{"as_of":"2026-08-12T12:21:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:7ce758fc4acc94d980b29771cc5ca74cf537c0721962d88cdf90e1bbeaf40fd4","coverage":[{"denominator":42,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":42,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T20:33:50.518719Z","state":"measured"},{"denominator":44,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":44,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T20:37:46.851695Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-08T14:41:54.121273Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.05709","snapshot_observed_at":"2026-08-11T20:37:46.851695Z","title":"Cai and J","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.05706","last_updated":"2025-01-27T16:56:43Z","snapshot_observed_at":"2026-08-11T20:23:50.823979Z","submitted_at":"2024-12-07T17:30:32Z","title":"Quasi-multiplicativity and regularity for metric graph Gaussian free fields","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-11T20:37:46.851695Z"},"links":{"cited_paper":"/paper/2412.05709","citing_paper":"/paper/2412.05706"},"observation_digest":"sha256:4a724753912b69c77d3810ef6630c1cd7d2907d9ec6fe520c0a6a1aa35249c88","observation_id":"50f51d2e-f81b-4bca-8f63-204e06603db7","resolution":{"observed_at":"2026-08-11T20:37:46.851695Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"cited_work":{"arxiv_id":"2412.05709","doi":null,"metadata_source":"pith","pith_arxiv_id":"2412.05709","snapshot_observed_at":"2026-08-08T14:41:54.121273Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","venue":"math.PR","work_id":"0e649a23-d054-4e77-a224-cad7bc7ae8f4","year":2024},"citing_paper":{"arxiv_id":"2502.06754","last_updated":"2025-07-03T17:46:29Z","snapshot_observed_at":"2026-08-12T05:33:37.769823Z","submitted_at":"2025-02-10T18:32:10Z","title":"A switching identity for cable-graph loop soups and Gaussian free fields","version":4},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-08T14:41:53.796788Z"},"links":{"cited_paper":"/paper/2412.05709","citing_paper":"/paper/2502.06754"},"observation_digest":"sha256:cbf90d914d5b1377623b85212de67342d0b5ab001bcb181bf0a076c4d62692ed","observation_id":"551930a3-cf7a-499e-86af-ce62114e4da4","resolution":{"observed_at":"2026-08-08T14:41:54.125072Z","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"}}],"links":{"evidence":"/evidence","html":"/paper/2412.05709/citation-record","integrity":"/paper/2412.05709/integrity","json":"/paper/2412.05709/citation-record.json","paper":"/paper/2412.05709"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:33:51.125834Z","title":"fractons","venue":null,"work_id":"78acdbb0-3140-478b-9b37-0b46456bffbf","year":1982},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.370934Z"},"links":{"citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:aefad9799f86c5c42e30d1b462f779e974572c92813c0aefb150f306cb503c3c","observation_id":"88fac10f-7033-4d6a-bbc0-2cb161e3d8ab","resolution":{"observed_at":"2026-08-11T20:33:51.129263Z","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":"2026-08-11T20:33:51.114032Z","title":"Basu and A","venue":null,"work_id":"3e73ba7f-8e89-4014-82e2-5270df1ced79","year":2017},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.375156Z"},"links":{"citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:0d522ac3666b6b3da8a94f6b3715f602e1a33c5b911cf0a509d840106cc8629d","observation_id":"4737ac45-3921-4426-82e9-49376f80a58b","resolution":{"observed_at":"2026-08-11T20:33:51.117663Z","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":"2026-08-11T20:33:51.103440Z","title":"Cai and J","venue":null,"work_id":"e678443f-2120-425d-89e0-5a8bdb66ab0c","year":2024},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.378653Z"},"links":{"citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:7b7f3a9defdfbeb30889e60a4293c7a9c6aeab81aeaca580b0060424d5a7f7e1","observation_id":"bd87786c-14de-4619-b678-d9c1b2a1c8e3","resolution":{"observed_at":"2026-08-11T20:33:51.106805Z","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":"2406.02397","last_updated":"2024-07-12T07:59:55Z","snapshot_observed_at":"2026-08-05T04:15:33.680480Z","submitted_at":"2024-06-04T15:11:49Z","title":"One-arm Probabilities for Metric Graph Gaussian Free Fields below