{"as_of":"2026-08-09T21:55:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:b065e0def53333ce2b1243c662e83e6f651d82a7a4ea49451b7565bce3095846","coverage":[{"denominator":78,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":78,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T21:49:15.932266Z","state":"measured"},{"denominator":78,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":78,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+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/2506.23344/citation-record","integrity":"/paper/2506.23344/integrity","json":"/paper/2506.23344/citation-record.json","paper":"/paper/2506.23344"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:49:27.374757Z","title":"https://ngsolve.org/","venue":null,"work_id":"b6ceb4b3-0478-47e4-9800-4e4250d9b829","year":null},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:08.503596Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:fec68f6cb7ec11af9f0f2968b0094a77cc1f81ae389d174599633017014b955a","observation_id":"74dae19f-ae77-4375-82bd-bf9c77729c9a","resolution":{"observed_at":"2026-08-06T21:49:27.404255Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:27.286641Z","title":"Ainsworth and I","venue":null,"work_id":"e2787541-71fe-4be6-bfb3-f7b8fe14b2a6","year":1999},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:08.601746Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:58d52e62e9811a26d8dacd7c350786c1c94687b97cd3ed35cf4276ff0bdd30b1","observation_id":"fa39455c-3945-43c7-8998-12c8c0a4e79e","resolution":{"observed_at":"2026-08-06T21:49:27.326347Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:27.199840Z","title":"Ainsworth and J.T","venue":null,"work_id":"fa6b528d-ff88-4b83-a344-64661a75ff31","year":2000},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:08.726106Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:296585882d64db8b657145d66f419200cbd52de1a7fb44a009318d99ecb7a580","observation_id":"c7a35fb5-c1e3-4e85-af2e-36b70571b42f","resolution":{"observed_at":"2026-08-06T21:49:27.242023Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:27.117640Z","title":"Ainsworth and T","venue":null,"work_id":"57151596-dbf7-4a5b-9059-338acf1fea68","year":2011},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:08.870439Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:5ffe01ed8afa07935f3549f8ce88a94a100c64de62f2020df0e3921780ff746d","observation_id":"17f448d3-d6a4-4847-b2c4-b1e8aca10a92","resolution":{"observed_at":"2026-08-06T21:49:27.142711Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:27.025954Z","title":"Galerkin neural networks: A framework for approxi- mating variational equations with error control","venue":null,"work_id":"d6e8dba3-4482-4d59-b6af-c5e992869d33","year":2021},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:08.945782Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:1324798aeb637c15e8b3e389ceadd6dc336b29c75c299987b5a277467f5e95f5","observation_id":"ea1aa25e-1c25-4dbb-8892-b2e43e839527","resolution":{"observed_at":"2026-08-06T21:49:27.065481Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:26.752830Z","title":null,"venue":null,"work_id":"a9d157db-c498-41ec-b47f-4c65cfa4224f","year":1998},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:09.090796Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:a6405839fab186f5a83f96377ddc5e182c72618722e9368f5cf4c6d28883eb32","observation_id":"fded4dc4-8ab3-4ab0-9e87-fb7afd421c17","resolution":{"observed_at":"2026-08-06T21:49:26.858715Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:26.639193Z","title":"Data2vec: A general framework for self-supervised learning in speech, vision and language","venue":null,"work_id":"29f955b5-7c58-4c1f-803a-869386d7f99a","year":2022},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:09.240841Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:bcd10334185b9692a49927cdfdbcd164fba44416ad0a21e63fb2708a86d78eed","observation_id":"4f6d1d4e-b222-4b6e-8146-1bd31bd96333","resolution":{"observed_at":"2026-08-06T21:49:26.690768Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:09.310721Z","title":"wav2vec 2.0: A framework for self-supervised learning of speech representations","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:09.310721Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:e8c54a8d6894c69b0005ff20dfb7cf1310df5e2efc46f5f4d9099bfc7cd20247","observation_id":"b6826c17-09e7-4435-81d7-684d2ab3e2b7","resolution":{"observed_at":"2026-08-06T21:49:09.310721Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2304.12210","last_updated":"2023-06-28T14:15:22Z","snapshot_observed_at":"2026-08-09T08:10:39.086440Z","submitted_at":"2023-04-24T15:49:53Z","title":"A Cookbook of Self-Supervised Learning","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2304.12210","snapshot_observed_at":"2026-08-06T21:49:09.380027Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:09.380027Z"},"links":{"cited_paper":"/paper/2304.12210","citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:a395ea6ae4d74872764e731d1754a884b9ff2fac7550b17e2ded88e764f3d61a","observation_id":"08df493e-0fc0-4371-8cb3-9c18fe6a6992","resolution":{"observed_at":"2026-08-06T21:49:09.380027Z","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":"2026-08-06T21:49:26.501827Z","title":"On