{"as_of":"2026-08-16T20:25:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:2243a2c4b46c67c54c70f5e1dbc596d9e831105140b583e325853d9906de2b4f","coverage":[{"denominator":65,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":65,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T13:12:02.715811Z","state":"measured"},{"denominator":66,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":66,"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":"2026-08-15T18:59:43.800895Z","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":"2026-08-15T18:59:45.129069Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"cited_work":{"arxiv_id":"1908.05573","doi":null,"metadata_source":"pith","pith_arxiv_id":"1908.05573","snapshot_observed_at":"2026-08-15T18:59:45.129069Z","title":"Random surfaces and Liouville quantum gravity","venue":"math.PR","work_id":"36ada197-aebb-491c-9a66-e30369d0fd7f","year":2019},"citing_paper":{"arxiv_id":"2506.18827","last_updated":"2026-06-30T02:14:53Z","snapshot_observed_at":"2026-08-16T16:09:47.977164Z","submitted_at":"2025-06-23T16:41:47Z","title":"Random walk reflected off of infinity, with applications to uniform spanning forests and supercritical Liouville quantum gravity","version":2},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-08-15T18:59:43.800895Z"},"links":{"cited_paper":"/paper/1908.05573","citing_paper":"/paper/2506.18827"},"observation_digest":"sha256:e514a96f628e46cb30acd9f6e4431db034ad7eb1637a265e0736899d61b9dd18","observation_id":"ff5168e3-b26f-4635-bb2f-1a79fec36dac","resolution":{"observed_at":"2026-08-15T18:59:45.143393Z","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"}}],"links":{"evidence":"/evidence","html":"/paper/1908.05573/citation-record","integrity":"/paper/1908.05573/integrity","json":"/paper/1908.05573/citation-record.json","paper":"/paper/1908.05573"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:12:03.623521Z","title":null,"venue":null,"work_id":"e710dbfa-e3b0-4453-8d93-bce6d2c1f0b3","year":2003},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.456894Z"},"links":{"citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:da7a5e2f696ced6f5eab8207a7d6a6949d3748a19ea77792e86905fc5cf5deb1","observation_id":"a784d2e6-47fc-4b05-898c-c437bc823c94","resolution":{"observed_at":"2026-08-14T13:12:03.627647Z","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":"1904.09285","last_updated":"2019-04-19T17:50:09Z","snapshot_observed_at":"2026-08-16T09:10:14.523281Z","submitted_at":"2019-04-19T17:50:09Z","title":"Comparison of discrete and continuum Liouville first passage percolation","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1904.09285","snapshot_observed_at":"2026-08-14T13:12:02.462987Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.462987Z"},"links":{"cited_paper":"/paper/1904.09285","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:6f49476f4f2fd1799a9eb622112998b8ef87a234a843a0fb7579b1e829dccc86","observation_id":"cf77f433-ee3b-4917-b59c-fdd526a85f71","resolution":{"observed_at":"2026-08-14T13:12:02.462987Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1709.04355","last_updated":"2020-04-29T07:06:49Z","snapshot_observed_at":"2026-08-15T13:42:54.432853Z","submitted_at":"2017-09-13T14:38:11Z","title":"Gaussian multiplicative chaos through the lens of the 2D Gaussian free field","version":3},"cited_work":{"arxiv_id":"1709.04355","doi":null,"metadata_source":"pith","pith_arxiv_id":"1709.04355","snapshot_observed_at":"2026-08-14T13:12:03.418001Z","title":"Gaussian multiplicative chaos through the lens of the 2D Gaussian free field","venue":"math.PR","work_id":"c9012cc3-3b6a-4342-a4d9-7af57843e28a","year":2017},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.467371Z"},"links":{"cited_paper":"/paper/1709.04355","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:3f73fa5cba874456805a8f0257620f9a2e681d236e678c13e485959a0085bfcc","observation_id":"87478785-cbed-4584-b9bb-3772055870e0","resolution":{"observed_at":"2026-08-14T13:12:03.422755Z","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":{"arxiv_id":"1908.09469","last_updated":"2019-08-26T04:51:46Z","snapshot_observed_at":"2026-08-15T21:09:39.574765Z","submitted_at":"2019-08-26T04:51:46Z","title":"Precision measurements of Hausdorff dimensions in two-dimensional quantum gravity","version":1},"cited_work":{"arxiv_id":"1908.09469","doi":null,"metadata_source":"pith","pith_arxiv_id":"1908.09469","snapshot_observed_at":"2026-08-14T13:12:03.399749Z","title":"Precision measurements of Hausdorff dimensions in two-dimensional quantum gravity","venue":"gr-qc","work_id":"c2bd7ec2-d5d0-4cf1-9670-3c2e24b4760b","year":2019},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.471635Z"},"links":{"cited_paper":"/paper/1908.09469","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:030e3b4b434a37b8d0b9686cd254eb73e97b136df62ee05af47fc298c9d8c1d9","observation_id":"a67c00df-1787-4d5b-ac2e-d2edcaaace85","resolution":{"observed_at":"2026-08-14T13:12:03.404787Z","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":{"arxiv_id":"math/0405099","last_updated":"2004-09-07T13:39:24Z","snapshot_observed_at":"2026-07-07T05:40:51.678048Z","submitted_at":"2004-05-06T15:35:03Z","title":"Planar maps as labeled mobiles","version":3},"cited_work":{"arxiv_id":"math/0405099","doi":null,"metadata_source":"pith","pith_arxiv_id":"math/0405099","snapshot_observed_at":"2026-08-14T13:12:03.380752Z","title":"Planar maps as labeled mobiles","venue":"math.CO","work_id":"1c709256-07c4-4728-84b5-e227af7e8a9f","year":2004},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.475945Z"},"links":{"cited_paper":"/paper/math/0405099","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:297e4c7fe8cad208cceb4bd64cfeab0c8c48d115e4476a9d7d4effd2fe9b87ef","observation_id":"7d6c584e-1c19-4f53-9489-8d3483c96469","resolution":{"observed_at":"2026-08-14T13:12:03.385668Z","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":"2026-08-14T13:12:03.611589Z","title":"Berestycki","venue":null,"work_id":"026a16a6-d7bc-4045-ac85-37696299c8a1","year":null},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.480165Z"},"links":{"citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:da248c73e8c4471eb7d1b14340e897a51f0c686424b79d851b6a31b18fd2c98a","observation_id":"754e386f-7be6-4fb0-8560-5c641fbb2790","resolution":{"observed_at":"2026-08-14T13:12:03.615812Z","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":"2026-08-14T13:12:03.600518Z","title":"Bernardi","venue":null,"work_id":"ec433a27-b094-4048-b658-9d126a018f74","year":2007},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.484519Z"},"links":{"citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:553b98332e002e50c6851d1f6a91699b563f292d39a8786ee2fd3ac2fa8b2b22","observation_id":"6da56f9c-6e68-4500-ac57-221ee9575e3d","resolution":{"observed_at":"2026-08-14T13:12:03.604185Z","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":"math/0601684","last_updated":"2006-01-27T18:51:04Z","snapshot_observed_at":"2026-08-15T17:56:21.250555Z","submitted_at":"2006-01-27T18:51:04Z","title":"Bijective