and at the Critical Dimension","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2406.02397","snapshot_observed_at":"2026-08-11T20:33:50.382491Z","title":"Cai and J","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.382491Z"},"links":{"cited_paper":"/paper/2406.02397","citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:61d6d761e7e32b80cc3bf7f78923c6163e462a59184e727b1bef6154178915fa","observation_id":"6d1eba94-3f36-497a-9b2a-608283572454","resolution":{"observed_at":"2026-08-11T20:33:50.382491Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.05706","last_updated":"2025-01-27T16:56:43Z","snapshot_observed_at":"2026-08-11T20:23:50.823979Z","submitted_at":"2024-12-07T17:30:32Z","title":"Quasi-multiplicativity and regularity for metric graph Gaussian free fields","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.05706","snapshot_observed_at":"2026-08-11T20:33:50.386375Z","title":"Cai and J","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.386375Z"},"links":{"cited_paper":"/paper/2412.05706","citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:be840b9c4ff28e438fa07436cfdfd09342c563aceb014469c3c562de42192b09","observation_id":"0252785e-86be-46e2-b75b-3a66ab272dfc","resolution":{"observed_at":"2026-08-11T20:33:50.386375Z","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":"2026-08-11T20:33:50.390933Z","title":"Chang, H","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.390933Z"},"links":{"citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:10d6db40ee1e7a6a5f8103f0f6b58b65a2d2d25b00d04aa08046f215dca63cd7","observation_id":"d252541d-310a-4916-ac0d-3442651be006","resolution":{"observed_at":"2026-08-11T20:33:50.390933Z","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":"2026-08-11T20:33:51.086417Z","title":"Ding and M","venue":null,"work_id":"5054bcdd-c4f2-4cdf-978a-259b8294ddfe","year":2020},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.395272Z"},"links":{"citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:ddeed27a880e05ca544853f7c1977825693ed78ad586e102812f323957708a36","observation_id":"41e21780-83b0-42ee-8dac-4561a94b17f7","resolution":{"observed_at":"2026-08-11T20:33:51.089924Z","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":"2026-08-11T20:33:51.076034Z","title":"Drewitz, A","venue":null,"work_id":"dc6779f7-1246-48c2-92e6-922a90e91a3b","year":2018},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.398757Z"},"links":{"citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:8132f77e8792004abb1de9894bbe739c216faefa71b90d0c5270c1564551d22f","observation_id":"84ef3fdc-91e7-47b3-b216-452b71308b91","resolution":{"observed_at":"2026-08-11T20:33:51.079690Z","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":"2026-08-11T20:33:51.064543Z","title":"Drewitz, A","venue":null,"work_id":"93271aa4-967b-40c1-aba4-242bd902da4f","year":2022},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.403462Z"},"links":{"citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:6a5510061a2d4a43bcec15101b2dfc101e25bf45c1e537f1c7538cb514ed14db","observation_id":"a8d9a420-2769-4762-a385-25f1bcb85a62","resolution":{"observed_at":"2026-08-11T20:33:51.068886Z","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":"2026-08-11T20:33:50.407166Z","title":"Drewitz, A","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.407166Z"},"links":{"citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:97ffb4de073d83ffc576e2c97cbf3dd1e21a52221182ee7a4ca6a60de58c62e2","observation_id":"cc7d8d33-f233-43eb-8441-a0461292c359","resolution":{"observed_at":"2026-08-11T20:33:50.407166Z","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":"2026-08-11T20:33:51.053198Z","title":"Drewitz, A","venue":null,"work_id":"6c67fa0b-4e11-4303-8a78-b100fa5fb910","year":2023},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.410248Z"},"links":{"citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:b52f94d7480a76ddbb92f4296c3df02360a6957fe58813ab9cde082c27685e23","observation_id":"701f62dd-c457-4ab3-b114-8e0d6df4a358","resolution":{"observed_at":"2026-08-11T20:33:51.056907Z","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":"2412.06772","last_updated":"2024-12-09T18:56:45Z","snapshot_observed_at":"2026-08-12T08:27:27.609047Z","submitted_at":"2024-12-09T18:56:45Z","title":"Cluster