the role of polynomials in RBF-FD approximations: II","venue":null,"work_id":"b5d11222-aa30-429c-92a1-a67c0c0fe31c","year":2017},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:09.465418Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:76d5c3b288ab98391e35800ae71357e887abb21a558e3296310c5bbf21842e83","observation_id":"fd41cf47-6db7-4c0a-ac08-cac22c816e9f","resolution":{"observed_at":"2026-08-06T21:49:26.556975Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:26.353560Z","title":"Bernardi and R","venue":null,"work_id":"435e0291-c279-44da-b6ab-4da67e066cb0","year":2000},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:09.550289Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:454b7e80d79e6e7187c818af74483af3aba651ff910adb848738cbc941638d97","observation_id":"09c7c362-326a-42ad-8c1e-8627ceb1d8f7","resolution":{"observed_at":"2026-08-06T21:49:26.420878Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:26.237412Z","title":"Bernhardsson","venue":null,"work_id":"42e76868-932e-47f5-a383-bfaf2578cd1a","year":null},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:09.687997Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:703f29ab3ffa86987d2493b9a361e15f9b4c8b8d79df1e901491d96699e6b3c3","observation_id":"d20b3cc3-4e3f-4d1c-8f25-880fcb334c74","resolution":{"observed_at":"2026-08-06T21:49:26.281321Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:09.790845Z","title":null,"venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:09.790845Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:2bd0469ba43ee4c530288eec57313ebdec05b060dde5aab3e280cd82b308adb4","observation_id":"edf36867-f474-4286-b18f-9f279dee6713","resolution":{"observed_at":"2026-08-06T21:49:09.790845Z","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":"2026-08-06T21:49:09.904811Z","title":"Convex optimization","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:09.904811Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:c444a866736d8c2b8456697c6eea7bfa9aab1fc8805674a1418e052a8eadb147","observation_id":"a0cc62d6-bf3c-4083-a35b-ae9069cf29c1","resolution":{"observed_at":"2026-08-06T21:49:09.904811Z","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":"2026-08-06T21:49:26.085625Z","title":"The neural network colloca- tion method for solving partial differential equations","venue":null,"work_id":"50ce62fa-9556-45b9-9908-443779be6266","year":2021},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:09.978586Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:af08ce83dfee8d52059b81dea2fd351b47537509bab0728c424d8e22ecd2deca","observation_id":"bb24a2e2-f7d4-4399-bd19-8c8a04bbc4d6","resolution":{"observed_at":"2026-08-06T21:49:26.145684Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:25.974921Z","title":"Cai and Z","venue":null,"work_id":"2f4353e5-1425-4a06-b918-2ab53998ab44","year":2018},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:10.036728Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:65660f1ccd161b6034e002ed3b8e1199bee0afaba25fb373749d7b563d0f023c","observation_id":"e769630e-3e9a-4a60-afe9-4e9fe46f7fd7","resolution":{"observed_at":"2026-08-06T21:49:26.027371Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:25.827995Z","title":null,"venue":null,"work_id":"8011ed5e-61fc-401b-99f2-6de943a7ce7c","year":2018},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:10.086764Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:00a81a4772775c4091e2138a4cc2c74045edfbd390bb745c635a43e2a4e0882c","observation_id":"cbd3e7a5-2bce-4202-a775-eed8eb0b30db","resolution":{"observed_at":"2026-08-06T21:49:25.894867Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:25.694269Z","title":null,"venue":null,"work_id":"73f308fd-9e67-4f59-8f33-897218429bc3","year":2024},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:10.156842Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:6d9e407ba62af4e2f2d7600d3b49bcd5247f800c974e1f3796162b7c6a56ab25","observation_id":"6effdb5c-6b74-4700-8067-354e93b1a8b3","resolution":{"observed_at":"2026-08-06T21:49:25.762345Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:25.488702Z","title":"Robust and Explicit a posteriori Error Estimation Techniques in Adaptive Finite Element Method","venue":null,"work_id":"6e2e5895-5a92-4136-939d-a9602aea1a0f","year":2019},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:10.251099Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:c047e26d8d9679787606528fc36365b08d31b68b82187a39a00dd6afa7108182","observation_id":"3324c7b6-e1b0-4dc3-95f5-e25f8db65fe8","resolution":{"observed_at":"2026-08-06T21:49:25.583327Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:25.337871Z","title":"Hybrid a posteriori error estimators for conforming finite element approximations to stationary convection-diffusion-reaction