{"as_of":"2026-08-17T15:57:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:61a8345b480c12ce52abe098184a40e0a1205e686a81e95a3a64c6b765a9eb18","coverage":[{"denominator":63,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":63,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T14:32:09.129211Z","state":"measured"},{"denominator":63,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":63,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-17T06:30:58.91139+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2608.09881/citation-record","integrity":"/paper/2608.09881/integrity","json":"/paper/2608.09881/citation-record.json","paper":"/paper/2608.09881"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"1609.02447","last_updated":"2019-07-18T17:08:59Z","snapshot_observed_at":"2026-08-15T17:05:41.883759Z","submitted_at":"2016-09-08T14:38:44Z","title":"Random coalescing geodesics in first-passage percolation","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1609.02447","snapshot_observed_at":"2026-08-15T14:32:08.555844Z","title":"Random coalescing geodesics in first-passage per- colation","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.555844Z"},"links":{"cited_paper":"/paper/1609.02447","citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:fc313def164299201c35cb97cdb05fb8f2e2504d8c5a995e711d1a7ec2e452f8","observation_id":"ccb2ded8-c5be-4a76-8910-bc48448d6c93","resolution":{"observed_at":"2026-08-15T14:32:08.555844Z","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":"2026-08-15T14:32:11.071243Z","title":"Rounding effects of quenched randomness on first-order phase transitions.Comm","venue":null,"work_id":"c6cfbaa2-b955-47e1-b0ef-597a85633f0e","year":1990},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.563109Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:30ea579c0d8d6625a16b680005bbc4b6d77f9df1d3fa32b0cb674479c7952fc1","observation_id":"30d54a66-a1c4-479c-8bb4-3c1f1039d464","resolution":{"observed_at":"2026-08-15T14:32:11.077805Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:11.046570Z","title":"Alexander","venue":null,"work_id":"50de2005-8914-4464-9c7e-1597905c41b4","year":2023},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.570422Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:68f9652dbb6414398441877e720452420b051c414ef2316fad83158f3f61e798","observation_id":"65047360-8bd9-43f8-a89f-d7f5e11825f9","resolution":{"observed_at":"2026-08-15T14:32:11.051992Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:11.025737Z","title":"Aliprantis and Kim C","venue":null,"work_id":"3b435b8c-9581-4436-bb87-c94a42b29689","year":2006},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.578705Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:b18689cc64f8a15372334e099abc7f19691cbeaf36fb6b879f6e38b0d67d4281","observation_id":"d3d28303-afaf-4884-bb08-96fd1970eb8c","resolution":{"observed_at":"2026-08-15T14:32:11.031522Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:10.994174Z","title":"American Mathematical Society, Providence, RI, 2017","venue":null,"work_id":"9e84fd94-5ff4-4f90-a481-1f6d784a05a0","year":2017},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.585956Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:2bb6262b79756c30857917dba00717ec9dae445960649d045d93f6dc98c7aaaf","observation_id":"0e3f2947-78f6-4fc9-a3a2-14d505e68118","resolution":{"observed_at":"2026-08-15T14:32:11.000624Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:10.970967Z","title":"The Burgers equation with Poisson random forcing.Ann","venue":null,"work_id":"536f9811-8e4f-4d11-a16c-cbb099b0d22f","year":2013},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.599394Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:8a33cb93f9d28b7a4bc4cef402deeb12125fd8e6ee0f63befda491fc80e151b7","observation_id":"b92460e6-eff3-483a-86a5-fdb0a87e4957","resolution":{"observed_at":"2026-08-15T14:32:10.977901Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:10.936162Z","title":"Inviscid Burgers equation with random kick forcing in noncompact