{"as_of":"2026-08-06T10:49:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:fee330ff9727352889554895e21ef93d85d4b7861669ef4499b98b059da4187a","coverage":[{"denominator":65,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":65,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-18T10:10:32.692581Z","state":"measured"},{"denominator":68,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":68,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-06T06:34:29.942622+00:00","state":"measured"},{"denominator":3,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":3,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-02T01:25:52.665357Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-06-30T17:14:57.079865Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"cited_work":{"arxiv_id":"2510.03989","doi":null,"metadata_source":"pith","pith_arxiv_id":"2510.03989","snapshot_observed_at":"2026-06-30T17:14:57.079865Z","title":"A Mathematical Explanation of Transformers","venue":"cs.LG","work_id":"1a11a933-ec80-4f8f-ae55-33688015e1e3","year":2025},"citing_paper":{"arxiv_id":"2605.22557","last_updated":"2026-05-26T09:40:19Z","snapshot_observed_at":"2026-07-06T23:32:54.127514Z","submitted_at":"2026-05-21T14:39:43Z","title":"Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations","version":1},"reference_index":173,"source":"arxiv_source","source_observed_at":"2026-05-22T07:28:49.152516Z"},"links":{"cited_paper":"/paper/2510.03989","citing_paper":"/paper/2605.22557"},"observation_digest":"sha256:aecdc0d3582ec692bafef789594c61fa2e901b4e5953e5f514e4fd38a6ee1bfe","observation_id":"c1a7acba-0964-4dde-ab06-34e19fd125ca","resolution":{"observed_at":"2026-05-22T07:31:14.016780Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"cited_work":{"arxiv_id":"2510.03989","doi":null,"metadata_source":"pith","pith_arxiv_id":"2510.03989","snapshot_observed_at":"2026-06-30T17:14:57.079865Z","title":"A Mathematical Explanation of Transformers","venue":"cs.LG","work_id":"1a11a933-ec80-4f8f-ae55-33688015e1e3","year":2025},"citing_paper":{"arxiv_id":"2605.22557","last_updated":"2026-05-26T09:40:19Z","snapshot_observed_at":"2026-07-06T23:32:54.127514Z","submitted_at":"2026-05-21T14:39:43Z","title":"Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations","version":2},"reference_index":77,"source":"arxiv_source","source_observed_at":"2026-06-30T17:08:54.066574Z"},"links":{"cited_paper":"/paper/2510.03989","citing_paper":"/paper/2605.22557"},"observation_digest":"sha256:eedf4840a0e7b0cc35254114607dc53d01b6db716e501897665e13f832b325df","observation_id":"c7b981ee-1787-443a-8bc0-577406d00893","resolution":{"observed_at":"2026-06-30T17:14:57.081354Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2510.03989","snapshot_observed_at":"2026-08-02T01:25:52.665357Z","title":"A mathematical explanation of transformers","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.14711","last_updated":"2026-07-17T20:57:29Z","snapshot_observed_at":"2026-08-02T01:25:50.435266Z","submitted_at":"2026-07-16T08:22:08Z","title":"VideoSEMA: a scalable and efficient Mamba-like attention for video understanding","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-02T01:25:52.665357Z"},"links":{"cited_paper":"/paper/2510.03989","citing_paper":"/paper/2607.14711"},"observation_digest":"sha256:f4d552d0fa26992e8ac223ffbc14fb80f0f9e36a64d4f777b3f8d3710dd5867b","observation_id":"d8f3b32e-d745-40a8-a67d-b3ccc66b2aa0","resolution":{"observed_at":"2026-08-02T01:25:52.665357Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2510.03989/citation-record","integrity":"/paper/2510.03989/integrity","json":"/paper/2510.03989/citation-record.json","paper":"/paper/2510.03989"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"1607.06450","last_updated":"2016-07-21T19:57:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2016-07-21T19:57:52Z","title":"Layer Normalization","version":1},"cited_work":{"arxiv_id":"1607.06450","doi":"10.1007/978-3-319-32025-0","metadata_source":"pith","pith_arxiv_id":"1607.06450","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Layer