{"as_of":"2026-08-08T10:35:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:38523d19fb4deb47b1bd46c7ee06660a4a4ab82fd1e2d46b744b5b762dd1a687","coverage":[{"denominator":69,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":69,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T20:07:28.726529Z","state":"measured"},{"denominator":69,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":69,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+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/2507.04098/citation-record","integrity":"/paper/2507.04098/integrity","json":"/paper/2507.04098/citation-record.json","paper":"/paper/2507.04098"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:07:30.998807Z","title":"Quantitative hydrodynamic limits of the L angevin dynamics for gradient interface models","venue":null,"work_id":"abb9ee52-a29b-49d0-a1fa-fbab94d86a74","year":2024},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:26.478362Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:1e99be91c7d255fec2ee3a9f01522333344b95fdd18b4c49c519e61fd43e19e4","observation_id":"9257cb33-bbe0-4e43-9361-8743b0a54e23","resolution":{"observed_at":"2026-08-06T20:07:31.004661Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2110.09498","last_updated":"2022-05-27T15:50:14Z","snapshot_observed_at":"2026-08-05T06:22:45.532782Z","submitted_at":"2021-10-18T17:48:36Z","title":"Depinning in integer-restricted Gaussian Fields and BKT phases of two-component spin models","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2110.09498","snapshot_observed_at":"2026-08-06T20:07:26.584842Z","title":"Depinning in integer-restricted G aussian F ields and BKT phases of two-component spin models","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:26.584842Z"},"links":{"cited_paper":"/paper/2110.09498","citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:54d112cf6bb02ab16b9cd48ae3032054d41a459a166362fe661225f819cd1e2b","observation_id":"daae20c1-e428-4bf4-9a75-ca3140af5ba5","resolution":{"observed_at":"2026-08-06T20:07:26.584842Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2210.06488","last_updated":"2024-09-18T17:39:05Z","snapshot_observed_at":"2026-08-04T19:18:26.680374Z","submitted_at":"2022-10-12T18:00:00Z","title":"Elliptic homogenization from qualitative to quantitative","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2210.06488","snapshot_observed_at":"2026-08-06T20:07:26.696738Z","title":"Elliptic homogenization from qualitative to quantitative","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:26.696738Z"},"links":{"cited_paper":"/paper/2210.06488","citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:9bfbd0d094097e92397ca6a77c2a47ff99e29b395b46933d18474849237d5050","observation_id":"14f966aa-8c58-4afa-93c9-8c4245cb6072","resolution":{"observed_at":"2026-08-06T20:07:26.696738Z","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":"2026-08-06T20:07:30.968090Z","title":"Armstrong, T","venue":null,"work_id":"bf4232ae-fb7b-4a5d-acca-4d6d3a4ff1d1","year":2016},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:26.731586Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:d8912e0211649f61ed4f99b52ec63ee60f48dc56781e57b3bf6e6178e96d54da","observation_id":"6e09f11f-8dc4-4750-8431-ffda481a4828","resolution":{"observed_at":"2026-08-06T20:07:30.975987Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:30.939830Z","title":"The additive structure of elliptic homogenization","venue":null,"work_id":"16a897a1-be3f-4897-a872-66a6f5c15511","year":2017},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:26.836375Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:48734af73d9cdf346d479d7149f79df7e2f11f798c58648d6277f7574495191f","observation_id":"42517c81-0c00-4031-8561-0148ff97a286","resolution":{"observed_at":"2026-08-06T20:07:30.947268Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:30.917436Z","title":"Quantitative stochastic homogenization and large-scale regularity , volume 352","venue":null,"work_id":"e19cfdde-13b8-42cb-b33a-abc448aedfe2","year":2019},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:26.942466Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:b1d3ac196f83a4cf05082f8c201301d11e728f83664f7df13eeba3cd1f05a598","observation_id":"2b9acb8a-d4a7-48fc-a3a7-1bfcdd05c612","resolution":{"observed_at":"2026-08-06T20:07:30.923469Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:30.892108Z","title":null,"venue":null,"work_id":"84b32df5-5dad-4065-9ce8-54a811ed8a58","year":1967},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:26.999208Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:82cbc07b41fb1b9aefeada94704dbbbbbaeb919c69c1926415c6fc268780399c","observation_id":"5f8b8272-1a8a-4c23-a862-cf32e77f64e4","resolution":{"observed_at":"2026-08-06T20:07:30.902013Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:30.862720Z","title":"Armstrong