volumes for the Gaussian free field on metric graphs","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.06772","snapshot_observed_at":"2026-08-11T20:33:50.413676Z","title":"Drewitz, A","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.413676Z"},"links":{"cited_paper":"/paper/2412.06772","citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:361995e5fab866b765f0ee4dc98fcadc37adc33e8cdf1f64d1cb6bdf3bf6bd96","observation_id":"80e5a270-1ca0-4f9a-a92c-a2981fa17458","resolution":{"observed_at":"2026-08-11T20:33:50.413676Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.17417","last_updated":"2024-05-27T17:58:44Z","snapshot_observed_at":"2026-07-06T18:20:44.070255Z","submitted_at":"2024-05-27T17:58:44Z","title":"Critical one-arm probability for the metric Gaussian free field in low dimensions","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.17417","snapshot_observed_at":"2026-08-11T20:33:50.417040Z","title":"Drewitz, A","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.417040Z"},"links":{"cited_paper":"/paper/2405.17417","citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:744f2d614b27423c0ef9f40b887983e2286b1118817c92669a62d5a0bb8c2a93","observation_id":"8799e27f-788c-4244-a0be-a064baedfd5b","resolution":{"observed_at":"2026-08-11T20:33:50.417040Z","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":"2026-08-11T20:33:51.041744Z","title":"Drewitz, B","venue":null,"work_id":"e1828514-efc1-4107-942b-2a849de7e938","year":2014},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.420668Z"},"links":{"citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:a7570fa8a78451cf42fbd5233ecc7fa87efd10debc2709bd8f7e6c8aeafd5cc4","observation_id":"e923df5e-a0ce-4928-80ac-7448b360b217","resolution":{"observed_at":"2026-08-11T20:33:51.045626Z","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":"2026-08-11T20:33:51.029773Z","title":"Drewitz, B","venue":null,"work_id":"fba05a28-d03f-4251-b1bf-f8289fef4dc8","year":2014},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.423661Z"},"links":{"citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:11e07956f6d04eb82a84854433bcf3102ae73dc0e3b83ef6f8a375453060e201","observation_id":"98d0dc8b-f6d1-466f-8a23-1c43da509e30","resolution":{"observed_at":"2026-08-11T20:33:51.033766Z","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":"2026-08-11T20:33:51.016010Z","title":"Fitzner and R","venue":null,"work_id":"358185a5-cb40-4937-af84-a9b8269240e0","year":2017},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.426465Z"},"links":{"citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:2aee187727dfcc8ed0cc393ff3364d4930cef7faf95ecf14669c164595bb276e","observation_id":"90d3af94-45f4-47da-b56b-48ef86ec6214","resolution":{"observed_at":"2026-08-11T20:33:51.019863Z","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":"2026-08-11T20:33:51.004835Z","title":"Gandolfi, M","venue":null,"work_id":"1e1e1d25-b0ec-43e8-9788-5fc9cb687354","year":1992},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.429558Z"},"links":{"citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:3959699b7b2c1be917ce03f901d47c9f92024ae8c6a19ea65816e50e82398505","observation_id":"83bfbe8e-4539-40e5-9ddc-1b063ac058c2","resolution":{"observed_at":"2026-08-11T20:33:51.008922Z","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":"2412.17768","last_updated":"2025-01-07T05:44:59Z","snapshot_observed_at":"2026-08-11T05:06:53.914771Z","submitted_at":"2024-12-23T18:28:40Z","title":"Critical level set percolation for the GFF in $d>6$: comparison principles and some consequences","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.17768","snapshot_observed_at":"2026-08-11T20:33:50.433110Z","title":"Ganguly and K","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.433110Z"},"links":{"cited_paper":"/paper/2412.17768","citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:73ea2d8f7e256d8426f4da86ce6ccd7c4cd0a232f4016c0f8a3fb417dc2ed0b9","observation_id":"0c116d5c-88b1-465b-81ec-0ef5779e5d51","resolution":{"observed_at":"2026-08-11T20:33:50.433110Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2403.02318","last_updated":"2024-03-04T18:54:10Z","snapshot_observed_at":"2026-07-06T17:39:24.823145Z","submitted_at":"2024-03-04T18:54:10Z","title":"The