{"as_of":"2026-08-18T12:59:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:ff697ad42e217217011ec9896ff69c12f497cb1c9bfd97e2a181a8480a95eb46","coverage":[{"denominator":36,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":36,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T12:18:05.057966Z","state":"measured"},{"denominator":36,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":36,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-18T06:34:40.430872+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2608.06226/citation-record","integrity":"/paper/2608.06226/integrity","json":"/paper/2608.06226/citation-record.json","paper":"/paper/2608.06226"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:18:10.590739Z","title":null,"venue":null,"work_id":"9f2545e6-47bb-4f2b-9b00-38cd6652acb5","year":1979},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:01.727003Z"},"links":{"citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:e4b0563783ca806296e553557f9eebd399ffd2ca8d5dd7675331d284ef68d03f","observation_id":"8d85d076-8308-4ea8-b7dc-12fe46bb5df1","resolution":{"observed_at":"2026-08-07T12:18:10.654515Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T12:18:10.445938Z","title":"Buckmaster, G","venue":null,"work_id":"b495443a-ed3a-48d9-9f50-c8fa8dd7f0d4","year":2025},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:01.767464Z"},"links":{"citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:6b215390803caea27ffd9dc2108de5c0f776d4110c75fc480513b485fdcf636d","observation_id":"64387639-dd2f-4659-a136-9319feb0c3b0","resolution":{"observed_at":"2026-08-07T12:18:10.506373Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T12:18:10.328481Z","title":"Cabr´ e and Y","venue":null,"work_id":"dcbff4d1-7182-43f1-b1a4-25a07f431306","year":2014},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:01.873188Z"},"links":{"citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:e3e6d76e9f3719705744ba1579c5bc2d89a88c40cfd58c0cb169dfc6b8e48ab0","observation_id":"53ce42a5-193a-49b3-84ea-37c425c438c1","resolution":{"observed_at":"2026-08-07T12:18:10.373655Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T12:18:10.190193Z","title":"Cabr´ e and Y","venue":null,"work_id":"9fef8fd0-bf44-4c85-b2da-ff23c93410f3","year":2015},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:01.952502Z"},"links":{"citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:9aacc8d145e49374acfda810890097f012ea08df40b6e7ad3aa81be3be0c220c","observation_id":"0b7c86ae-1ed7-459c-9131-c90dc4614a58","resolution":{"observed_at":"2026-08-07T12:18:10.232498Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T12:18:10.041539Z","title":"Cabr´ e and J","venue":null,"work_id":"778dd9b7-b064-466c-8e65-b122702fabc3","year":2005},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:02.059183Z"},"links":{"citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:df25cb050d37ad2b0dfa0a246c3a2d31675ab58520c843ef918d9f60e111cf65","observation_id":"eb2c68c7-914f-49b6-b8f4-c80030bfa24d","resolution":{"observed_at":"2026-08-07T12:18:10.096904Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T12:18:09.900185Z","title":null,"venue":null,"work_id":"2146feeb-486f-4b23-b865-f6a875707591","year":2025},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:02.145588Z"},"links":{"citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:3dd225ac964df77b4435512a1de4f71460966a44d737fa4ca282011d5ed9e240","observation_id":"f9e631fe-0597-4a47-a3bd-9a9992188431","resolution":{"observed_at":"2026-08-07T12:18:09.960581Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2607.13567","last_updated":"2026-07-15T08:06:19Z","snapshot_observed_at":"2026-08-18T03:05:38.893518Z","submitted_at":"2026-07-15T08:06:19Z","title":"Global Bifurcation and the Constructive Existence of Overhanging Periodic Steady Water Waves","version":1},"cited_work":{"arxiv_id":"2607.13567","doi":null,"metadata_source":"pith","pith_arxiv_id":"2607.13567","snapshot_observed_at":"2026-08-07T12:18:05.421138Z","title":"Global