{"as_of":"2026-08-05T20:41:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:d35b826a04fb675965c545dc56fdb6274d94d2b2358e480a4e89afa3e4c750ab","coverage":[{"denominator":32,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":32,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-26T19:21:29.846750Z","state":"measured"},{"denominator":32,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":32,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-05T06:32:48.257954+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/2606.18752/citation-record","integrity":"/paper/2606.18752/integrity","json":"/paper/2606.18752/citation-record.json","paper":"/paper/2606.18752"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"1303.3573","last_updated":"2013-03-14T19:48:01Z","snapshot_observed_at":"2026-08-04T09:26:06.878574Z","submitted_at":"2013-03-14T19:48:01Z","title":"On properties of Parisi measures","version":1},"cited_work":{"arxiv_id":"1303.3573","doi":null,"metadata_source":"pith","pith_arxiv_id":"1303.3573","snapshot_observed_at":"2026-07-04T02:49:24.108011Z","title":"On properties of Parisi measures","venue":"math.PR","work_id":"f854c22e-9b29-4843-b4be-c6c1d3663f5b","year":2013},"citing_paper":{"arxiv_id":"2606.18752","last_updated":"2026-06-18T13:29:17Z","snapshot_observed_at":"2026-08-02T13:01:02.852581Z","submitted_at":"2026-06-17T06:56:55Z","title":"Self-averaging of replica overlaps in the random field Edwards-Anderson model","version":2},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-06-26T19:21:29.846750Z"},"links":{"cited_paper":"/paper/1303.3573","citing_paper":"/paper/2606.18752"},"observation_digest":"sha256:3539b92f4c980f37905bd13aa360be932f9b55a335afccc59d42e84c5958dd05","observation_id":"c0a90570-b01e-43d3-9e7e-8ce7d186f99a","resolution":{"observed_at":"2026-07-04T02:49:24.109515Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"cond-mat/9712129","last_updated":"1998-06-08T16:33:09Z","snapshot_observed_at":"2026-07-07T02:50:07.875335Z","submitted_at":"1997-12-11T20:47:36Z","title":"On the Stability of the Quenched State in Mean Field Spin Glass Models","version":3},"cited_work":{"arxiv_id":"cond-mat/9712129","doi":null,"metadata_source":"pith","pith_arxiv_id":"cond-mat/9712129","snapshot_observed_at":"2026-07-04T02:49:24.115913Z","title":"On the Stability of the Quenched State in Mean Field Spin Glass Models","venue":"cond-mat.stat-mech","work_id":"1951bd8d-5de4-4c56-a945-944d828fe6bd","year":1997},"citing_paper":{"arxiv_id":"2606.18752","last_updated":"2026-06-18T13:29:17Z","snapshot_observed_at":"2026-08-02T13:01:02.852581Z","submitted_at":"2026-06-17T06:56:55Z","title":"Self-averaging of replica overlaps in the random field Edwards-Anderson model","version":2},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-06-26T19:21:29.846750Z"},"links":{"cited_paper":"/paper/cond-mat/9712129","citing_paper":"/paper/2606.18752"},"observation_digest":"sha256:4a61272b4d7fb911502ea55c88295e65cbbbf8e66496557db83816812fe6635f","observation_id":"7c83bcc1-94f4-4f43-9f05-b028aeac23eb","resolution":{"observed_at":"2026-07-04T02:49:24.117742Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-26T19:21:29.846750Z","title":null,"venue":null,"work_id":null,"year":1978},"citing_paper":{"arxiv_id":"2606.18752","last_updated":"2026-06-18T13:29:17Z","snapshot_observed_at":"2026-08-02T13:01:02.852581Z","submitted_at":"2026-06-17T06:56:55Z","title":"Self-averaging of replica overlaps in the random field Edwards-Anderson model","version":2},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-06-26T19:21:29.846750Z"},"links":{"citing_paper":"/paper/2606.18752"},"observation_digest":"sha256:74b5a9deb8ec52b575685df77372a62f8cfc2acb04187c59e59033286e0e8fdd","observation_id":"d9d6a2d8-652a-4af4-ac87-47ebaaa513b0","resolution":{"observed_at":"2026-06-26T19:21:29.846750Z","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":"2026-06-26T19:21:29.846750Z","title":"Statistical