{"as_of":"2026-08-16T20:21:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:117de67f3ef650a2cc1c90698c77606181c53c8e5872fdcb17223306b48f6aa1","coverage":[{"denominator":59,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":59,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T13:24:39.243859Z","state":"measured"},{"denominator":60,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":60,"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":"2026-08-14T13:24:43.971134Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-14T13:24:44.350441Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"cited_work":{"arxiv_id":"1908.05677","doi":null,"metadata_source":"pith","pith_arxiv_id":"1908.05677","snapshot_observed_at":"2026-08-14T13:24:44.350441Z","title":"Lifting countable to uncountable mathematics","venue":"math.LO","work_id":"a10a7221-abf8-4321-b1ca-af2aa5908b24","year":2019},"citing_paper":{"arxiv_id":"1908.05676","last_updated":"2020-08-13T10:18:01Z","snapshot_observed_at":"2026-08-16T04:43:06.395582Z","submitted_at":"2019-08-15T12:33:48Z","title":"Plato and the foundations of mathematics","version":6},"reference_index":76,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:43.971134Z"},"links":{"cited_paper":"/paper/1908.05677","citing_paper":"/paper/1908.05676"},"observation_digest":"sha256:5deeb9928736fefeac5feeb7c53827809d02dd25c46f7efbae902dba37b8b4d7","observation_id":"3b8d60ac-a406-4667-87d3-0d854e9cda3a","resolution":{"observed_at":"2026-08-14T13:24:44.356981Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"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"}}],"links":{"evidence":"/evidence","html":"/paper/1908.05677/citation-record","integrity":"/paper/1908.05677/integrity","json":"/paper/1908.05677/citation-record.json","paper":"/paper/1908.05677"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:24:40.571523Z","title":"Dialectica","venue":null,"work_id":"261925eb-e3a0-4a6c-b5f1-624909993534","year":1998},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:38.954147Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:49fc72a565519ad48c35b77e3c043472f7a5b6d361afec94734de9b21c168f71","observation_id":"1c251051-bad9-410f-b486-80c826abdfb4","resolution":{"observed_at":"2026-08-14T13:24:40.575924Z","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":"2026-08-14T13:24:40.556805Z","title":"Bartle, Nets and filters in topology , Amer","venue":null,"work_id":"5cd30b2b-11fa-4955-8b66-1f972f15e48d","year":1955},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:38.959377Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:336bf14a2fcdbd837091f660ae8ca92dde2a81ec20525affcee383e212208742","observation_id":"1114741a-c6cd-46a7-8868-956623345438","resolution":{"observed_at":"2026-08-14T13:24:40.562056Z","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":"2026-08-14T13:24:40.539947Z","title":"Pure Appl","venue":null,"work_id":"4b32120a-211c-484b-bfdc-8eaf284bf3e3","year":2012},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:38.963856Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:e3ec3288df02ca0be23c36d44f4e5e319a5db922a226197e86adb1a190efa3c1","observation_id":"a35d8f7c-f925-4716-bd1d-13fe938e4c24","resolution":{"observed_at":"2026-08-14T13:24:40.545367Z","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":"2026-08-14T13:24:40.523912Z","title":"Brown, Notions of closed subsets of a complete separable metric spa ce in weak subsystems of second-order arithmetic , Logic and computation (Pittsburgh, PA, 1987), Con- temp","venue":null,"work_id":"a928ae44-bf0a-4f93-adc3-ea1860d29dec","year":1987},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:38.969720Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:a1cd9d8ece412fdacbb69d770a9b070b40659fe5e33f0697372244560fd053ba","observation_id":"15578779-a254-4042-b38e-a91b9eb40f8e","resolution":{"observed_at":"2026-08-14T13:24:40.528712Z","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":"2026-08-14T13:24:40.496316Z","title":"Notes