setting","venue":null,"work_id":"2a7b6b3c-eff1-4a6e-9fae-aeb97f0d07e8","year":2016},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.612711Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:c1399e09d534a50fbac3b0005cc67ea26e60718d52d83225f80c52117380a848","observation_id":"5ed4934d-99e1-4cfa-ba20-dbe1cceae790","resolution":{"observed_at":"2026-08-15T14:32:10.947520Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:10.910589Z","title":"Space-time stationary solutions for the Burgers equation.J","venue":null,"work_id":"21e054bb-48b5-42d9-9769-9883c7e7d359","year":2014},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.626733Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:61de4d04582cf6259374fa1769a79afd73aca5160a607a4b7b1ffc9dc0d2a36d","observation_id":"1a08fdab-5552-438a-9a5d-39a7cdb4c044","resolution":{"observed_at":"2026-08-15T14:32:10.918363Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:10.877868Z","title":"Thermodynamic limit for directed polymers and stationary solu- tions of the Burgers equation.Comm","venue":null,"work_id":"a91eb062-bcc7-4ac2-b320-aa2a14eddb30","year":2019},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.637134Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:7f4d46dcc5dba8385514873c469d82de9790c0204d1abfd8f5c521e9de437710","observation_id":"9b9f2c7e-9375-48dc-813a-bcb35a7ee8df","resolution":{"observed_at":"2026-08-15T14:32:10.886039Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:10.844531Z","title":"Non-existence of bi-infinite geodesics in the exponential corner growth model.Forum Math","venue":null,"work_id":"2983cd08-afe5-438c-b359-bdcf9bb43a12","year":2020},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.649908Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:33d74108f55c3535d5fa568cd6256847193f7041980d7e0ecd1d9b05ab03af48","observation_id":"dc5dba33-e363-47e9-80be-36c75003d563","resolution":{"observed_at":"2026-08-15T14:32:10.851948Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:10.813583Z","title":"Nonexistence of bigeodesics in planar exponential last passage percolation.Comm","venue":null,"work_id":"165f2295-e77c-4d0b-ae8f-1c2f15a51fa5","year":2022},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.663304Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:4bfcb747488b174343102a25b301dd900ad7f4737d95b02c43b1c5374dbfa543","observation_id":"056a6dae-f1c0-42b6-b0f0-9dc262cbb0e2","resolution":{"observed_at":"2026-08-15T14:32:10.822759Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:10.781123Z","title":"Geodesic trees and exceptional directions in FPP on hyperbolic groups.Adv","venue":null,"work_id":"64b0f6ab-a490-4661-b087-36a308947936","year":2026},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.669285Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:bd2454cf3e6aaa3b7c57c6bde586a130286c5879040754753769401874347d26","observation_id":"b289095b-28ad-45b0-9b0f-115978163297","resolution":{"observed_at":"2026-08-15T14:32:10.787633Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:10.753134Z","title":"Intertwining the Busemann process of the directed polymer model.Electron","venue":null,"work_id":"95c6bfff-b457-4de8-bbe3-7f72c62960f2","year":2025},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.676730Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:5632dff9a198080b7799519a8ef2974fe818ed39ed03bacb2869c9028fdadbfb","observation_id":"573343e9-fb3c-4123-937a-e314f0f4432a","resolution":{"observed_at":"2026-08-15T14:32:10.760565Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:10.707343Z","title":"Kluwer Academic Publishers Group, Dordrecht, 1993","venue":null,"work_id":"babadef7-d2fc-4286-a679-16ab1a371b11","year":1993},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.684382Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:18cc46fcf4bebf602778336c1e7360e8e4831ca9d7ae2ca8ec89fb41dc24b2ef","observation_id":"00fe6c61-fe0c-4a37-aaa3-0722f5375fbd","resolution":{"observed_at":"2026-08-15T14:32:10.731993Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:32:08.690746Z","title":null,"venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.690746Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:6c7eb53307d7c61aa535722d9768b8d93372ce624f92ad8975bcb6ed7fea7ffb","observation_id":"baaba056-67b0-499d-aa53-90532a0cd802","resolution":{"observed_at":"2026-08-15T14:32:08.690746Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:32:08.697085Z","title":null,"venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.697085Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:f0b21f79e50386a172a46fb11e4e503b12f90a5d05f25306f5ed6dd57111344f","observation_id":"b79fb178-5c15-4e84-a5e4-781b5c3b754f","resolution":{"observed_at":"2026-08-15T14:32:08.697085Z","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":"2026-08-15T14:32:10.633260Z","title":"Non-existence