{"as_of":"2026-08-12T16:36:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:cfbc0c483041e446baa7816a152536d973a9581fea1a09e4cd08f629f4fd8c0f","coverage":[{"denominator":39,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":39,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T14:48:48.861667Z","state":"measured"},{"denominator":39,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":39,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+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/2412.11708/citation-record","integrity":"/paper/2412.11708/integrity","json":"/paper/2412.11708/citation-record.json","paper":"/paper/2412.11708"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:48:50.708015Z","title":"Aizenman, D","venue":null,"work_id":"24847d42-575e-4e10-bedb-d344a1e7de3b","year":1987},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:47.853233Z"},"links":{"citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:f5bd811af1a7796e73e50b4603a666fccedf533310d0e394759f8c040abcfa17","observation_id":"7b98218b-35c6-401f-adac-366435a6141a","resolution":{"observed_at":"2026-08-11T14:48:50.714793Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T14:48:50.685628Z","title":null,"venue":null,"work_id":"e545d4c2-65e0-42af-b666-2392229fec9b","year":2023},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:47.903368Z"},"links":{"citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:5644b1b1ef46cb15774a97a5cd0bbc632b18424b066b3c9a8bf290130ec9368d","observation_id":"2f80a0bb-b7b9-471d-b6f8-7b05e7191cc4","resolution":{"observed_at":"2026-08-11T14:48:50.692346Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T14:48:50.564576Z","title":"Aizenman, Translation invariance and instability of phase coexistence in the two-dimensional I sing system , Comm","venue":null,"work_id":"b8bfee8b-8ba5-4c41-b55f-1ea172aba345","year":1980},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:47.909434Z"},"links":{"citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:e59dac883f3ebe172a2e9cffe8295378530ba403936821616c37a9135f1b5f9d","observation_id":"2f293bd9-5a0d-476c-b10a-36babdf78e93","resolution":{"observed_at":"2026-08-11T14:48:50.640840Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T14:48:50.415339Z","title":"4, 2049--2086","venue":null,"work_id":"6e1f3515-3647-4033-9dc3-48de4325e75d","year":2019},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:47.914924Z"},"links":{"citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:c7222598ccd87fd53de7d9ecb2384e30a97d707882ba03879fd032da1ae18712","observation_id":"af483b50-01df-4b35-abcb-d3ccef603986","resolution":{"observed_at":"2026-08-11T14:48:50.503384Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T14:48:50.351372Z","title":null,"venue":null,"work_id":"abadce3e-3a78-4f06-be79-1d906c0bca6e","year":1989},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:47.920975Z"},"links":{"citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:2b6707e38b99157589e8387cf418897c5af8760d12cdd0ab6c2e1383f6577667","observation_id":"ca1e0c95-9452-41b8-822c-12e99968899b","resolution":{"observed_at":"2026-08-11T14:48:50.357880Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T14:48:50.331082Z","title":"Bl \\\"o te and Bernard Nienhuis, The phase diagram of the O (n) model , Physica A: Statistical Mechanics and its Applications 160 (1989), no","venue":null,"work_id":"79e8af9e-1892-40bd-b16f-dda267792831","year":1989},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:47.925784Z"},"links":{"citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:026945f11d21fea02cac333079f2ba744051fb1c42fa8e1a29f64bf0f5a34a6e","observation_id":"62d747e7-cfb0-49d6-91da-82802b6fd631","resolution":{"observed_at":"2026-08-11T14:48:50.337728Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T14:48:47.932437Z","title":null,"venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:47.932437Z"},"links":{"citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:bdbd9bd53ce3c54602b0bff5a00376fc09931fb83bf07fbe2f73e82bb2c56103","observation_id":"c1b7a984-c8ec-4d66-b5ea-7d71e89c54a1","resolution":{"observed_at":"2026-08-11T14:48:47.932437Z","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":"2026-08-11T14:48:50.300170Z","title":"Theory Related Fields 158 (2014), no","venue":null,"work_id":"98a678bc-39dc-4731-8944-5f9279cab0ea","year":2014},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:47.938193Z"},"links":{"citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:8c99934ebb9f90665e6c5d9dd0509083b909c7f580788dd07af56eaea9ac2f50","observation_id":"b970ba08-7ffb-40db-972f-2a70aba144cd","resolution":{"observed_at":"2026-08-11T14:48:50.306002Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2001.11977","last_updated":"2024-06-13T10:07:50Z","snapshot_observed_at":"2026-07-06T08:54:06.146857Z","submitted_at":"2020-01-31T17:50:59Z","title":"Macroscopic loops in the loop O(n) model via the XOR trick","version":2},"cited_work":{"arxiv_id":"2001.11977","doi":null,"metadata_source":"pith","pith_arxiv_id":"2001.11977","snapshot_observed_at":"2026-08-11T14:48:49.076245Z","title":"Macroscopic loops in the loop O(n) model via the XOR trick","venue":"math.PR","work_id":"5c8c5d36-3774-4c69-92ac-fcd9454a2630","year":2020},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:47.943671Z"},"links":{"cited_paper":"/paper/2001.11977","citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:a59236a32b64211c72b7bec4718aea50cd88906e5a8cd5572e38c7c9d237ed25","observation_id":"32910be4-6ead-4f4c-b020-77d0aec98e82","resolution":{"observed_at":"2026-08-11T14:48:49.097347Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T14:48:50.279844Z","title":"2, 297--346","venue":null,"work_id":"9d4c3b88-a251-45a2-966d-b2e1e0395b3e","year":2001},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:47.950238Z"},"links":{"citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:f9f1bd694217d175c3315c52be3350f52fa34027ef1468cbd98d611da37dec55","observation_id":"b514fcf8-b658-40bf-9453-14d575763406","resolution":{"observed_at":"2026-08-11T14:48:50.287208Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T14:48:50.255199Z","title":"Newman, Two-dimensional critical percolation: the full scaling limit, Comm","venue":null,"work_id":"fd2ad598-98c9-40b3-a569-967d2020d224","year":2006},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:47.955512Z"},"links":{"citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:d812bf48ec37f1ffff04464a9b29768379340858321c2a30170c3377ed364724","observation_id":"c5850843-7bd6-4867-9072-a91c94ecd3b1","resolution":{"observed_at":"2026-08-11T14:48:50.260977Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T14:48:47.961310Z","title":null,"venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:47.961310Z"},"links":{"citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:7d6bfff39553b3ce94d3d1cdce1c9c25df1e0317e4c107b3c5e49727e052c213","observation_id":"e38263a9-77d7-45d1-8af1-0c2628ab7e33","resolution":{"observed_at":"2026-08-11T14:48:47.961310Z","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":"2026-08-11T14:48:50.159805Z","title":null,"venue":null,"work_id":"a38bdae4-1509-47c4-aa8a-416a567cdc62","year":2019},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:47.966761Z"},"links":{"citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:bd43c4a1a40b42de9eaa5a6d171237ebd9227be2d665042f51cd1f6ba8c8b35c","observation_id":"77497990-ab57-44c9-b5cc-dc8b52a8d644","resolution":{"observed_at":"2026-08-11T14:48:50.213810Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T14:48:50.009810Z","title":"Duminil-Copin and V","venue":null,"work_id":"b2b96634-56ad-41a2-a77e-d71d48c19b87","year":2016},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:48.004501Z"},"links":{"citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:9d3f1f67296e759749a280a043b68a5c9cee9e0d1d0291c612ba68be9a34988f","observation_id":"64a0c52b-9678-466d-bb5e-16e73ca0bdd6","resolution":{"observed_at":"2026-08-11T14:48:50.059811Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T14:48:49.977809Z","title":"Fisher, On the dimer solution of planar I sing models , Journal of Math","venue":null,"work_id":"af9c064d-3de7-4d6f-bf8d-5f245c2c0d3d","year":1966},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:48.048905Z"},"links":{"citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:2bdd719049540435fe1434b2ea91274fb450a6b97f366c7af13a884bcbbfb0ea","observation_id":"175918a4-dad3-4038-a65b-8d7ad2f52d14","resolution":{"observed_at":"2026-08-11T14:48:49.985155Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2306.01527","last_updated":"2023-10-27T15:03:08Z","snapshot_observed_at":"2026-08-12T06:12:32.640307Z","submitted_at":"2023-06-02T13:27:12Z","title":"Delocalisation and continuity in 2D: loop O(2), six-vertex, and