counting of tree-rooted maps and shuffles of parenthesis systems","version":1},"cited_work":{"arxiv_id":"math/0601684","doi":null,"metadata_source":"pith","pith_arxiv_id":"math/0601684","snapshot_observed_at":"2026-08-14T13:12:03.363850Z","title":"Bijective counting of tree-rooted maps and shuffles of parenthesis systems","venue":"math.CO","work_id":"a82d8ab2-2df8-4af5-973f-9b147d9cd57d","year":2006},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.488670Z"},"links":{"cited_paper":"/paper/math/0601684","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:d354783ef41b99d7ed71bee42b24c464fec1ec2f2bfdbe42768c17df1cb1b40c","observation_id":"ddcdff88-9d09-4bb1-ae21-07a6b70016be","resolution":{"observed_at":"2026-08-14T13:12:03.367958Z","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":{"arxiv_id":"1506.09113","last_updated":"2017-10-27T20:01:37Z","snapshot_observed_at":"2026-08-14T22:42:20.953253Z","submitted_at":"2015-06-30T14:56:58Z","title":"An elementary approach to Gaussian multiplicative chaos","version":2},"cited_work":{"arxiv_id":"1506.09113","doi":null,"metadata_source":"pith","pith_arxiv_id":"1506.09113","snapshot_observed_at":"2026-08-14T13:12:03.347196Z","title":"An elementary approach to Gaussian multiplicative chaos","venue":"math.PR","work_id":"30dd6b6a-d2ee-4f7e-a7fa-830b4c0cf540","year":2015},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.492985Z"},"links":{"cited_paper":"/paper/1506.09113","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:99ea493fadb47566ef755395990539c754785661b191fb5c5f9ecc607a26eda3","observation_id":"45346790-fba7-4f09-8891-637effc2350a","resolution":{"observed_at":"2026-08-14T13:12:03.352201Z","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":{"arxiv_id":"1807.01684","last_updated":"2021-06-02T17:57:28Z","snapshot_observed_at":"2026-08-16T01:36:02.715957Z","submitted_at":"2018-07-04T17:05:36Z","title":"Percolation on triangulations: a bijective path to Liouville quantum gravity","version":5},"cited_work":{"arxiv_id":"1807.01684","doi":null,"metadata_source":"pith","pith_arxiv_id":"1807.01684","snapshot_observed_at":"2026-08-14T13:12:03.330875Z","title":"Percolation on triangulations: a bijective path to Liouville quantum gravity","venue":"math.PR","work_id":"8e037f0c-e83a-452f-8504-362df97b8fa5","year":2018},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.497353Z"},"links":{"cited_paper":"/paper/1807.01684","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:cf5eb91f695a5a534186467d1bc5ad290faf597fd48058733cc93be2b6025761","observation_id":"86ad136a-50c4-469d-9d40-f848bd39e9db","resolution":{"observed_at":"2026-08-14T13:12:03.335696Z","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":{"arxiv_id":"1202.5296","last_updated":"2013-02-25T14:32:41Z","snapshot_observed_at":"2026-08-15T04:18:18.231295Z","submitted_at":"2012-02-23T20:46:55Z","title":"Gaussian multiplicative chaos and KPZ duality","version":4},"cited_work":{"arxiv_id":"1202.5296","doi":null,"metadata_source":"pith","pith_arxiv_id":"1202.5296","snapshot_observed_at":"2026-08-14T13:12:03.313205Z","title":"Gaussian multiplicative chaos and KPZ duality","venue":"math.PR","work_id":"6c140edb-2efd-4bee-80c7-15add8051042","year":2012},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.501363Z"},"links":{"cited_paper":"/paper/1202.5296","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:ce0ef063a51f11f8a67c899e4db185382a7bd6206efe6512ef289f55f4c12564","observation_id":"7e771e72-8f9d-4ef1-95ba-028d36bba88c","resolution":{"observed_at":"2026-08-14T13:12:03.317386Z","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":"2026-08-14T13:12:03.589188Z","title":"B erestycki and J","venue":null,"work_id":"4ce049ef-0dfa-43b4-a991-0d7b81fb2b71","year":null},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.505525Z"},"links":{"citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:18f0c9a2225a0cc67a0a1d49ed46ec21295c8f91534ef6df81f694cc97865433","observation_id":"cfd2d1a0-2fcf-4977-a11e-266d98908fcc","resolution":{"observed_at":"2026-08-14T13:12:03.592887Z","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":"2026-08-14T13:12:03.578534Z","title":null,"venue":null,"work_id":"eac559ae-8c82-4f12-9631-0be8317468b4","year":1955},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.509376Z"},"links":{"citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:19c21ff3d114cef34008de50e50876826b59bd7215250da4362859c3d073fea6","observation_id":"402b3e45-33be-4fc3-8e3a-f02900ed9107","resolution":{"observed_at":"2026-08-14T13:12:03.582272Z","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":"2026-08-14T13:12:03.565428Z","title":null,"venue":null,"work_id":"029387ec-2f44-41d7-8372-c4dcd077b02e","year":2016},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.513357Z"},"links":{"citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:b98273ca45ed98f577332438a08290033948e8d77384eee0659fb23715bdb535","observation_id":"17de3aa5-1ffa-42df-bce6-1e811a37195c","resolution":{"observed_at":"2026-08-14T13:12:03.570268Z","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":"1904.08021","last_updated":"2020-11-16T20:17:19Z","snapshot_observed_at":"2026-08-14T16:45:20.609650Z","submitted_at":"2019-04-16T23:45:42Z","title":"Tightness of Liouville first passage percolation for $\\gamma \\in (0,2)$","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1904.08021","snapshot_observed_at":"2026-08-14T13:12:02.516899Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.516899Z"},"links":{"cited_paper":"/paper/1904.08021","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:a355517ba38d08038289489104910684549133460f90699b3b64996713650746","observation_id":"4902cdc5-e1d0-4f8b-8409-0f9195c1c88f","resolution":{"observed_at":"2026-08-14T13:12:02.516899Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1905.00380","last_updated":"2020-06-02T15:48:21Z","snapshot_observed_at":"2026-08-14T16:38:40.804753Z","submitted_at":"2019-05-01T17:00:00Z","title":"Weak LQG metrics and Liouville first passage percolation","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1905.00380","snapshot_observed_at":"2026-08-14T13:12:02.520751Z","title":"Dub \\'e