of three non-coalescing infinite geodesics with the same direction in the directed landscape.Probab","venue":null,"work_id":"f6804a3c-a00f-4706-8daf-058d8505df98","year":2025},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.704367Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:cf1a865e6e8dba0fe7afc7d8ff147d132f60b480517890843d479f78ce62a314","observation_id":"0aee1714-7de3-49ad-97b4-6e98070e768d","resolution":{"observed_at":"2026-08-15T14:32:10.641330Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:10.594661Z","title":"Non-existence of bi-infinite polymers.Electron","venue":null,"work_id":"535c003e-5bb1-4bbf-8ee1-fd526c03794f","year":2022},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.712265Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:3f892db91a93f2abb47476986a8ece402f3d1d564bdfe75bf9cb817f27ecef4c","observation_id":"c06e6103-0796-49f0-a91d-496fc7de998d","resolution":{"observed_at":"2026-08-15T14:32:10.611930Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:10.553964Z","title":"The stationary horizon and semi-infinite geodesics in the directed landscape.Ann","venue":null,"work_id":"6b8f4408-e917-4ad5-b2b8-7713cdcea790","year":2024},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.717006Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:384cae5fafbce59e5f3cad24173aa3ca8e340f3e316fed330d5db636e168c928","observation_id":"2b896512-d63d-445a-b684-0b8f42c28610","resolution":{"observed_at":"2026-08-15T14:32:10.563045Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:10.515410Z","title":"Souganidis","venue":null,"work_id":"dec83aea-dcbc-4959-a766-832fe4a841d1","year":2017},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.722882Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:d6968cd711e368caf46d00033a326fe49a60e2ced6d381ee77af2b9f22b7b162","observation_id":"4e3b183e-63d4-4e32-b9b9-40714cd50933","resolution":{"observed_at":"2026-08-15T14:32:10.528989Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:10.485727Z","title":"Castaing and M","venue":null,"work_id":"7c10b75a-9593-4de3-8391-3ffc9658812b","year":1977},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.729544Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:3dc077919b7c1346869fc1e9f9133bb554b5621e159e9b65fc4af13df50557b9","observation_id":"8dc96682-7955-48aa-83d2-7a1703b04e71","resolution":{"observed_at":"2026-08-15T14:32:10.494553Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:10.445394Z","title":"On the input-output map of aG{G{1 queue.J","venue":null,"work_id":"8ae4ce4a-fd2d-458e-882a-481859c5710e","year":1994},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.739863Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:85a26bf5932f7fe37b2d66ad790c5ea49282fe90e5335a0c37cc6324070515c2","observation_id":"f1a0d617-e7b7-4a6b-839c-0aa4e8c97f15","resolution":{"observed_at":"2026-08-15T14:32:10.457920Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:10.406232Z","title":"Springer, Cham, 2017","venue":null,"work_id":"cad5d99d-6af8-4bcf-a9d1-720d573bc98c","year":2017},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.746197Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:af10c9bcd96fdf83605ebd446fe56072626664361844d5ca0f4a44202eafd134","observation_id":"e0e6dbee-2fef-4d93-abfc-22f196aa220a","resolution":{"observed_at":"2026-08-15T14:32:10.418775Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:10.369704Z","title":"Directed polymers in random environment are diffusive at weak disorder.Ann","venue":null,"work_id":"d378da81-8d81-4538-9ecd-60627a721aef","year":2006},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.751717Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:73445fced2d9be6f8c681e9e0eb7cfc292397abe0a07fbffe88c9644d9fd25be","observation_id":"b3563569-9902-4efe-88c8-e7f21622c796","resolution":{"observed_at":"2026-08-15T14:32:10.377256Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:10.340958Z","title":"Multiple