Mechanics of Disordered Systems: A Mathematical Perspective , Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge University Press, 2006","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2606.18752","last_updated":"2026-06-18T13:29:17Z","snapshot_observed_at":"2026-08-02T13:01:02.852581Z","submitted_at":"2026-06-17T06:56:55Z","title":"Self-averaging of replica overlaps in the random field Edwards-Anderson model","version":2},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-06-26T19:21:29.846750Z"},"links":{"citing_paper":"/paper/2606.18752"},"observation_digest":"sha256:b65b49adda7e059802b2a5d72b4d1b6965f1c35ea81f270d066408e2cb431752","observation_id":"bb57c38a-c6e3-4aeb-aa93-473a81b0ff7e","resolution":{"observed_at":"2026-06-26T19:21:29.846750Z","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":"2026-06-26T19:21:29.846750Z","title":null,"venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2606.18752","last_updated":"2026-06-18T13:29:17Z","snapshot_observed_at":"2026-08-02T13:01:02.852581Z","submitted_at":"2026-06-17T06:56:55Z","title":"Self-averaging of replica overlaps in the random field Edwards-Anderson model","version":2},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-06-26T19:21:29.846750Z"},"links":{"citing_paper":"/paper/2606.18752"},"observation_digest":"sha256:34098a952e79c8ff2301b7ef25fd3a40b6df211a5a1f915397e3d0c3fc9336fd","observation_id":"5e5d8109-0287-4491-9f4e-698fa63d5ae5","resolution":{"observed_at":"2026-06-26T19:21:29.846750Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1404.7178","last_updated":"2014-07-29T22:52:35Z","snapshot_observed_at":"2026-07-06T03:42:17.811981Z","submitted_at":"2014-04-28T21:50:29Z","title":"Absence of replica symmetry breaking in the random field Ising model","version":2},"cited_work":{"arxiv_id":"1404.7178","doi":null,"metadata_source":"pith","pith_arxiv_id":"1404.7178","snapshot_observed_at":"2026-07-04T02:49:24.100551Z","title":"Absence of replica symmetry breaking in the random field Ising model","venue":"math-ph","work_id":"dcb25576-d2ae-40ba-a043-a073def5e892","year":2014},"citing_paper":{"arxiv_id":"2606.18752","last_updated":"2026-06-18T13:29:17Z","snapshot_observed_at":"2026-08-02T13:01:02.852581Z","submitted_at":"2026-06-17T06:56:55Z","title":"Self-averaging of replica overlaps in the random field Edwards-Anderson model","version":2},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-06-26T19:21:29.846750Z"},"links":{"cited_paper":"/paper/1404.7178","citing_paper":"/paper/2606.18752"},"observation_digest":"sha256:18b22a30471becde77aef63c0161d16b9670d7f90e8d9773790a71d0a0f05b22","observation_id":"ad325f26-3549-4a8a-805a-7fa7060d60c8","resolution":{"observed_at":"2026-07-04T02:49:24.102133Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2103.04802","last_updated":"2021-11-05T01:19:39Z","snapshot_observed_at":"2026-07-06T10:47:51.102861Z","submitted_at":"2021-03-08T14:53:03Z","title":"On the Almeida-Thouless transition line in the Sherrington-Kirkpatrick model with centered Gaussian external field","version":2},"cited_work":{"arxiv_id":"2103.04802","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2103.04802","snapshot_observed_at":"2026-07-04T02:49:24.116190Z","title":null,"venue":null,"work_id":"6185b0f4-6977-4088-b031-0d7abd8587d1","year":null},"citing_paper":{"arxiv_id":"2606.18752","last_updated":"2026-06-18T13:29:17Z","snapshot_observed_at":"2026-08-02T13:01:02.852581Z","submitted_at":"2026-06-17T06:56:55Z","title":"Self-averaging of replica overlaps in the random field Edwards-Anderson