and Charles K","venue":null,"work_id":"061e8304-b5af-494c-8fd8-e6b705c07894","year":2016},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:27.104867Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:f76585beeac316238bba735526474b1c0103d1182c13e14e1111fcdb8e141a65","observation_id":"3c207daf-8c1a-4ea3-92f0-8b24bb5cc601","resolution":{"observed_at":"2026-08-06T20:07:30.871817Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:30.839630Z","title":"Local limit theorems for the random conductance model and applications to the Ginzburg--Landau interface model","venue":null,"work_id":"79503d59-3cb3-440b-bb7e-1901b344b102","year":2021},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:27.202087Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:ed8ae23efd60daa6d4218a57d598dc4e20a293184d53a2f714740110db136236","observation_id":"14a26b67-680a-403f-9fb7-df3a3cea93bf","resolution":{"observed_at":"2026-08-06T20:07:30.845706Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:30.815704Z","title":"C^2 regularity of the surface tension for the interface model","venue":null,"work_id":"1e213289-731c-4b9d-be2c-2aea81aeabbe","year":2022},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:27.264035Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:02342dc388db9da14f12cb259116e656bb6ba3d7ed60031af3716cbe1a7a6a46","observation_id":"d82b1d1a-a66d-41ac-98af-7d6b085561bc","resolution":{"observed_at":"2026-08-06T20:07:30.822388Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2310.13630","last_updated":"2023-10-23T01:05:37Z","snapshot_observed_at":"2026-07-06T16:36:15.820331Z","submitted_at":"2023-10-20T16:26:40Z","title":"The scaling limit of the continuous solid-on-solid model","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2310.13630","snapshot_observed_at":"2026-08-06T20:07:27.364260Z","title":"The scaling limit of the continuous solid-on-solid model","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:27.364260Z"},"links":{"cited_paper":"/paper/2310.13630","citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:fa69bf9bec5de1e2b3b8f4fe65329f3526a957a9ae12816b4e8211a619dae5a7","observation_id":"44628141-da6f-4cb6-9524-3048ad94ebc9","resolution":{"observed_at":"2026-08-06T20:07:27.364260Z","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":"2026-08-06T20:07:30.786929Z","title":"Bauerschmidt","venue":null,"work_id":"ad3841ed-7d88-44ea-ad78-1ac0fd62fb48","year":null},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:27.466445Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:958e0e6150ce2c74b7d79052768e628eb241e1e089f175161709200d1daac364","observation_id":"914d89e4-25c9-409d-abaa-56da1929cf1c","resolution":{"observed_at":"2026-08-06T20:07:30.795336Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:30.758262Z","title":"Percolation transition for random forests in d 3","venue":null,"work_id":"7bbc7384-339c-4829-8314-d4179a66545c","year":2024},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:27.543005Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:93cc90f9eebf07af5897ac79ce9b54f2ca31ae3eab006061ee65f2a9090c382e","observation_id":"db5ff1e1-5434-4e8f-b3fc-f2ac0a6198cc","resolution":{"observed_at":"2026-08-06T20:07:30.765672Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:30.731740Z","title":"Bricmont, J","venue":null,"work_id":"54f46606-d492-43ef-a6e3-7c6c49907529","year":1977},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:27.650625Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:0cb06cdc4459b14edba0282c004b4f010bdb0f1973d04631e5ae63434aa64092","observation_id":"5dc4ace0-586b-403b-918b-20c21d4bd2d2","resolution":{"observed_at":"2026-08-06T20:07:30.738774Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:30.702198Z","title":"Lebowitz, Elliott H","venue":null,"work_id":"191d2026-24fa-42bb-a66a-0ef47dfc7676","year":1980},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:27.729282Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:4a903c98ce7b5d0eb23c320650d5e2d7d39ce186a1649a7f84193a5c2eb0fb20","observation_id":"ee8a4a89-25e6-4112-90ff-8d9a67e98ace","resolution":{"observed_at":"2026-08-06T20:07:30.710344Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:30.675795Z","title":"Phase coexistence of gradient G ibbs states","venue":null,"work_id":"ad170d09-8988-4da4-a819-ed17e92efac2","year":2007},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:27.828320Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:3f0802094d8b189ee18a40a3dde934ae9e03b2408dd59a909eb95c101c2036e3","observation_id":"955992a4-1d7b-4c2c-a102-1597709f51ec","resolution":{"observed_at":"2026-08-06T20:07:30.681593Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:30.647255Z","title":null,"venue":null,"work_id":"509d32bd-c1ac-4ce7-8cd8-d0a6a17686ad","year":1976},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:27.930411Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:aa465c60311bea71898d77323c066308a4cc9deb66dc0de56141b1a21f0018bf","observation_id":"d596b6ba-45ea-4fc0-9503-dbf1c293b87c","resolution":{"observed_at":"2026-08-06T20:07:30.652944Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:30.615812Z","title":"Low