geodesics with the same direction.Electron","venue":null,"work_id":"2d88a97a-47af-4bdc-a0d9-5f661497a745","year":2011},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.759598Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:9f4fa6b67cb2cb139665b9a8d509e844cef220f965fbd970117ae18507d507db","observation_id":"90034bd9-6be9-40ee-aa3c-deeeb4f55ee4","resolution":{"observed_at":"2026-08-15T14:32:10.351792Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:10.310587Z","title":"Busemann functions and infinite geodesics in two- dimensional first-passage percolation.Comm","venue":null,"work_id":"ff29792e-b7b2-495f-b4c1-a5e98e99c946","year":2014},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.766146Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:ef364c4c1d8441de40d1c37cc379084f2516da1d3060217dca11b2d9a7213d77","observation_id":"ce1387f3-a375-4f13-bb61-746eb3409b10","resolution":{"observed_at":"2026-08-15T14:32:10.319940Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:10.277574Z","title":"Springer-Verlag, New York, second edition, 1998","venue":null,"work_id":"40f2accf-d3c3-4b6a-b68f-29a33e30b600","year":1998},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.779178Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:15150db4fd17809aa00cc77977771ed8f991aa1a433dc153330e44a4f647b379","observation_id":"349b8ef4-cd5b-43de-8f9b-60cbf3f350d1","resolution":{"observed_at":"2026-08-15T14:32:10.289404Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:10.252252Z","title":"Anomalous geodesics in the inhomogeneous corner growth model.Comm","venue":null,"work_id":"56f08210-769f-4c48-b36d-350fb28f97da","year":2025},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.787398Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:9360c639ae4fc319a91cbd83d7736babfa2126e40a4aedb830de686861414bed","observation_id":"c557ea32-b520-474b-9890-97adecd14fb7","resolution":{"observed_at":"2026-08-15T14:32:10.260754Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:10.221964Z","title":"Ethier and Thomas G","venue":null,"work_id":"532d247e-582e-4e13-abe8-7fe2194cc026","year":1986},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.798667Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:a5d5bef346ece8e8a482db689076e274685e38b4a4dabcd29d4ec7098e7e786b","observation_id":"5f375ad2-b8d6-4969-81e6-e8abba617724","resolution":{"observed_at":"2026-08-15T14:32:10.228989Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:10.195038Z","title":"Joint distribution of Busemann functions in the exactly solvable corner growth model.Prob","venue":null,"work_id":"3689a632-eb51-46a8-93a3-45f9d8c41147","year":2020},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.805465Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:d8fb230f53ae68ea97fb7e5f79834512e465ed7ba9778d2fb9017470de1437f5","observation_id":"70ad705b-4961-4b14-a108-96c83e9f680f","resolution":{"observed_at":"2026-08-15T14:32:10.203315Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:10.170273Z","title":"Coexistence in two-type first-passage percolation models","venue":null,"work_id":"650dd2b0-58a4-4118-9d88-756aa818aa5e","year":2005},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.819675Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:c290071c4fe8ae31dc4dd879b0c0f579b468a0700a74aba8157d38ad29b86e60","observation_id":"6879a698-74cd-41d4-9711-b6c75dcc40ba","resolution":{"observed_at":"2026-08-15T14:32:10.177760Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:10.145226Z","title":"Walter de Gruyter & Co., Berlin, 1988","venue":null,"work_id":"c6935fe8-eb01-42b9-855b-e39a319e8af7","year":1988},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.830475Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:9b4928052c0d58ed54e2d07ccded44108d94fd6a0e5d1dec8a00372e2bb8e47f","observation_id":"d4b74279-386c-4317-8e1d-c3b247a94fa3","resolution":{"observed_at":"2026-08-15T14:32:10.152563Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:10.121035Z","title":"Geodesics and the competition interface for the corner growth model.Probab","venue":null,"work_id":"f3673ead-ec27-4afa-88fb-cd25d3390b75","year":2017},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.841495Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:96d02e488b5a67bbb060c2d29126d79d332322c8644f00109f0929fed183080f","observation_id":"d5bf6191-54c9-4fd7-90f9-0d06c6ed1be1","resolution":{"observed_at":"2026-08-15T14:32:10.128696Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:10.099308Z","title":"Stationary cocycles and Buse- mann functions for the corner growth model.Probab","venue":null,"work_id":"8e1fb7d8-697c-426f-a170-d35c5998d7a8","year":2017},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.848890Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:50ac16e94aec6118e92328c0f18d12bf4578cb9f6436df03bfada2cf45ffaecc","observation_id":"38035bdb-d61f-4ddf-a438-b40d8a964ff7","resolution":{"observed_at":"2026-08-15T14:32:10.106749Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:10.073963Z","title":"Ratios of partition functions for the log-gamma polymer.Ann","venue":null,"work_id":"e46559da-b31c-4736-a773-18adcc9fbcba","year":2015},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.856212Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:8a72876d92a847a52abe93516c61f653d594730bb1adc8f3b1ba946bacac479b","observation_id":"4a3fce8d-a0b8-411c-b133-f9dbb47222da","resolution":{"observed_at":"2026-08-15T14:32:10.082236Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:10.045031Z","title":"Maximal coupling.Z","venue":null,"work_id":"acc3ded5-8e95-4c11-af15-b6c7b9d9f3ce","year":1978},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.869472Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:f4b529b33fe1b1090b98d53ec166a4402e4b75ee00fcb72513cea1e77f4a97eb","observation_id":"d37334ef-cc76-444c-b541-397548da5388","resolution":{"observed_at":"2026-08-15T14:32:10.053570Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:10.021018Z","title":"Shape of territories in some competing growth models.Ann","venue":null,"work_id":"dd1d528e-3759-4c43-8f93-e46ea55c17cc","year":2007},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.877826Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:0a93a6a8a7ca1eccca3efbeef5adc95f7e97bd0944e43f1988a9de9c1de57415","observation_id":"48234335-d290-4604-a29e-4cc3718291a7","resolution":{"observed_at":"2026-08-15T14:32:10.029182Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:09.989144Z","title":"Existence of generalized Busemann functions and Gibbs measures for random walks in random potentials.Trans","venue":null,"work_id":"a743a490-e700-4bc5-9e6e-ac83ad6f8e6d","year":2025},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.886248Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:6597bdee5596f020e26b292737984b39f23df4fcb33fe5aadcb69f7b601653dd","observation_id":"a9a91bb2-e5cf-465a-aa64-69c8dd64922e","resolution":{"observed_at":"2026-08-15T14:32:10.002332Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:09.963515Z","title":"Non-existence of non-trivial bi-infinite geodesics in Geometric Last Passage Percolation.J","venue":null,"work_id":"453626fc-af52-4a82-8f10-8d901715ef38","year":2025},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.903554Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:5fcee9892cf12598b421a14a27b4a030726c72a2d2d723db01e125b913fb4513","observation_id":"54225a1a-cf96-418b-b5aa-70bcb9f6970e","resolution":{"observed_at":"2026-08-15T14:32:09.969279Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:09.928004Z","title":"Geodesics in first passage percolation.Ann","venue":null,"work_id":"de4c1bfd-005d-4b17-ae92-8d11e133487e","year":1944},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.910678Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:2ac63c9941ad187266008442acef0cde807c7532a786cd2cea7c7a2f0b9453e7","observation_id":"7e04d983-3964-4f9f-ae22-f809eef9b152","resolution":{"observed_at":"2026-08-15T14:32:09.937005Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:09.901427Z","title":"Huse and Christopher L","venue":null,"work_id":"0290c3ba-9739-4f66-9b0b-a1fdd5368b60","year":1985},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.917110Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:9b862859c10a10dded91929a61387419003c5e6a7a20a0c0cf42cf62e28690c3","observation_id":"9d9ad34e-3eb9-440b-a0bd-8cf03f3ca5fb","resolution":{"observed_at":"2026-08-15T14:32:09.911050Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:09.875298Z","title":"Existence of weak solutions