model","version":2},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-06-26T19:21:29.846750Z"},"links":{"cited_paper":"/paper/2103.04802","citing_paper":"/paper/2606.18752"},"observation_digest":"sha256:4e7b4977e6e94a9acdf09b2de60a691d7a54572ec6aa988186be1122838205d4","observation_id":"a9e139be-7638-47da-8aee-a62cf104e3ad","resolution":{"observed_at":"2026-07-04T02:49:24.117761Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-26T19:21:29.846750Z","title":null,"venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"2606.18752","last_updated":"2026-06-18T13:29:17Z","snapshot_observed_at":"2026-08-02T13:01:02.852581Z","submitted_at":"2026-06-17T06:56:55Z","title":"Self-averaging of replica overlaps in the random field Edwards-Anderson model","version":2},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-06-26T19:21:29.846750Z"},"links":{"citing_paper":"/paper/2606.18752"},"observation_digest":"sha256:16186b856ee91a9e80532af5349168ef8f9c7bc9c01ec1f8c068abb0e3f5bf18","observation_id":"86684dc8-ab17-4161-8fae-7bcb59357960","resolution":{"observed_at":"2026-06-26T19:21:29.846750Z","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":"cmp/1103940","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-04T02:49:24.103599Z","title":"Deift and B","venue":null,"work_id":"86f21973-67e5-4b2d-b5e9-077328aeedb4","year":1983},"citing_paper":{"arxiv_id":"2606.18752","last_updated":"2026-06-18T13:29:17Z","snapshot_observed_at":"2026-08-02T13:01:02.852581Z","submitted_at":"2026-06-17T06:56:55Z","title":"Self-averaging of replica overlaps in the random field Edwards-Anderson model","version":2},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-06-26T19:21:29.846750Z"},"links":{"citing_paper":"/paper/2606.18752"},"observation_digest":"sha256:67df8ddca65edde843558355a3ef8cb53f1ffd40ed2063f64e97f847d9e97ffb","observation_id":"63933d30-2cee-445d-8ec4-5e38a472cdf2","resolution":{"observed_at":"2026-07-04T02:49:24.105405Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-26T19:21:29.846750Z","title":null,"venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2606.18752","last_updated":"2026-06-18T13:29:17Z","snapshot_observed_at":"2026-08-02T13:01:02.852581Z","submitted_at":"2026-06-17T06:56:55Z","title":"Self-averaging of replica overlaps in the random field Edwards-Anderson model","version":2},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-06-26T19:21:29.846750Z"},"links":{"citing_paper":"/paper/2606.18752"},"observation_digest":"sha256:463f19413cc439188460147d05cf18aa511cd17bb14a58bbd3f62bae77e663ab","observation_id":"59b3d6ab-254d-478f-a819-98e17f934b42","resolution":{"observed_at":"2026-06-26T19:21:29.846750Z","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":"2026-06-26T19:21:29.846750Z","title":null,"venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2606.18752","last_updated":"2026-06-18T13:29:17Z","snapshot_observed_at":"2026-08-02T13:01:02.852581Z","submitted_at":"2026-06-17T06:56:55Z","title":"Self-averaging of replica overlaps in the random field Edwards-Anderson model","version":2},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-06-26T19:21:29.846750Z"},"links":{"citing_paper":"/paper/2606.18752"},"observation_digest":"sha256:02ae3a585ba74b63a3b074617ae84edfa6907cd7b774c4d37e87ddac8b1feed6","observation_id":"94a3f3eb-1020-44ad-a700-da32e29fd9c0","resolution":{"observed_at":"2026-06-26T19:21:29.846750Z","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":"2026-06-26T19:21:29.846750Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2606.18752","last_updated":"2026-06-18T13:29:17Z","snapshot_observed_at":"2026-08-02T13:01:02.852581Z","submitted_at":"2026-06-17T06:56:55Z","title":"Self-averaging of replica overlaps in the random field Edwards-Anderson model","version":2},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-06-26T19:21:29.846750Z"},"links":{"citing_paper":"/paper/2606.18752"},"observation_digest":"sha256:6d8acbf4b0e54bfc4f3c25a4bf5636cb59480f8de6aeb45348b846b3634e3d05","observation_id":"d16933e7-5225-4d44-9b55-95452c4f239f","resolution":{"observed_at":"2026-06-26T19:21:29.846750Z","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":"2026-06-26T19:21:29.846750Z","title":"M., Kasteleyn