{"as_of":"2026-08-16T07:54:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:8c430743722e89083efb4f04f57432a6065aa16cf15305a8875ef989f138ecec","coverage":[{"denominator":12,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":12,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T11:23:58.929290Z","state":"measured"},{"denominator":13,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":13,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+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":"2026-07-11T19:45:27.699165Z","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":[{"citation":{"cited_paper":{"arxiv_id":"1908.09420","last_updated":"2021-06-26T18:19:08Z","snapshot_observed_at":"2026-08-16T04:43:21.009389Z","submitted_at":"2019-08-26T00:52:57Z","title":"On the third largest prime divisor of an odd perfect number","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1908.09420","snapshot_observed_at":"2026-07-11T19:45:27.699165Z","title":"Integers , volume =","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.04365","last_updated":"2026-07-05T15:47:30Z","snapshot_observed_at":"2026-08-08T13:47:37.521869Z","submitted_at":"2026-07-05T15:47:30Z","title":"Certified Minimal-Prime Branch Closures for Odd Perfect Numbers","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-07-11T19:45:27.699165Z"},"links":{"cited_paper":"/paper/1908.09420","citing_paper":"/paper/2607.04365"},"observation_digest":"sha256:8426cb659e074a0dba234f25e92dd6171c88b9ba745d8e1f10be3c6c0add2141","observation_id":"1436ad2f-610c-4bc8-b982-2f78cc9f5c5f","resolution":{"observed_at":"2026-07-11T19:45:27.699165Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/1908.09420/citation-record","integrity":"/paper/1908.09420/integrity","json":"/paper/1908.09420/citation-record.json","paper":"/paper/1908.09420"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:23:59.136657Z","title":"Acquaa and S","venue":null,"work_id":"5adb42d6-58b2-4622-8b98-76593e697a33","year":2012},"citing_paper":{"arxiv_id":"1908.09420","last_updated":"2021-06-26T18:19:08Z","snapshot_observed_at":"2026-08-16T04:43:21.009389Z","submitted_at":"2019-08-26T00:52:57Z","title":"On the third largest prime divisor of an odd perfect number","version":3},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-14T11:23:58.872924Z"},"links":{"citing_paper":"/paper/1908.09420"},"observation_digest":"sha256:706f35e720be027e1ad385bf10a13e4ae2b8570dab58f01162a7badf041d38c8","observation_id":"7de9a12c-567b-4532-b0fb-94fb03a80dc7","resolution":{"observed_at":"2026-08-14T11:23:59.141649Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:23:59.122041Z","title":null,"venue":null,"work_id":"4f356d22-3920-45c2-89ea-1fa0c80a7532","year":2017},"citing_paper":{"arxiv_id":"1908.09420","last_updated":"2021-06-26T18:19:08Z","snapshot_observed_at":"2026-08-16T04:43:21.009389Z","submitted_at":"2019-08-26T00:52:57Z","title":"On the third largest prime divisor of an odd perfect number","version":3},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-14T11:23:58.878366Z"},"links":{"citing_paper":"/paper/1908.09420"},"observation_digest":"sha256:b8d582d40bbb191eabf9197327f46c7fd1d55b097d26d72ed8f544a3c8c61201","observation_id":"eaf5af21-e858-444f-9f13-1bbea152ca3f","resolution":{"observed_at":"2026-08-14T11:23:59.126505Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:23:59.105975Z","title":null,"venue":null,"work_id":"2b02ecd8-c121-4ea7-8fb3-566ccd21125d","year":1975},"citing_paper":{"arxiv_id":"1908.09420","last_updated":"2021-06-26T18:19:08Z","snapshot_observed_at":"2026-08-16T04:43:21.009389Z","submitted_at":"2019-08-26T00:52:57Z","title":"On the third largest prime divisor of an odd perfect number","version":3},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-14T11:23:58.883307Z"},"links":{"citing_paper":"/paper/1908.09420"},"observation_digest":"sha256:923d13f4c99d8d0a6f1b1198724fbab525f3b9fc44672a702b0a4b3912217629","observation_id":"4e14988c-7731-4b94-9811-2f51b192497a","resolution":{"observed_at":"2026-08-14T11:23:59.110934Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:23:59.090754Z","title":"Ellia, A