random-cluster models","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2306.01527","snapshot_observed_at":"2026-08-11T14:48:48.145225Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:48.145225Z"},"links":{"cited_paper":"/paper/2306.01527","citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:5de3797fb561880b8b293668fb10127c75e2b4c5b07f38cd4cb79809a8181341","observation_id":"20db707a-38e5-4952-a7e2-25dd3eba9131","resolution":{"observed_at":"2026-08-11T14:48:48.145225Z","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":"2026-08-11T14:48:48.237107Z","title":"2, 209--256","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:48.237107Z"},"links":{"citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:b0e17acfe8f33158db7bd3267a57cfb72e30bf172abb04520706c036b0457d68","observation_id":"68855bf4-cc6d-4fe6-82a4-4c247f191bc2","resolution":{"observed_at":"2026-08-11T14:48:48.237107Z","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":"2026-08-11T14:48:49.936569Z","title":"Grimmett, Percolation, second ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol","venue":null,"work_id":"b4b12585-4605-4137-87e8-0f11e7418312","year":1999},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:48.290460Z"},"links":{"citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:3c3afa826f38e020eb34e3e421c419396d7cd0f9596475b3df5cd808e115aeff","observation_id":"893d734c-1050-45db-b868-101703fa350e","resolution":{"observed_at":"2026-08-11T14:48:49.947280Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T14:48:49.913383Z","title":"Higuchi, On the absence of non-translation invariant G ibbs states for the two-dimensional I sing model , Random fields, V ol","venue":null,"work_id":"c98acf17-85d7-4c05-833a-d00fc287a7ef","year":1979},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:48.302057Z"},"links":{"citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:27680bedd49c1860bb7a81add8f310e9dd9b0d7339274bda731270afd22adfe3","observation_id":"05d69f49-0d9f-49bc-a51c-2795fd956c01","resolution":{"observed_at":"2026-08-11T14:48:49.920102Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2304.10930","last_updated":"2024-06-09T18:07:28Z","snapshot_observed_at":"2026-07-06T15:18:22.636996Z","submitted_at":"2023-04-21T13:06:11Z","title":"Local dimer dynamics in higher dimensions","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2304.10930","snapshot_observed_at":"2026-08-11T14:48:48.309495Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:48.309495Z"},"links":{"cited_paper":"/paper/2304.10930","citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:15c71e5738ea0a32a8c1c60a4907eb0824d1e2fe2fba53a2c0d2c72e80fe781d","observation_id":"5f0f016e-832f-4887-a0cc-993c2738c383","resolution":{"observed_at":"2026-08-11T14:48:48.309495Z","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":"2026-08-11T14:48:49.848217Z","title":null,"venue":null,"work_id":"a77c0b12-79c7-4169-8de1-ca31caccab06","year":1961},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:48.318333Z"},"links":{"citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:b1531d6385828c93f2a68aeebbaf3578efe167fab3f4bdb31be27e504ae9c995","observation_id":"1e90cccd-89c1-411d-a6eb-1be5d2a6000c","resolution":{"observed_at":"2026-08-11T14:48:49.895813Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T14:48:49.655543Z","title":null,"venue":null,"work_id":"feb4f1e7-501e-4a9c-b81b-56903b5eb54f","year":1967},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:48.326601Z"},"links":{"citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:65d0854fe9b66f127c48d6baae5cb533af4fcf709d61bfa5c9d36ca9e1fb2e3c","observation_id":"d1a52764-6a5c-4e61-acd2-84dcddfa5391","resolution":{"observed_at":"2026-08-11T14:48:49.743206Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T14:48:49.629581Z","title":null,"venue":null,"work_id":"8f7cc14e-e139-46e1-99f0-aa26bb8759a4","year":1997},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:48.332822Z"},"links":{"citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:70d02f8df4a77bb955c4e4f935da8f92bb19304fdbe3d27c65fdba09ce6e5e8c","observation_id":"47cd5882-e2b6-4903-b0d2-8e8de7024bf0","resolution":{"observed_at":"2026-08-11T14:48:49.635476Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T14:48:49.600464Z","title":null,"venue":null,"work_id":"9f5c88ca-69a2-459a-92a4-3e56fbd57791","year":2001},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:48.339181Z"},"links":{"citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:d98fcace6c17d7bb9f98eeef52a565b2e58d999765f65359ba07d6a521572cc1","observation_id":"00f05181-5b76-43ad-babd-c6ec48adef36","resolution":{"observed_at":"2026-08-11T14:48:49.610932Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T14:48:49.574586Z","title":"Kenyon, The