Bifurcation and the Constructive Existence of Overhanging Periodic Steady Water Waves","venue":"math.AP","work_id":"0c332299-9b2b-4376-9179-dd355261b078","year":2026},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:02.222884Z"},"links":{"cited_paper":"/paper/2607.13567","citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:0bdc57638764f74a5e85d1de7a083b2c4598131cf98adaa4162a597cfc3ab6a5","observation_id":"c36b3eec-5407-4a92-b1b7-45e7a7699e45","resolution":{"observed_at":"2026-08-07T12:18:05.473906Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T12:18:09.756101Z","title":"Cadiot, J.-P","venue":null,"work_id":"65d2ad46-d710-485b-a3f0-2a2700147728","year":1966},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:02.341369Z"},"links":{"citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:03373781ca8f800f19d095d6d15d5e723ee79c1894d4cc9da5b5141ffef04694","observation_id":"45315987-3ea8-430e-9f54-a32f68a1dc52","resolution":{"observed_at":"2026-08-07T12:18:09.827169Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T12:18:09.585086Z","title":null,"venue":null,"work_id":"0f01be43-58f6-4c2c-8430-93d807a38ad8","year":2010},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:02.432481Z"},"links":{"citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:c76675682c293ddfc90750f5469c5cc5ecde0b2236b4dc044cd0d441096be823","observation_id":"fa0941e9-06ed-4378-8197-33401187b05b","resolution":{"observed_at":"2026-08-07T12:18:09.682682Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T12:18:02.548179Z","title":"Cao-Labora, M","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:02.548179Z"},"links":{"citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:da87cb377e2507e7592cff4dc6d1b09e812751ba7e4bb1c53b60b78bc9b4eeff","observation_id":"6e791904-37e7-4f8a-8c6c-849b8179dc05","resolution":{"observed_at":"2026-08-07T12:18:02.548179Z","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":"2026-08-07T12:18:09.408731Z","title":"Carballeira, D","venue":null,"work_id":"39022458-4b44-46a1-9680-d3cda1d65ee8","year":2026},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:02.667893Z"},"links":{"citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:e6a0061dacc46fcbee27cddbcc368565304b44aeaca69a352e63b7846c2ea036","observation_id":"84dc205c-1069-4b9f-8753-25d6641a1d18","resolution":{"observed_at":"2026-08-07T12:18:09.489472Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T12:18:09.237600Z","title":"Castro, D","venue":null,"work_id":"a52d387c-7730-4055-9140-84c6c792c36c","year":2020},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:02.756908Z"},"links":{"citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:9b1fb5abc44eeceabde1c6ff60febd3910a82c8059731890c074b6a667cd6f18","observation_id":"e22d821d-8192-4fa4-a0ce-0a5aa66a95f4","resolution":{"observed_at":"2026-08-07T12:18:09.323362Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2605.03920","last_updated":"2026-06-08T13:51:51Z","snapshot_observed_at":"2026-07-06T23:16:44.876986Z","submitted_at":"2026-05-05T16:16:50Z","title":"Linear instability of a Burgers--Hilbert traveling wave","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2605.03920","snapshot_observed_at":"2026-08-07T12:18:02.897396Z","title":"Castro, J","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:02.897396Z"},"links":{"cited_paper":"/paper/2605.03920","citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:80a709b5c9786110d1564dba434ef2516382406bab04cea783cd0bd939f8930f","observation_id":"3e78a905-b376-4e99-90be-da991584e72e","resolution":{"observed_at":"2026-08-07T12:18:02.897396Z","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":"2026-08-07T12:18:09.010126Z","title":"Cayama, C","venue":null,"work_id":"0b185305-c468-4c6f-af16-b72e562c6940","year":2020},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:02.987743Z"},"links":{"citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:91d34834fbe81972034235309b8363e6f7edd6692fa32ff0dc820a9295ec8335","observation_id":"5ee7f2bc-e34f-4894-b8b2-ee653f27fef5","resolution":{"observed_at":"2026-08-07T12:18:09.119790Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2210.07191","last_updated":"2026-08-16T08:46:30Z","snapshot_observed_at":"2026-08-18T12:13:38.307161Z","submitted_at":"2022-10-13T17:13:08Z","title":"Stable