , Trigonometric series","venue":null,"work_id":"92135ac1-7dc3-4dbe-9872-d90eb24e68ec","year":2002},"citing_paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T22:48:08.768483Z"},"links":{"citing_paper":"/paper/2506.21642"},"observation_digest":"sha256:797d8c061a135f3f1008258e8bf8c8b1c2ba80004d7e8fce4eb44a0f8e2912c9","observation_id":"a2473438-fccd-40c6-9244-80ad2dc3b08c","resolution":{"observed_at":"2026-08-06T22:48:09.161449Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.21642","last_updated":"2025-07-10T16:00:37Z","latest_version":2,"primary_category":"math.NT","snapshot_observed_at":"2026-08-10T07:40:07.945734Z","submitted_at":"2025-06-25T20:56:01Z","title":"Prime numbers with an almost prime reverse"},"reference_resolution":{"displayed":34,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":10,"verified_exact":0,"verified_fuzzy":24},"total_outbound_references":34},"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":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 3 inbound Pith citation observations for arXiv:2506.21642."}