for stochastic differential equations with driving semimartingales.Stochastics, 4(4):317–337, 1980/81","venue":null,"work_id":"0437a377-8614-4a85-ab15-88d99cb67c80","year":1980},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.927336Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:b8d4e01b876449096341658eaed4a8719ae77d15bd7f541a49b1a754b3ddbbe5","observation_id":"7c6ad053-cb8d-4a41-a662-46101a445bca","resolution":{"observed_at":"2026-08-15T14:32:09.882261Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:09.844611Z","title":"Sur un type de convergence interm´ ediaire entre la convergence en loi et la convergence en probabilit´ e","venue":null,"work_id":"91c4e395-60d1-4daf-9a79-ecfdef4981ed","year":1979},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.938489Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:b4e9b9949761c4c7ece3b0a6ccbf1860d5bf47b25db6e4949d0001c109a6b2e2","observation_id":"447f1226-e843-4c65-a0e9-55b45595390a","resolution":{"observed_at":"2026-08-15T14:32:09.854510Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:09.811787Z","title":"A shape theorem and a variational formula for the quenched Lyapunov exponent of random walk in a random potential","venue":null,"work_id":"52858db6-e9cf-43f8-ac5c-38f3fb6a3e01","year":2022},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.946176Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:494f572c6b9f2ad550f7b30ab3c185e457554745aa751f219340901d9833481d","observation_id":"bbdb050c-48a3-45d0-aae0-9823794fd946","resolution":{"observed_at":"2026-08-15T14:32:09.820817Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1810.03580","last_updated":"2019-10-09T20:32:49Z","snapshot_observed_at":"2026-08-14T18:17:52.396054Z","submitted_at":"2018-10-08T17:03:10Z","title":"Busemann functions and Gibbs measures in directed polymer models on $\\mathbb{Z}^2$","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1810.03580","snapshot_observed_at":"2026-08-15T14:32:08.957987Z","title":"Busemann functions and Gibbs measures in directed polymer models onZ 2","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.957987Z"},"links":{"cited_paper":"/paper/1810.03580","citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:0f37e57da9424c9b3d8aa9ed41045c5e72e36d0b54bacf03371d097af41ea231","observation_id":"a30ec669-57b9-4ddd-a1e4-eb3649b36df6","resolution":{"observed_at":"2026-08-15T14:32:08.957987Z","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":"2026-08-15T14:32:09.776962Z","title":"Busemann functions and Gibbs measures in directed polymer models onZ 2.Ann","venue":null,"work_id":"0c93de37-a24e-4662-be5b-c756081edb62","year":2020},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.971616Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:80b675ebf0efe5e1b9efa26f4b891076ed95532314423b93a8f52b82689a6ab7","observation_id":"aef94030-f5bc-4be9-a2a4-c135ec57fb61","resolution":{"observed_at":"2026-08-15T14:32:09.786704Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:09.746909Z","title":"Uniqueness and Ergodicity of Stationary Di- rected Polymers onZ 2.J","venue":null,"work_id":"700edbda-55a8-47e1-aeb8-33546d1df855","year":2020},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.977621Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:ef82dcc5a19edc648f467aa0ed86d6c0322875595c5f4391067687c49b6448e2","observation_id":"c90c3855-a3a2-4aa4-946f-796f931abcdd","resolution":{"observed_at":"2026-08-15T14:32:09.757466Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2211.06779","last_updated":"2022-11-13T01:15:51Z","snapshot_observed_at":"2026-08-16T16:16:39.717222Z","submitted_at":"2022-11-13T01:15:51Z","title":"Ergodicity and synchronization of the Kardar-Parisi-Zhang equation","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2211.06779","snapshot_observed_at":"2026-08-15T14:32:08.985786Z","title":"Ergodicity and synchro- nization of the Kardar-Parisi-Zhang equation","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.985786Z"},"links":{"cited_paper":"/paper/2211.06779","citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:4ed28ac1ddcce3c5ff55419d718235247187b4ecdd095e3e599d16c720150800","observation_id":"ef62c3c5-e510-4057-ae74-e4aefcd2e0c7","resolution":{"observed_at":"2026-08-15T14:32:08.985786Z","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":"2026-08-15T14:32:09.725087Z","title":"Geometry