nearly self-similar blowup of the 2D Boussinesq and 3D Euler equations with smooth data I: Analysis","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2210.07191","snapshot_observed_at":"2026-08-07T12:18:03.065484Z","title":"Chen and T","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:03.065484Z"},"links":{"cited_paper":"/paper/2210.07191","citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:faac63ba8a5544259128a6d2161c6786f56d307f5b4950dfd4b7a82d00ff8761","observation_id":"f5e56762-2755-49f1-9427-853b17b9126a","resolution":{"observed_at":"2026-08-07T12:18:03.065484Z","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":"2026-08-07T12:18:08.840317Z","title":"Chen and T","venue":null,"work_id":"696da637-e14f-4bdc-9a92-e505cd4ba109","year":2025},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:03.179156Z"},"links":{"citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:a98e60cd4905a27dabc25eab5bf3ab828d83abddb406ea781a941446a95ea35e","observation_id":"340a83b8-1895-42f9-abb1-cffedae47ac5","resolution":{"observed_at":"2026-08-07T12:18:08.934300Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T12:18:08.710051Z","title":null,"venue":null,"work_id":"25496ed5-185d-4963-bf8e-effe9b9e616c","year":2024},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:03.276619Z"},"links":{"citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:6a56dff4fcc159fc9d2bb8583db6a8e1cefaec79e880a8a423cb2658f4b55b86","observation_id":"b84fa9fa-f28b-47e9-96ed-d83a3f99b82f","resolution":{"observed_at":"2026-08-07T12:18:08.771424Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2410.05480","last_updated":"2024-12-20T14:38:37Z","snapshot_observed_at":"2026-08-17T09:26:41.705090Z","submitted_at":"2024-10-07T20:23:27Z","title":"Self-Similar Singular Solutions to the Nonlinear Schr\\\"odinger and the Complex Ginzburg-Landau Equations","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2410.05480","snapshot_observed_at":"2026-08-07T12:18:03.349836Z","title":"Dahne and J.-L","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:03.349836Z"},"links":{"cited_paper":"/paper/2410.05480","citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:3f59e24ae99ee5ac657e8113034bfc8b0224993e840d286ec930d22aeceadfef","observation_id":"4752f6bf-92c3-4d1c-a77e-c210bcd12049","resolution":{"observed_at":"2026-08-07T12:18:03.349836Z","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":"2026-08-07T12:18:08.544677Z","title":"Dahne and J","venue":null,"work_id":"dc9772ad-55a6-4995-ae1d-dab5eab90799","year":2023},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:03.461055Z"},"links":{"citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:a3a01ea45177f607ea8c26eae1fdc0cc7997c92be31bf64514b838fa9db52d05","observation_id":"be028f2e-5a26-49da-8693-a6d1af9b692e","resolution":{"observed_at":"2026-08-07T12:18:08.626050Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T12:18:03.542272Z","title":"Dahne, J","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:03.542272Z"},"links":{"citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:81f787945843f1c95f66fe3d0de1a6f09b34aae5ef0f4d690a78488ade20b9da","observation_id":"9d28f9fc-cee3-429a-9631-ae67a300c11e","resolution":{"observed_at":"2026-08-07T12:18:03.542272Z","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":"2026-08-07T12:18:08.334316Z","title":"Di Nezza, G","venue":null,"work_id":"9f7f3c4a-cd8a-497c-8a48-45ac4e3ea8af","year":2012},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:03.619074Z"},"links":{"citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:d131cc4db5abc07c3efa44fc06957fa42f1d6ba33cac4ea5464b7cb8d937d5c9","observation_id":"7ca3cda0-5775-4640-9867-9b6ab8a034e5","resolution":{"observed_at":"2026-08-07T12:18:08.447979Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T12:18:03.693672Z","title":"Donninger