L aplacian and D irac operators on critical planar graphs , Invent","venue":null,"work_id":"68ca2e44-812e-411c-8a98-61b136f76455","year":2002},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:48.391209Z"},"links":{"citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:f3de649a93c8640bbcf0c9bd1973d77db1cc17192fc69ab4fcc40b8d25a6464d","observation_id":"7a6ed0ed-041f-403c-bd47-9f2e0096e545","resolution":{"observed_at":"2026-08-11T14:48:49.581414Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T14:48:49.544267Z","title":"Ser., vol","venue":null,"work_id":"719e88a4-767d-4932-a5ef-5329a6ffe999","year":2009},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:48.469393Z"},"links":{"citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:bd1f61045acb404c4e9e434bb26163df1c479fed5b4fd258ea2844f080de234d","observation_id":"fc48b5ad-a347-43b2-b0c8-167d02bf58c0","resolution":{"observed_at":"2026-08-11T14:48:49.552816Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T14:48:49.521854Z","title":null,"venue":null,"work_id":"5bb24b67-d4ac-4e09-8a05-2b48cdb6ff98","year":2004},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:48.563880Z"},"links":{"citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:2b48cb97f44426b2400c317d5dcc138b9a3a5dc0de889586b23f84b074508a5c","observation_id":"45cdd1a4-f37d-4693-94b3-62e693cb7060","resolution":{"observed_at":"2026-08-11T14:48:49.528379Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T14:48:49.501873Z","title":null,"venue":null,"work_id":"9fa8cfb4-3490-4ab0-a4ef-ecc1de743e4d","year":2006},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:48.634789Z"},"links":{"citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:8c48e558beb24fb317553adb9dacce583843efaed148e8b9043b8f557da1ed25","observation_id":"4547a972-fe7e-4e6d-804d-ceb26a80ee2f","resolution":{"observed_at":"2026-08-11T14:48:49.507680Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2111.15612","last_updated":"2021-11-30T18:03:19Z","snapshot_observed_at":"2026-08-06T02:23:54.397497Z","submitted_at":"2021-11-30T18:03:19Z","title":"Percolation and $O(1)$ loop model","version":1},"cited_work":{"arxiv_id":"2111.15612","doi":null,"metadata_source":"pith","pith_arxiv_id":"2111.15612","snapshot_observed_at":"2026-08-11T14:48:48.935219Z","title":"Percolation and $O(1)$ loop model","venue":"math.PR","work_id":"0734d604-1e5b-498c-9ef0-292cbd25aa32","year":2021},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:48.785491Z"},"links":{"cited_paper":"/paper/2111.15612","citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:17ef20fd0a9c0a5361de5cf39749892b62d9c4341263f7aee0e0989ae40d4b2f","observation_id":"45d024cc-67d2-42ae-a5db-92dfbaaf93a1","resolution":{"observed_at":"2026-08-11T14:48:48.954035Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00440","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:48:48.906032Z","title":"3-4, 1243--1264, http://doi.org/10.1007/s00440\\","venue":null,"work_id":"4b158292-3735-4d94-8840-55af6cfbba94","year":2018},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:48.803207Z"},"links":{"citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:1505f4556667e5ef7b243ec638ac585e952658fd90780c18f72f2b934b37a664","observation_id":"84c64b26-4f9a-48b8-8c51-7f72a8d9af04","resolution":{"observed_at":"2026-08-11T14:48:48.913502Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T14:48:49.480110Z","title":"Newman, Ising models and dependent percolation, Topics in statistical dependence ( S omerset, PA , 1987), IMS Lecture Notes