Log., vol","venue":null,"work_id":"0e51e7c0-13ba-4d33-9143-3304e468010c","year":2001},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:38.974478Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:7ed1bd010335a2a4b4846eeec360374729bcb95941fec382f8c72b89b37a09be","observation_id":"46bf4d2b-515c-4f9e-873c-eadd88de7f2b","resolution":{"observed_at":"2026-08-14T13:24:40.512223Z","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":"2026-08-14T13:24:40.477658Z","title":null,"venue":null,"work_id":"efa4005d-6613-4114-b3c9-c326db509728","year":1981},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:38.979129Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:5148e26dd2c59f1d856cf359d009c1531b9f6ae0775785a0c3ae5d0b041aa4fa","observation_id":"5ce6f58f-3496-42cd-abb0-ef66476134ad","resolution":{"observed_at":"2026-08-14T13:24:40.486009Z","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":"2026-08-14T13:24:40.463912Z","title":"19 (1895), 1–61","venue":null,"work_id":"7a05e869-b8cc-4cd4-becc-f236332b6936","year":null},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:38.984499Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:7ebe01368d7d461e47061730def23f4e53119624c45d2f4b7917b9b3824ec4f4","observation_id":"ac422442-733e-478c-b953-d721034bac5e","resolution":{"observed_at":"2026-08-14T13:24:40.468800Z","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":{"arxiv_id":"1209.4944","last_updated":"2013-05-10T14:26:50Z","snapshot_observed_at":"2026-08-15T00:45:43.995985Z","submitted_at":"2012-09-22T00:19:53Z","title":"Reverse Mathematics and Algebraic Field Extensions","version":2},"cited_work":{"arxiv_id":"1209.4944","doi":null,"metadata_source":"pith","pith_arxiv_id":"1209.4944","snapshot_observed_at":"2026-08-14T13:24:39.422486Z","title":"Reverse Mathematics and Algebraic Field Extensions","venue":"math.LO","work_id":"f921bf3f-be94-4503-9d3f-fc263e9cea29","year":2012},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:38.989494Z"},"links":{"cited_paper":"/paper/1209.4944","citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:a416fee9b7eade025e01f7ee325ecabb88650042fdb43ade0b70b287899ad19b","observation_id":"fcb58b76-4a9d-475d-81c6-28920aa5f32f","resolution":{"observed_at":"2026-08-14T13:24:39.426899Z","resolver_source":"local_arxiv","status":"verified_exact"},"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":"2026-08-14T13:24:40.450258Z","title":"2, 75–92","venue":null,"work_id":"aa0a0f7f-535e-4182-8181-c3d541890012","year":2013},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:38.994126Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:6c7205d109022274bdfaff55a3e8586d32dd2bf38c6a6b055a321e57f8906ee3","observation_id":"0235b44e-5cc4-4151-a71d-8b1d555f15a2","resolution":{"observed_at":"2026-08-14T13:24:40.454869Z","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":"2026-08-14T13:24:40.437988Z","title":null,"venue":null,"work_id":"b46bd408-e1ba-48e8-86db-47408b154eba","year":1977},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:38.998549Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:0878bb2b8434ae949809d1590f52c427b65a89cc9629dbe0a9d5ed4d4b725e38","observation_id":"89e503f7-a034-4c2b-86fa-56760d4c8a7d","resolution":{"observed_at":"2026-08-14T13:24:40.442082Z","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":"2026-08-14T13:24:40.425648Z","title":null,"venue":null,"work_id":"e2ed1d6c-3982-43bb-99ee-54c640fb546b","year":1998},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.003481Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:31e528e54f1fe381b78f2fe96c1f321c2621c7f83953d6c72ded793932338fce","observation_id":"ce106ee0-b561-49b6-b37d-d3f338fa6cce","resolution":{"observed_at":"2026-08-14T13:24:40.429713Z","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":"2026-08-14T13:24:40.412928Z","title":"unpublished notes from 1977-1981 with updated intro duction, https://math.stanford.edu/~feferman/papers/pfa(1).pdf","venue":null,"work_id":"e97aeee4-7069-412a-b80a-4bc05fce2b62","year":2013},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.007940Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:e616998958cb621def8f893b266b9f516fcefda1632ce01b17a24a8f535dace8","observation_id":"df13ce05-56d6-4881-a371-814b4beedf8f","resolution":{"observed_at":"2026-08-14T13:24:40.417330Z","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":"2026-08-14T13:24:40.399762Z","title":"C ., 