P","venue":null,"work_id":null,"year":1971},"citing_paper":{"arxiv_id":"2606.18752","last_updated":"2026-06-18T13:29:17Z","snapshot_observed_at":"2026-08-02T13:01:02.852581Z","submitted_at":"2026-06-17T06:56:55Z","title":"Self-averaging of replica overlaps in the random field Edwards-Anderson model","version":2},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-06-26T19:21:29.846750Z"},"links":{"citing_paper":"/paper/2606.18752"},"observation_digest":"sha256:115e8da227ce8d2af8518c4e2c64890ae3d2fc3b9b4008cdc176d85c98582dc7","observation_id":"1efd7d5e-851b-408a-95c7-985164e56600","resolution":{"observed_at":"2026-06-26T19:21:29.846750Z","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":"2026-06-26T19:21:29.846750Z","title":null,"venue":null,"work_id":null,"year":1966},"citing_paper":{"arxiv_id":"2606.18752","last_updated":"2026-06-18T13:29:17Z","snapshot_observed_at":"2026-08-02T13:01:02.852581Z","submitted_at":"2026-06-17T06:56:55Z","title":"Self-averaging of replica overlaps in the random field Edwards-Anderson model","version":2},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-06-26T19:21:29.846750Z"},"links":{"citing_paper":"/paper/2606.18752"},"observation_digest":"sha256:0f109426de9d12f403b4ef1c3ff9febc30944069ed566c857ed7ba50a7f07f34","observation_id":"8a4a9b3d-fb71-4f12-8222-f534555fec7e","resolution":{"observed_at":"2026-06-26T19:21:29.846750Z","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":"2026-06-26T19:21:29.846750Z","title":": General properties of overlap probability distributions in disordered spin systems","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2606.18752","last_updated":"2026-06-18T13:29:17Z","snapshot_observed_at":"2026-08-02T13:01:02.852581Z","submitted_at":"2026-06-17T06:56:55Z","title":"Self-averaging of replica overlaps in the random field Edwards-Anderson model","version":2},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-06-26T19:21:29.846750Z"},"links":{"citing_paper":"/paper/2606.18752"},"observation_digest":"sha256:2b5c5085939ef495acc28c64b1c35b2550445c1eaf7ab882ec0c266a68442125","observation_id":"ebcf0db8-10e8-483b-9249-2c635852f10d","resolution":{"observed_at":"2026-06-26T19:21:29.846750Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2310.04775","last_updated":"2024-02-24T23:49:13Z","snapshot_observed_at":"2026-07-06T16:29:07.961823Z","submitted_at":"2023-10-07T10:58:00Z","title":"Griffiths-type theorems for short-range spin glass models","version":2},"cited_work":{"arxiv_id":"2310.04775","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2310.04775","snapshot_observed_at":"2026-07-04T02:49:24.102121Z","title":"Mukaida, H","venue":null,"work_id":"a0c2e946-97fc-432b-9195-738ecea36989","year":2024},"citing_paper":{"arxiv_id":"2606.18752","last_updated":"2026-06-18T13:29:17Z","snapshot_observed_at":"2026-08-02T13:01:02.852581Z","submitted_at":"2026-06-17T06:56:55Z","title":"Self-averaging of replica overlaps in the random field Edwards-Anderson model","version":2},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-06-26T19:21:29.846750Z"},"links":{"cited_paper":"/paper/2310.04775","citing_paper":"/paper/2606.18752"},"observation_digest":"sha256:962f2703939b2dc5d57bd9d98351600622564c0bc67385c3f7e0cbc5968bea8a","observation_id":"a559d2b1-6a06-4620-898d-d5eabfa9b420","resolution":{"observed_at":"2026-07-04T02:49:24.103678Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"cmp/1104254","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-04T02:49:24.110047Z","title":null,"venue":null,"work_id":"62e589bf-e4d4-4c29-aeec-08e80af49a8a","year":1993},"citing_paper":{"arxiv_id":"2606.18752","last_updated":"2026-06-18T13:29:17Z","snapshot_observed_at":"2026-08-02T13:01:02.852581Z","submitted_at":"2026-06-17T06:56:55Z","title":"Self-averaging