dat, H","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.520751Z"},"links":{"cited_paper":"/paper/1905.00380","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:833ca805342a733bb72db69efa863ae85b94c3da3e37e1f82e8b807bad17f335","observation_id":"ffc6ae66-3979-4d58-a459-44a05bd82994","resolution":{"observed_at":"2026-08-14T13:12:02.520751Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1610.09998","last_updated":"2018-08-01T18:01:20Z","snapshot_observed_at":"2026-08-16T01:41:08.476388Z","submitted_at":"2016-10-31T16:21:35Z","title":"Upper bounds on Liouville first passage percolation and Watabiki's prediction","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1610.09998","snapshot_observed_at":"2026-08-14T13:12:02.524663Z","title":"Ding and S","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.524663Z"},"links":{"cited_paper":"/paper/1610.09998","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:396f074a2c1004c5ae776f31392ee8612dbb931f13b69a76a1577515a224c8e7","observation_id":"534b607c-ebe3-434c-ad5f-5120ae183582","resolution":{"observed_at":"2026-08-14T13:12:02.524663Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1807.01072","last_updated":"2019-04-22T11:04:07Z","snapshot_observed_at":"2026-08-16T01:33:29.241395Z","submitted_at":"2018-07-03T10:37:38Z","title":"The fractal dimension of Liouville quantum gravity: universality, monotonicity, and bounds","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1807.01072","snapshot_observed_at":"2026-08-14T13:12:02.529558Z","title":"Ding and E","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.529558Z"},"links":{"cited_paper":"/paper/1807.01072","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:a3781bbc8b4676495a55f8e5b054d5be25dc4446499fbe71e383c6d9706c7d9a","observation_id":"150ac723-f12c-4ea2-bcf0-944954eca6fb","resolution":{"observed_at":"2026-08-14T13:12:02.529558Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1410.7318","last_updated":"2015-06-05T16:36:27Z","snapshot_observed_at":"2026-08-16T14:42:15.955926Z","submitted_at":"2014-10-27T17:14:03Z","title":"Liouville Quantum Gravity on the Riemann sphere","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1410.7318","snapshot_observed_at":"2026-08-14T13:12:02.533519Z","title":"David, A","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.533519Z"},"links":{"cited_paper":"/paper/1410.7318","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:4c754e2223dab278d72e381040fd087b241e98601fafcf35a84c235672db4dfa","observation_id":"0d7290fe-71ff-474c-969a-37c9dcb342fd","resolution":{"observed_at":"2026-08-14T13:12:02.533519Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1409.7055","last_updated":"2020-08-18T21:52:15Z","snapshot_observed_at":"2026-08-16T02:54:38.329870Z","submitted_at":"2014-09-24T19:50:15Z","title":"Liouville quantum gravity as a mating of trees","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1409.7055","snapshot_observed_at":"2026-08-14T13:12:02.537540Z","title":"Duplantier , J","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.537540Z"},"links":{"cited_paper":"/paper/1409.7055","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:8ec20dc18762b43516e0ef4d184d6468ad86ee785e0bfe49b4fd158a3c4c4f0a","observation_id":"f4d86498-8ff9-4fa6-8221-528b0009d16c","resolution":{"observed_at":"2026-08-14T13:12:02.537540Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1407.5605","last_updated":"2014-07-21T19:21:30Z","snapshot_observed_at":"2026-08-14T23:25:58.394426Z","submitted_at":"2014-07-21T19:21:30Z","title":"Log-correlated Gaussian fields: an overview","version":1},"cited_work":{"arxiv_id":"1407.5605","doi":null,"metadata_source":"pith","pith_arxiv_id":"1407.5605","snapshot_observed_at":"2026-08-14T13:12:03.228127Z","title":"Log-correlated Gaussian fields: an overview","venue":"math.PR","work_id":"d78d4088-5994-4fbe-9d94-67ffdf3a16c3","year":2014},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.541377Z"},"links":{"cited_paper":"/paper/1407.5605","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:b7ba0c85ca85adf8243456a0116515618e9727906981fbdafa42dce51cf9bbce","observation_id":"7722787b-f16d-4b2e-8f5c-c9f8f7cef3a1","resolution":{"observed_at":"2026-08-14T13:12:03.233147Z","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":{"arxiv_id":"1206.1671","last_updated":"2014-09-02T13:20:05Z","snapshot_observed_at":"2026-08-15T00:57:32.378810Z","submitted_at":"2012-06-08T06:08:39Z","title":"Critical Gaussian multiplicative chaos: Convergence of the derivative martingale","version":3},"cited_work":{"arxiv_id":"1206.1671","doi":null,"metadata_source":"pith","pith_arxiv_id":"1206.1671","snapshot_observed_at":"2026-08-14T13:12:03.211708Z","title":"Critical Gaussian multiplicative chaos: Convergence of the derivative martingale","venue":"math.PR","work_id":"68eef94f-e0fc-42bd-a97d-625a479ef14b","year":2012},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.545305Z"},"links":{"cited_paper":"/paper/1206.1671","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:f8bd8a7c5757655036a6e581043aa3f43e42593dc153d3af597d779259e70611","observation_id":"682857fc-5e1d-47ec-af05-a25d5dfa4d98","resolution":{"observed_at":"2026-08-14T13:12:03.216104Z","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":{"arxiv_id":"1212.0529","last_updated":"2013-09-24T22:30:02Z","snapshot_observed_at":"2026-08-15T00:37:17.382367Z","submitted_at":"2012-12-03T20:30:17Z","title":"Renormalization of Critical Gaussian Multiplicative Chaos and KPZ formula","version":3},"cited_work":{"arxiv_id":"1212.0529","doi":null,"metadata_source":"pith","pith_arxiv_id":"1212.0529","snapshot_observed_at":"2026-08-14T13:12:03.195054Z","title":"Renormalization of Critical Gaussian Multiplicative Chaos and KPZ formula","venue":"math.PR","work_id":"d6638f59-0d84-421e-9a39-2e793304ddde","year":2012},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.549110Z"},"links":{"cited_paper":"/paper/1212.0529","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:3ff97085e035fe7c47e66eec2bcac6f9c76aeaef5234415f898079f3e28e137d","observation_id":"def02f35-06b6-441a-9f2c-2fbea61b96a5","resolution":{"observed_at":"2026-08-14T13:12:03.199699Z","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":{"arxiv_id":"1206.0212","last_updated":"2012-06-01T14:59:23Z","snapshot_observed_at":"2026-08-16T14:38:11.404084Z","submitted_at":"2012-06-01T14:59:23Z","title":"Quantum gravity and the KPZ formula","version":1},"cited_work":{"arxiv_id":"1206.0212","doi":null,"metadata_source":"pith","pith_arxiv_id":"1206.0212","snapshot_observed_at":"2026-08-14T13:12:03.178169Z","title":"Quantum gravity and the KPZ formula","venue":"math.PR","work_id":"b605d824-6308-4689-910c-8ceaa98cb510","year":2012},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.553613Z"},"links":{"cited_paper":"/paper/1206.0212","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:191ac738962d28a4f8fd0f75725ff02e5347c5b55d9793b95bd47345964c99f5","observation_id":"f980e41c-f63d-40ff-bdc9-6c01b869a1c6","resolution":{"observed_at":"2026-08-14T13:12:03.182778Z","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":"2026-08-14T13:12:03.552283Z","title":"Duplantier","venue":null,"work_id":"8d1ac757-6a89-447e-8ce6-13371797a486","year":2010},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.557317Z"},"links":{"citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:9c4281efa071ee28cf7065eedba3aa0bcd17fa1b662cea839235c70bb2486d9a","observation_id":"80e93030-712f-401f-ac6c-c44a3228fc14","resolution":{"observed_at":"2026-08-14T13:12:03.556647Z","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":"1807.00422","last_updated":"2018-07-02T00:26:16Z","snapshot_observed_at":"2026-08-15T22:42:23.799749Z","submitted_at":"2018-07-02T00:26:16Z","title":"Heat kernel for Liouville Brownian motion and Liouville graph distance","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1807.00422","snapshot_observed_at":"2026-08-14T13:12:02.561133Z","title":"Ding , O","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.561133Z"},"links":{"cited_paper":"/paper/1807.00422","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:19a780ab43686cb5050ba079688853ed00efef420641c369bd4fc4f88d7bcf58","observation_id":"9885ec3c-66f6-42a1-b788-2ca3671ba764","resolution":{"observed_at":"2026-08-14T13:12:02.561133Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1807.01512","last_updated":"2020-07-04T14:29:39Z","snapshot_observed_at":"2026-08-16T04:12:33.634218Z","submitted_at":"2018-07-04T10:47:16Z","title":"Anomalous diffusion of random walk on random planar maps","version":3},"cited_work":{"arxiv_id":"1807.01512","doi":null,"metadata_source":"pith","pith_arxiv_id":"1807.01512","snapshot_observed_at":"2026-08-14T13:12:03.150065Z","title":"Anomalous diffusion of random walk on random planar maps","venue":"math.PR","work_id":"ad42c083-72d8-47aa-8d24-7ae34b3c4c31","year":2018},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.564734Z"},"links":{"cited_paper":"/paper/1807.01512","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:61639c58cd4943ad3ca6dfabd830b08ef6071a00834be829da904419d9205460","observation_id":"1ab3f8c2-5158-422b-9eb9-02fe20e23f58","resolution":{"observed_at":"2026-08-14T13:12:03.154975Z","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":{"arxiv_id":"1711.00723","last_updated":"2020-03-11T12:06:41Z","snapshot_observed_at":"2026-08-16T01:46:53.129596Z","submitted_at":"2017-11-02T13:22:09Z","title":"A mating-of-trees approach for graph distances in random planar maps","version":3},"cited_work":{"arxiv_id":"1711.00723","doi":null,"metadata_source":"pith","pith_arxiv_id":"1711.00723","snapshot_observed_at":"2026-08-14T13:12:03.133861Z","title":"A mating-of-trees approach for graph distances in random planar maps","venue":"math.PR","work_id":"02de70c0-4c92-4eca-8df6-b6c4ff5375f0","year":2017},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.568370Z"},"links":{"cited_paper":"/paper/1711.00723","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:b1b79d9162d741c393483642383cf6adeea7fe1e17065eb159f9fb8cc7ec69ff","observation_id":"aa6ab8e0-3c20-4e52-a881-f590e4d2208a","resolution":{"observed_at":"2026-08-14T13:12:03.138286Z","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":"2026-08-14T13:12:03.539088Z","title":"Gwynne, N","venue":null,"work_id":"b63f63b6-3a89-4802-bdd5-5679683e22b6","year":2019},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.572230Z"},"links":{"citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:dd324c3c31620ea238dd0de6730a8fc34b229195f26527116682467eb0b2ff99","observation_id":"acb979ae-f133-4a5b-b0ab-16e936c0b09f","resolution":{"observed_at":"2026-08-14T13:12:03.543514Z","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":"1905.06757","last_updated":"2021-06-08T13:13:16Z","snapshot_observed_at":"2026-08-16T04:13:02.092310Z","submitted_at":"2019-05-16T13:58:10Z","title":"Joint scaling limit of site percolation on random triangulations in the metric and peanosphere sense","version":3},"cited_work":{"arxiv_id":"1905.06757","doi":null,"metadata_source":"pith","pith_arxiv_id":"1905.06757","snapshot_observed_at":"2026-08-14T13:12:03.116047Z","title":"Joint scaling limit of site percolation on random triangulations in the metric and peanosphere sense","venue":"math.PR","work_id":"9ff7a134-eb5c-40de-b6e1-dc3d5ff34d1d","year":2019},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.575807Z"},"links":{"cited_paper":"/paper/1905.06757","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:028aa18d9e7833eb7dfeaee987101b044ac161bbf004fe7b6094488807d13c0f","observation_id":"aab14716-a9d6-429e-8d8d-f0ff28189ee4","resolution":{"observed_at":"2026-08-14T13:12:03.120735Z","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":{"arxiv_id":"1711.00836","last_updated":"2020-08-25T21:24:18Z","snapshot_observed_at":"2026-08-15T22:41:14.845848Z","submitted_at":"2017-11-02T17:42:32Z","title":"Random walk on random planar maps: spectral dimension, resistance, and displacement","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1711.00836","snapshot_observed_at":"2026-08-14T13:12:02.579833Z","title":"Gwynne and J","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.579833Z"},"links":{"cited_paper":"/paper/1711.00836","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:7c0cfbe42928900817cff7a385f0c69aad40624e1dd43ca6922a127d1eeff45c","observation_id":"f603dc5d-cae6-46fc-b210-6c62b6b2c573","resolution":{"observed_at":"2026-08-14T13:12:02.579833Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1905.00381","last_updated":"2020-02-01T12:11:53Z","snapshot_observed_at":"2026-08-14T16:38:41.074808Z","submitted_at":"2019-05-01T17:01:15Z","title":"Confluence of geodesics in Liouville quantum gravity for $\\gamma \\in (0,2)$","version":3},"cited_work":{"arxiv_id":"1905.00381","doi":null,"metadata_source":"pith","pith_arxiv_id":"1905.00381","snapshot_observed_at":"2026-08-14T13:12:03.088584Z","title":"Confluence of geodesics in Liouville quantum gravity for $\\gamma \\in (0,2)$","venue":"math.PR","work_id":"1b49dfb5-c646-4e75-a4a6-731d93d698ca","year":2019},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.583806Z"},"links":{"cited_paper":"/paper/1905.00381","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:b536ab437a2f1dcc7144416fc82389c657687bf76f4dee5b8c26609079e57469","observation_id":"5b5b920c-fc5e-43ec-8811-a46efc9b8cfd","resolution":{"observed_at":"2026-08-14T13:12:03.092630Z","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":{"arxiv_id":"1905.00384","last_updated":"2020-09-09T22:46:55Z","snapshot_observed_at":"2026-08-16T03:04:01.290379Z","submitted_at":"2019-05-01T17:02:23Z","title":"Conformal covariance