equations","venue":null,"work_id":"faac5cbc-0fec-483f-bb8c-ebd4c15366e2","year":2025},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:10.347781Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:f06856ce09da87aa5ca96e29a129fb279f8b922d37dffc08992cdf941cb9568d","observation_id":"3f8105d1-f40f-4915-9f8f-33e12bedbec6","resolution":{"observed_at":"2026-08-06T21:49:25.429037Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:24.971405Z","title":"Posterior covariance structures in gaussian processes","venue":null,"work_id":"6146c157-3b44-46d4-8f2c-cd51076a8e28","year":null},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:10.440000Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:72c551eae3689f009421c63a33034e686f8673b4bbcd350fac2e8d0f7572da93","observation_id":"8de28e27-b540-44a1-8846-a2df862d7288","resolution":{"observed_at":"2026-08-06T21:49:25.148735Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:24.670412Z","title":"Cai and S","venue":null,"work_id":"eaa8ef91-fc57-4fbf-b672-763604478f48","year":2009},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:10.553670Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:139a95316e95586014407da7422f5e179c8862055e9706451e91a0f81fd7f461","observation_id":"e853e009-8a89-411f-8dcc-97a432a3b9f1","resolution":{"observed_at":"2026-08-06T21:49:24.788327Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:24.342288Z","title":"Flux recovery and a posteriori error estimators: conforming elements for scalar elliptic equations","venue":null,"work_id":"227934ff-8d27-4e31-a1f5-1c4afb1578b2","year":2010},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:10.685032Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:85391795ed0eb11fa8fd7d92eb07f5d6a2c768dec33a8e3444644a83ebad19c5","observation_id":"7cd4e614-5ee2-45b0-a723-cdf8bf1176d2","resolution":{"observed_at":"2026-08-06T21:49:24.528787Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:24.090221Z","title":"Adaptive radial basis function partition of unity interpolation: A bivariate algorithm for unstructured data","venue":null,"work_id":"608f041d-ea58-45d7-9d54-931dd58a1ab3","year":2021},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:10.814961Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:107d80aa56f918d7170e68dbf82191add8437f246eeb8b81584c53f02ae78df0","observation_id":"5347c171-e74c-4abc-9cf8-1f50d0c52a50","resolution":{"observed_at":"2026-08-06T21:49:24.180349Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:23.852252Z","title":"Davydov, D","venue":null,"work_id":"a174c5f3-a222-4592-a202-80811782a53d","year":2023},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:10.926357Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:4aeb7b5d4a52a4d4b9b26de8732034c0adfe9b2ed02b4c3e1622f9e6aaa21af4","observation_id":"338dbd54-ce04-4f99-baa0-2cebd30e0681","resolution":{"observed_at":"2026-08-06T21:49:23.970131Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:23.513156Z","title":"Deng and H","venue":null,"work_id":"3e38e02f-3454-49b8-bb88-9d50b8f7fdde","year":2011},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:11.097930Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:7f73e1140f467df8a49db470ba23b28bb96129f3737658388c1a736a9699763d","observation_id":"fe7d9ba0-af95-4a39-b8b7-f72c31840127","resolution":{"observed_at":"2026-08-06T21:49:23.643448Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:23.213839Z","title":"BERT: Pre-training of deep bidirectional transformers for language understanding","venue":null,"work_id":"2a06371d-631d-4815-9b8a-7ccf6ed3333d","year":2019},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:11.243783Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:81a6d9418ff7c2304c78adb88ea8db057da9f3fcb6f0781583543c17a4aaf021","observation_id":"f0cc6f92-b0ac-4fa2-873a-b7a4e2d610a4","resolution":{"observed_at":"2026-08-06T21:49:23.352606Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:22.966453Z","title":"Efficient k-nearest neighbor graph construction for generic similarity measures","venue":null,"work_id":"1239093d-d0cc-4d54-a047-178bc746271c","year":2011},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:11.388421Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:b46253b97cc5ceadf10aa8c8d08762afff2a01a9194105211cfdbf6bc2dcd12f","observation_id":"323cc46e-292a-431f-b231-d2f3b338a9a8","resolution":{"observed_at":"2026-08-06T21:49:23.069631Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:22.876971Z","title":"Dosovitskiy, L","venue":null,"work_id":"fd538aef-061d-41e2-b97a-679568a4ec34","year":2021},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:11.533227Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:9e8c2717e3ee6bc4db8e4864798aa9055af7725257301f4e4aeb416da67dfd09","observation_id":"9b7fed12-68e0-41ed-b1f1-74befec50fe0","resolution":{"observed_at":"2026-08-06T21:49:22.907291Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:22.714841Z","title":"Adaptive residual refinement in an RBF finite difference scheme for 2D time-dependent