Normalization","venue":"stat.ML","work_id":"20a2d720-0046-4c7c-bcd6-327ec8143f69","year":2016},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"cited_paper":"/paper/1607.06450","citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:bf34790add3d122c792a8bbcf62c1ecbcac4afe2d7eb122f76d600b17366ff8d","observation_id":"19dc7265-4698-40ea-9a81-737e41a3b4fd","resolution":{"observed_at":"2026-05-18T10:11:13.771044Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Benning, E","venue":null,"work_id":"80d9e5a6-ec96-490b-afcd-b6580643a20f","year":2019},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:1adab8c2f6e2e44cf8732e3966401895de5061b126d4b3d433fb0676655f2e37","observation_id":"6529469f-7410-4c19-a573-71ea38405860","resolution":{"observed_at":"2026-05-18T10:11:14.784579Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Bryutkin, J","venue":null,"work_id":"7ef0a92c-0bf5-49f5-aac6-269c12e76297","year":2024},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:36f65c4deca3adb088729f2e224d7f48a98970c46290586c8cf883d24577f7cd","observation_id":"f8d193d4-3cc8-42d9-b6ea-b62719ea0ee7","resolution":{"observed_at":"2026-05-18T10:11:14.757515Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"74326fc0-4b72-480b-8711-16ed9979d83f","year":2022},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:6ce5d4e24d893fdbbfc187802e63b5e14ff971ff8d587c95aedb5596798c5350","observation_id":"1b445e97-e6b8-49d8-9b2a-ac475c867d37","resolution":{"observed_at":"2026-05-18T10:11:14.684790Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-07-06T05:11:58.059330Z","title":null,"venue":null,"work_id":"a3af36b6-28eb-4416-812a-c686feefdbda","year":2018},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:fcda3e534249ce20b0a4090871d55608503a6c05dde921d7489a6954e3d912aa","observation_id":"0b46bec2-2027-4c42-b872-7baf0b666ac3","resolution":{"observed_at":"2026-05-18T10:11:14.694928Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2410.02113","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Cheng, J","venue":null,"work_id":"c9292293-da8c-46c4-81ee-afc7fbf256a6","year":2024},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:acd9522e649aa1949b0e7dd794d30b63ff9f72b8e1a4b0d1349356d44f3f232d","observation_id":"0428c010-f7aa-43c7-b568-7ed72623e1f3","resolution":{"observed_at":"2026-05-18T10:11:13.748993Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"a2b25652-5615-46b0-bfad-ffc941b946a2","year":2022},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:8459d2c1ae96bd140ed0a004deaad5c43e1bec3dfd622acaf3436cededc4600c","observation_id":"56103c6c-4fb5-491f-ab34-2cb2e88fbcbe","resolution":{"observed_at":"2026-05-18T10:11:14.691632Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Dosovitskiy, L","venue":null,"work_id":"43e5d3fd-325c-46e2-8ef4-238ee852d12c","year":2021},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:5aeae1d347a7537c73d0b32e2f7a683eb1857a3be4ddfac7e80d924c03f3b660","observation_id":"147ecd25-090a-4c93-b153-51b4dcf11834","resolution":{"observed_at":"2026-05-18T10:11:14.688337Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Dutta, T","venue":null,"work_id":"69369264-19b8-4348-a72d-a4ad457a4338","year":2021},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:ce0b70b27ebd3164250f96297610bd8a0a46193677305b3ec23852344d4f8fdc","observation_id":"8d6fd979-5bff-4465-a162-689f09954438","resolution":{"observed_at":"2026-05-18T10:11:14.855956Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2408.01367","last_updated":"2024-10-03T02:43:59Z","snapshot_observed_at":"2026-08-05T07:34:36.379159Z","submitted_at":"2024-08-02T16:21:48Z","title":"Transformers are Universal In-context Learners","version":2},"cited_work":{"arxiv_id":"2408.01367","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2408.01367","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Furuya, M","venue":null,"work_id":"6a71aabc-b486-4317-9cca-92276db3d6ed","year":2024},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"cited_paper":"/paper/2408.01367","citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:5a239d10d5969b0952bdb224f00bb7b58c9ae727a01ad52919edb506e87c03e1","observation_id":"0835f6f9-cd6f-4519-9c93-aac76bfc3386","resolution":{"observed_at":"2026-05-18T10:11:13.753014Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2312.10794","last_updated":"2025-08-21T11:31:09Z","snapshot_observed_at":"2026-07-06T17:04:17.738921Z","submitted_at":"2023-12-17T19:06:29Z","title":"A