temperature properties for correlation functions in classical N -vector spin models","venue":null,"work_id":"f48e6e6f-3923-4ab4-935c-acb91e143235","year":1999},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.062551Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:12a671ad3bddc8d4084c5f25486e0d87104c868f2e0c31840bcc8138f1ebf8fa","observation_id":"68609528-b37b-4b7b-9515-bc1fa451297e","resolution":{"observed_at":"2026-08-06T20:07:30.625244Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:30.585245Z","title":"The discrete G aussian model, I","venue":null,"work_id":"b8ccb90f-87bb-47de-9797-1be331ebef47","year":2024},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.109993Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:547d340299d41fb26892af482f7cc644f6a6b34535b4f447959c0114b88d99ef","observation_id":"0aa797d3-1e08-4be2-bd49-8cb03d11c72d","resolution":{"observed_at":"2026-08-06T20:07:30.592541Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:30.560919Z","title":"The discrete G aussian model, II","venue":null,"work_id":"d8d33f2e-9f07-458d-9994-8957a9c358dc","year":2024},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.222992Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:412313ae978757f08712e36dd966d3b9ccf0faaecbfc6ab1e9e211ee2ba37bbc","observation_id":"fd17677c-870c-4c79-b4ff-b404252bd2bf","resolution":{"observed_at":"2026-08-06T20:07:30.566231Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:30.541271Z","title":"Scaling limit for a class of gradient fields with nonconvex potentials","venue":null,"work_id":"44a40991-7d23-4c39-bd3f-ca704cb34cbc","year":2011},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.289209Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:88277962c068be53b483ba14127d24f726e856082db031d7886482290c039691","observation_id":"b31f8826-a966-4ca5-88ef-aa2235bbc003","resolution":{"observed_at":"2026-08-06T20:07:30.546637Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:30.516525Z","title":"Decay of covariances, uniqueness of ergodic component and scaling limit for a class of systems with non-convex potential","venue":null,"work_id":"30926d99-a09d-4f52-9694-4cef31b9404f","year":2012},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.358070Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:8adc4efa09347f133edd1a7aaa7bbf6e9bd08639d9ded3cc6ff33018f9d8c1b1","observation_id":"0c3adb83-0ec5-426e-ac6e-99dbe67b0863","resolution":{"observed_at":"2026-08-06T20:07:30.523472Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:30.489948Z","title":"Strict convexity of the free energy for a class of non-convex gradient models","venue":null,"work_id":"4cb7f114-7b5a-40e0-8387-f7d1b2ea2c95","year":2009},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.405296Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:6dbf2ba2bf39b46f4aff0eaaa4afe6478e9b80399207bf042955b235df8923ee","observation_id":"e05fa39f-6728-45ab-9a78-36427f57a93b","resolution":{"observed_at":"2026-08-06T20:07:30.501145Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:30.464265Z","title":"Validity of the spin-wave approximation for the free energy of the H eisenberg ferromagnet","venue":null,"work_id":"79797d61-95c3-47e3-9c54-7c360e3d5f2c","year":2015},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.413479Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:634e919b5b83217ef9cad54b805ad473e1a3b446fe2d5d3449ad4fa051b41f83","observation_id":"77305688-8278-4e54-9619-ed1f128ea2bb","resolution":{"observed_at":"2026-08-06T20:07:30.472140Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:30.438540Z","title":"Wilson loops in I sing lattice gauge theory","venue":null,"work_id":"b7847f5a-fba6-44cc-b796-652cf573e581","year":2020},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.419110Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:b5175e38fe804c4057b7a69a1f14a684378a86e7590932b566687dd7136394eb","observation_id":"9d38f57d-5a82-44a1-930a-5f984d6de0bd","resolution":{"observed_at":"2026-08-06T20:07:30.448143Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:30.405056Z","title":"A strong central limit theorem for a class of random