of replica overlaps in the random field Edwards-Anderson model","version":2},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-06-26T19:21:29.846750Z"},"links":{"citing_paper":"/paper/2606.18752"},"observation_digest":"sha256:7bd3733dd05ea0a30d6f7445b66603dcbb24e36bf69fe70833af9c842ce98ba8","observation_id":"36f31737-1ba9-49c7-808c-66e66feded72","resolution":{"observed_at":"2026-07-04T02:49:24.111651Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"cond-mat/0002055","last_updated":"2000-09-05T15:49:14Z","snapshot_observed_at":"2026-07-07T01:34:44.438408Z","submitted_at":"2000-02-03T14:52:28Z","title":"Spin and link overlaps in 3-dimensional spin glasses","version":2},"cited_work":{"arxiv_id":"cond-mat/0002055","doi":null,"metadata_source":"pith","pith_arxiv_id":"cond-mat/0002055","snapshot_observed_at":"2026-07-04T02:49:24.096258Z","title":"Spin and link overlaps in 3-dimensional spin glasses","venue":"cond-mat.dis-nn","work_id":"331a62f1-4f02-44a5-b76f-ce427670ba47","year":2000},"citing_paper":{"arxiv_id":"2606.18752","last_updated":"2026-06-18T13:29:17Z","snapshot_observed_at":"2026-08-02T13:01:02.852581Z","submitted_at":"2026-06-17T06:56:55Z","title":"Self-averaging of replica overlaps in the random field Edwards-Anderson model","version":2},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-06-26T19:21:29.846750Z"},"links":{"cited_paper":"/paper/cond-mat/0002055","citing_paper":"/paper/2606.18752"},"observation_digest":"sha256:9f3193912c45938148fa9da2f118cf62d389725bd05db8db1141e78f3dbb9744","observation_id":"035d2bdb-03aa-4c65-a178-662795748661","resolution":{"observed_at":"2026-07-04T02:49:24.098013Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"cond-mat/9804266","last_updated":"1998-08-21T07:58:36Z","snapshot_observed_at":"2026-07-07T02:51:43.478381Z","submitted_at":"1998-04-24T12:51:24Z","title":"New phenomena in the random field Ising model","version":2},"cited_work":{"arxiv_id":"cond-mat/9804266","doi":null,"metadata_source":"pith","pith_arxiv_id":"cond-mat/9804266","snapshot_observed_at":"2026-07-04T02:49:24.110781Z","title":"New phenomena in the random field Ising model","venue":"cond-mat","work_id":"d2003482-4df4-4825-a514-2380c8713788","year":1998},"citing_paper":{"arxiv_id":"2606.18752","last_updated":"2026-06-18T13:29:17Z","snapshot_observed_at":"2026-08-02T13:01:02.852581Z","submitted_at":"2026-06-17T06:56:55Z","title":"Self-averaging of replica overlaps in the random field Edwards-Anderson model","version":2},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-06-26T19:21:29.846750Z"},"links":{"cited_paper":"/paper/cond-mat/9804266","citing_paper":"/paper/2606.18752"},"observation_digest":"sha256:fecebd0f0c8f9307b09e3513aeabd99ff97cf329492f64c9907ed1f995cd7b14","observation_id":"19a6b33f-b44e-439a-894d-7bc58e23978f","resolution":{"observed_at":"2026-07-04T02:49:24.112197Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"adap-org/9508006","last_updated":"1995-08-25T22:06:30Z","snapshot_observed_at":"2026-07-07T00:08:06.269337Z","submitted_at":"1995-08-25T22:06:30Z","title":"Non-Mean-Field Behavior of Realistic Spin Glasses","version":1},"cited_work":{"arxiv_id":"adap-org/9508006","doi":null,"metadata_source":"pith","pith_arxiv_id":"adap-org/9508006","snapshot_observed_at":"2026-07-04T02:49:24.121361Z","title":"Non-Mean-Field Behavior of Realistic Spin Glasses","venue":"adap-org","work_id":"cba8007d-21ca-4a07-96ca-cf8d945adb28","year":1995},"citing_paper":{"arxiv_id":"2606.18752","last_updated":"2026-06-18T13:29:17Z","snapshot_observed_at":"2026-08-02T13:01:02.852581Z","submitted_at":"2026-06-17T06:56:55Z","title":"Self-averaging of replica overlaps in the random field Edwards-Anderson