of geodesics through Busemann measures in directed last-passage percolation.J","venue":null,"work_id":"ca18af31-7f25-4bb0-a721-7c63a724b05f","year":2023},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:08.996047Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:eb1808f45b604f57de3ca96f46e1c5c903e050602a2d1b3352a17d445f547b83","observation_id":"64562455-2532-47b5-8032-e031362f796d","resolution":{"observed_at":"2026-08-15T14:32:09.731051Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2507.08757","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:32:09.316925Z","title":"Strong existence and uniqueness of the tilt-indexed Busemann process in the planar corner growth model","venue":null,"work_id":"fdb387f7-0867-42fa-bd69-366f4cce7bc3","year":2025},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:09.003906Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:87c5935160f87d686b474be95a3b2def98d4b0031537a5b116c95fed97f08cbd","observation_id":"5004ba9c-b650-46d4-bcec-8027dd70dfe3","resolution":{"observed_at":"2026-08-15T14:32:09.332002Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:32:09.010681Z","title":"Kechris.Classical descriptive set theory, volume 156 ofGraduate Texts in Math- ematics","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:09.010681Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:16a36c86ff20f8369177da4ff28a871b990fc30ee95cec950d142a7196dd6628","observation_id":"4f63bffc-1fae-4fa9-b692-8db07e470507","resolution":{"observed_at":"2026-08-15T14:32:09.010681Z","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":"2026-08-15T14:32:09.678664Z","title":null,"venue":null,"work_id":"9b860324-e96d-4429-a4cc-2e9e0027898d","year":2007},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:09.040055Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:2ac995bb194b15a784cf3942e162fd74f1ffdbbe021c9c8709b51007eed87239","observation_id":"4202311b-b79e-486e-b259-c5418cc8af3e","resolution":{"observed_at":"2026-08-15T14:32:09.686151Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:09.652033Z","title":null,"venue":null,"work_id":"7d92a60c-7eab-4c50-8bcb-13f3643995ec","year":1996},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:09.046612Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:3921af677b3a9767db9e485355a5e7ece803842a9236353197f294b7f687835d","observation_id":"239e41d3-c6dd-41c2-84d8-552151a3b7e1","resolution":{"observed_at":"2026-08-15T14:32:09.660586Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:09.625943Z","title":null,"venue":null,"work_id":"55cd6d7a-644e-4659-a219-b0fc9d97fa12","year":2004},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:09.056921Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:508d024cdc374d4e22e226c28fa69e98f191b6fdbcbfb5229c9072abf4691a34","observation_id":"ee9fedee-935f-4d57-a64b-59651bfa600f","resolution":{"observed_at":"2026-08-15T14:32:09.633210Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:09.601613Z","title":null,"venue":null,"work_id":"8a82777e-e4cc-4526-a116-1e3815fa8eb9","year":1994},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:09.064604Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:8151b2c504f587ac53446460aedac03ffab2263d0b85a0d08966934581729e09","observation_id":"a29881fa-56d0-416f-b907-cd7ccc981761","resolution":{"observed_at":"2026-08-15T14:32:09.609316Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:09.576218Z","title":"Newman.Topics in disordered systems","venue":null,"work_id":"8dfc5cbb-2c26-41af-9e4c-26e60845cf71","year":1997},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:09.071788Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:045a1c7c34bbf1305334d7a9abc15ebd109f67f55dbeeb4580b70d0463f0a929","observation_id":"21b2dfe9-d7e4-469d-a428-94c6e42ee20e","resolution":{"observed_at":"2026-08-15T14:32:09.583574Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:09.554150Z","title":"Phelps.Lectures on Choquet’s theorem, volume 1757 ofLecture Notes in