surfaces","venue":null,"work_id":"cbf60012-2521-4085-95fe-ccc09182d797","year":2014},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.424892Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:b716f8d57840dadaa9b1e5223b69ed9b974e6b82dc476323fe79cc8446f69513","observation_id":"7746777a-ba7b-4f04-b4a4-4ce2b99e64c8","resolution":{"observed_at":"2026-08-06T20:07:30.415677Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2409.20405","last_updated":"2024-09-30T15:34:25Z","snapshot_observed_at":"2026-08-05T11:59:32.616683Z","submitted_at":"2024-09-30T15:34:25Z","title":"Hydrodynamic limit for a class of degenerate convex $\\nabla \\varphi$-interface models","version":1},"cited_work":{"arxiv_id":"2409.20405","doi":null,"metadata_source":"pith","pith_arxiv_id":"2409.20405","snapshot_observed_at":"2026-08-06T20:07:28.861325Z","title":"Hydrodynamic limit for a class of degenerate convex $\\nabla \\varphi$-interface models","venue":"math.PR","work_id":"ef3d2909-d337-4838-8679-1f202275f071","year":2024},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.430212Z"},"links":{"cited_paper":"/paper/2409.20405","citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:293157fa71d92d79fe1b869370b7323d2482254ba76d739f881e80ca752ccd06","observation_id":"059e9fe0-597f-4194-9863-4175c7d898ee","resolution":{"observed_at":"2026-08-06T20:07:28.870631Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:30.362812Z","title":"Delmotte and J.-D","venue":null,"work_id":"b9117043-19d6-4795-af7a-573ad7bcb685","year":2005},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.436944Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:a8e934f11ef9851ffe7c8144d9e4f695f7b8c139245855c315e2a442eb510da4","observation_id":"43aba182-11da-4a20-8c8e-39d89ebf8c92","resolution":{"observed_at":"2026-08-06T20:07:30.371198Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:30.325488Z","title":"Entropic repulsion for massless fields","venue":null,"work_id":"1bae01b3-a730-4a19-81e7-959eceb730de","year":2000},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.445789Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:1539a772792d7a2660655a72f3e2bc6372bc858fe10b398bc9fdfcf7d0a91919","observation_id":"00efe568-adbf-402a-a618-b290679ef13b","resolution":{"observed_at":"2026-08-06T20:07:30.335814Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:30.295741Z","title":"Large deviations and concentration properties for interface models","venue":null,"work_id":"923088f1-db4d-4101-9ecf-a1d3c7e6c39a","year":2000},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.453320Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:812d60c5c136a4ef213f69da2c2cce6696873d55e17d10f357775caafe11ba7e","observation_id":"a87187c8-b962-4b79-be6b-8f1cc8b092e4","resolution":{"observed_at":"2026-08-06T20:07:30.306602Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:30.249282Z","title":"Dyson, Elliott H","venue":null,"work_id":"80658340-0eca-41a7-a0e9-3ce9a7b051a8","year":1978},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.460163Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:9bf88e67b602cf9bbf19b2131deaf35a6fd7021d46d831c02e72459e91a7fbab","observation_id":"bf5c419a-2b2e-4db9-a696-c505e4ae1236","resolution":{"observed_at":"2026-08-06T20:07:30.259556Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:30.222066Z","title":null,"venue":null,"work_id":"1a43fabb-8fa5-4ce7-845b-089d24334b38","year":1975},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.466357Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:3f171c10bb4ac3b3aa4f43265db08519e2e4ba4d8bf599d864875e33dafc2e05","observation_id":"2f29cad9-b389-4560-ae26-7b465fb8cd23","resolution":{"observed_at":"2026-08-06T20:07:30.233161Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:30.189886Z","title":"A Ray--Knight theorem for interface models and scaling limits","venue":null,"work_id":"5367c305-f89f-4824-9e0f-be0a9d98c731","year":2024},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.471207Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:d6c69ae505c46730f90f24b634c1beca48cad54f24d4ac622167aa8ff4911676","observation_id":"7ac96881-8bb1-4061-b4a7-e17102ad0e31","resolution":{"observed_at":"2026-08-06T20:07:30.197291Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:29.980051Z","title":"Massless phases for the V illain model in d 3","venue":null,"work_id":"82795c50-1aba-4a56-b249-f527158ac21f","year":2024},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.477099Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:993bf117f02fab04996e555518a124a1907f6f679f97441833a9c6ea4edb911c","observation_id":"c4651cca-6f0d-440e-b81b-ba65fa6eed69","resolution":{"observed_at":"2026-08-06T20:07:29.989103Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:29.949614Z","title":null,"venue":null,"work_id":"e8ffe197-6b65-451b-a138-19732471b899","year":1956},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.483704Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:45d746c33c2ab83ac6b79e9241c76dd8d9672a0317ca49b465ba6ece5c3ebdab","observation_id":"cf11964a-6810-4345-b737-fba7d50bfb8d","resolution":{"observed_at":"2026-08-06T20:07:29.961622Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:29.922863Z","title":"Kosterlitz- T