model","version":2},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-06-26T19:21:29.846750Z"},"links":{"cited_paper":"/paper/adap-org/9508006","citing_paper":"/paper/2606.18752"},"observation_digest":"sha256:a9c86759639732936247f284865cf6659907d9017c71594b983f2eb5746b6a00","observation_id":"5e758e3b-261e-491c-8ea7-c03f9af79851","resolution":{"observed_at":"2026-07-04T02:49:24.123006Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"cond-mat/9612097","last_updated":"1996-12-10T22:21:31Z","snapshot_observed_at":"2026-07-07T02:46:55.950080Z","submitted_at":"1996-12-10T22:21:31Z","title":"The metastate approach to thermodynamic chaos","version":1},"cited_work":{"arxiv_id":"cond-mat/9612097","doi":null,"metadata_source":"pith","pith_arxiv_id":"cond-mat/9612097","snapshot_observed_at":"2026-07-04T02:49:24.118895Z","title":"The metastate approach to thermodynamic chaos","venue":"cond-mat.dis-nn","work_id":"fd23a237-d31a-405d-be40-114c1b7f0586","year":1996},"citing_paper":{"arxiv_id":"2606.18752","last_updated":"2026-06-18T13:29:17Z","snapshot_observed_at":"2026-08-02T13:01:02.852581Z","submitted_at":"2026-06-17T06:56:55Z","title":"Self-averaging of replica overlaps in the random field Edwards-Anderson model","version":2},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-06-26T19:21:29.846750Z"},"links":{"cited_paper":"/paper/cond-mat/9612097","citing_paper":"/paper/2606.18752"},"observation_digest":"sha256:48e92fd8b25c2e44d02f5fc2e12e5b9a66e5e9da4317f9efc1e90a4b85854712","observation_id":"b4d7f1ae-8d3f-41af-86e4-fe862b641c12","resolution":{"observed_at":"2026-07-04T02:49:24.120383Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"cond-mat/0105282","last_updated":"2001-08-29T19:48:47Z","snapshot_observed_at":"2026-07-07T01:42:34.292480Z","submitted_at":"2001-05-14T23:07:44Z","title":"The State(s) of Replica Symmetry Breaking: Mean Field Theories vs. Short-Ranged Spin Glasses","version":3},"cited_work":{"arxiv_id":"cond-mat/0105282","doi":null,"metadata_source":"pith","pith_arxiv_id":"cond-mat/0105282","snapshot_observed_at":"2026-07-04T02:49:24.113042Z","title":"The State(s) of Replica Symmetry Breaking: Mean Field Theories vs. Short-Ranged Spin Glasses","venue":"cond-mat.dis-nn","work_id":"4d0528e1-d84b-4d0f-816c-7972af1dc261","year":2001},"citing_paper":{"arxiv_id":"2606.18752","last_updated":"2026-06-18T13:29:17Z","snapshot_observed_at":"2026-08-02T13:01:02.852581Z","submitted_at":"2026-06-17T06:56:55Z","title":"Self-averaging of replica overlaps in the random field Edwards-Anderson model","version":2},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-06-26T19:21:29.846750Z"},"links":{"cited_paper":"/paper/cond-mat/0105282","citing_paper":"/paper/2606.18752"},"observation_digest":"sha256:a36789902ee263e3d7a3cfd3ebe9b1c12549820f78b90d080dc097b176c4a271","observation_id":"98360d71-2b9a-47cd-b3e3-56b486f01540","resolution":{"observed_at":"2026-07-04T02:49:24.114622Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-26T19:21:29.846750Z","title":"Statistical Physics of Spin Glasses and Information","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.18752","last_updated":"2026-06-18T13:29:17Z","snapshot_observed_at":"2026-08-02T13:01:02.852581Z","submitted_at":"2026-06-17T06:56:55Z","title":"Self-averaging of replica overlaps in the random field Edwards-Anderson model","version":2},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-06-26T19:21:29.846750Z"},"links":{"citing_paper":"/paper/2606.18752"},"observation_digest":"sha256:c5af1ef92c4e2d4961aa8f94a3d06dee872ad8e134958f15f7558da9fb680b02","observation_id":"443c39e8-33f2-4b05-a4f7-ddbd14880d6d","resolution":{"observed_at":"2026-06-26T19:21:29.846750Z","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":"2026-06-26T19:21:29.846750Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.18752","last_updated":"2026-06-18T13:29:17Z","snapshot_observed_at":"2026-08-02T13:01:02.852581Z","submitted_at":"2026-06-17T06:56:55Z","title":"Self-averaging