Monogr","venue":null,"work_id":"fa0021c8-4ef1-4929-b9a2-34402f1538f6","year":1987},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:48.810231Z"},"links":{"citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:e36fbdf5a8f3404461c54f6fd70d4f6f322ed7261ba0a191445dd4702b532ca3","observation_id":"f13e8ac6-781f-4f6e-98ef-eba18fa1ecd5","resolution":{"observed_at":"2026-08-11T14:48:49.486524Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T14:48:49.320696Z","title":null,"venue":null,"work_id":"ded25d78-ed70-49a1-979a-e149c32a36a4","year":1982},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:48.815838Z"},"links":{"citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:8288760fb612e30a55c9a53b9da38f4fb4e2300d47d4ac4883946e1246186300","observation_id":"e5412b90-23aa-41b9-a902-000232739e78","resolution":{"observed_at":"2026-08-11T14:48:49.394684Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T14:48:49.231721Z","title":null,"venue":null,"work_id":"63439322-6b26-414d-98d9-1b2a0dc9493e","year":2019},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:48.821651Z"},"links":{"citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:a767e5ac8cc8aecdf3a01463ae04001a61e6fcf84ab59eda89bc277d170a0469","observation_id":"e62575ab-f9c3-4c88-80f8-bd82fcf0fc37","resolution":{"observed_at":"2026-08-11T14:48:49.254287Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T14:48:49.213785Z","title":"304, vi+175","venue":null,"work_id":"be2ace88-6fc1-4db5-b889-d1359f066ac5","year":2005},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:48.829680Z"},"links":{"citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:2c8754a6a61bceb34842a77fe3ea2286c86446481d0faedf994cbfe00e358813","observation_id":"fe93a595-fd3f-433c-bfb4-9e38d333dc89","resolution":{"observed_at":"2026-08-11T14:48:49.219455Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T14:48:49.192385Z","title":null,"venue":null,"work_id":"d2d08da0-9e8a-4158-9554-22e16da3425f","year":2001},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:48.836052Z"},"links":{"citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:de8cc36e76634d6db9a8b7bbb91cd2888a16d2136bdc8e0d9337854668a89d8e","observation_id":"07648332-683c-4160-b972-082b1df4fead","resolution":{"observed_at":"2026-08-11T14:48:49.198414Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T14:48:49.174140Z","title":null,"venue":null,"work_id":"d64fcaf6-a2d6-47f0-a19d-dbaa470bac55","year":2010},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:48.841860Z"},"links":{"citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:9ce5d83c7fafcc9f75730ae163d037f56a71e57ee01a73f18fc32ecdd62d76aa","observation_id":"7fd749e1-e3eb-4346-89ad-98783856a8cd","resolution":{"observed_at":"2026-08-11T14:48:49.179285Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T14:48:49.153233Z","title":"2, 239--252","venue":null,"work_id":"ea4f5379-c5c0-41d3-9ba8-e5ae369c3ec0","year":1996},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:48.849576Z"},"links":{"citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:fca0c3d7a67989a74c4c7e535a8838510f927184ecdd53a92e9ae3d52344aac1","observation_id":"a68f9061-cbb0-4fab-8b5e-9385d00dae87","resolution":{"observed_at":"2026-08-11T14:48:49.159982Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T14:48:49.133122Z","title":null,"venue":null,"work_id":"c255ae83-6494-46dd-80db-fc7a2d30c291","year":2016},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:48.856357Z"},"links":{"citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:bf48fe8d0573748c2ca9a2c80e3662b8390577cfbe3630f8438b25845aea3ca2","observation_id":"c8f4a770-2df5-4010-b6be-40dd5ddafd42","resolution":{"observed_at":"2026-08-11T14:48:49.138765Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T14:48:49.111948Z","title":"Thurston, Conway's tiling groups, Am","venue":null,"work_id":"5ed2cd77-d527-497e-8778-9bd968e8083d","year":1990},"citing_paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers","version":1},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-08-11T14:48:48.861667Z"},"links":{"citing_paper":"/paper/2412.11708"},"observation_digest":"sha256:98435fc9b9ff32ff8fe95ee9060bf2ae748c0da61afc90d328155c957f9822da","observation_id":"be748f73-e43a-44d2-ba7d-8a2c982b2b79","resolution":{"observed_at":"2026-08-11T14:48:49.118126Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2412.11708","last_updated":"2024-12-16T12:31:11Z","latest_version":1,"primary_category":"math.PR","snapshot_observed_at":"2026-08-12T06:13:00.601480Z","submitted_at":"2024-12-16T12:31:11Z","title":"On loops in the complement to dimers"},"reference_resolution":{"displayed":39,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":19,"verified_exact":3,"verified_fuzzy":17},"total_outbound_references":39},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 39 of 39 outbound references and 0 inbound Pith citation observations for arXiv:2412.11708."}