1974), Vol","venue":null,"work_id":"e1093668-c78f-4d66-96b2-eaf9070c76dd","year":1974},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.012028Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:d26be8492afc75c936762bb571b37d195aacf96cd533671129f148c60fca1fba","observation_id":"433933c5-26e0-4cb5-88d6-bcafcab5982b","resolution":{"observed_at":"2026-08-14T13:24:40.403994Z","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":"2026-08-14T13:24:40.382115Z","title":"Symbolic Logic 41 (1976), 557–559","venue":null,"work_id":"c13a8e84-c38c-4851-b1b9-600adadb45b0","year":1976},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.017143Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:5ea1aaff334260b8a33a081a3c6bb6307029b2336914d898b7a687def20ef84d","observation_id":"5ad30b85-c67f-4f28-a20b-367255729990","resolution":{"observed_at":"2026-08-14T13:24:40.386436Z","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":"2026-08-14T13:24:40.363023Z","title":"Simpson, and Rick L","venue":null,"work_id":"2ea3cd90-192a-41cd-ae6d-8304eb75a960","year":1983},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.022390Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:c91a2bd1f23adf92928242ac152972081c6ad6dff7c31428ccf67e1a4449d5ab","observation_id":"092b169a-381f-4b9e-8c31-a46bcf1e20a9","resolution":{"observed_at":"2026-08-14T13:24:40.369315Z","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":"2026-08-14T13:24:40.344309Z","title":"Fr¨ ohlich and J","venue":null,"work_id":"ea3e735f-e3be-41b9-a838-d50c565a475a","year":1956},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.028873Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:90f88580972ec7ddb0ceb89342b777d0696292c3ae265152657c3c24f5309da9","observation_id":"062a077b-ddcd-4f50-9769-db2b4d440c2d","resolution":{"observed_at":"2026-08-14T13:24:40.350600Z","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":"2026-08-14T13:24:40.329270Z","title":null,"venue":null,"work_id":"8ef04dd9-73e4-4af0-92e3-bdf397057c8c","year":1967},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.035235Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:bbef63f863d3b5c65803c67b3615d7f72fd1a961aec431abeffb90949c1a85f2","observation_id":"3c31bf42-da72-4fb8-9162-28f2d950dfe8","resolution":{"observed_at":"2026-08-14T13:24:40.334655Z","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":"2026-08-14T13:24:40.312090Z","title":"Symbolic Logic 56 (1991), no","venue":null,"work_id":"82ecea93-9622-417c-bd45-502fbdf4a24c","year":1991},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.041325Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:f823f25007b418559b2aa758a897a5f2ea71afd4d688460fb311a13ebb5bf808","observation_id":"96ca09c4-87b5-4b67-9a71-21921e187190","resolution":{"observed_at":"2026-08-14T13:24:40.316957Z","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":"2026-08-14T13:24:40.299235Z","title":"Thesis (Ph.D.)–The Pennsylvania State University","venue":null,"work_id":"828ad490-cf93-4fbe-bca5-b4dcb169bae7","year":1987},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.047212Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:4fb66bcbd5b5061bd496df3c28cd25cfe3757af78183b4ecb719a6fc3078da86","observation_id":"391f213c-877b-45dc-9c7d-d89db80af0fe","resolution":{"observed_at":"2026-08-14T13:24:40.303587Z","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":"2026-08-14T13:24:40.285866Z","title":"1876, Springer, 2006","venue":null,"work_id":"baf0ee5d-a4c9-44aa-853a-6d8fa1ba5244","year":2006},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.053435Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:8fac5b1adc116402548dfe0d0c9d4d6625a2a32cd466f1dcb835607ec7857506","observation_id":"47ee759f-cc7e-4ac0-83f3-2e59763c084a","resolution":{"observed_at":"2026-08-14T13:24:40.290695Z","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":"2026-08-14T13:24:40.273055Z","title":"I , Zweite Auflage","venue":null,"work_id":"3edeaebd-486a-4202-b53d-f7ee901ff797","year":1968},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.058101Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:b6a9e70105242ce278526fd134882de13cb6859fe70466aca4291f5f13156b56","observation_id":"3bd88c26-76da-4f04-b72b-0cfd03139e52","resolution":{"observed_at":"2026-08-14T13:24:40.276981Z","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":"2026-08-14T13:24:40.258822Z","title":"II , Zweite Auflage","venue":null,"work_id":"16bd3d22-e801-4338-afdb-8d6a1b7d909e","year":1970},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.064446Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:16025fc765bc2bb0051007df0586ea3de60845502efb3a465b952ccb8f00c7a7","observation_id":"8976ef66-9f1a-4522-9795-e4a304217de0","resolution":{"observed_at":"2026-08-14T13:24:40.262620Z","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":"2026-08-14T13:24:40.242337Z","title":"Thesis (Ph.D.)