houless transition line for the two dimensional C oulomb gas","venue":null,"work_id":"2098ca3e-e21a-454e-abf7-962d9e9fe803","year":2012},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.493441Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:6cb42dfe24656d419cf3e047620ad73b3812212c024f3a53bfdc641de0afce69","observation_id":"9bc15b2e-6314-4f8b-910d-5d68bf4f3b6c","resolution":{"observed_at":"2026-08-06T20:07:29.933508Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1311.2237","last_updated":"2013-11-25T21:18:30Z","snapshot_observed_at":"2026-07-06T03:27:47.946581Z","submitted_at":"2013-11-10T01:31:16Z","title":"Critical exponents of the two dimensional Coulomb gas at the Berezinskii-Kosterlitz-Thouless transition","version":2},"cited_work":{"arxiv_id":"1311.2237","doi":null,"metadata_source":"pith","pith_arxiv_id":"1311.2237","snapshot_observed_at":"2026-08-06T20:07:28.813403Z","title":"Critical exponents of the two dimensional Coulomb gas at the Berezinskii-Kosterlitz-Thouless transition","venue":"math-ph","work_id":"00456191-0ff1-473e-8b48-524ffe577218","year":2013},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.507072Z"},"links":{"cited_paper":"/paper/1311.2237","citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:a213c1442dabbaec471644d28c1ec1cc222ee92c5eaaec7dc383929a5e0c40b8","observation_id":"8e79dec3-8f37-4c90-9182-545305d5e411","resolution":{"observed_at":"2026-08-06T20:07:28.822488Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:29.890188Z","title":"u rg Fr\\","venue":null,"work_id":"7f1db80c-9bd3-42e6-a06f-380244502d03","year":1981},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.514232Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:7f91fd7f68a520a5d1b4c601037bd24179215d3a4d437bcafcdac8fccc17c22a","observation_id":"b26cc460-ed19-4609-bebb-3a1663507ae4","resolution":{"observed_at":"2026-08-06T20:07:29.901434Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:29.863558Z","title":"u rg Fr\\","venue":null,"work_id":"ba4e49b0-5c52-4f42-a051-486dcd75b59e","year":1982},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.519758Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:71efd5ec31e6e84e4e78de9d778fd6b8214dcda864f174c4d3ffcdaa01fcc6c1","observation_id":"22abdf30-157c-4a3f-b61f-d13767b180d6","resolution":{"observed_at":"2026-08-06T20:07:29.872423Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:29.840839Z","title":"Funaki and H","venue":null,"work_id":"2a77bf24-027c-4c54-92ef-d02bea551dd3","year":1997},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.527292Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:56228decb4e60189f24e6522472b07b03d90bb5a529fda6e5cd33b05894cdc8c","observation_id":"203120f3-61df-4749-badd-5c563d5017cb","resolution":{"observed_at":"2026-08-06T20:07:29.846566Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:29.813609Z","title":"Fr\\\" o hlich, B","venue":null,"work_id":"b0389ca7-f0f2-4b35-8753-183c8382f815","year":1976},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.535143Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:8f5e3b542c275abedca9a82318562077774ed5ba139a018bfb808b82deb27b1d","observation_id":"204b8d53-08e6-4f9c-a8e3-723dba455e0a","resolution":{"observed_at":"2026-08-06T20:07:29.819793Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:29.789031Z","title":"Stochastic interface models","venue":null,"work_id":"ff47d6d3-c6de-477e-84fa-b470703dacf6","year":2005},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":42,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.542743Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:e0522bf951866d26cb6d94c0f361ce969637dd73daf6a70e0cb2b1281f56acaa","observation_id":"7739313c-1a1c-450b-a745-f4fd9ab808ba","resolution":{"observed_at":"2026-08-06T20:07:29.794682Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:29.765634Z","title":null,"venue":null,"work_id":"76a8eb67-3b13-4e0a-8ac1-96925a01e791","year":1970},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":43,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.547828Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:4fb777b24fef02bfb64d512afac175ca58ae1e234c76fe3e981de4da7bcbf2cc","observation_id":"0451842c-7218-4340-a6b3-a1b97ce38b06","resolution":{"observed_at":"2026-08-06T20:07:29.771635Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:29.741583Z","title":"Gloria, S","venue":null,"work_id":"ce4052f9-250f-4c63-88e8-a723ae57a034","year":2015},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":44,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.553647Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:96a1056e6f06435f65a349577f3f44c64ebc0b3af5c782660743b1eaa03688a4","observation_id":"91a0c10a-6a63-4101-a7a4-dbccd6fee8bf","resolution":{"observed_at":"2026-08-06T20:07:29.749117Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:28.558610Z","title":"Gloria