of replica overlaps in the random field Edwards-Anderson model","version":2},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-06-26T19:21:29.846750Z"},"links":{"citing_paper":"/paper/2606.18752"},"observation_digest":"sha256:e7b9f5f621b52e33e2b6bbda53c25c26276f8f33484e59d7af4f89282a67e860","observation_id":"b0c67082-33b9-47d3-9ab0-ab3a8bf110cc","resolution":{"observed_at":"2026-06-26T19:21:29.846750Z","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":"2026-06-26T19:21:29.846750Z","title":"Infinite Number of Order Parameters for Spin-Glasses, Phys","venue":null,"work_id":null,"year":1979},"citing_paper":{"arxiv_id":"2606.18752","last_updated":"2026-06-18T13:29:17Z","snapshot_observed_at":"2026-08-02T13:01:02.852581Z","submitted_at":"2026-06-17T06:56:55Z","title":"Self-averaging of replica overlaps in the random field Edwards-Anderson model","version":2},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-06-26T19:21:29.846750Z"},"links":{"citing_paper":"/paper/2606.18752"},"observation_digest":"sha256:69bed3fb5ed60937eb0ab44651ca4dec081f7e02cb517bf7b69328e2d98369cf","observation_id":"63569c09-a7fb-4245-8748-eb101ea39ba6","resolution":{"observed_at":"2026-06-26T19:21:29.846750Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1112.4409","last_updated":"2014-03-31T05:35:15Z","snapshot_observed_at":"2026-07-06T02:39:40.270645Z","submitted_at":"2011-12-19T17:11:11Z","title":"The Parisi formula for mixed $p$-spin models","version":2},"cited_work":{"arxiv_id":"1112.4409","doi":null,"metadata_source":"pith","pith_arxiv_id":"1112.4409","snapshot_observed_at":"2026-07-04T02:49:24.093074Z","title":"The Parisi formula for mixed $p$-spin models","venue":"math.PR","work_id":"1d64bebb-b670-4567-89e8-4c4916f6445d","year":2011},"citing_paper":{"arxiv_id":"2606.18752","last_updated":"2026-06-18T13:29:17Z","snapshot_observed_at":"2026-08-02T13:01:02.852581Z","submitted_at":"2026-06-17T06:56:55Z","title":"Self-averaging of replica overlaps in the random field Edwards-Anderson model","version":2},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-06-26T19:21:29.846750Z"},"links":{"cited_paper":"/paper/1112.4409","citing_paper":"/paper/2606.18752"},"observation_digest":"sha256:01fee05682fb217ca5aa610c2ff669afb3ccddf14e8ee6c3023c0feb7e7bf06f","observation_id":"8bc9c2e2-d853-4b4a-a73c-b713eed0c662","resolution":{"observed_at":"2026-07-04T02:49:24.094707Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-26T19:21:29.846750Z","title":null,"venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"2606.18752","last_updated":"2026-06-18T13:29:17Z","snapshot_observed_at":"2026-08-02T13:01:02.852581Z","submitted_at":"2026-06-17T06:56:55Z","title":"Self-averaging of replica overlaps in the random field Edwards-Anderson model","version":2},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-06-26T19:21:29.846750Z"},"links":{"citing_paper":"/paper/2606.18752"},"observation_digest":"sha256:dbd1a1b030e79e0df649c3bcc92d997263ea312f11dcaef2a631d8172faa982a","observation_id":"fa5a476e-ead8-4388-9cd9-802931d4e037","resolution":{"observed_at":"2026-06-26T19:21:29.846750Z","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":"2026-06-26T19:21:29.846750Z","title":"The statistical mechanics of lattice gases, Vol","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2606.18752","last_updated":"2026-06-18T13:29:17Z","snapshot_observed_at":"2026-08-02T13:01:02.852581Z","submitted_at":"2026-06-17T06:56:55Z","title":"Self-averaging of replica overlaps in the random field Edwards-Anderson model","version":2},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-06-26T19:21:29.846750Z"},"links":{"citing_paper":"/paper/2606.18752"},"observation_digest":"sha256:194e0510133cf3427786750b1f2d8c4dcba63dc63f9909b86e712b215e3f0d2b","observation_id":"07a62a06-ed2f-41d3-957d-d97d9816a5a5","resolution":{"observed_at":"2026-06-26T19:21:29.846750Z","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":"2026-06-26T19:21:29.846750Z","title":"Spin