–The University of Wisconsin - Madison","venue":null,"work_id":"fcdeb3c5-d7cd-4ef1-a505-3939b25e2cf5","year":2008},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.069502Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:d851dc27a086ec027fdb9bbfabd234f226cc00adbb8a3b927f89c4d08ca573a8","observation_id":"65037731-25d0-4ba9-982d-c6da76c60ae4","resolution":{"observed_at":"2026-08-14T13:24:40.249911Z","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":"2026-08-14T13:24:40.227921Z","title":"87, American Mathematical Society, Providen ce, RI; Mathematics Advanced Study Semesters, University Park, PA, 2018","venue":null,"work_id":"f6c788bf-cf9c-4d7c-b04f-e2a4f681f484","year":2018},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.074215Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:5aab75a42adca4a7c517285eff9ca811f6bab554a6fb0df520923f7ed5577821","observation_id":"a808be8d-306b-42db-921c-320eaa620a87","resolution":{"observed_at":"2026-08-14T13:24:40.232565Z","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":"2026-08-14T13:24:40.208539Z","title":"Kelley, General topology, Springer-Verlag, 1975","venue":null,"work_id":"84faf1e6-84e7-4663-a249-7a5ed110f8e8","year":1975},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.079171Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:08637f4ee387a67c3e193046851f027d6f794ccb8582f92e1b794ad954d871a1","observation_id":"c47f339b-c4cd-4aa2-82e8-6d2abac9206e","resolution":{"observed_at":"2026-08-14T13:24:40.216199Z","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":"2026-08-14T13:24:40.190507Z","title":"Notes Log., vol","venue":null,"work_id":"4a2b2a27-b569-410e-a3b8-c36f66f5e47c","year":2002},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.083624Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:42bcebb3af7ac80fd9b759579fa0badc83ba06b55a18f326f822bc22a19ff7f6","observation_id":"b956ad8c-ee6b-4e6d-ab12-efc16050e19a","resolution":{"observed_at":"2026-08-14T13:24:40.196543Z","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":"2026-08-14T13:24:40.170967Z","title":"Notes Log., vol","venue":null,"work_id":"4e558fc7-b0f2-4d1c-800c-f94f2069b7b2","year":2001},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.088464Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:82abfa5d86b4a756639c542a215ad13008d93e761ec9b75334f74ce8268e4155","observation_id":"e1e0c8c8-d3df-4f55-9173-99fd602985fd","resolution":{"observed_at":"2026-08-14T13:24:40.176158Z","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":"2026-08-14T13:24:39.987750Z","title":"Kreisel and A","venue":null,"work_id":"2f58de44-6ad4-4a20-b7a8-604207fbcec7","year":1970},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.093964Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:a3c03ff6d2f16ec9f9a692b82519229c2f5919c7b682ec907509f4f26eb059eb","observation_id":"a6b7cb88-bf05-40db-aa9c-1f5b690aad8d","resolution":{"observed_at":"2026-08-14T13:24:39.993482Z","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":"2026-08-14T13:24:39.970599Z","title":null,"venue":null,"work_id":"f2c912e9-e1ef-4304-b5d0-00e73b98af04","year":1989},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.098142Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:f32e5d74063d00e62a73b4694043efa284bc037b4059d25aacd28da7d9a0eea3","observation_id":"c06f0c27-8601-41f1-a5d0-7cb2eaefbb84","resolution":{"observed_at":"2026-08-14T13:24:39.974770Z","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":"2026-08-14T13:24:39.948689Z","title":null,"venue":null,"work_id":"e79f6787-c747-4f63-9117-a02adfe208f5","year":1922},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.101981Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:fe1f9125263a7d13b9fd40b81a9aefe64d25e53fbff70acdab5435c9bdb89ebb","observation_id":"8b96f41a-62ea-4ba3-a363-e039ab24dbdd","resolution":{"observed_at":"2026-08-14T13:24:39.954546Z","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":"2026-08-14T13:24:39.928844Z","title":"Muldowney, A