and F","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.558610Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:f901324ff9ff8d528196380f13ecd8c4ca62e4ea95e0dfcfd55a4bdd633d192f","observation_id":"f672c308-a22c-4398-9ce0-a3d0d21a5c01","resolution":{"observed_at":"2026-08-06T20:07:28.558610Z","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":"2026-08-06T20:07:28.565149Z","title":"Gloria and F","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":46,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.565149Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:d4fbc769a042e447aa59214f4aba277d1b17b0cc573c0ea7c1011284d9076304","observation_id":"729ffa3c-c7ee-4e49-9ea3-f4a4c2a502b7","resolution":{"observed_at":"2026-08-06T20:07:28.565149Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1510.08290","last_updated":"2016-05-04T22:14:58Z","snapshot_observed_at":"2026-07-06T04:34:31.968768Z","submitted_at":"2015-10-28T12:46:57Z","title":"The corrector in stochastic homogenization: optimal rates, stochastic integrability, and fluctuations","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1510.08290","snapshot_observed_at":"2026-08-06T20:07:28.570499Z","title":"The corrector in stochastic homogenization: optimal rates, stochastic integrability, and fluctuations","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":47,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.570499Z"},"links":{"cited_paper":"/paper/1510.08290","citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:beaff6624a16f8e0eaeb2ff2ff134819af027fa97dab2f86eb670c51378ff8c1","observation_id":"55204ccc-7595-45cd-b248-60119cdeb3b6","resolution":{"observed_at":"2026-08-06T20:07:28.570499Z","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":"2026-08-06T20:07:29.664978Z","title":"Quantitative results on the corrector equation in stochastic homogenization","venue":null,"work_id":"ab4b9f23-5d66-4b08-9446-71508051ac28","year":2017},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":48,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.576745Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:96a7b8d4ea3c1f3a6a9b9b7e814ff100861374938056df4c994b0907c346f133","observation_id":"78c1d0ec-77be-41a8-bf49-ac0a00e12726","resolution":{"observed_at":"2026-08-06T20:07:29.670908Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:29.630819Z","title":"Low-temperature asymptotic expansion for classical O ( N ) vector models","venue":null,"work_id":"9d1c24c1-f844-4d0e-aed6-ba5880164f6c","year":2025},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":49,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.584769Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:eb0826c42039ebc767230d84d4da50db53e37ce75e87ec9d8b3ead3ede264fe7","observation_id":"93ff1981-a434-4f48-8fa6-edb01817e5e7","resolution":{"observed_at":"2026-08-06T20:07:29.640474Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:29.597461Z","title":"Goldstone","venue":null,"work_id":"86e5f657-9460-4517-86f1-f59afae727ce","year":1961},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":50,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.595479Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:93442c49f92f2b763eb604f663a7a538cae426223f47f5569010a61b004b8448","observation_id":"d848baa2-8e40-4271-8040-bf7cfb78553b","resolution":{"observed_at":"2026-08-06T20:07:29.605951Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:29.572106Z","title":"Equilibrium fluctuations for interface model","venue":null,"work_id":"d293b18f-8cc8-45a7-9f0e-c5f066d39f0c","year":2001},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":51,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.604056Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:6d38c9dc751392b9dfff5d56db0592a34fc64ab33e97887fe404a73299ef307a","observation_id":"ed3cf72d-63f4-478d-a43b-959f65200138","resolution":{"observed_at":"2026-08-06T20:07:29.580526Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:29.542377Z","title":"Improved spin-wave estimate for W ilson loops in U(1) lattice gauge