mathematical perspective on Transformers","version":5},"cited_work":{"arxiv_id":"2312.10794","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2312.10794","snapshot_observed_at":"2026-07-04T13:29:51.095693Z","title":"Letrouit, Y","venue":null,"work_id":"d081e886-f9fa-4d25-9355-b6f6d2e2af62","year":2023},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"cited_paper":"/paper/2312.10794","citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:7a29e8c612c048917cdc7d833b5e56330ec4bbf3ef7078d99136165fb25f4a93","observation_id":"b1b0e0c6-7824-40b4-9351-ea8bcb8cbefa","resolution":{"observed_at":"2026-05-18T10:11:13.744455Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Glowinski and P","venue":null,"work_id":"791c6364-1450-4ab7-b592-532437e287c3","year":1989},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:5706e9b2ac4d3fc879c3917b15334f6136dbe721cfb4d0dff69f934ff1fc9988","observation_id":"f2bd92ba-cab5-4c93-b138-bbffae550542","resolution":{"observed_at":"2026-05-18T10:11:14.833965Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Glowinski, S","venue":null,"work_id":"74d4f10d-62ed-42fe-9869-15a9b726e878","year":2017},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:f4dd5ad8206d030b01afbf8713260ae7ee64c85a52f883b712b2e7c93bc9bfe1","observation_id":"a9a83cfd-758a-46ea-a0e6-303f1d46c22e","resolution":{"observed_at":"2026-05-18T10:11:14.817243Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Glowinski, T.-W","venue":null,"work_id":"abbd8fae-5ca5-42c3-a714-bf51a843dde6","year":2016},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:73491cfeaa652439d349fe0c0dbcdd48fe39a28e7d4dcb15bfab47c42bee6055","observation_id":"e27613a6-1175-4d85-9e87-6fa54df062d5","resolution":{"observed_at":"2026-05-18T10:11:14.714930Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Graves, A.-r","venue":null,"work_id":"1f6727cd-31f6-48cb-bd9b-a64ef100fe63","year":2013},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:e984887a5920b9aebb4c88706825632d28bc7f22a44100c67a8910e8ae8b103e","observation_id":"01e5745c-7596-4a5e-ab44-f1b77fbd5a6c","resolution":{"observed_at":"2026-05-18T10:11:14.750091Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Gregor and Y","venue":null,"work_id":"93def5a8-9837-4f92-9d17-08b530317703","year":2010},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:e99cb554783bb4f7395a1e16f93a6b6f10ddff6566f837137a2890c31014762c","observation_id":"201ec9fa-ad69-45ec-b391-eb40c2915343","resolution":{"observed_at":"2026-05-18T10:11:14.728573Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Haber, L","venue":null,"work_id":"f22d83f5-b796-4b48-b5e6-f41b101968cc","year":2018},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:64232956cac04fe5df7d7bd2e2a1c97444f57e9a4f3ba8912f37544c918614bd","observation_id":"8f12e32d-2c1c-45bc-a144-e27c7709247e","resolution":{"observed_at":"2026-05-18T10:11:14.781993Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Hagemann, J","venue":null,"work_id":"1d2fc382-b288-45ea-a262-7664d4da6279","year":2022},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:4bf607fed601b4da8ffde0dbedbbf0f1de6e7a6ff942a07833a69cb0d472b9aa","observation_id":"69375b66-f08a-4cad-8239-3f570c19edee","resolution":{"observed_at":"2026-05-18T10:11:14.703744Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Havrilla and W","venue":null,"work_id":"390d884c-377b-47e7-9976-0ebce956af21","year":2024},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:0f72d593463d23b739b58af799ac649abdbc91dbb309199bccd78c0146b0d7af","observation_id":"361aa13e-1a6f-4b59-8b15-7456bf883a11","resolution":{"observed_at":"2026-05-18T10:11:14.746860Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Mgnet: Aunifiedframeworkofmultigridandconvolutionalneuralnetwork","venue":null,"work_id":"8af4b81d-ca08-4a74-8eb0-c109c5e1f531","year":2019},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:6d46252e80a8666b69381bfe7d2cfd5b63fcc0b00dc01c3af8ef5d658265e02e","observation_id":"d88dc355-4792-460a-8b87-c35ead697298","resolution":{"observed_at":"2026-05-18T10:11:14.740459Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Jelassi, M","venue":null,"work_id":"f08e0ee1-54c0-4454-bf6f-884ed76d966a","year":2022},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:f87f9c0b8e04172548c456e042b420c209ca0e00848b855ee8606baeb03f810e","observation_id":"0b205dd2-3ddd-4f22-8347-ca7f2408fee5","resolution":{"observed_at":"2026-05-18T10:11:14.736711Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Jiang, Y","venue":null,"work_id":"4d858726-ac6e-4dba-b66d-20a338adb12e","year":2017},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:961c8c7052a457cafa852a1b11cf7722cfec9ccde29c338af260ffe95758bd89","observation_id":"dbe750c2-cb13-4e4c-8b46-8ab29a059c3f","resolution":{"observed_at":"2026-05-18T10:11:14.843458Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Krizhevsky, I","venue":null,"work_id":"5f6f47c2-b57a-4645-b3d3-4d8873a60f5e","year":2012},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:e474efdd944847ed7ea83b479c2b68e3a8c31c230f5ff3ed473ae80da5ec6931","observation_id":"f2fbf548-2cc2-40cc-94da-e784b7a47454","resolution":{"observed_at":"2026-05-18T10:11:14.846388Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2408.09624","last_updated":"2024-08-19T00:56:44Z","snapshot_observed_at":"2026-07-06T19:02:11.267510Z","submitted_at":"2024-08-19T00:56:44Z","title":"Attention is a smoothed cubic spline","version":1},"cited_work":{"arxiv_id":"2408.09624","doi":"10.48550/arxiv.2408.09624","metadata_source":"arxiv_reference","pith_arxiv_id":"2408.09624","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Attention is a smoothed cubic spline","venue":"arXiv (Cornell University)","work_id":"93da86e8-db7c-45c8-9fb6-7dfc92ce9a31","year":2024},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"cited_paper":"/paper/2408.09624","citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:317da0820b06163dc338f57d6b646adc1ce94546eacc0f5cb6a394ea3ec31c88","observation_id":"afab02ad-efe8-46ac-a57f-73e3fe6cac0c","resolution":{"observed_at":"2026-05-18T10:11:13.766867Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-05-24T04:55:27.497514+00:00","source":"crossref_status_cache"},{"observed_at":"2026-05-24T04:55:27.497514+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"c3897eda-d3a0-4313-a0f2-3b8de91def42","year":2023},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:fc836a93f2f0c47d9e13308712ae9c46aa6e2c453b1ff239fa38cace3cb89aa9","observation_id":"5a114d6b-cd31-474a-8db0-077006967377","resolution":{"observed_at":"2026-05-18T10:11:14.849548Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2010.08895","last_updated":"2021-05-17T03:12:33Z","snapshot_observed_at":"2026-07-06T10:05:26.653366Z","submitted_at":"2020-10-18T00:34:21Z","title":"Fourier Neural Operator for Parametric Partial Differential Equations","version":3},"cited_work":{"arxiv_id":"2010.08895","doi":"10.1016/0375-9601(81)90165-1","metadata_source":"pith","pith_arxiv_id":"2010.08895","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Fourier Neural Operator for Parametric Partial Differential Equations","venue":"cs.LG","work_id":"cc647655-121e-4055-85f0-fad4530ea964","year":2020},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"cited_paper":"/paper/2010.08895","citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:e1767ea4f00fb5f44e8d70bc2a1de8067fe32b3b5b68aa6a9449f4c61696a640","observation_id":"29a06aa3-6cfa-4bd1-b81b-785b40bf7243","resolution":{"observed_at":"2026-05-18T10:11:13.785992Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"bf04d8a4-692e-4e8e-9f97-a2c2e37bec36","year":2025},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:efb325aa6efa83110acd1609c644977c64b6fea28a646445ccbbb40e26a3274a","observation_id":"9269da19-f018-47f4-a332-2ccad64267ea","resolution":{"observed_at":"2026-05-18T10:11:14.830886Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"e6e6ca4e-5f71-458e-b3ea-bd2e41dc9f57","year":2024},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:3668b14c2f202d9c7223ee011d0e8e23bb718b57cb2a67f2ebcf7c4c730b5ae7","observation_id":"638981d1-836c-4cea-a53e-7257a2b21813","resolution":{"observed_at":"2026-05-18T10:11:14.837166Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2005.07476","last_updated":"2020-05-15T11:36:04Z","snapshot_observed_at":"2026-08-06T09:37:21.486621Z","submitted_at":"2020-05-15T11:36:04Z","title":"Convex Shape Prior for Deep Neural Convolution Network based Eye Fundus Images