general theory of integration in function spaces, includi ng Wiener and Feynman integration, Vol","venue":null,"work_id":"bd890e87-2be2-45a3-baa7-48b5d5860a0d","year":1987},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.105763Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:802f76fb3b47d0d863a0b56f03689852b296e3d58d072397b2b88409058c5391","observation_id":"fe1c447f-52c7-4772-a0eb-9c10b1c511d1","resolution":{"observed_at":"2026-08-14T13:24:39.935071Z","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":"10.1142/s0219061319500016","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:24:39.309983Z","title":null,"venue":null,"work_id":"b9cee42b-6e79-4064-946a-c61067bd6e1c","year":2019},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.109472Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:d093bfacf2de1230934b6e2f76301742f543ed9363d58616056b9561439cff91","observation_id":"bb24d492-1fd1-43c5-803d-3e7737e819ab","resolution":{"observed_at":"2026-08-14T13:24:39.315583Z","resolver_source":"doi","status":"verified_exact"},"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":{"arxiv_id":"1902.02756","last_updated":"2022-04-05T13:02:08Z","snapshot_observed_at":"2026-08-16T12:13:18.382220Z","submitted_at":"2019-02-07T18:26:56Z","title":"On the logical and computational properties of the Vitali covering theorem","version":4},"cited_work":{"arxiv_id":"1902.02756","doi":null,"metadata_source":"pith","pith_arxiv_id":"1902.02756","snapshot_observed_at":"2026-08-14T13:24:39.401408Z","title":"On the logical and computational properties of the Vitali covering theorem","venue":"math.LO","work_id":"b2837155-b1e6-4463-b10c-4f4c62642f8d","year":2019},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.113392Z"},"links":{"cited_paper":"/paper/1902.02756","citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:a24b4198dc87e9010cdccef1da4118db31794f3dd2fc2a75742b135ae7b05ff0","observation_id":"5b891e7b-4d47-40c6-9b61-94125fd070af","resolution":{"observed_at":"2026-08-14T13:24:39.407646Z","resolver_source":"local_arxiv","status":"verified_exact"},"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":"2026-08-14T13:24:39.909206Z","title":null,"venue":null,"work_id":"5f6a1cb1-721a-4d90-a468-f863f455be2f","year":2020},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.117818Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:6aafa319daaef528c1aad287d5857883840d057b0cc306ad56b31f137610c045","observation_id":"7288f39d-8041-4f63-bfb1-b915a1eede79","resolution":{"observed_at":"2026-08-14T13:24:39.916807Z","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":"2026-08-14T13:24:39.886767Z","title":"Pure Appl","venue":null,"work_id":"19f14a32-4b21-46a3-b7e1-3e0798288ae2","year":2020},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.122262Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:c081b21830b3d140c0cc6a89d7f53a82c3b5229b6830e67cdb845af0430c6cb0","observation_id":"410f42a4-ec2e-472e-a8e4-90405d917b00","resolution":{"observed_at":"2026-08-14T13:24:39.896069Z","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":{"arxiv_id":"2006.01614","last_updated":"2020-11-03T15:05:21Z","snapshot_observed_at":"2026-08-09T06:53:16.923031Z","submitted_at":"2020-05-30T08:47:49Z","title":"The Axiom of Choice in Computability Theory and Reverse Mathematics, with a cameo for the Continuum Hypothesis","version":2},"cited_work":{"arxiv_id":"2006.01614","doi":null,"metadata_source":"pith","pith_arxiv_id":"2006.01614","snapshot_observed_at":"2026-08-14T13:24:39.381266Z","title":"The Axiom of Choice in Computability Theory and Reverse Mathematics, with a cameo for the Continuum Hypothesis","venue":"math.LO","work_id":"a2d8cfb5-2444-4172-ba7a-d94527e8e39d","year":2020},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.126312Z"},"links":{"cited_paper":"/paper/2006.01614","citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:711f3f81693c45317b1bed0aeda0cde4064eacd7a5df7597f8de19a4aa74e4c7","observation_id":"df439b0e-0cb0-4ab7-acfc-b6984f681b14","resolution":{"observed_at":"2026-08-14T13:24:39.385917Z","resolver_source":"local_arxiv","status":"verified_exact"},"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":"2026-08-14T13:24:39.862881Z","title":null,"venue":null,"work_id":"d5436dab-69de-49b3-ab87-e1ce6c9a61ec","year":2020},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.132280Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:e85bcd11a3e16fd75ab718c75d5f5dfba777febd2f7dca343de5e7bc454174a6","observation_id":"be0f5d0f-b792-47ea-aee4-5ea676966521","resolution":{"observed_at":"2026-08-14T13:24:39.868086Z","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":"2026-08-14T13:24:39.842734Z","title":"Rado, Axiomatic