of the Liouville quantum gravity metric for $\\gamma \\in (0,2)$","version":2},"cited_work":{"arxiv_id":"1905.00384","doi":null,"metadata_source":"pith","pith_arxiv_id":"1905.00384","snapshot_observed_at":"2026-08-14T13:12:03.070879Z","title":"Conformal covariance of the Liouville quantum gravity metric for $\\gamma \\in (0,2)$","venue":"math.PR","work_id":"4ea56d35-62fb-4225-bfb6-65f9e468e0e4","year":2019},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.587740Z"},"links":{"cited_paper":"/paper/1905.00384","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:e5829c118d32b5bb22732523b9240ecdac34c7e8233f20e1e62801cea39283d8","observation_id":"b77def12-7689-41a6-a2ee-bded3fa98021","resolution":{"observed_at":"2026-08-14T13:12:03.075181Z","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":{"arxiv_id":"1905.00383","last_updated":"2020-07-22T13:43:09Z","snapshot_observed_at":"2026-08-15T22:41:14.258636Z","submitted_at":"2019-05-01T17:01:59Z","title":"Existence and uniqueness of the Liouville quantum gravity metric for $\\gamma \\in (0,2)$","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1905.00383","snapshot_observed_at":"2026-08-14T13:12:02.591864Z","title":"Gwynne and J","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.591864Z"},"links":{"cited_paper":"/paper/1905.00383","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:21664e0982ae1ff6c8bc57dc1aeefd075a39814d3f3c27fa3822f8df4c3db422","observation_id":"d6cc3f26-4d34-4b47-8434-c5840e6daac4","resolution":{"observed_at":"2026-08-14T13:12:02.591864Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1905.00379","last_updated":"2020-02-01T12:16:32Z","snapshot_observed_at":"2026-08-14T16:38:41.304871Z","submitted_at":"2019-05-01T16:59:04Z","title":"Local metrics of the Gaussian free field","version":2},"cited_work":{"arxiv_id":"1905.00379","doi":null,"metadata_source":"pith","pith_arxiv_id":"1905.00379","snapshot_observed_at":"2026-08-14T13:12:03.045086Z","title":"Local metrics of the Gaussian free field","venue":"math.PR","work_id":"35757477-d894-4d1d-97fd-8768becf3eb5","year":2019},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.595815Z"},"links":{"cited_paper":"/paper/1905.00379","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:7ba5d37ab639fed0201d1aeb0d13fd6208a76cd9d0704b7f423ffa2c7d267d20","observation_id":"2697bf5c-ee76-45e8-ad7d-2383e1b067a3","resolution":{"observed_at":"2026-08-14T13:12:03.049112Z","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":{"arxiv_id":"1705.11161","last_updated":"2021-02-20T21:48:33Z","snapshot_observed_at":"2026-08-16T19:42:06.746417Z","submitted_at":"2017-05-31T16:12:34Z","title":"The Tutte embedding of the mated-CRT map converges to Liouville quantum gravity","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1705.11161","snapshot_observed_at":"2026-08-14T13:12:02.599660Z","title":"Gwynne , J","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.599660Z"},"links":{"cited_paper":"/paper/1705.11161","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:87f39a922f99e3c803fda524365d7a3355c53419a801591fa759f415ba76942e","observation_id":"ef955c30-f658-46d9-bca5-29f34687936e","resolution":{"observed_at":"2026-08-14T13:12:02.599660Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1809.02091","last_updated":"2019-09-23T20:11:43Z","snapshot_observed_at":"2026-08-16T08:04:27.719428Z","submitted_at":"2018-09-06T17:02:04Z","title":"The Tutte embedding of the Poisson-Voronoi tessellation of the Brownian disk converges to $\\sqrt{8/3}$-Liouville quantum gravity","version":3},"cited_work":{"arxiv_id":"1809.02091","doi":null,"metadata_source":"pith","pith_arxiv_id":"1809.02091","snapshot_observed_at":"2026-08-14T13:12:03.017339Z","title":"The Tutte embedding of the Poisson-Voronoi tessellation of the Brownian disk converges to $\\sqrt{8/3}$-Liouville quantum gravity","venue":"math.PR","work_id":"de74b4fd-2789-4ac5-901b-32d20dcffe45","year":2018},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.603576Z"},"links":{"cited_paper":"/paper/1809.02091","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:4c055193a851b199b0bae5c3b19deba4a5ae8926ddceb21856c8bc0866650f76","observation_id":"73ae73b1-f06f-4782-bd46-33441e8cb23d","resolution":{"observed_at":"2026-08-14T13:12:03.021773Z","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":{"arxiv_id":"1903.09561","last_updated":"2019-06-23T19:15:40Z","snapshot_observed_at":"2026-08-15T22:41:07.527662Z","submitted_at":"2019-03-22T15:37:28Z","title":"Bounds for distances and geodesic dimension in Liouville first passage percolation","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1903.09561","snapshot_observed_at":"2026-08-14T13:12:02.607368Z","title":"Gwynne and J","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.607368Z"},"links":{"cited_paper":"/paper/1903.09561","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:6cd2fae79c7093fd9b0db17012ff50636dab38e7adcd2ce72427a4287d5ce342","observation_id":"5233203c-ca58-41bc-81f5-bb0fc0f00b7c","resolution":{"observed_at":"2026-08-14T13:12:02.607368Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1901.06860","last_updated":"2021-02-26T17:07:14Z","snapshot_observed_at":"2026-08-16T01:41:06.711902Z","submitted_at":"2019-01-21T10:25:33Z","title":"External diffusion limited aggregation on a spanning-tree-weighted random planar map","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1901.06860","snapshot_observed_at":"2026-08-14T13:12:02.611297Z","title":"Gwynne and J","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.611297Z"},"links":{"cited_paper":"/paper/1901.06860","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:e285c840cec72886f24ae0e2f670e90609466af5b891b12f9ffa7a581af3ef34","observation_id":"3eeb4511-99cc-4dbb-aad0-5f596a9d1076","resolution":{"observed_at":"2026-08-14T13:12:02.611297Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1905.11790","last_updated":"2019-12-28T22:19:26Z","snapshot_observed_at":"2026-08-14T16:25:14.884817Z","submitted_at":"2019-05-28T13:10:55Z","title":"KPZ formulas for the Liouville quantum gravity metric","version":3},"cited_work":{"arxiv_id":"1905.11790","doi":null,"metadata_source":"pith","pith_arxiv_id":"1905.11790","snapshot_observed_at":"2026-08-14T13:12:02.980485Z","title":"KPZ formulas for the Liouville quantum gravity metric","venue":"math.PR","work_id":"2ddee2c8-e7aa-40a3-83f0-33d1ea43ed74","year":2019},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.615638Z"},"links":{"cited_paper":"/paper/1905.11790","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:4b14c533d736ed5aa437475aea663d8e80510abfaf7a0e8e13dc9dfe1205890d","observation_id":"33a38688-b073-42e9-baf8-a2b8a732944d","resolution":{"observed_at":"2026-08-14T13:12:02.985120Z","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":{"arxiv_id":"0902.3842","last_updated":"2010-10-02T06:40:59Z","snapshot_observed_at":"2026-08-16T13:51:34.045128Z","submitted_at":"2009-02-23T03:34:33Z","title":"Thick