Segmentation","version":1},"cited_work":{"arxiv_id":"2005.07476","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2005.07476","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Convex shape prior for deep neural convolution network based eye fun- dus images segmentation.arXiv preprint arXiv:2005.07476","venue":null,"work_id":"6cd14da7-8236-44e3-b4d3-574356bb7754","year":2005},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"cited_paper":"/paper/2005.07476","citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:974f8adac716a933b8dbe1247851250f26a2413a21cc8c47fa4058e8c77fd91a","observation_id":"7e78ae75-54b3-42e1-a40a-a44100f0299c","resolution":{"observed_at":"2026-05-18T10:11:13.757253Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"e9c4547e-8e7c-410f-94ba-3e13cc50c8c7","year":2022},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:b84ae33455d3693da2b29a414cf1f6eb4a20e19a8a83fa3fa2f8c09d9247d0d8","observation_id":"30ce50c7-6ebe-4088-8031-5f6152ca22a5","resolution":{"observed_at":"2026-05-18T10:11:14.825018Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"398826c0-e176-461a-9eac-90213d21c54e","year":2024},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:f55732e83609265def6999e0e99f43c522f8c705ed1890506cc6c41a3acf9fc9","observation_id":"5d708bcc-f62f-48e6-bcdd-26f20aaba230","resolution":{"observed_at":"2026-05-18T10:11:14.827744Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"963b9692-978f-4b78-b8d5-2786677d830c","year":2018},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:0f84b1f79dac1f7a9f62dfaefc33010f4b86a9cfe4524385d652f6198bccd42c","observation_id":"a4b73140-e70b-4876-86b1-65c3af396818","resolution":{"observed_at":"2026-05-18T10:11:14.840184Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"a49db10e-6c0a-43cd-b35a-f4a138da7171","year":2021},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:d90a41c3341baa0febb86ddfbda0715a0ccd1754f14ac297007d25d5aed9964e","observation_id":"7632e106-63a6-4682-bd60-3e8c18f0778e","resolution":{"observed_at":"2026-05-18T10:11:14.852807Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-07-06T23:03:01.240813Z","title":null,"venue":null,"work_id":"d9529d1e-2a5b-4988-a02d-1bf4f78049a2","year":2021},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:55b790f4874121ed107c0cf4ba4240eabc25b97ac00bff81f5aecea27140a276","observation_id":"22161c44-74a8-4da2-91c1-cc863aa5192b","resolution":{"observed_at":"2026-05-18T10:11:14.718838Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"910f8bb2-9fcf-42ab-a1ed-ebaf6773cc03","year":1992},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:f78d819254ff9438704cd5c0d8ae59241eb52fda0c744bd06617e19a2d4b4012","observation_id":"64078488-af22-4ab0-bc65-e86784f53aeb","resolution":{"observed_at":"2026-05-18T10:11:14.814556Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"12e0b97e-902f-422b-be7f-073797bae30d","year":2020},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:ce22fd53293578d0fc14f9f58ea078cf90e73185d8be081ee8a52a56395c5baf","observation_id":"9951cae4-daf8-4abf-b3a2-ade229a88805","resolution":{"observed_at":"2026-05-18T10:11:14.808494Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2410.02423","last_updated":"2025-09-09T07:43:19Z","snapshot_observed_at":"2026-08-03T18:54:30.811068Z","submitted_at":"2024-10-03T12:13:56Z","title":"PnP-Flow: Plug-and-Play Image Restoration with Flow Matching","version":3},"cited_work":{"arxiv_id":"2410.02423","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2410.02423","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Pnp-flow: Plug-and-play image restoration with flow matching","venue":null,"work_id":"f33adfdd-d6d4-453a-b1df-a52b27d0f308","year":2024},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"cited_paper":"/paper/2410.02423","citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:8488d82024c1368aa3cc051a516024ba47cfbcd58b2464516832b2fd053be21a","observation_id":"ffbe0164-bf1c-4a19-8a88-212ca62efdb0","resolution":{"observed_at":"2026-05-18T10:11:13.776220Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"8fc8ecf6-fba2-4be0-a9e2-52d9901102db","year":2024},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:19d0d5facdfa852c1f96d3c6854727bd00c6e3ca73e6286bb8fdc53a1f44f0e4","observation_id":"a99aaad1-dbf9-4ada-b61b-15