treatment of rank in infinite sets , Canadian J","venue":null,"work_id":"6be38ade-b560-47bf-b778-df0a5dbffd4c","year":1949},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.137379Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:16bd27b2d825bce6a53d93a3bef0f15f5aa794e12681fb0ac5062cf9e605b278","observation_id":"353de0a4-2fbb-4812-b4de-81e28e1c5dd5","resolution":{"observed_at":"2026-08-14T13:24:39.849261Z","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":"2026-08-14T13:24:39.822143Z","title":null,"venue":null,"work_id":"c5c327c0-35a3-4e66-baaf-577b11aebc3b","year":1988},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.144459Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:869d17c3a6fad3b8297a269676ed56b0284df1fe0d32edc05e162f1019324e20","observation_id":"af69942d-1c82-4325-bee2-2cbc4e6eac7a","resolution":{"observed_at":"2026-08-14T13:24:39.827390Z","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":"2026-08-14T13:24:39.795209Z","title":null,"venue":null,"work_id":"ab87c543-a1d0-4e89-95d8-59268e3081e0","year":1987},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.149260Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:9888b26f9810d9ac5690fe24f4796f2df0925a150c47571e2229bdce4c24a25e","observation_id":"7974fa49-8ba6-49c5-aa45-354a6ca699d9","resolution":{"observed_at":"2026-08-14T13:24:39.804140Z","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":"2026-08-14T13:24:39.770761Z","title":null,"venue":null,"work_id":"74f2225e-28b4-4183-b10b-cd7d3c10f7c3","year":2004},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.154262Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:9d167ecb7e9d0120f0ce034b4fde2196ded83a7344c7f7be43593ba8a59247e9","observation_id":"90857e6c-1b6f-4fee-ab89-c450a11966f4","resolution":{"observed_at":"2026-08-14T13:24:39.778719Z","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":"2026-08-14T13:24:39.749588Z","title":null,"venue":null,"work_id":"37b2b8e1-b54c-4c3f-99d7-c8042f7ae26e","year":2019},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.159534Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:c82556b9b7a193c917344767fb95235c26a4a7b8c77a18f7e8cd06ab5a5684ed","observation_id":"e980d26f-72e6-4b54-8979-440a6b4da688","resolution":{"observed_at":"2026-08-14T13:24:39.756372Z","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":"2026-08-14T13:24:39.721711Z","title":null,"venue":null,"work_id":"f87eacbe-890f-42b5-a572-c24dde62ee37","year":2019},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.163947Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:5e3c6021bd35a14729bc8d884265eb136201cfee05f81449776f2aa6e2e518ef","observation_id":"e16780cb-4478-4c40-8ae0-bec0109ba657","resolution":{"observed_at":"2026-08-14T13:24:39.731427Z","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":"10.3233/com-190265","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:24:39.288785Z","title":null,"venue":null,"work_id":"96518524-bac8-4f3a-be8d-ee431dce74cb","year":2019},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.168957Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:c6eecfd9369c5a2e1696f0ae3420a25d9f64f176fbc81aa0468b5bf28fdc3a62","observation_id":"86177026-9428-4acf-90c6-b0a7948b6d05","resolution":{"observed_at":"2026-08-14T13:24:39.295199Z","resolver_source":"doi","status":"verified_exact"},"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":{"arxiv_id":"1908.05676","last_updated":"2020-08-13T10:18:01Z","snapshot_observed_at":"2026-08-16T04:43:06.395582Z","submitted_at":"2019-08-15T12:33:48Z","title":"Plato and the foundations of mathematics","version":6},"cited_work":{"arxiv_id":"1908.05676","doi":null,"metadata_source":"pith","pith_arxiv_id":"1908.05676","snapshot_observed_at":"2026-08-14T13:24:39.359205Z","title":"Plato and the foundations of