Mathemat- ics","venue":null,"work_id":"404b1605-be8c-45a2-8101-ce225a7caa5a","year":2001},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:09.077528Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:a76726b042bfc69988dc1e6c91d676d2d4d931a155acc81da7f247a4038a5151","observation_id":"2be25c56-d43a-4a19-94d2-a009e8def472","resolution":{"observed_at":"2026-08-15T14:32:09.561756Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:09.531238Z","title":"Quenched point-to-point free energy for random walks in random potentials.Probab","venue":null,"work_id":"48ad277a-26a6-4b7c-8042-5fef9cf0226a","year":2014},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:09.084836Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:884ccef8cf878ee1270319b901e41bd7280b38a32180140bcab6ee95348ce39d","observation_id":"9e2a17c6-3044-4938-9503-45195db59275","resolution":{"observed_at":"2026-08-15T14:32:09.537670Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:09.511415Z","title":"American Mathematical Society, Providence, RI, 2015","venue":null,"work_id":"e029c5bd-5cd6-4a2f-be27-8bd642f28a34","year":2015},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:09.093465Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:bc9116081083d909ec24905df9a59fb519693cb5dde5de5e44bf5545e204646b","observation_id":"aa74cce6-427c-4aae-bcd7-90bb863f7c84","resolution":{"observed_at":"2026-08-15T14:32:09.517424Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:09.490308Z","title":"Quenched free energy and large deviations for random walks in random potentials.Comm","venue":null,"work_id":"e3fd0ddc-f90f-444c-9214-8ae4b5cc02f7","year":2013},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:09.103399Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:499124cc80e43b54493badea90d625843959d3cd5156bcb119d3abe9b8213e66","observation_id":"0dfd7393-124b-4954-b2ec-0483726a5904","resolution":{"observed_at":"2026-08-15T14:32:09.497154Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:32:09.461806Z","title":"Tyrrell Rockafellar.Convex analysis","venue":null,"work_id":"2895da06-d7fa-4f94-96bb-36fc2d27b72f","year":1970},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:09.111511Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:9dbae53bcd6b42cc7c913f80ee9d02edbfb6bc73de5e7836015c2cbc1855f30d","observation_id":"f6535a65-7f82-41a1-9656-460981a8897e","resolution":{"observed_at":"2026-08-15T14:32:09.468104Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0911.2446","last_updated":"2015-08-26T23:08:03Z","snapshot_observed_at":"2026-08-15T05:34:04.948727Z","submitted_at":"2009-11-12T19:03:20Z","title":"Scaling for a one-dimensional directed polymer with boundary conditions","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0911.2446","snapshot_observed_at":"2026-08-15T14:32:09.122516Z","title":"Scaling for a one-dimensional directed polymer with boundary conditions","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:09.122516Z"},"links":{"cited_paper":"/paper/0911.2446","citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:a85620218d8f45c0d653e32d31808f6c7fd6b111c988e455459aea2ac9719638","observation_id":"9b51ea30-3542-47fa-8561-e5fc82378369","resolution":{"observed_at":"2026-08-15T14:32:09.122516Z","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":"2026-08-15T14:32:09.436670Z","title":"Strassen","venue":null,"work_id":"4339a854-103c-491f-9a65-1c820d8d0f32","year":1965},"citing_paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-15T14:32:09.129211Z"},"links":{"citing_paper":"/paper/2608.09881"},"observation_digest":"sha256:bcbc76a85e59a1dd4cbf89d04f7f8a32f8cce7a2c2b43efda0d91663fe384b40","observation_id":"1f358373-2966-48f5-999b-531fde4b6ab8","resolution":{"observed_at":"2026-08-15T14:32:09.443388Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2608.09881","last_updated":"2026-08-10T17:33:42Z","latest_version":1,"primary_category":"math.PR","snapshot_observed_at":"2026-08-15T14:20:31.131811Z","submitted_at":"2026-08-10T17:33:42Z","title":"Rooted Gibbs-DLR Measures in Planar Directed Polymers"},"reference_resolution":{"displayed":63,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":11,"verified_exact":1,"verified_fuzzy":51},"total_outbound_references":63},"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":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"thesis":"As of 17 August 2026, this Paper Citation Record lists 63 of 63 outbound references and 0 inbound Pith citation observations for arXiv:2608.09881."}