dfb86d6c01","resolution":{"observed_at":"2026-05-18T10:11:14.811792Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Miotto, F","venue":null,"work_id":"5a2ab292-a2d1-48c3-af9b-7f8237b0858d","year":2018},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:e048006c3ad3b504b6afa62e97177813130fcbc895fffe7e2de9510ab8388ce6","observation_id":"6281ad43-350d-4f5f-8495-5fe3a6ae11a9","resolution":{"observed_at":"2026-05-18T10:11:14.819990Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Raissi, P","venue":null,"work_id":"1687f7bb-9209-4d0a-ad02-53ce858a0c80","year":2019},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:4b4def348c32a07cabf3673f1c2432f2fc4127c7e60cd76b3db4a9d9f5ad7d59","observation_id":"67fbd88a-e234-4719-87a2-959e049078b0","resolution":{"observed_at":"2026-05-18T10:11:14.732820Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Ronneberger, P","venue":null,"work_id":"38911027-72cb-4a74-8e9b-10545a68e157","year":2015},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:d084fccc67afcce21b22c7865e394a82f3bf18e859c6491795f02d77077c64b6","observation_id":"fd2b367d-b837-4829-976a-b59856383bef","resolution":{"observed_at":"2026-05-18T10:11:14.799433Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Ruiz-Balet and E","venue":null,"work_id":"7eca87bf-29b7-448e-b508-f2b93c8aeb33","year":2023},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:f7485133f725b4e36575fb1cafb0ce26157ef793829985ed5724b9755af9c3d1","observation_id":"fa3c8eb8-38c1-4c15-9f63-4a0520e3eb63","resolution":{"observed_at":"2026-05-18T10:11:14.802446Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Ruthotto and E","venue":null,"work_id":"a9fa8a13-bac1-4a22-9f55-ad6762095b76","year":2020},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:ced3a10963f7870eb7cd134fac8c78a4e5a50b51cb528c0b17e90833467e6542","observation_id":"00257d06-32bc-4740-b0c8-07d139bbaaf0","resolution":{"observed_at":"2026-05-18T10:11:14.793214Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2505.03205","last_updated":"2026-05-17T05:57:50Z","snapshot_observed_at":"2026-08-02T11:29:44.461952Z","submitted_at":"2025-05-06T05:41:46Z","title":"Transformers for Learning on Noisy and Task-Level Manifolds: Approximation and Generalization Insights","version":3},"cited_work":{"arxiv_id":"2505.03205","doi":null,"metadata_source":"pith","pith_arxiv_id":"2505.03205","snapshot_observed_at":"2026-07-03T16:38:40.639778Z","title":"Transformers for Learning on Noisy and Task-Level Manifolds: Approximation and Generalization Insights","venue":"cs.LG","work_id":"7fce5064-ff22-4c96-a066-055ed6194bd4","year":2025},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"cited_paper":"/paper/2505.03205","citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:19dc9575b79ec409df1fe0c8bcfe58d1c59248a4818c4240dfab3258c50e7a6b","observation_id":"17554625-5df4-4ec2-b118-0a6a46609f5a","resolution":{"observed_at":"2026-05-20T00:02:49.976542Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Strudel, R","venue":null,"work_id":"1870faf3-1ed9-4e02-8602-65ede7e08ae5","year":2021},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:c1f791a4a32aa15c4194ec17512519c2d7772870d092d201a214af0b1073876a","observation_id":"cbea65cf-63d8-45e7-b523-fd1ea2ba1416","resolution":{"observed_at":"2026-05-18T10:11:14.790661Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"d3b70e03-18bb-483b-ab2c-02e8afeef710","year":2024},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:bf665c64f88e1c977a1aa73d83094cdc99b4e88a950117bc63c0b08daafa8b16","observation_id":"739b008c-36ff-4f36-b1a1-cd01fb627b7e","resolution":{"observed_at":"2026-05-18T10:11:14.796526Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Tai, H.Liu, R","venue":null,"work_id":"e8914ef3-9ccc-4fa2-9dd8-1b71763f1547","year":2024},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:6c2b2cf2095271b69d4a71533b3eeea0aebe205e7b4604965cc76f12ab2258eb","observation_id":"63395770-3896-4a34-9454-31195958db89","resolution":{"observed_at":"2026-05-18T10:11:14.805389Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Takakura and