problems","venue":null,"work_id":"2901a57b-521b-49c3-90ce-67ba3a439ad3","year":2024},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:11.630878Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:5db0ee58e4c166fa50c3508de600d033e612b4e0773b5f9ce2892150b28d098c","observation_id":"2dad62da-8c61-43b1-85f5-7cb5922563c0","resolution":{"observed_at":"2026-08-06T21:49:22.777519Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:22.503170Z","title":"Adaptive residual refinement in an rbf finite difference scheme for 2d time-dependent problems","venue":null,"work_id":"82098b81-c2cb-4973-ab2f-80f9dbdf6bd6","year":2024},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:11.746940Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:f7091f1499fba4aa142bd3f3b1848182e434e0e059f54e2e10c192a77f8e763e","observation_id":"94b1c5c5-4b83-44a6-9c96-f4c44f8e6dfd","resolution":{"observed_at":"2026-08-06T21:49:22.606898Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2202.08360","last_updated":"2022-02-22T18:15:21Z","snapshot_observed_at":"2026-08-05T01:07:03.567692Z","submitted_at":"2022-02-16T22:26:47Z","title":"Vision Models Are More Robust And Fair When Pretrained On Uncurated Images Without Supervision","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2202.08360","snapshot_observed_at":"2026-08-06T21:49:11.864829Z","title":"Goyal, Q","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:11.864829Z"},"links":{"cited_paper":"/paper/2202.08360","citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:dff4faf89b2d520448c0abbcb098e9b818a112fb0d35bb269a73cb4b4eb580df","observation_id":"f3cba657-06aa-439d-83b6-dc58ec640525","resolution":{"observed_at":"2026-08-06T21:49:11.864829Z","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":"2026-08-06T21:49:22.349220Z","title":"Gray and A","venue":null,"work_id":"2840466a-4ec5-4bf4-9b0e-6c9bb9b52c91","year":2000},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:11.976854Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:5f2e2bec8a3cea3ed146f47276a41e5abc803b3dbb5f16581041b13eb05bf8ca","observation_id":"9785b3a3-1c39-4a6d-82fb-4cfe232ec389","resolution":{"observed_at":"2026-08-06T21:49:22.416746Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:22.203404Z","title":"Gray and A","venue":null,"work_id":"2b7a65db-4b75-4e02-91df-361ff034f5d6","year":2003},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:12.124768Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:e2295a9a45516250f166454ae47c02139c66465e6026978c24d80e05f3ae4d1e","observation_id":"2f7080f1-9e17-4ae1-aecf-65daaa29d5b1","resolution":{"observed_at":"2026-08-06T21:49:22.260034Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:22.031101Z","title":"Greengard and J","venue":null,"work_id":"a56f61d6-2647-4f93-b98c-a395aba01e39","year":1991},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:12.246137Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:80c670f2c034ed58ae991147e8126064d5441a23d80ed757232587bb4d4551e4","observation_id":"ce7ee8b0-bc50-4fed-a749-5daa23080041","resolution":{"observed_at":"2026-08-06T21:49:22.118338Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:21.853580Z","title":"Bootstrap your own latent-a new approach to self-supervised learning","venue":null,"work_id":"a19a0125-fdfc-4b78-b012-4696bf86d3eb","year":2020},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:12.353485Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:1584e883f2dd797ae59d641b24e54ad4accf83709724dd9203938b22520e6b65","observation_id":"8a3572f9-6a9a-4b9e-bd41-1949fc09cd5a","resolution":{"observed_at":"2026-08-06T21:49:21.937840Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:21.664836Z","title":"Hackbusch","venue":null,"work_id":"8e5c5590-2235-42bd-8b97-09b592b44f0a","year":2015},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:12.482658Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:a7cb7c9e18e529b5b8aa224b88b89f8aae612958df10ec4a990fbb38775fa961","observation_id":"5886a987-5857-4a0d-95df-d5bacee30477","resolution":{"observed_at":"2026-08-06T21:49:21.756665Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:21.529741Z","title":"Tetgen, a delaunay-based quality tetrahedral mesh generator","venue":null,"work_id":"70664320-9953-4dd2-8b35-ecf7e9ced0a3","year":2015},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:12.598129Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:cd3c8a550c733af6bfd4ca260d11e75b37196ebee43d55776c1ea08a5372cc5a","observation_id":"d58ec86c-fe30-45bf-b028-2ad705b049b2","resolution":{"observed_at":"2026-08-06T21:49:21.588784Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:21.404314Z","title":null,"venue":null,"work_id":"45b0c9a7-a212-40f6-83dd-73f90f896dd7","year":2022},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:12.710819Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:12a85d0502feaabd19c41d093cd34703862af9b8d03ce0809bb4bcfff2f94aa1","observation_id":"18b72808-66b0-4abb-a385-32898c89a085","resolution":{"observed_at":"2026-08-06T21:49:21.465387Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:12.806309Z","title":"Masked autoencoders