points of the Gaussian free field","version":3},"cited_work":{"arxiv_id":"0902.3842","doi":null,"metadata_source":"pith","pith_arxiv_id":"0902.3842","snapshot_observed_at":"2026-08-14T13:12:02.964493Z","title":"Thick points of the Gaussian free field","venue":"math.PR","work_id":"4077ae0f-fe84-4da6-81a8-498fe4b34704","year":2009},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.619573Z"},"links":{"cited_paper":"/paper/0902.3842","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:5e08b5fea835cb9edf8cc347433dd443f275daa9f642add04f16cd47639c06ec","observation_id":"2b6b62ab-6ecb-4867-aae6-6906b205e7af","resolution":{"observed_at":"2026-08-14T13:12:02.968845Z","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":{"arxiv_id":"1905.13207","last_updated":"2021-06-02T21:48:11Z","snapshot_observed_at":"2026-08-16T01:41:09.583678Z","submitted_at":"2019-05-30T17:49:31Z","title":"Convergence of uniform triangulations under the Cardy embedding","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1905.13207","snapshot_observed_at":"2026-08-14T13:12:02.623864Z","title":"Holden and X","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":42,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.623864Z"},"links":{"cited_paper":"/paper/1905.13207","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:1cc391767f13b1c9c9900c77a8405127808bcc80c30c54aa07ecdd0b15cb762a","observation_id":"c55f2cf7-09ae-4769-97bd-d291f8a1ecc2","resolution":{"observed_at":"2026-08-14T13:12:02.623864Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:12:03.524435Z","title":null,"venue":null,"work_id":"3af9ba1f-2877-4c5c-aa61-a91f73176f8b","year":1985},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":43,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.627862Z"},"links":{"citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:20973241a8f40a4e8457947f4e2097cf8bde1b5dbe174c4f8a61aaef7561ce5d","observation_id":"67ce4118-9de7-499d-aacd-f27a729fcdf7","resolution":{"observed_at":"2026-08-14T13:12:03.529906Z","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":"1511.04068","last_updated":"2016-11-10T00:30:05Z","snapshot_observed_at":"2026-08-15T22:42:34.237075Z","submitted_at":"2015-11-12T20:52:36Z","title":"Bipolar orientations on planar maps and SLE$_{12}$","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1511.04068","snapshot_observed_at":"2026-08-14T13:12:02.631373Z","title":"Kenyon, J","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":44,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.631373Z"},"links":{"cited_paper":"/paper/1511.04068","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:91cdba0828aaa6281787cd5ff933c7404f027cc99df1fba21d6d734935d4cc9d","observation_id":"a32af9ef-22b0-4005-b42c-111611213e6a","resolution":{"observed_at":"2026-08-14T13:12:02.631373Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1707.08785","last_updated":"2019-08-30T12:57:25Z","snapshot_observed_at":"2026-08-16T03:08:06.971769Z","submitted_at":"2017-07-27T09:00:06Z","title":"Integrability of Liouville theory: proof of the DOZZ Formula","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1707.08785","snapshot_observed_at":"2026-08-14T13:12:02.635675Z","title":"Kupiainen , R","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.635675Z"},"links":{"cited_paper":"/paper/1707.08785","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:759307f6c4d7f147185ba15a28f181107b671daade99e98b64b4452b630bba32","observation_id":"d2922d9a-d91c-4fca-99a8-b94acd2dabbb","resolution":{"observed_at":"2026-08-14T13:12:02.635675Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:12:03.509930Z","title":null,"venue":null,"work_id":"ad0c4b8d-7f0d-43ba-b439-16d44e772fa9","year":2005},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":46,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.639489Z"},"links":{"citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:bf25f9543988e098d5e45afcdd949f708f13b6b0836fb6513284f8d393f8a2f6","observation_id":"ed904f89-4b32-42e5-8065-d138d08fed55","resolution":{"observed_at":"2026-08-14T13:12:03.514165Z","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":"1105.4842","last_updated":"2013-07-25T11:54:12Z","snapshot_observed_at":"2026-08-16T04:13:25.523234Z","submitted_at":"2011-05-24T17:34:48Z","title":"Uniqueness and universality of the Brownian map","version":2},"cited_work":{"arxiv_id":"1105.4842","doi":null,"metadata_source":"pith","pith_arxiv_id":"1105.4842","snapshot_observed_at":"2026-08-14T13:12:02.918942Z","title":"Uniqueness and universality of the Brownian map","venue":"math.PR","work_id":"d1fec55b-bd4b-4120-ba22-f5dd3f6d45db","year":2011},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":47,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.644329Z"},"links":{"cited_paper":"/paper/1105.4842","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:beb5b419051c83eae08132ca21a12fad8927ee3b88821b91723147d6841c1d62","observation_id":"d983c25a-0432-45e7-9d19-1ca717103020","resolution":{"observed_at":"2026-08-14T13:12:02.923293Z","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":{"arxiv_id":"1403.7943","last_updated":"2014-03-31T10:50:54Z","snapshot_observed_at":"2026-08-16T01:42:21.888575Z","submitted_at":"2014-03-31T10:50:54Z","title":"Random geometry on the sphere","version":1},"cited_work":{"arxiv_id":"1403.7943","doi":null,"metadata_source":"pith","pith_arxiv_id":"1403.7943","snapshot_observed_at":"2026-08-14T13:12:02.902875Z","title":"Random geometry on the sphere","venue":"math.PR","work_id":"01c67af3-5361-4103-a61a-9bba6b0b4440","year":2014},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":48,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.648242Z"},"links":{"cited_paper":"/paper/1403.7943","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:8195421ded9bf97e090321830771132a60f95651dfce6e1df0e6281c7e31a5a2","observation_id":"1add0d2c-3e35-4172-86a7-77ebaf65dd4c","resolution":{"observed_at":"2026-08-14T13:12:02.907132Z","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":{"arxiv_id":"1908.02259","last_updated":"2020-01-17T20:15:55Z","snapshot_observed_at":"2026-08-16T05:32:00.125238Z","submitted_at":"2019-08-06T17:12:59Z","title":"Iterated foldings of discrete spaces and their limits: candidates for the role of Brownian map in higher dimensions","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1908.02259","snapshot_observed_at":"2026-08-14T13:12:02.652196Z","title":"Lioni and J.