and B","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:03.693672Z"},"links":{"citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:8e0c5fb19f2d0c535c6dbad4407e2c765456a340c8767383460cf0569a7cf40d","observation_id":"4eaf9db3-4658-43e7-bc6e-7e171941a556","resolution":{"observed_at":"2026-08-07T12:18:03.693672Z","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":"2026-08-07T12:18:08.158660Z","title":"G´ omez-Serrano","venue":null,"work_id":"75673a43-7b7d-4463-9892-79411e1f00b2","year":2019},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:03.804586Z"},"links":{"citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:cd2dd86caf0312b6c1effc09795ca77622f0d3d0f2bc98fdacad76a4bf784f3d","observation_id":"6c4b5fe5-b19d-46e0-8b61-541830198650","resolution":{"observed_at":"2026-08-07T12:18:08.240780Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T12:18:07.996705Z","title":"Johansson","venue":null,"work_id":"6445c5b9-44c6-47a1-9779-d2fc821c532d","year":2017},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:03.894862Z"},"links":{"citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:76736fb6cf5d1072d567cc41bf1b32b8ce2afcd73c760e559d180db62b11fe93","observation_id":"f251031b-4f61-4c6c-865c-32cfe868e076","resolution":{"observed_at":"2026-08-07T12:18:08.075954Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T12:18:07.820635Z","title":"Kato.Perturbation Theory for Linear Operators, volume 132 ofGrundlehren der mathematischen Wis- senschaften","venue":null,"work_id":"0382a463-ef8f-4024-a427-0f34b0047c57","year":1976},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:04.010070Z"},"links":{"citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:8851ed8ea5a53ebe4a4b060ad5a42d6503f879e59096dcfaaa77cf4b89ba003b","observation_id":"59561808-5003-4455-b16a-a09939fc773f","resolution":{"observed_at":"2026-08-07T12:18:07.896177Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T12:18:07.651798Z","title":null,"venue":null,"work_id":"63c6ab73-b197-49d6-abb5-4954748f5cb5","year":2021},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:04.117664Z"},"links":{"citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:962507ce5a84099eed8be627a0d4927b10870c8745bc045a870d8dbcf7d856bb","observation_id":"bbc6f38f-a182-4add-a04c-a00ebaa97ea0","resolution":{"observed_at":"2026-08-07T12:18:07.729822Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T12:18:07.429366Z","title":null,"venue":null,"work_id":"9da55d10-0e1e-47b2-b8f0-fe41550e32e0","year":1987},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:04.218053Z"},"links":{"citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:4cda2c1e2dd8c74ef3d2a3aee6cb64a48bafecc47aa3b546900c1b74eb60e940","observation_id":"bd46e598-b828-44e4-acf8-1a16a72f002e","resolution":{"observed_at":"2026-08-07T12:18:07.536025Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T12:18:07.267067Z","title":"Modica and S","venue":null,"work_id":"a6244142-9a07-4cf3-bbae-9e367a165f9c","year":1977},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:04.368777Z"},"links":{"citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:a78f19ec4e5360e053471b980bfd7e2a59429a0a7f158ff26b09c1f295ab146b","observation_id":"9e711da4-4096-49a7-b7b0-0965ba86bce1","resolution":{"observed_at":"2026-08-07T12:18:07.348081Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T12:18:07.103704Z","title":null,"venue":null,"work_id":"0f4bcf51-e313-4075-8407-b176fe8db598","year":2019},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:04.458430Z"},"links":{"citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:6816cb5c148bf2cedc34ea74a565c107ae5b49e86e4a9bd7fe323d09def009f8","observation_id":"25ce968a-62d9-45d1-8497-e3b6817439b8","resolution":{"observed_at":"2026-08-07T12:18:07.175795Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T12:18:06.921866Z","title":null,"venue":null,"work_id":"d536