remark on the radical of odd perfect numbers, Fibonacci Quarterly 50 3 (2012) 231--234","venue":null,"work_id":"a61a196e-9782-4ea3-839f-cc293c41df2a","year":2012},"citing_paper":{"arxiv_id":"1908.09420","last_updated":"2021-06-26T18:19:08Z","snapshot_observed_at":"2026-08-16T04:43:21.009389Z","submitted_at":"2019-08-26T00:52:57Z","title":"On the third largest prime divisor of an odd perfect number","version":3},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-14T11:23:58.888105Z"},"links":{"citing_paper":"/paper/1908.09420"},"observation_digest":"sha256:d1cb3440eb441d3445f5495eaf34df5aa5e4bf304a85bb895bbc110cfc0e4d5e","observation_id":"ab3aba93-efa7-46ea-9d52-9139ac5ec794","resolution":{"observed_at":"2026-08-14T11:23:59.095988Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:23:59.074728Z","title":"Iannucci, The third largest prime divisor of an odd perfect number exceeds one hundred, Mathematics of Computation 69 230 (2000), 867--879","venue":null,"work_id":"a725659a-5a5c-44d8-9c56-bb44f845d404","year":2000},"citing_paper":{"arxiv_id":"1908.09420","last_updated":"2021-06-26T18:19:08Z","snapshot_observed_at":"2026-08-16T04:43:21.009389Z","submitted_at":"2019-08-26T00:52:57Z","title":"On the third largest prime divisor of an odd perfect number","version":3},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-14T11:23:58.893873Z"},"links":{"citing_paper":"/paper/1908.09420"},"observation_digest":"sha256:e75381bfdaecc4041df5efbbab4f87b5e8ef4dc94b5ad3e023868169bb5bb76e","observation_id":"ec890007-ef61-40bf-a884-66a7e25d768a","resolution":{"observed_at":"2026-08-14T11:23:59.080001Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:23:59.059728Z","title":"Klurman, Radical of perfect numbers and perfect numbers among polynomial values, International Journal of Number Theory 12 3 (2016), 585--591","venue":null,"work_id":"a5fa244f-ba66-4a40-8d21-9ecf08de9096","year":2016},"citing_paper":{"arxiv_id":"1908.09420","last_updated":"2021-06-26T18:19:08Z","snapshot_observed_at":"2026-08-16T04:43:21.009389Z","submitted_at":"2019-08-26T00:52:57Z","title":"On the third largest prime divisor of an odd perfect number","version":3},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-14T11:23:58.898933Z"},"links":{"citing_paper":"/paper/1908.09420"},"observation_digest":"sha256:fc5e3771b1e56fe81c14129813e28280306f5a4454b88df4368e39b37730101f","observation_id":"c6500a7f-eced-45c9-ad8c-9d65aa980fbf","resolution":{"observed_at":"2026-08-14T11:23:59.064480Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:23:59.043555Z","title":null,"venue":null,"work_id":"419076c0-4a8a-4de1-b87d-89d0fe26ec69","year":1953},"citing_paper":{"arxiv_id":"1908.09420","last_updated":"2021-06-26T18:19:08Z","snapshot_observed_at":"2026-08-16T04:43:21.009389Z","submitted_at":"2019-08-26T00:52:57Z","title":"On the third largest prime divisor of an odd perfect number","version":3},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-14T11:23:58.904178Z"},"links":{"citing_paper":"/paper/1908.09420"},"observation_digest":"sha256:5aa705c72727ac37778f30cf2dd61b7853551905f7357f48bcefd111983f23c0","observation_id":"bda1f235-d19a-4001-be2e-c77922dc08ac","resolution":{"observed_at":"2026-08-14T11:23:59.048890Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:23:59.026853Z","title":"Nielsen, Odd perfect numbers, Diophantine equations, and upper bounds, Mathematics of Computation 84 295 (2015), 2549--2567","venue":null,"work_id":"f2bf8d2e-0a5d-4b8a-b610-1a524b354192","year":2015},"citing_paper":{"arxiv_id":"1908.09420","last_updated":"2021-06-26T18:19:08Z","snapshot_observed_at":"2026-08-16T04:43:21.009389Z","submitted_at":"2019-08-26T00:52:57Z","title":"On the third largest prime divisor of an odd perfect