theory","venue":null,"work_id":"b8dcc046-72fd-4002-b86c-b9eb2309f74a","year":2023},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":52,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.614757Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:9203f346750924c80299eebe7e4c98c4c7267fa9f473a5ca12538f2f6f4c5ae2","observation_id":"6bca7e5f-2c22-4483-9d34-01e19a383e76","resolution":{"observed_at":"2026-08-06T20:07:29.548973Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:28.620085Z","title":"Trudinger","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":53,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.620085Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:3e35c5fe3cc61e61af4ae2245a9344f3f2848aa04e93410f515d7f4dd6e10bcd","observation_id":"2c187026-b6c9-44d3-ac39-a657ae437f7f","resolution":{"observed_at":"2026-08-06T20:07:28.620085Z","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":"2026-08-06T20:07:29.474698Z","title":null,"venue":null,"work_id":"5a29aa5a-f8ff-4d92-8d94-8ba084e97f9a","year":1980},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":54,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.625992Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:116de4bd765f2cb9f12873093f3acbfa4213ba91168189a9ab2c630d8152b3a7","observation_id":"910611e3-7b09-4682-8f3d-e4b40b176430","resolution":{"observed_at":"2026-08-06T20:07:29.491114Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:29.437335Z","title":"On the correlation for K ac-like models in the convex case","venue":null,"work_id":"90cc5280-fd42-4511-94fd-350b4ce12887","year":1994},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":55,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.631283Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:9398993d91bc238646fb195ea7ac41c48d0f8181e07c54f85ff3ef3aae06a90f","observation_id":"1fb00741-91e2-489d-8d67-e37281df6eaf","resolution":{"observed_at":"2026-08-06T20:07:29.443449Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:29.407475Z","title":"Spontaneous symmetry breakdown in the abelian H iggs model","venue":null,"work_id":"8135d6e4-ada2-4a83-835c-92d191dc8deb","year":1986},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":56,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.638030Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:0c6cce05828290bf72eb4d87cb1c28e45719aaefe7ea88f3fd5d4a9f1c2000ab","observation_id":"28542f5c-a5ac-4709-9d3c-37509481ad75","resolution":{"observed_at":"2026-08-06T20:07:29.420501Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:29.375663Z","title":"Ordering, metastability and phase transitions in two-dimensional systems","venue":null,"work_id":"c86bc2f8-3627-4292-8a4d-1885e9516519","year":1973},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":57,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.643690Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:641058b512e22f625f4353cc77e546864a21db61027078d5aa3ffe58abeed7bb","observation_id":"3a10c753-e236-44c0-b5eb-29aa478f9ba9","resolution":{"observed_at":"2026-08-06T20:07:29.383934Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:28.649947Z","title":"Random walk: a modern introduction , volume 123","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":58,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.649947Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:299bd345a4edd7183cad42304cc5e1b9cde0fe492dfbea911c8ee6f74b3c67c0","observation_id":"11954102-da04-45f3-8318-5fad3c00e84c","resolution":{"observed_at":"2026-08-06T20:07:28.649947Z","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":"2026-08-06T20:07:29.307966Z","title":"Fluctuations for the G inzburg- L andau interface model on a bounded domain","venue":null,"work_id":"6964f992-4c59-4cc7-bcac-cc24469b10c8","year":2011},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":59,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.656532Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:f63233067bd78fae78a45f7189892069311a6bf8f4702a9c38119a5ab9e904bb","observation_id":"d5ba89a2-010c-45f2-aba5-03ec7ac0ea0d","resolution":{"observed_at":"2026-08-06T20:07:29.316099Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:29.269603Z","title":"Absence of ferromagnetism or antiferromagnetism in one-or two-dimensional isotropic H eisenberg models","venue":null,"work_id":"84efe4df-294f-40a1-9722-77b03a0b10e3","year":1966},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":60,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.663835Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:180c8b249b0145df490e53d3e39b6f59ede1bfec3b46043efb86ce96bff30c2b","observation_id":"531aedd9-df51-4f40-a23b-9cf295fbaaef","resolution":{"observed_at":"2026-08-06T20:07:29.280096Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:28.671897Z","title":"Naddaf and T","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":61,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.671897Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:b86cbfb98f0d9e928a5bf910dd0c8e037a5aebff7cf8ce6e65ad92aebba7bfab","observation_id":"73f87b41-a39d-42d6-88a3-8f3a3f90ef7d","resolution":{"observed_at":"2026-08-06T20:07:28.671897Z","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":"2026-08-06T20:07:29.209593Z","title":"Newman and Wei