are scalable vision learners","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:12.806309Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:d651e1bbe386051a6f28bef7d210c94e453bfd5affd963cda500549aadb62111","observation_id":"70f3bbbe-bb37-45a4-8f6b-7b8c92b8d82f","resolution":{"observed_at":"2026-08-06T21:49:12.806309Z","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":"2026-08-06T21:49:21.226644Z","title":"Hendrycks, M","venue":null,"work_id":"4516b155-05d6-466a-8e71-d7d546c25134","year":2019},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:12.924728Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:8a9a42d58dceef9874c15ba82d7817a807aebd1e1787cec5ce447e59c63ce18e","observation_id":"6112e4ee-2381-4047-9705-e179af1489c6","resolution":{"observed_at":"2026-08-06T21:49:21.324574Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:21.023332Z","title":null,"venue":null,"work_id":"4eabd003-b61a-417c-b22d-f27d1b127a60","year":2014},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:13.043985Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:d4f84ad75cee142da46d58a178a7592df82c17cf449e5934f06a617c9c7146e9","observation_id":"cb2f4de1-0a2a-4632-b76c-278d08576621","resolution":{"observed_at":"2026-08-06T21:49:21.121780Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:13.146055Z","title":"A software package for sequential quadratic programming","venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:13.146055Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:9163d715b43034a192e7c12246694cdd8926ea0da19c41e4cefa76ecfe047579","observation_id":"ad852401-813a-45d9-bc31-1d0c09579258","resolution":{"observed_at":"2026-08-06T21:49:13.146055Z","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":"2026-08-06T21:49:20.814505Z","title":"Empirical testing of fast kernel density estimation algorithms","venue":null,"work_id":"179c3cf6-179b-44bd-aa14-19c94cba83ec","year":2005},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:13.227814Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:8936e2c39d41ef9f0207411e0b606920e6e58089041500d74dd5e312ea30979d","observation_id":"f89124bc-da7a-498a-acc1-ded52b2e1623","resolution":{"observed_at":"2026-08-06T21:49:20.908750Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:20.692357Z","title":null,"venue":null,"work_id":"36738153-f3d9-4316-b2ae-50668dae5f37","year":2021},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:13.372382Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:5d157d4db9adbf03667cdbe7ffb094c20a48ec853e7aa202bdedc1ee4b423e5e","observation_id":"cb147140-e3e6-4c8d-844b-7602e3a0ae13","resolution":{"observed_at":"2026-08-06T21:49:20.738122Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:20.594331Z","title":"Stable high order FD methods for interface and internal layer problems based on non-matching grids","venue":null,"work_id":"32e2da42-b5a4-4b22-a137-853ba001dbe6","year":2024},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:13.449117Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:c54a58665750214341a84729f0bb8bec3d160ec974b584bf417791f3635f14f0","observation_id":"3466b810-9c8a-40da-b57a-811d86a41d9e","resolution":{"observed_at":"2026-08-06T21:49:20.632224Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:20.452911Z","title":"An explicit link between gaussian fields and gaussian markov random fields: The stochastic partial differential equation approach","venue":null,"work_id":"2d47161f-d5d3-4ac9-ab2c-3c5a0fecccc2","year":2011},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:13.532213Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:2204b5de71f999c7ac09c6bdae5867d0c911a8ab813315c313c7373f74e0a7fb","observation_id":"685942db-bdf1-4d7d-ac25-7894f213e8c4","resolution":{"observed_at":"2026-08-06T21:49:20.539024Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:20.244785Z","title":"CPAFT: A consistent parallel advanc- ing front technique for unstructured triangular/tetrahedral mesh generation","venue":null,"work_id":"652f3af5-3cf7-4eb3-a68e-9d3829ab4ae6","year":2025},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:13.623372Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:6cf971685b099d9338f1de3ad8647450520c896196aacc677fb66d547bbf8902","observation_id":"1405666c-9db4-4378-92f1-777b980bb2af","resolution":{"observed_at":"2026-08-06T21:49:20.329232Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:20.103222Z","title":null,"venue":null,"work_id":"680a7f8a-5e3c-4ebe-907d-09e8bfe40ea1","year":2018},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:13.690928Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:b2072e8628293bdef2f25b954cda5cfcaacaa93eb3177a472ea2bbd72ebe0076","observation_id":"1c8a7b80-a21f-4f6e-bcf8-b5db972754f6","resolution":{"observed_at":"2026-08-06T21:49:20.171316Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:19.917119Z","title":"An artificial neural network based deep collocation method for the solution of transient linear and nonlinear partial differen- tial