number","version":3},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-14T11:23:58.908903Z"},"links":{"citing_paper":"/paper/1908.09420"},"observation_digest":"sha256:67c65c6ed0466734dc229c485c4da373581ae13dd58a21046af00328691b2842","observation_id":"7f6e4eea-31e1-427d-b47d-b287b4c83985","resolution":{"observed_at":"2026-08-14T11:23:59.031825Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:23:59.011396Z","title":"Ochem, M","venue":null,"work_id":"c83ccbac-d63c-4c39-b764-522e71afb6fd","year":2014},"citing_paper":{"arxiv_id":"1908.09420","last_updated":"2021-06-26T18:19:08Z","snapshot_observed_at":"2026-08-16T04:43:21.009389Z","submitted_at":"2019-08-26T00:52:57Z","title":"On the third largest prime divisor of an odd perfect number","version":3},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-14T11:23:58.913787Z"},"links":{"citing_paper":"/paper/1908.09420"},"observation_digest":"sha256:16687fa875c90e301f30c4eaa30753d2251f65aaa475f1d709647d9457570d3d","observation_id":"06e53ad8-027b-4c89-b10f-ef86d5374354","resolution":{"observed_at":"2026-08-14T11:23:59.016286Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:23:58.994982Z","title":"Luca and C","venue":null,"work_id":"4992536c-6b43-4210-8bd0-f4f2ecde0280","year":2010},"citing_paper":{"arxiv_id":"1908.09420","last_updated":"2021-06-26T18:19:08Z","snapshot_observed_at":"2026-08-16T04:43:21.009389Z","submitted_at":"2019-08-26T00:52:57Z","title":"On the third largest prime divisor of an odd perfect number","version":3},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-14T11:23:58.918985Z"},"links":{"citing_paper":"/paper/1908.09420"},"observation_digest":"sha256:3cfb629d314595e743f79d8ccff8a270c00bd234a1e66ccdc9477e8f5dc28292","observation_id":"d00de3fa-690b-45a0-8bdc-33b39bb09bc6","resolution":{"observed_at":"2026-08-14T11:23:58.999974Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:23:58.978695Z","title":"Zelinsky, Upper bounds on the second largest prime factor of an odd perfect number","venue":null,"work_id":"5c28c7e4-ffbe-44b4-9f1f-12dd400bc313","year":2019},"citing_paper":{"arxiv_id":"1908.09420","last_updated":"2021-06-26T18:19:08Z","snapshot_observed_at":"2026-08-16T04:43:21.009389Z","submitted_at":"2019-08-26T00:52:57Z","title":"On the third largest prime divisor of an odd perfect number","version":3},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-14T11:23:58.924459Z"},"links":{"citing_paper":"/paper/1908.09420"},"observation_digest":"sha256:6d9b50ba825cd04bc477870923734de63b9e60fdb11396a52ba6f5e754aae39a","observation_id":"8aeab62d-632f-499b-b7be-5fd4fd0ae904","resolution":{"observed_at":"2026-08-14T11:23:58.983829Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:23:58.959581Z","title":"Zelinsky, An improvement of an inequality of Ochem and Rao concerning odd perfect numbers, Integers 18 (2018)","venue":null,"work_id":"783fc204-e5d6-48ab-a250-47f33b01d67a","year":2018},"citing_paper":{"arxiv_id":"1908.09420","last_updated":"2021-06-26T18:19:08Z","snapshot_observed_at":"2026-08-16T04:43:21.009389Z","submitted_at":"2019-08-26T00:52:57Z","title":"On the third largest prime divisor of an odd perfect number","version":3},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-14T11:23:58.929290Z"},"links":{"citing_paper":"/paper/1908.09420"},"observation_digest":"sha256:7e6bc9fdfe9188e6139cbab535f78e38c137b158315a18cb1b5b6d76f7e311b4","observation_id":"2e1e6d78-de28-4461-af3e-a53f3cb61e21","resolution":{"observed_at":"2026-08-14T11:23:58.967313Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"1908.09420","last_updated":"2021-06-26T18:19:08Z","latest_version":3,"primary_category":"math.NT","snapshot_observed_at":"2026-08-16T04:43:21.009389Z","submitted_at":"2019-08-26T00:52:57Z","title":"On the third largest prime divisor of an odd perfect number"},"reference_resolution":{"displayed":12,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":3,"verified_exact":0,"verified_fuzzy":9},"total_outbound_references":12},"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":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 1 inbound Pith citation observation for arXiv:1908.09420."}