ant on loops: Alexander-Orbach conjecture for the critical level set of the Gaussian free field","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.02318","snapshot_observed_at":"2026-08-11T20:33:50.437360Z","title":"Ganguly and K","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.437360Z"},"links":{"cited_paper":"/paper/2403.02318","citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:87ce1603a06b5635be813ea8c86c98a57bc25a94a6720a0bd8d3167a87f564f9","observation_id":"19f53d0e-be1a-4687-93a0-ecc44c0b5c64","resolution":{"observed_at":"2026-08-11T20:33:50.437360Z","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":"2026-08-11T20:33:50.441086Z","title":"Hara and G","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.441086Z"},"links":{"citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:795ea97fb91fcbc867cd3545b4cf4564429718052887b197baa6e16b20bca95c","observation_id":"44913e94-36d8-4cd3-ba69-24fbfb27ca1d","resolution":{"observed_at":"2026-08-11T20:33:50.441086Z","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":"2026-08-11T20:33:50.986310Z","title":"Hara and G","venue":null,"work_id":"4f2c80f7-2125-418d-8243-e1c36494284e","year":2000},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.444341Z"},"links":{"citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:5b7ce4c00c74228882229a7fb1df585a37757162ddf57b29668592f4807ec773","observation_id":"c79deb35-91fc-4ae1-b1ae-4523dced8407","resolution":{"observed_at":"2026-08-11T20:33:50.990461Z","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":"2026-08-11T20:33:50.975240Z","title":"Hara and G","venue":null,"work_id":"dfcb1d74-d97b-45fb-8ab1-b3d932086a8d","year":2000},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.448325Z"},"links":{"citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:4a7d65b2eac92a8f4eaa0c57ccea835ea434cca4636091990df9e0432d9c0ee0","observation_id":"4f65550f-c0a5-4c85-99a3-d18b0e5dcf3e","resolution":{"observed_at":"2026-08-11T20:33:50.979274Z","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":"2026-08-11T20:33:50.451544Z","title":"Heydenreich, R","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.451544Z"},"links":{"citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:56a56a30f3921992dbb5c5be7e80dd85b4d6f15c2ad72b465bce887687cb362e","observation_id":"9da13dd5-6ec1-4a8c-affd-db11f476b1bc","resolution":{"observed_at":"2026-08-11T20:33:50.451544Z","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":"2026-08-11T20:33:50.958550Z","title":"Heydenreich, R","venue":null,"work_id":"6b776256-1299-4119-aef6-ad09ff1a7b4b","year":2014},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.454804Z"},"links":{"citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:315c795ae7cea42b913ef737cd5bdbb28dc7ad7e308e609e3d700f2ac2f307fc","observation_id":"c57ac354-39a2-4703-b7e8-b80ae2674031","resolution":{"observed_at":"2026-08-11T20:33:50.961684Z","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":"2026-08-11T20:33:50.949192Z","title":null,"venue":null,"work_id":"83dafd8a-8fb7-4df9-87b1-f1b1e8b27ab6","year":1963},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.457948Z"},"links":{"citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:b55c3c5a8fb2e06d7d3dc8b396e07450f9cfed5908088e4a034ae3043f013f15","observation_id":"44562c98-1c9b-4bad-a230-7af67099b653","resolution":{"observed_at":"2026-08-11T20:33:50.952458Z","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":"2026-08-11T20:33:50.940408Z","title":null,"venue":null,"work_id":"3affb8e3-bb9f-4545-90d0-5082d6e33a11","year":1986},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.464191Z"},"links":{"citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:71d63fd712328859e0fec54e737d6647d13833d2eabd9254c4dbcf226574c83e","observation_id":"bf12ebc0-1d34-4916-b32c-c05ef98fb304","resolution":{"observed_at":"2026-08-11T20:33:50.943234Z","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":"2026-08-11T20:33:50.930586Z","title":"Kozma and