equations","venue":null,"work_id":"f5d68b3b-be98-4082-bb31-a202a35fd8b6","year":2024},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:13.764745Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:f43a137a2173ed6682bebdb9429199b771b6dad13f1d15e8114595dbc99adf47","observation_id":"035deaf5-2227-41af-be23-77884f12c4f4","resolution":{"observed_at":"2026-08-06T21:49:20.026110Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:19.718407Z","title":null,"venue":null,"work_id":"f5209b7a-55a0-4b83-a218-3e54061266f7","year":null},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:13.833764Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:67fe0329b652bb66071b335e85f8cccc0707d063e1abc3b36f4cd6a03c4dca86","observation_id":"0bad47f5-3b7b-4814-a8e2-c3ec04aa6d1f","resolution":{"observed_at":"2026-08-06T21:49:19.797276Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:19.429422Z","title":"Mitchell","venue":null,"work_id":"30aaf6a3-b478-4599-97ee-402066a0db4a","year":2013},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:13.971295Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:14ebaf06c9b1ee1aa0de851f41d6eece9d5ecb9e7b8844f35e97f84e1511760e","observation_id":"60779442-850d-48ac-895a-d69bf8f8c051","resolution":{"observed_at":"2026-08-06T21:49:19.472725Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:19.316701Z","title":"Muja and D","venue":null,"work_id":"7c8ecacb-e7f8-4c83-ae82-dd88022bd79c","year":2009},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:14.086993Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:fa9b7eeb0204838443b55fa1f57b99ea9a88b30c2509519425d567c243f99a08","observation_id":"ac2a9231-495f-423a-bacf-50a0036e8160","resolution":{"observed_at":"2026-08-06T21:49:19.383615Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:19.148766Z","title":"Adaptive RBF-FD method for elliptic problems with point singularities in 2D","venue":null,"work_id":"78e763db-dbce-4ad7-b43c-0744153e4d64","year":2017},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:14.181026Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:f7dc9e9d51afc54b2a1f6450554fe5375a80db8bea0d47eb0275ae523704d4f2","observation_id":"7e3598c2-5969-49dc-b33f-cc4b1095ea95","resolution":{"observed_at":"2026-08-06T21:49:19.231488Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:18.975943Z","title":"A multilevel, hierarchical sam- pling technique for spatially correlated random fields","venue":null,"work_id":"d122bcb4-3193-41fc-8ba2-d1ab38d64d91","year":2017},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:14.280869Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:f2a21c9dbe3b62807c26db236933a2e54ec0c32fd65715ae6531d01b3707b5c5","observation_id":"a89fe8c4-12b8-4c4e-b384-1600770d1cc1","resolution":{"observed_at":"2026-08-06T21:49:19.044978Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:18.878621Z","title":null,"venue":null,"work_id":"19652fe4-d3bf-4b95-b031-eee13897d57c","year":1962},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:14.380140Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:5542986979397110f067e13835ff9c609749f80f352b11725de89ee8a0c8e6fb","observation_id":"bcd5b1c4-8c44-4681-975a-848de4d2512f","resolution":{"observed_at":"2026-08-06T21:49:18.911409Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:18.783933Z","title":"Adaptive mesh refinement: Quantitative computation of a rising bubble using comsol multiphysics ®","venue":null,"work_id":"e0437707-7f71-45b1-95f7-88eb042f482c","year":2016},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:14.434225Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:c43cf36596e43b40154672a4493cf0e25b652ebb0f05ae87234a89a48b2f6b51","observation_id":"ca807e55-b0d9-4fe8-a003-33ca6f39ff72","resolution":{"observed_at":"2026-08-06T21:49:18.821944Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:18.689662Z","title":"Raffel, N","venue":null,"work_id":"2d4a1651-52fe-4ffe-97ec-dc07bdcf4baf","year":2020},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:14.527914Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:1ee6e7c82cd48cf4dfc4ede534bb9bfb84fbbbb10593be3dcd0d447ae6bdd664","observation_id":"e9b481d1-fc78-40f7-b75b-3d0203400656","resolution":{"observed_at":"2026-08-06T21:49:18.720213Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1711.10561","last_updated":"2017-11-28T21:21:59Z","snapshot_observed_at":"2026-07-06T06:11:42.746828Z","submitted_at":"2017-11-28T21:21:59Z","title":"Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1711.10561","snapshot_observed_at":"2026-08-06T21:49:14.633957Z","title":"Physics informed deep learn- ing (part i): Data-driven solutions of nonlinear partial differential