b92c-cd6f-4840-95a2-0f1129f3cb65","year":1988},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:04.524204Z"},"links":{"citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:329f19bf228004c99ec4a0a4bfeba6545e9dd3bf9d8d8c77f96af426acb0d126","observation_id":"f31cef4a-2a11-43b5-a4b9-8683fdc0d59d","resolution":{"observed_at":"2026-08-07T12:18:07.010122Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T12:18:06.758398Z","title":"Palatucci, O","venue":null,"work_id":"522c2d0e-257c-47bb-a6b2-a8db4f4637d0","year":2013},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:04.612439Z"},"links":{"citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:d163f3b06bf3afc98aa756f005a8cc606a2e457d8c15964d021b46fcd81a68c1","observation_id":"bc564456-1c14-4052-aeb4-b793fc1ae877","resolution":{"observed_at":"2026-08-07T12:18:06.831028Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T12:18:06.534757Z","title":"Savin and E","venue":null,"work_id":"bd5930e3-9b4f-4ed1-b653-b2c32a2ba3a1","year":2012},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:04.701731Z"},"links":{"citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:1c6d2a5fbba61cde533e6c36bb4d83f5b61231c3fe785a59b19255834af66f2b","observation_id":"905bacdc-9f36-4359-ab13-da8b2b8ae020","resolution":{"observed_at":"2026-08-07T12:18:06.634734Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T12:18:06.369699Z","title":"Savin and E","venue":null,"work_id":"899f3e5a-b493-477d-8c2c-81db99307935","year":2014},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:04.780881Z"},"links":{"citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:7f511fc7112ad795bcf122b0fdc558d1cc3e42a54c4923e338c5667259d19c1a","observation_id":"6ff57b42-6cf8-404b-8001-7d5b1d9a6a25","resolution":{"observed_at":"2026-08-07T12:18:06.470487Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T12:18:06.126843Z","title":"Sire and E","venue":null,"work_id":"f6948517-f441-4177-bd79-bedd8b20b5e7","year":2009},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:04.873964Z"},"links":{"citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:c41171fc230efa2ee049eaa2f5ffcd8db172e26897aa956b2352047f234bc7b2","observation_id":"f0c05f07-8c5a-435f-854c-55f8467f0632","resolution":{"observed_at":"2026-08-07T12:18:06.261405Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T12:18:05.881772Z","title":null,"venue":null,"work_id":"70dfc666-4154-4d9d-aee7-10641824e3fb","year":1970},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:04.957724Z"},"links":{"citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:3eb6f366acf702c932516199aa5f1305708b524635d04b117053d7af11e1f323","observation_id":"baf3b093-043a-4447-8d95-e5f05739547e","resolution":{"observed_at":"2026-08-07T12:18:06.001467Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T12:18:05.590827Z","title":"Tucker.Validated Numerics: A Short Introduction to Rigorous Computations","venue":null,"work_id":"8a9df174-3f2d-4553-8c65-7c1ac5c832af","year":2011},"citing_paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-07T12:18:05.057966Z"},"links":{"citing_paper":"/paper/2608.06226"},"observation_digest":"sha256:2a08dafd10acb007e23d17d2f8199553a22776319e8b1a8d28d9df636e6cc5b9","observation_id":"80f4d3bd-49ca-431d-b42f-2e80a9520215","resolution":{"observed_at":"2026-08-07T12:18:05.718336Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2608.06226","last_updated":"2026-08-06T16:15:18Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-12T01:22:14.287127Z","submitted_at":"2026-08-06T16:15:18Z","title":"The energy of fractional Allen--Cahn layers in dimension one"},"reference_resolution":{"displayed":36,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":15,"verified_exact":1,"verified_fuzzy":20},"total_outbound_references":36},"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":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"thesis":"As of 18 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 0 inbound Pith citation observations for arXiv:2608.06226."}