mathematics","venue":"math.LO","work_id":"b30c9d87-4d05-4292-be0a-bc7a0b7bec19","year":2019},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.173397Z"},"links":{"cited_paper":"/paper/1908.05676","citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:cda4a83f9c4999f3de342aae0bc2c6f8fd0b2d0c027db1c187a05a0b3eeb34f0","observation_id":"f040861a-1772-4e1e-810e-f29dc5b3c892","resolution":{"observed_at":"2026-08-14T13:24:39.364489Z","resolver_source":"local_arxiv","status":"verified_exact"},"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":"2026-08-14T13:24:39.701430Z","title":null,"venue":null,"work_id":"cb6eae94-4bb0-43d3-b4ac-f917605c6104","year":2020},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.177697Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:b7c4be2972800b382551af781b569a092957d4b0539b243df6f496c7b84fbe3d","observation_id":"6bc23362-cb45-404d-8e94-c11e083938b5","resolution":{"observed_at":"2026-08-14T13:24:39.710184Z","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":"2026-08-14T13:24:39.676044Z","title":null,"venue":null,"work_id":"159e422f-1c9f-4878-a188-eb7343f40b17","year":2020},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.181365Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:578b5cd196f62e1bb73aa202ca5fd3ff28415db2d734ea8011af2778c5d4a064","observation_id":"bb20fe12-af03-4375-ad4d-28c8a71f1326","resolution":{"observed_at":"2026-08-14T13:24:39.685367Z","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":{"arxiv_id":"1808.08785","last_updated":"2020-05-28T06:54:35Z","snapshot_observed_at":"2026-08-16T10:57:46.182524Z","submitted_at":"2018-08-27T11:17:44Z","title":"Reverse Mathematics of topology: dimension, paracompactness, and splittings","version":3},"cited_work":{"arxiv_id":"1808.08785","doi":null,"metadata_source":"pith","pith_arxiv_id":"1808.08785","snapshot_observed_at":"2026-08-14T13:24:39.333110Z","title":"Reverse Mathematics of topology: dimension, paracompactness, and splittings","venue":"math.LO","work_id":"2e5f9477-b091-497e-b47c-6282ab4bd38e","year":2018},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.185734Z"},"links":{"cited_paper":"/paper/1808.08785","citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:6492ddfd155cdae202890fda71dfea3c75bbd045265d885e546c7ece6f965e08","observation_id":"14251db5-9bff-454b-a3cf-c806d57e38f0","resolution":{"observed_at":"2026-08-14T13:24:39.339849Z","resolver_source":"local_arxiv","status":"verified_exact"},"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":"2026-08-14T13:24:39.658388Z","title":"Simpson and J","venue":null,"work_id":"8fb4ff8d-7630-4d3d-9ea1-6493b31b78df","year":1998},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.190262Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:de4886353912d22bafd05879fbfeea3a6deabd68074cd118d203cb4b4ed02350","observation_id":"91c716d5-2b20-49ec-a7b8-fbc2a7b431c2","resolution":{"observed_at":"2026-08-14T13:24:39.662465Z","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":"2026-08-14T13:24:39.640415Z","title":"Simpson (ed.), Reverse mathematics 2001 , Lecture Notes in Logic, vol","venue":null,"work_id":"e56fa74e-eb1f-445c-a960-c4a1bc15a4e7","year":2001},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.195501Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:fb1bdfb56defcf2298bb2dd49f3d4b09458e098ed3af5c4897f72883cb4b3689","observation_id":"86e62ad6-ee8e-4c4c-8b61-bfb3b4757e2e","resolution":{"observed_at":"2026-08-14T13:24:39.646503Z","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":"2026-08-14T13:24:39.622405Z","title":null,"venue":null,"work_id":"f360a255-267e-402b-95af-2da76187c4e3","year":2009},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.201032Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:7ad6aa4e98108e0b2f11a727e0fd79730c7fce35a20cdd6bbcb1fb3e603a63a8","observation_id":"78c14e39-d91a-4302-b97c-4a55897c5937","resolution":{"observed_at":"2026-08-14T13:24:39.627435Z","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":"2026-08-14T13:24:39.606761Z","title":"Symbolic Logic 14 (1949), 145–158 (German)","venue":null,"work_id":"1643bdda-daaf-4909-97fe-9813405d3f77","year":1949},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.205750Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:3ee48996942adc86e4d2caf88aaefbbc9479344ee99fb990f8158a6fcfd6db69","observation_id":"453937e6-6a69-4de5-aed4-9352cc430bfa","resolution":{"observed_at":"2026-08-14T13:24:39.612227Z","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":"2026-08-14T13:24:39.578737Z","title":"Stillwell, Reverse mathematics, proofs from the inside out , Princeton Univ","venue":null,"work_id":"fbc9ec2f-44df-4a69-9fc6-3eb68de10366","year":2018},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.209974Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:494d2189e0a4c5f6892d55d7e39a2a83be37f1d4c62ca9fe9c1d327ac75d5f8f","observation_id":"6ab8e14c-5e8d-4d62-9080-6cd84e385216","resolution":{"observed_at":"2026-08-14T13:24:39.588279Z","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":"2026-08-14T13:24:39.559263Z","title":null,"venue":null,"work_id":"c1b3764c-5c38-49c1-b8c1-e25f0cd9b91a","year":2001},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.216075Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:87d29b6a5db99de8972de8c69a338152b6c24266e11e4c5fa284086f99734d7a","observation_id":"fc0c43e0-e8a4-4320-81a7-9944b2aa43c3","resolution":{"observed_at":"2026-08-14T13:24:39.565956Z","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":"2026-08-14T13:24:39.538329Z","title":"81, North-Holland, 1987","venue":null,"work_id":"26c5cedb-5ba2-4ae2-8b56-cb99f3b3a49e","year":1987},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.220735Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:00614f213dd0a1edfe0c254a4984951b2159b43e286935aea4141d3dc9c4d561","observation_id":"7d6f0a66-1035-4bcd-a6e5-4638e58e2cde","resolution":{"observed_at":"2026-08-14T13:24:39.545707Z","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":"2026-08-14T13:24:39.512330Z","title":"Lecture Notes in Mathematics, Vol","venue":null,"work_id":"c97e576e-0d5c-4ef3-8c3e-1fb4f16cbe4d","year":1973},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.225662Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:a37a0dfee8db934c52a1484874dcece4c8ac3ff3b312670b15cafe0716a3622a","observation_id":"fecbba77-5ab2-4ec2-ba4b-f34ec7026353","resolution":{"observed_at":"2026-08-14T13:24:39.518847Z","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":"2026-08-14T13:24:39.492595Z","title":null,"venue":null,"work_id":"916aa73e-9b08-47a4-8aef-b88edeedf118","year":1988},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.230825Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:feca6c49b2506b8e24002cb5805429186f9ad4fb45cef754bab1952ca082b9bc","observation_id":"c5c1d959-2ab8-45ee-a00e-36716755ea55","resolution":{"observed_at":"2026-08-14T13:24:39.496797Z","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":"2026-08-14T13:24:39.467285Z","title":null,"venue":null,"work_id":"e4a742ac-61bb-4b4e-9b42-24e923762284","year":1936},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.238487Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:76d5b226225d06020137482cbe18442c2aac5eb511f290ef3b619224667a6eba","observation_id":"325f7eaa-44db-483a-97da-233c38574026","resolution":{"observed_at":"2026-08-14T13:24:39.475106Z","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":"2026-08-14T13:24:39.435646Z","title":null,"venue":null,"work_id":"8b113248-b044-4729-b0e4-8954ad12c7ed","year":1921},"citing_paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics","version":4},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-14T13:24:39.243859Z"},"links":{"citing_paper":"/paper/1908.05677"},"observation_digest":"sha256:93ee63a7613ce76f76ba91a95efd522d27db0a8d17d9e3b616e23bc293ddfa64","observation_id":"9105216f-ab9a-49af-869c-007408ea3b53","resolution":{"observed_at":"2026-08-14T13:24:39.447306Z","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"}}],"paper":{"arxiv_id":"1908.05677","last_updated":"2020-06-21T19:39:10Z","latest_version":4,"primary_category":"math.LO","snapshot_observed_at":"2026-08-16T14:19:24.225341Z","submitted_at":"2019-08-15T12:50:20Z","title":"Lifting countable to uncountable mathematics"},"reference_resolution":{"displayed":59,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":20,"verified_exact":7,"verified_fuzzy":32},"total_outbound_references":59},"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 59 of 59 outbound references and 1 inbound Pith citation observation for arXiv:1908.05677."}