Wu","venue":null,"work_id":"988d410e-2442-4fd9-ae02-f8be88827d25","year":2019},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":62,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.677330Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:bc6ba0926af02f70f89e52fd66f9bca5d114f68b6958b20217d2ee584e1faaea","observation_id":"1fe65c02-d195-4131-85bc-a046c36a7b5e","resolution":{"observed_at":"2026-08-06T20:07:29.221830Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:29.183868Z","title":"Sheffield","venue":null,"work_id":"cfb8ea7a-61eb-4f89-a987-9d533ee8c3ea","year":2005},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":63,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.683850Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:75c3064ed85f44a64d7992b1c6d062c5094edc3febba5cfb74f24e6550e32c05","observation_id":"3f07d64d-db61-4d47-8615-1af48c73d031","resolution":{"observed_at":"2026-08-06T20:07:29.190360Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:29.153876Z","title":"Sj \\\"o strand","venue":null,"work_id":"54c6b3d6-cc21-4fec-b776-529715c66287","year":1996},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":64,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.689512Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:cb7211ad858e5f9cac1f1c775caf8141c8bedffee1782a88e6631e946a98716c","observation_id":"4dca1d17-4058-4505-a605-3b422dc8e853","resolution":{"observed_at":"2026-08-06T20:07:29.162491Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:29.119888Z","title":"Euclidean proof of the G oldstone T heorem","venue":null,"work_id":"7bd92805-f5c3-4ad6-845b-b3e01eea666f","year":1967},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":65,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.696984Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:984de7806e00a86b1321bb8bc50026e7651a67e04c4383aaee293e13c06d4840","observation_id":"c28aae12-4e0d-4510-a1e3-3b827988f646","resolution":{"observed_at":"2026-08-06T20:07:29.128652Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:29.094690Z","title":"Symanzik","venue":null,"work_id":"6ac56a21-43bb-46de-b373-e1f824838af7","year":1970},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":66,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.702986Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:12c82b4c6aedbecb12f98fb7e126ca7df6b7c1b5c6896cfa00d36bde99fdd769","observation_id":"10e15010-1b7b-485c-8ec5-2eb1ba8d2d34","resolution":{"observed_at":"2026-08-06T20:07:29.100766Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:29.054248Z","title":"Localization and delocalization of random interfaces","venue":null,"work_id":"b51c9f53-caa7-4e5c-9b93-93f46d744433","year":2006},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":67,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.711899Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:8c91b60e80e3f42aa5f1ae665d19081b8fede4918553eab6c67fab79185d4ece","observation_id":"4967c4b5-1863-4ca4-83ba-daee2ed75e2b","resolution":{"observed_at":"2026-08-06T20:07:29.060595Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:29.011486Z","title":"Theory of one-and two-dimensional magnets with an easy magnetization plane","venue":null,"work_id":"134e72f1-cb78-4474-8e23-f6856ef3b6fc","year":1975},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":68,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.719228Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:7f06c8382ae4bc87261d8c1183c310fbc4be5ed4f0579ff482537e5561b5fd78","observation_id":"f2111c16-a852-49ae-8e49-f1c195eb0422","resolution":{"observed_at":"2026-08-06T20:07:29.023021Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:07:28.984878Z","title":"Local central limit theorem for gradient field models","venue":null,"work_id":"33776098-dfdc-4908-8120-ec827a102340","year":2025},"citing_paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model","version":1},"reference_index":69,"source":"arxiv_source","source_observed_at":"2026-08-06T20:07:28.726529Z"},"links":{"citing_paper":"/paper/2507.04098"},"observation_digest":"sha256:2be6ddc5005f203bce629a6039d2e400fae7641c52d910cc60c3710bd5e6b7fa","observation_id":"ee62d1a4-6784-4f51-bbfa-b8dbc75ad672","resolution":{"observed_at":"2026-08-06T20:07:28.992629Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.04098","last_updated":"2025-07-05T16:48:01Z","latest_version":1,"primary_category":"math.PR","snapshot_observed_at":"2026-08-06T19:53:19.976281Z","submitted_at":"2025-07-05T16:48:01Z","title":"Parallel spin wave for the Villain model"},"reference_resolution":{"displayed":69,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":15,"verified_exact":2,"verified_fuzzy":52},"total_outbound_references":69},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 69 of 69 outbound references and 0 inbound Pith citation observations for arXiv:2507.04098."}