-F","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":49,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.652196Z"},"links":{"cited_paper":"/paper/1908.02259","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:e3b50f499dbed5f0025e1b45b21b95e104333e8853a635a5e6d86cbecd038b77","observation_id":"ada6c697-d1c7-4487-9af2-3cbb59b3f946","resolution":{"observed_at":"2026-08-14T13:12:02.652196Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1104.1606","last_updated":"2011-05-09T23:43:56Z","snapshot_observed_at":"2026-08-15T04:49:51.448569Z","submitted_at":"2011-04-08T16:37:01Z","title":"The Brownian map is the scaling limit of uniform random plane quadrangulations","version":2},"cited_work":{"arxiv_id":"1104.1606","doi":null,"metadata_source":"pith","pith_arxiv_id":"1104.1606","snapshot_observed_at":"2026-08-14T13:12:02.873858Z","title":"The Brownian map is the scaling limit of uniform random plane quadrangulations","venue":"math.PR","work_id":"4acd11f5-6a26-4604-b582-2a38194ef0c9","year":2011},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":50,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.656293Z"},"links":{"cited_paper":"/paper/1104.1606","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:d378d40b4c2be01e2fbc04eb36e0a33cf03eaa1583ee5be1aece375e784c676b","observation_id":"cbbec4d1-c55b-4665-90df-a52993b7adce","resolution":{"observed_at":"2026-08-14T13:12:02.878528Z","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":{"arxiv_id":"1507.00719","last_updated":"2019-07-29T12:58:43Z","snapshot_observed_at":"2026-08-14T22:41:56.937943Z","submitted_at":"2015-07-02T19:54:32Z","title":"Liouville quantum gravity and the Brownian map I: The QLE(8/3,0) metric","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1507.00719","snapshot_observed_at":"2026-08-14T13:12:02.660470Z","title":"Miller and S","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":51,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.660470Z"},"links":{"cited_paper":"/paper/1507.00719","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:0342113239f452f452f048faf3589e6373d0e0b5a076ffb5881996ded027e73e","observation_id":"fef6d37c-6298-4043-b313-f4bee0d4bd0f","resolution":{"observed_at":"2026-08-14T13:12:02.660470Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1605.03563","last_updated":"2021-04-19T13:12:23Z","snapshot_observed_at":"2026-08-16T16:14:41.219043Z","submitted_at":"2016-05-11T19:52:10Z","title":"Liouville quantum gravity and the Brownian map II: geodesics and continuity of the embedding","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1605.03563","snapshot_observed_at":"2026-08-14T13:12:02.664226Z","title":"Miller and S","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":52,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.664226Z"},"links":{"cited_paper":"/paper/1605.03563","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:a320e0d3d087df06e11ae0ae616cd2d01833da8aef8a8462eb620bf76266be78","observation_id":"c9a7b502-b329-46ca-b0fd-42baf7416ec5","resolution":{"observed_at":"2026-08-14T13:12:02.664226Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1608.05391","last_updated":"2020-11-20T14:07:52Z","snapshot_observed_at":"2026-08-14T21:43:38.708702Z","submitted_at":"2016-08-18T19:50:37Z","title":"Liouville quantum gravity and the Brownian map III: the conformal structure is determined","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1608.05391","snapshot_observed_at":"2026-08-14T13:12:02.668141Z","title":"Miller and S","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":53,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.668141Z"},"links":{"cited_paper":"/paper/1608.05391","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:62efcf4100a7526107dc701cb1bec9a44afff4c853ca63f4c44794156e33575a","observation_id":"036c66db-2b53-4c01-8591-791cec32d43a","resolution":{"observed_at":"2026-08-14T13:12:02.668141Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:12:03.497043Z","title":null,"venue":null,"work_id":"fd4ee3c0-86cb-47af-900a-7b1f8571b774","year":1967},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":54,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.672207Z"},"links":{"citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:f4ccff1816950821fad1048ed608e9396cda70553f01d0d4a07d580bf7a01955","observation_id":"40394a20-5a53-47a8-a575-90e502c364b9","resolution":{"observed_at":"2026-08-14T13:12:03.501165Z","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":"2026-08-14T13:12:03.484655Z","title":null,"venue":null,"work_id":"ae6428dc-05c9-420e-adaa-5569de04e19c","year":1981},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":55,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.676811Z"},"links":{"citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:1d769d11c81626ff57ddcf384c4f2711aa7acb8d08c586fe878e436a9c235f2a","observation_id":"6dd0104e-2375-4e7e-9b47-653c0ab81831","resolution":{"observed_at":"2026-08-14T13:12:03.488549Z","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":"1305.6221","last_updated":"2013-05-27T13:54:17Z","snapshot_observed_at":"2026-08-15T00:16:29.851894Z","submitted_at":"2013-05-27T13:54:17Z","title":"Gaussian multiplicative chaos and applications: a review","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1305.6221","snapshot_observed_at":"2026-08-14T13:12:02.680362Z","title":"Rhodes and V","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":56,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.680362Z"},"links":{"cited_paper":"/paper/1305.6221","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:575000c651ee85279f1b181dad87caaae66161c5ed4b32700fd5664f76297343","observation_id":"e2e63927-6627-40ff-99c1-fbc7fa73caaa","resolution":{"observed_at":"2026-08-14T13:12:02.680362Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:12:03.473338Z","title":"Schaeffer","venue":null,"work_id":"1d577420-7a1f-4420-bb95-7f60d3aed7ea","year":1997},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":57,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.684588Z"},"links":{"citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:481f3bcc6580a2bf5ac680a98095ed9ca994ea8b5baaf85e8e012c10add8e6d7","observation_id":"c9a2f169-8b52-4e85-8b52-2e467158351d","resolution":{"observed_at":"2026-08-14T13:12:03.477259Z","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":"math/9904022","last_updated":"1999-04-18T07:48:03Z","snapshot_observed_at":"2026-07-07T06:10:27.116847Z","submitted_at":"1999-04-05T09:45:10Z","title":"Scaling limits of loop-erased random walks and uniform spanning