{"as_of":"2026-08-08T10:16:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:d9b70d6abb95d04ba28dd39d3bd9c49cb14a670b178b481eae8ede25dc6bc694","coverage":[{"denominator":7,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":7,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T11:47:51.013813Z","state":"measured"},{"denominator":7,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":7,"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/2506.01830/citation-record","integrity":"/paper/2506.01830/integrity","json":"/paper/2506.01830/citation-record.json","paper":"/paper/2506.01830"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:47:51.923146Z","title":"196, 857–868.↑2 [Eul49] Leonhard Euler, De numeris amicibilibus , Euler Archive - All Works","venue":null,"work_id":"51695b1b-0897-47a7-a28b-77e2c502def8","year":1991},"citing_paper":{"arxiv_id":"2506.01830","last_updated":"2025-06-03T06:56:11Z","snapshot_observed_at":"2026-08-07T19:37:34.783003Z","submitted_at":"2025-06-02T16:18:03Z","title":"On a Recursive Integer Sequence Implying the Nonexistence of Odd Perfect Numbers","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T11:47:50.721011Z"},"links":{"citing_paper":"/paper/2506.01830"},"observation_digest":"sha256:a32544aebcffe1dbc425ce9b67f9d8d6d6077d71e0ccb57bfd28bdce0676349a","observation_id":"4037e7b4-e78e-4f60-a02f-ace4ae4ca720","resolution":{"observed_at":"2026-08-07T11:47:51.955415Z","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":"2026-08-07T11:47:51.264870Z","title":"Suryanarayana, Super perfect numbers, Elem","venue":null,"work_id":"92448333-5b8a-41e0-ac2b-e79eeb0e6559","year":1969},"citing_paper":{"arxiv_id":"2506.01830","last_updated":"2025-06-03T06:56:11Z","snapshot_observed_at":"2026-08-07T19:37:34.783003Z","submitted_at":"2025-06-02T16:18:03Z","title":"On a Recursive Integer Sequence Implying the Nonexistence of Odd Perfect Numbers","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T11:47:50.938251Z"},"links":{"citing_paper":"/paper/2506.01830"},"observation_digest":"sha256:fc5246af3d9c08efd7931fe6f6b48a767c099e9c5ee8447e6fecd0fcd7571db5","observation_id":"5da2e951-4c4d-4de4-86b6-711f85a81b3a","resolution":{"observed_at":"2026-08-07T11:47:51.387205Z","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":"2026-08-07T11:47:51.110464Z","title":"19 (1953), 35–39","venue":null,"work_id":"64a466c6-180c-4d04-9b67-5bde888dd3fc","year":1953},"citing_paper":{"arxiv_id":"2506.01830","last_updated":"2025-06-03T06:56:11Z","snapshot_observed_at":"2026-08-07T19:37:34.783003Z","submitted_at":"2025-06-02T16:18:03Z","title":"On a Recursive Integer Sequence Implying the Nonexistence of Odd Perfect Numbers","version":2},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-07T11:47:51.013813Z"},"links":{"citing_paper":"/paper/2506.01830"},"observation_digest":"sha256:defa71f26863f217d821cc97e6c662cd67bf961ca7ac99fd4881208e79647554","observation_id":"069d56cf-484e-47a8-bf7d-938460cb85f9","resolution":{"observed_at":"2026-08-07T11:47:51.171228Z","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":"2026-08-07T11:47:51.491558Z","title":"Satyanarayana, Odd perfect numbers, Math","venue":null,"work_id":"f9e3073f-4569-42ad-a334-75980a91be18","year":1959},"citing_paper":{"arxiv_id":"2506.01830","last_updated":"2025-06-03T06:56:11Z","snapshot_observed_at":"2026-08-07T19:37:34.783003Z","submitted_at":"2025-06-02T16:18:03Z","title":"On a Recursive Integer Sequence Implying the