Glasses","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2606.18752","last_updated":"2026-06-18T13:29:17Z","snapshot_observed_at":"2026-08-02T13:01:02.852581Z","submitted_at":"2026-06-17T06:56:55Z","title":"Self-averaging of replica overlaps in the random field Edwards-Anderson model","version":2},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-06-26T19:21:29.846750Z"},"links":{"citing_paper":"/paper/2606.18752"},"observation_digest":"sha256:c97edf0817127622589620723ebca92bdccd7c1c41be9be2ec66f92d1a3813f4","observation_id":"4fe839a2-ff58-4089-a507-279ec22497c6","resolution":{"observed_at":"2026-06-26T19:21:29.846750Z","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":"2026-06-26T19:21:29.846750Z","title":"The Parisi formula, Ann","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2606.18752","last_updated":"2026-06-18T13:29:17Z","snapshot_observed_at":"2026-08-02T13:01:02.852581Z","submitted_at":"2026-06-17T06:56:55Z","title":"Self-averaging of replica overlaps in the random field Edwards-Anderson model","version":2},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-06-26T19:21:29.846750Z"},"links":{"citing_paper":"/paper/2606.18752"},"observation_digest":"sha256:597974e23a58a5667787a12f41daca34ac86e51697d5ea8380d2d04213b21592","observation_id":"fc9e8a64-a9ec-4844-84cb-1dc6c292df87","resolution":{"observed_at":"2026-06-26T19:21:29.846750Z","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":"2026-06-26T19:21:29.846750Z","title":"Mean Field Models for Spin Glasses , Vol","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2606.18752","last_updated":"2026-06-18T13:29:17Z","snapshot_observed_at":"2026-08-02T13:01:02.852581Z","submitted_at":"2026-06-17T06:56:55Z","title":"Self-averaging of replica overlaps in the random field Edwards-Anderson model","version":2},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-06-26T19:21:29.846750Z"},"links":{"citing_paper":"/paper/2606.18752"},"observation_digest":"sha256:950e2995db5ad9dd59ade5bd88ca0f7d5e53c5f23487547cb0895fb0d5806088","observation_id":"0ceab892-94e0-4b77-b516-3f52035d1978","resolution":{"observed_at":"2026-06-26T19:21:29.846750Z","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":"2026-06-26T19:21:29.846750Z","title":"On the upper critical dimensions of random spin systems, J","venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2606.18752","last_updated":"2026-06-18T13:29:17Z","snapshot_observed_at":"2026-08-02T13:01:02.852581Z","submitted_at":"2026-06-17T06:56:55Z","title":"Self-averaging of replica overlaps in the random field Edwards-Anderson model","version":2},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-06-26T19:21:29.846750Z"},"links":{"citing_paper":"/paper/2606.18752"},"observation_digest":"sha256:b7939a944605382a2cbc29c6fa62e28f09b17b2b288f822f9b7e2509cf028468","observation_id":"3523cd9d-da13-4732-964b-d6ce6127d77e","resolution":{"observed_at":"2026-06-26T19:21:29.846750Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2606.18752","last_updated":"2026-06-18T13:29:17Z","latest_version":2,"primary_category":"math-ph","snapshot_observed_at":"2026-08-02T13:01:02.852581Z","submitted_at":"2026-06-17T06:56:55Z","title":"Self-averaging of replica overlaps in the random field Edwards-Anderson model"},"reference_resolution":{"displayed":32,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":19,"verified_exact":13,"verified_fuzzy":0},"total_outbound_references":32},"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":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"thesis":"As of 5 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 0 inbound Pith citation observations for arXiv:2606.18752."}