equations","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:14.633957Z"},"links":{"cited_paper":"/paper/1711.10561","citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:6841e0aedbe6259fee8049dc757249d50c09440ef0aadb02fc2cac75fc7d55c8","observation_id":"92a92bf8-6cc1-42c1-8afa-930535fe44c5","resolution":{"observed_at":"2026-08-06T21:49:14.633957Z","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":"2026-08-06T21:49:18.517377Z","title":"Rosenblatt","venue":null,"work_id":"556fc431-5182-4c63-b139-73436ee1f8cf","year":1956},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:14.738721Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:fe884f41952afd33bce19b1554a4b3d66e47acd44eabcbe553cb740eaae1e999","observation_id":"14641d14-73f9-4fe5-9c7f-e0aa6c780e1d","resolution":{"observed_at":"2026-08-06T21:49:18.609205Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:18.356910Z","title":null,"venue":null,"work_id":"47e041fb-cfc1-4d94-a4b1-4490cc48e3aa","year":1984},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:14.795794Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:e5e43d296869b3039b06d776dcc4fdbfc2d33f5e8141459fa529616e3e860af4","observation_id":"6e6df4a0-9d83-407f-ab72-3362508fbf5b","resolution":{"observed_at":"2026-08-06T21:49:18.438092Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:18.159427Z","title":"Netgen an advancing front 2d/3d-mesh generator based on abstract rules","venue":null,"work_id":"77ab2a3a-e2a9-4d11-9023-bd8f053da661","year":1997},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:14.861075Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:a70d4a1379443950f7c86b95b80251cd46fe466e101b2813b370142ef55efa15","observation_id":"139072e9-2595-4bc6-a5f8-88c0432bc102","resolution":{"observed_at":"2026-08-06T21:49:18.206380Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:17.992646Z","title":null,"venue":null,"work_id":"a7d5dfaa-7229-4152-b52e-bc3bc0de1e18","year":1972},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:14.927956Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:cb2488afecb48ee630b88351079b893c88b20928393a3955bdbf7fb43f8f3d94","observation_id":"5bb1fec6-4382-4d36-b713-337f156ef99e","resolution":{"observed_at":"2026-08-06T21:49:18.040024Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:17.879335Z","title":null,"venue":null,"work_id":"437bd220-af8d-443a-a6b2-43f1ac35e069","year":1986},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:14.986461Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:99905fd3fa593936f2155907feceb76b0872e44d087e3790e751fb3a92121c97","observation_id":"7077ac79-6fca-4e69-90ac-202950629ae8","resolution":{"observed_at":"2026-08-06T21:49:17.939089Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:15.049432Z","title":"Density estimation for statistics and data analysis","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:15.049432Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:45498a8295163f96f7d98894c0e147d7b9d3cda92eee3b0f313b41b4534f1c9f","observation_id":"a818b082-aa55-4a73-9897-bb1b23a6f755","resolution":{"observed_at":"2026-08-06T21:49:15.049432Z","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":"2026-08-06T21:49:17.703484Z","title":"Slak and G","venue":null,"work_id":"21524d73-cdc3-4ac3-a4a8-3ff249fd08f0","year":2019},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:15.099822Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:246cf6960e4b2754a51156c1a96d9fe9ebcb83a3530455474e4d37347c2b74fd","observation_id":"a925337f-b593-4888-970b-07931afab259","resolution":{"observed_at":"2026-08-06T21:49:17.775011Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:17.528601Z","title":null,"venue":null,"work_id":"012b6849-0588-49e8-8cbb-5931fdec63f2","year":2005},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:15.217829Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:4f1e05a6fa55e8f407eea4cc5aa43978800735053062f3fec02ece559bf05aec","observation_id":"bbddc24a-97bc-422b-b1b5-6540b1c3c410","resolution":{"observed_at":"2026-08-06T21:49:17.610017Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:17.349745Z","title":"Adaptive mesh methods for one- and two-dimensional hyperbolic conservation laws","venue":null,"work_id":"321c9cff-c2de-4389-ba26-c32aae69d299","year":2003},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:15.303507Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:8c352d90fb37fd6beddfd5728b1a28f96ed9f3aaca96c2f620d11b62ed3f0520","observation_id":"34eeadf7-43f2-47ca-8737-ea458ff95d97","resolution":{"observed_at":"2026-08-06T21:49:17.418762Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:15.354150Z","title":"Variable kernel density estimation","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:15.354150Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:10314d87b060042262228e03c5e507cd588f15f49d6953ccd107fd10aa08077f","observation_id":"f3d893cd-e436-4e43-857a-b499888feb88","resolution":{"observed_at":"2026-08-06T21:49:15.354150Z","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":"2026-08-06T21:49:17.175402Z","title":"Verf¨ urth","venue":null,"work_id":"7aa7d5b4-3904-4b7c-96c6-ea71607d9b40","year":1998},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:15.419039Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:342e2a6efc155c924b4223d7b878f61f70bd779a56f574935ff28b7527c4ff99","observation_id":"5da08485-6f87-4d24-87f7-76b75eab69b6","resolution":{"observed_at":"2026-08-06T21:49:17.248179Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:17.056266Z","title":"Verf¨ urth","venue":null,"work_id":"0c07a5a5-2f75-4404-bff1-97a3980a1b18","year":2005},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:15.487654Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:e8a1fb80fc555e94a593d619b3a7eb694f18d28ec367515ce57fc4ff40ff35f7","observation_id":"b76f18da-c6b8-4a2f-9fae-a6d85cdd9089","resolution":{"observed_at":"2026-08-06T21:49:17.113741Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:16.940801Z","title":"Verf¨ urth.A Posteriori Error Estimation Techniques for Finite Element Methods","venue":null,"work_id":"1e066e2f-40e2-4f21-81f4-ddfe6619fbc8","year":2013},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":72,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:15.569965Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:0d59f940a67ca37ec760f25887b5d17f545238875c43f750c6d39ebd8093187a","observation_id":"a6d804b7-2551-40d6-99bc-5934f1f3fe08","resolution":{"observed_at":"2026-08-06T21:49:17.000504Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:16.800410Z","title":"Wald and V","venue":null,"work_id":"855540a5-5d4e-4b32-ac00-d052a215ce92","year":2006},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":73,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:15.653197Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:8d76cbafe02a721e3d3e89c2a785dc62fae0b3b72a4b9a5b860690a0641e4dcd","observation_id":"a6096563-234b-4ccc-8c57-d0d1b8a2c909","resolution":{"observed_at":"2026-08-06T21:49:16.860910Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:16.638942Z","title":"Optimal smoothing parameters for multivariate fized and adaptive kernel methods","venue":null,"work_id":"77dacab3-0bfd-4578-b8c7-d1bdf9b2a54d","year":1989},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":74,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:15.714646Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:ef4fa2258743f28ba5d4152dac0566958f3620f9f587070897c127c397bca71d","observation_id":"203f0d13-703b-4bc1-bc26-c5ac8225abd9","resolution":{"observed_at":"2026-08-06T21:49:16.712220Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:16.497268Z","title":null,"venue":null,"work_id":"6b719ed1-7137-4ba2-918c-cc3f87c7f649","year":2003},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":75,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:15.785601Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:88e834ff69b9808f75f3f759dd0c7eb13eae0686c9d42db9b030b44998363b2c","observation_id":"df69a4e6-c51b-4cdb-bf76-b36daf66a77e","resolution":{"observed_at":"2026-08-06T21:49:16.565832Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:16.342055Z","title":"Yu and W","venue":null,"work_id":"8d760e70-37ae-4156-801f-863334d3c0aa","year":2018},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":76,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:15.864233Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:68efe0bcb0bfc7ac095c65983db78b7e0ea96ff5413a3f619070c47b21447f46","observation_id":"f943c040-ff1a-46cf-8547-e463faa7acb9","resolution":{"observed_at":"2026-08-06T21:49:16.432478Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:16.090524Z","title":"Amrex: a framework for block- structured adaptive mesh refinement","venue":null,"work_id":"e440bccd-8a7e-45bf-8801-d0bbcb8375bd","year":2019},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":77,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:15.932266Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:3197009cf4df1ae44fcbc868f2eaa1ec5a693fc6696bd3253ec3315b41523265","observation_id":"2ce28640-aa1b-4418-b7cf-a898ac9e8250","resolution":{"observed_at":"2026-08-06T21:49:16.206059Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T21:49:19.529006Z","title":null,"venue":null,"work_id":"c8016a4d-2817-468d-85dd-56c208ddf57e","year":2016},"citing_paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations","version":1},"reference_index":1738,"source":"pdf_text","source_observed_at":"2026-08-06T21:49:13.916908Z"},"links":{"citing_paper":"/paper/2506.23344"},"observation_digest":"sha256:fc1a12bfd665cc4fc37208307913bc0578c94cb74180a0f32406758124f8e40e","observation_id":"38c4a08a-2ca1-48bb-8a77-ce0937e40c01","resolution":{"observed_at":"2026-08-06T21:49:19.605931Z","resolver_source":"raw_fallback","status":"parse_uncertain"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.23344","last_updated":"2025-06-29T17:39:41Z","latest_version":1,"primary_category":"math.NA","snapshot_observed_at":"2026-08-09T15:09:38.022194Z","submitted_at":"2025-06-29T17:39:41Z","title":"Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations"},"reference_resolution":{"displayed":78,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":1,"unresolved":24,"verified_exact":0,"verified_fuzzy":53},"total_outbound_references":78},"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":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 78 of 78 outbound references and 0 inbound Pith citation observations for arXiv:2506.23344."}