Nonexistence of Odd Perfect Numbers","version":2},"reference_index":170,"source":"pdf_text","source_observed_at":"2026-08-07T11:47:50.899539Z"},"links":{"citing_paper":"/paper/2506.01830"},"observation_digest":"sha256:9aee21a6879b1966cbc50ec51e52f544d4931c97f437d98889b02ac4f0e8b33c","observation_id":"c5392579-6843-45c8-92b2-f81910e8d519","resolution":{"observed_at":"2026-08-07T11:47:51.572342Z","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":"2026-08-07T11:47:51.863759Z","title":"↑2 [Gal22] Luis H","venue":null,"work_id":"bbfb153f-44e2-4e25-8b5a-d8cae696387d","year":2022},"citing_paper":{"arxiv_id":"2506.01830","last_updated":"2025-06-03T06:56:11Z","snapshot_observed_at":"2026-08-07T19:37:34.783003Z","submitted_at":"2025-06-02T16:18:03Z","title":"On a Recursive Integer Sequence Implying the Nonexistence of Odd Perfect Numbers","version":2},"reference_index":798,"source":"pdf_text","source_observed_at":"2026-08-07T11:47:50.760983Z"},"links":{"citing_paper":"/paper/2506.01830"},"observation_digest":"sha256:3fee8c33a7607222fb9f71349a7681eccb5cf585d74ca0ac2e97a7728c9ebcf5","observation_id":"fcdeb6f9-f738-471d-aced-89f9415f7b2e","resolution":{"observed_at":"2026-08-07T11:47:51.893219Z","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":"2026-08-07T11:47:51.802865Z","title":"super perfect numbers","venue":null,"work_id":"370b52e1-93b3-4d46-bcd5-0c06e7d0f0e5","year":2006},"citing_paper":{"arxiv_id":"2506.01830","last_updated":"2025-06-03T06:56:11Z","snapshot_observed_at":"2026-08-07T19:37:34.783003Z","submitted_at":"2025-06-02T16:18:03Z","title":"On a Recursive Integer Sequence Implying the Nonexistence of Odd Perfect Numbers","version":2},"reference_index":2004,"source":"pdf_text","source_observed_at":"2026-08-07T11:47:50.812583Z"},"links":{"citing_paper":"/paper/2506.01830"},"observation_digest":"sha256:b92c7f6e58bcd5aeb08e505a49f39a783d2fd2f842468f4a6cb920ab2714fc02","observation_id":"de6fb555-9dae-4aa8-bb7c-6facf94bdcc4","resolution":{"observed_at":"2026-08-07T11:47:51.821219Z","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":"2026-08-07T11:47:51.663157Z","title":null,"venue":null,"work_id":"7394d4f9-e01f-49ed-9a92-1fb1ecda53cd","year":2012},"citing_paper":{"arxiv_id":"2506.01830","last_updated":"2025-06-03T06:56:11Z","snapshot_observed_at":"2026-08-07T19:37:34.783003Z","submitted_at":"2025-06-02T16:18:03Z","title":"On a Recursive Integer Sequence Implying the Nonexistence of Odd Perfect Numbers","version":2},"reference_index":2010,"source":"pdf_text","source_observed_at":"2026-08-07T11:47:50.864744Z"},"links":{"citing_paper":"/paper/2506.01830"},"observation_digest":"sha256:33d18bb0732c4cd08a490c5d9d73f3d40d9c2431de50530dd22ce8a1e138549e","observation_id":"9e19818e-ec91-4f02-9fbd-611586eca050","resolution":{"observed_at":"2026-08-07T11:47:51.766034Z","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":"2506.01830","last_updated":"2025-06-03T06:56:11Z","latest_version":2,"primary_category":"math.NT","snapshot_observed_at":"2026-08-07T19:37:34.783003Z","submitted_at":"2025-06-02T16:18:03Z","title":"On a Recursive Integer Sequence Implying the Nonexistence of Odd Perfect Numbers"},"reference_resolution":{"displayed":7,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":1,"verified_exact":0,"verified_fuzzy":6},"total_outbound_references":7},"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 7 of 7 outbound references and 0 inbound Pith citation observations for arXiv:2506.01830."}