A","venue":null,"work_id":"1dbbdbc7-0be8-4f66-b73e-c21e85e6a632","year":2009},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.467937Z"},"links":{"citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:608355b97c9f0f0998681bd54de9bac037e45d89d84b62c786acbe8bb064878d","observation_id":"ec4890f1-4e0e-4b8e-8c42-76fbf0fd5877","resolution":{"observed_at":"2026-08-11T20:33:50.934247Z","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":"2026-08-11T20:33:50.920181Z","title":null,"venue":null,"work_id":"e3b8ca0d-1f6c-4885-b776-77414e40fbe1","year":2010},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.471673Z"},"links":{"citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:0ed8ccf96c6a5bd526f4745327f2e3628d8dc6003b7816c8706fcd884cb4b7fd","observation_id":"c0705d4d-f5a5-4f15-b7bd-8876a36e5ff9","resolution":{"observed_at":"2026-08-11T20:33:50.923817Z","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":"2026-08-11T20:33:50.910327Z","title":null,"venue":null,"work_id":"0e4588ed-9415-4969-b4b2-a1d6272c554a","year":2016},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.475033Z"},"links":{"citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:4006366cf2af7db9de8fa03a14af65fb11393e0f00e18146c992a30c267af62f","observation_id":"35c38618-88f5-408e-82e3-91a4f70bfc9a","resolution":{"observed_at":"2026-08-11T20:33:50.913721Z","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":"2209.07901","last_updated":"2023-10-11T15:39:11Z","snapshot_observed_at":"2026-08-11T20:52:16.100491Z","submitted_at":"2022-09-16T12:53:03Z","title":"An equivalence between gauge-twisted and topologically conditioned scalar Gaussian free fields","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2209.07901","snapshot_observed_at":"2026-08-11T20:33:50.478513Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.478513Z"},"links":{"cited_paper":"/paper/2209.07901","citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:38a976d1d9dd5dbdaa3c859eb650374af5320cd16ae03aa7558f01a16bf92301","observation_id":"3403e6a6-7439-41b2-ad87-26dae3615385","resolution":{"observed_at":"2026-08-11T20:33:50.478513Z","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":"2026-08-11T20:33:50.899007Z","title":"Lupu and W","venue":null,"work_id":"4d87ce3e-832f-4bd9-9d84-de9c0aba815d","year":2018},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.482048Z"},"links":{"citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:dc46dbc85045e769a370de153af8690602429ee5550eccb6bf3c2f737a27c24a","observation_id":"878d791b-df69-4cf5-a42b-7c61afd0906f","resolution":{"observed_at":"2026-08-11T20:33:50.902899Z","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":"2026-08-11T20:33:50.888785Z","title":"M¨ orters and Y","venue":null,"work_id":"9146b037-35f3-4bfb-88d4-802784b6174e","year":2010},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.485419Z"},"links":{"citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:5cfe94d9dd9ea72dc1a95d7f3adee3a28823cecae35b9c49a955791ec22e64a4","observation_id":"f7e01286-f040-42ce-92d7-f652eec395d9","resolution":{"observed_at":"2026-08-11T20:33:50.892440Z","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":"2406.15243","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:33:50.636594Z","title":null,"venue":null,"work_id":"537c0f7d-8349-4027-9be5-58cd963b796d","year":2024},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.488627Z"},"links":{"citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:5b0d4f52b0a92a0315d6dca06716e7357f9f7cb1eea8a70f8025c8a313687612","observation_id":"51b35936-273e-4a68-9678-548d92a02430","resolution":{"observed_at":"2026-08-11T20:33:50.643099Z","resolver_source":"raw_fallback","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":"2026-08-11T20:33:50.878297Z","title":"Popov and B","venue":null,"work_id":"90a7fd2b-d11c-4b04-8b6e-f49701c61a48","year":2015},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.492054Z"},"links":{"citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:15379a3822b88e4aa38e7d410e74c31601d17d5e678b18895627c8c5b22fd079","observation_id":"d9fd92d6-6fe1-4130-8ba9-395f2d9f0576","resolution":{"observed_at":"2026-08-11T20:33:50.882098Z","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":"2026-08-11T20:33:50.865986Z","title":"Rath and A","venue":null,"work_id":"31827d7f-833a-4c2e-b5f5-3dd19d1d0940","year":2011},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.495268Z"},"links":{"citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:bca36779916b2aa77b14be1bf9611ce0da0028b7ef3437cb5b53eb4f705c983f","observation_id":"1f964ee8-cccd-4ffe-8a10-4e8958d4d46d","resolution":{"observed_at":"2026-08-11T20:33:50.869724Z","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":"2026-08-11T20:33:50.854795Z","title":"Rodriguez and A.