trees","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"math/9904022","snapshot_observed_at":"2026-08-14T13:12:02.688492Z","title":null,"venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":58,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.688492Z"},"links":{"cited_paper":"/paper/math/9904022","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:ae113517404e372ba39335fece0acb417c35458daf9c7f7b8d2daf8568503432","observation_id":"e0b3a675-6ce3-4197-bbaf-e42ef1cc1d3f","resolution":{"observed_at":"2026-08-14T13:12:02.688492Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"math/0312099","last_updated":"2006-11-23T04:58:14Z","snapshot_observed_at":"2026-08-16T19:20:00.255131Z","submitted_at":"2003-12-04T11:06:29Z","title":"Gaussian free fields for mathematicians","version":3},"cited_work":{"arxiv_id":"math/0312099","doi":null,"metadata_source":"pith","pith_arxiv_id":"math/0312099","snapshot_observed_at":"2026-08-14T13:12:02.804237Z","title":"Gaussian free fields for mathematicians","venue":"math.PR","work_id":"5be41d70-8e1d-4e0a-a8e2-b20b08f9c7b7","year":2003},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":59,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.692519Z"},"links":{"cited_paper":"/paper/math/0312099","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:24fc087d5bd0c0119f46382090ce83a53c62cf8569384acfffa66e017e67cb5a","observation_id":"e4445dea-1fe6-4e9e-9af1-e6c158a29d55","resolution":{"observed_at":"2026-08-14T13:12:02.808779Z","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":{"arxiv_id":"1012.4797","last_updated":"2015-09-23T19:28:03Z","snapshot_observed_at":"2026-08-16T00:09:59.677445Z","submitted_at":"2010-12-21T20:55:36Z","title":"Conformal weldings of random surfaces: SLE and the quantum gravity zipper","version":2},"cited_work":{"arxiv_id":"1012.4797","doi":null,"metadata_source":"pith","pith_arxiv_id":"1012.4797","snapshot_observed_at":"2026-08-14T13:12:02.788558Z","title":"Conformal weldings of random surfaces: SLE and the quantum gravity zipper","venue":"math.PR","work_id":"5acaf930-872d-4ddf-9d96-41399d7eacf2","year":2010},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":60,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.696485Z"},"links":{"cited_paper":"/paper/1012.4797","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:35e69615c33fb15171fa42a37ed1d6dba186dc0715389d2cab9a3b532153a80a","observation_id":"224a9293-2d41-4ba9-b0c6-b59bb348a27b","resolution":{"observed_at":"2026-08-14T13:12:02.792742Z","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":{"arxiv_id":"1108.2241","last_updated":"2015-09-23T19:36:10Z","snapshot_observed_at":"2026-08-15T04:38:33.957640Z","submitted_at":"2011-08-10T18:49:34Z","title":"Quantum gravity and inventory accumulation","version":2},"cited_work":{"arxiv_id":"1108.2241","doi":null,"metadata_source":"pith","pith_arxiv_id":"1108.2241","snapshot_observed_at":"2026-08-14T13:12:02.770342Z","title":"Quantum gravity and inventory accumulation","venue":"math.PR","work_id":"7ae138bf-7566-4a53-ad77-c8aa41314fe5","year":2011},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":61,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.700427Z"},"links":{"cited_paper":"/paper/1108.2241","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:c481870ec41eda44b67e34df547e9139042fe368ca244832a156a213f3cb0b0b","observation_id":"61ab7f82-ea16-43b6-9a03-18c9d3760fd2","resolution":{"observed_at":"2026-08-14T13:12:02.776376Z","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":{"arxiv_id":"1712.00829","last_updated":"2017-12-03T20:10:32Z","snapshot_observed_at":"2026-08-15T05:29:13.629116Z","submitted_at":"2017-12-03T20:10:32Z","title":"Lecture notes on Liouville theory and the DOZZ formula","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1712.00829","snapshot_observed_at":"2026-08-14T13:12:02.704199Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":62,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.704199Z"},"links":{"cited_paper":"/paper/1712.00829","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:20b5aac8422ddfbd05a6d1095fad6411a2e5a128dab43d4be548cc1c8f96eec7","observation_id":"3ad3eff2-fa00-4556-a2a7-b177425620b3","resolution":{"observed_at":"2026-08-14T13:12:02.704199Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:12:03.458970Z","title":"Watabiki","venue":null,"work_id":"80568179-4fd3-4304-9341-cdb2c40ce46b","year":1993},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":63,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.708130Z"},"links":{"citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:ed1fe7e8378a34d23dc2caf23d018662ffe6c9420d248bb1b11c40439a63b50b","observation_id":"4c6bc48f-e255-4737-a8ef-c816795e6158","resolution":{"observed_at":"2026-08-14T13:12:03.463815Z","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":"1410.0939","last_updated":"2015-10-02T13:18:34Z","snapshot_observed_at":"2026-08-14T23:17:02.859430Z","submitted_at":"2014-10-03T18:51:07Z","title":"The characteristic polynomial of a random unitary matrix and Gaussian multiplicative chaos - The $L^2$-phase","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1410.0939","snapshot_observed_at":"2026-08-14T13:12:02.711859Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":64,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.711859Z"},"links":{"cited_paper":"/paper/1410.0939","citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:d5ffdc8cf483ebacda0abdeb4080a684518a96e9138d39c62074029e57f593d5","observation_id":"2ce9be4d-6a9c-444c-953a-925f6aeb29bc","resolution":{"observed_at":"2026-08-14T13:12:02.711859Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:12:03.445125Z","title":null,"venue":null,"work_id":"25fa92e9-bf16-443d-b80d-5c0df25da8c8","year":2004},"citing_paper":{"arxiv_id":"1908.05573","last_updated":"2021-02-28T00:03:52Z","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity","version":3},"reference_index":65,"source":"arxiv_source","source_observed_at":"2026-08-14T13:12:02.715811Z"},"links":{"citing_paper":"/paper/1908.05573"},"observation_digest":"sha256:5c39084e5321ba715184f57a3d2ef0e43d41a80775caf9b3f654f21e233d0be8","observation_id":"9a0a6855-062f-4d69-a802-ce4a33ec4550","resolution":{"observed_at":"2026-08-14T13:12:03.449605Z","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":"1908.05573","last_updated":"2021-02-28T00:03:52Z","latest_version":3,"primary_category":"math.PR","snapshot_observed_at":"2026-08-16T13:39:00.138625Z","submitted_at":"2019-08-15T15:03:56Z","title":"Random surfaces and Liouville quantum gravity"},"reference_resolution":{"displayed":65,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":32,"verified_exact":26,"verified_fuzzy":7},"total_outbound_references":65},"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 65 of 65 outbound references and 1 inbound Pith citation observation for arXiv:1908.05573."}