T","venue":null,"work_id":"40d95da1-37ad-4f52-b94e-d2f94ff8de1e","year":2023},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:a70b1b07f04bcdb98b0bc4ee6229fd7b6de58931ea9ebc42c59f15847acef0c7","observation_id":"3ab210a7-3b80-4d80-9277-97758412e64e","resolution":{"observed_at":"2026-05-18T10:11:14.822362Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2304.10557","doi":"10.48550/arxiv.2304.10557","metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":", month = feb, year =","venue":"arXiv (Cornell University)","work_id":"c30a0477-fbfd-4045-a768-f1bc3f79f21c","year":2023},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:a4e19f488deac96a37ae04439e345505628049d3940b09974bdf82de164a887b","observation_id":"d0006589-0cd3-4c7e-9421-bd68476d6cbc","resolution":{"observed_at":"2026-05-18T10:11:13.739427Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-07-18T14:51:21.112105+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-18T14:51:21.112105+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-07-08T13:34:54.851188Z","title":"Vaswani, N","venue":null,"work_id":"835895df-34ce-4f32-896d-3b0616e2cfe9","year":2017},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:93a589ac3085be90c0462d9c81f57e6c708844423e23d2000e2a7ec2385c8ea4","observation_id":"96bcada9-6c8b-4e29-8ab5-dad746472488","resolution":{"observed_at":"2026-05-18T10:11:14.776311Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"7d62ce37-daf5-4ccb-9278-d21053d82dfe","year":2023},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:e677b386b6ccbac9d6e7c08d72b1b10a6e7a7474a73b8a766044b94416da5a7d","observation_id":"b9b5a133-af6e-42da-8dca-a0ce0a3bd823","resolution":{"observed_at":"2026-05-18T10:11:14.770075Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"b110c617-2647-476e-a73a-5bb5cd9ac41b","year":2017},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:71fe7a6f419b4fec13f974a1a8168d2663c066b013a59b6c49f2916a8df0d1bb","observation_id":"fcec7646-e35b-451d-9dc9-1970e79fcb8d","resolution":{"observed_at":"2026-05-18T10:11:14.787975Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Weinan, C","venue":null,"work_id":"800d83eb-815b-4174-9a5f-dce88ea8c007","year":2020},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:b83a8e36bb59c36f39f1b0786a5c756430046a7ea6abf8a454d312492397b118","observation_id":"83a14114-13f9-4325-b3db-891be95bf213","resolution":{"observed_at":"2026-05-18T10:11:14.767451Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"52e5121c-eecc-4d8e-8c5f-c9ae7d01b586","year":2021},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:72e039123781b08e145a7b047ab71dd442e876f5fe7706e861e71eb83238d2bd","observation_id":"c470c3c8-99c1-4af2-9686-5631cf5c4538","resolution":{"observed_at":"2026-05-18T10:11:14.773039Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"3ae7deb7-0dda-48e9-a9d5-0c351fba4bdb","year":2019},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:88c340d0afba88eb9f85549c8d4b47890bcc598ddc66bc4a2b698bbfc19abde2","observation_id":"f790415e-0566-4a8c-a45b-07895916c873","resolution":{"observed_at":"2026-05-18T10:11:14.779330Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"9c566ccc-7587-4203-9f45-e9577015d72e","year":2018},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:06549d04248ca9a8abd32b62572cd01dbde79ee8a54305d17a53c80a35d349b2","observation_id":"fe2f5afa-781a-481e-be02-6f8f18455f91","resolution":{"observed_at":"2026-05-18T10:11:14.760875Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Yarotsky","venue":null,"work_id":"6fa7ebe0-c951-48f1-bf28-60bb452d12fa","year":2017},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:3a19d535dda5cf5626df57cb7fa09d8f7b4f97820fd7d59a6446d35d283488b6","observation_id":"98ff5674-d3b9-49b7-abc1-0e300b807f4d","resolution":{"observed_at":"2026-05-18T10:11:14.764258Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.12652","last_updated":"2025-01-27T10:11:21Z","snapshot_observed_at":"2026-08-04T19:09:42.261856Z","submitted_at":"2024-02-20T02:02:29Z","title":"PDEformer: Towards a Foundation Model for One-Dimensional Partial Differential Equations","version":3},"cited_work":{"arxiv_id":"2402.12652","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2402.12652","snapshot_observed_at":"2026-07-04T09:29:43.186082Z","title":"Pdeformer: Towards a foundation model for one- dimensional partial differential equations.arXiv preprint