-S","venue":null,"work_id":"f7684e19-c0ab-4f2b-aa42-2b4217345007","year":2013},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.498878Z"},"links":{"citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:73a8186f950be7b7fe2635298700ee4b1e3d1bb75da68772f2e944bf101770ff","observation_id":"ea0a57fe-c13a-4032-8017-090ec9da7e45","resolution":{"observed_at":"2026-08-11T20:33:50.858778Z","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":"2026-08-11T20:33:50.843573Z","title":"Sznitman","venue":null,"work_id":"34380c83-0f3f-4208-a613-406d8f0d0655","year":2010},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.502387Z"},"links":{"citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:c88af932b7fbf858fa87361e6fc2bbdadb343438274b7939fd101eae68d65ba7","observation_id":"0f26797b-c9df-4fed-b48b-b4ec3f227de4","resolution":{"observed_at":"2026-08-11T20:33:50.847475Z","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":"2026-08-11T20:33:50.831210Z","title":"Sznitman","venue":null,"work_id":"4daad552-1bb8-4272-b464-b1de9da5d145","year":2016},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.505835Z"},"links":{"citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:6d0aba0fdfcd8e0260147fbf7d8e61649b4d2077e7c278b7aa4eb6352929e1b0","observation_id":"1f89ea4a-3dc7-4a82-9268-0b8ec70a3fff","resolution":{"observed_at":"2026-08-11T20:33:50.835295Z","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":"2026-08-11T20:33:50.820820Z","title":"Cames van Batenburg","venue":null,"work_id":"6bbe662d-8078-4915-be1c-0263f2948384","year":2015},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.509041Z"},"links":{"citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:fdacb624a1d13e185ff6f6c6af1821eaf868ecdd50c7ef73e8766de640cb84da","observation_id":"4b7fdfc7-b802-42ce-991f-39c8611a09ea","resolution":{"observed_at":"2026-08-11T20:33:50.824353Z","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":"2026-08-11T20:33:50.810812Z","title":"Van der Hofstad and A","venue":null,"work_id":"1e97ece3-d75b-438f-8b7c-4e62d415e05d","year":2004},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.512316Z"},"links":{"citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:cf170cef1d92f26b55a83dd1ff348e238bd84b6b3f2c3f3e3ed6fa66065f09c2","observation_id":"6b84b484-a5d6-400f-9a5c-fa479b17c443","resolution":{"observed_at":"2026-08-11T20:33:50.814322Z","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":"2026-08-11T20:33:50.515479Z","title":"Vershynin","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.515479Z"},"links":{"citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:5df9fa0c8db4bba4dd35b367427120b8237fe0d15aadce9c93a9172face87d4b","observation_id":"fe39d4a9-5845-450c-bd4e-7f74ee23439b","resolution":{"observed_at":"2026-08-11T20:33:50.515479Z","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":"2026-08-11T20:33:50.794618Z","title":null,"venue":null,"work_id":"c6bf5f42-4f2c-4f24-80c2-c4785ae6f5d5","year":2021},"citing_paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs","version":2},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-11T20:33:50.518719Z"},"links":{"citing_paper":"/paper/2412.05709"},"observation_digest":"sha256:afe3ba18d79ddf7b80512ab8941bd269fbaaff7bbc1a1766cad324dc8482eca9","observation_id":"afb52683-5843-459c-a351-e7c36db782ae","resolution":{"observed_at":"2026-08-11T20:33:50.797907Z","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"}}],"paper":{"arxiv_id":"2412.05709","last_updated":"2025-01-27T17:24:39Z","latest_version":2,"primary_category":"math.PR","snapshot_observed_at":"2026-08-11T20:23:44.817406Z","submitted_at":"2024-12-07T17:48:37Z","title":"Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs"},"reference_resolution":{"displayed":42,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":17,"verified_exact":1,"verified_fuzzy":24},"total_outbound_references":42},"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 42 of 42 outbound references and 2 inbound Pith citation observations for arXiv:2412.05709."}