arXiv:2402.12652","venue":null,"work_id":"3d0be60b-da99-44c4-9a03-4023c463fa2d","year":2024},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"cited_paper":"/paper/2402.12652","citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:8991b60b06d651ca235116c9dba8349f23d48d2e656b9f40d9fd5c362105bf6a","observation_id":"f4b3bff0-767b-4962-842f-8a37344a156a","resolution":{"observed_at":"2026-05-18T10:11:13.790596Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Young, D","venue":null,"work_id":"fc30c396-5288-4c9a-ba97-8713c2e82d5f","year":2018},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:fe62fc62f3cafc335fe679fd8443f46ea299e8a57bb90ef3cf6c8cf63c917b4b","observation_id":"95362abf-46da-46e2-a75e-d2f5d3359422","resolution":{"observed_at":"2026-05-18T10:11:14.743447Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"6d65b9b2-288f-4c77-ad62-9224ffa33a9c","year":2019},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:f2eac06fc2080172c3ea01ab81d0c70a9c85bb41f639032477e6945b1ba7155f","observation_id":"8b74ab77-e6b2-4aae-9111-62131a2a9223","resolution":{"observed_at":"2026-05-18T10:11:14.754203Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Zhang and R","venue":null,"work_id":"2d47d707-3fe2-4383-b448-108e289cbc2e","year":2019},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:d51c5be522123356d926a8fac2f75b5a2a4c8d49370faf40dd35f4df59fd0d5a","observation_id":"bdc328e5-f3a2-47bf-b92f-7c2b0c7ae70d","resolution":{"observed_at":"2026-05-18T10:11:14.708096Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Zhang, L","venue":null,"work_id":"2c0a685d-50df-4d26-8c31-6bf05ebbb5b7","year":2025},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:adf0d9195e7fdcc797acc09d497a848b67144d16ae2b99df2c80b2e8d7b432b9","observation_id":"cf0cbf72-975d-4aee-a594-a6ce32da1078","resolution":{"observed_at":"2026-05-18T10:11:14.724040Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"43170054-83b8-43ac-848f-2445914092bf","year":2020},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:415467d531b7868eab995892a52ae5363f6e3f10cb179c40eea4f82ad55d9863","observation_id":"4af8ddc5-5c12-4c89-9448-f94ae190db5c","resolution":{"observed_at":"2026-05-18T10:11:14.711526Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2503.10622","last_updated":"2025-06-14T08:10:48Z","snapshot_observed_at":"2026-07-06T20:52:09.743730Z","submitted_at":"2025-03-13T17:59:06Z","title":"Transformers without Normalization","version":2},"cited_work":{"arxiv_id":"2503.10622","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2503.10622","snapshot_observed_at":"2026-07-01T22:36:17.334878Z","title":"Transformers without Normalization","venue":null,"work_id":"21b0eff6-a7f6-4825-ace9-3a7156a074eb","year":2025},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"cited_paper":"/paper/2503.10622","citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:159e391be63ad43e6d8f086c8410e21ecba80d660f1f0df3e7a2bd1f0f89e12b","observation_id":"bdca079b-b28c-4221-ac8d-1504cb4751ad","resolution":{"observed_at":"2026-05-18T10:11:13.780648Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Ziaee and E","venue":null,"work_id":"7cdb4a54-f532-45d0-a8e1-0fc8af451414","year":2022},"citing_paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers","version":2},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-05-18T10:10:32.692581Z"},"links":{"citing_paper":"/paper/2510.03989"},"observation_digest":"sha256:c1b4a32a1559f412083013fab39dcf4549ee72d966ca60e07884e1acf35d43e0","observation_id":"dd5f0e80-150f-4a39-bdf9-ca541dacb181","resolution":{"observed_at":"2026-05-18T10:11:14.698572Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2510.03989","last_updated":"2026-04-12T14:04:19Z","latest_version":2,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-05T12:20:04.752383Z","submitted_at":"2025-10-05T01:16:08Z","title":"A Mathematical Explanation of Transformers"},"reference_resolution":{"displayed":65,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":22,"verified_exact":12,"verified_fuzzy":31},"total_outbound_references":65},"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":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"thesis":"As of 6 August 2026, this Paper Citation Record lists 65 of 65 outbound references and 3 inbound Pith citation observations for arXiv:2510.03989."}