{"as_of":"2026-08-15T08:19:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:f62dfb0f9dffa580c04dbe3c56e92fa2d9447d203f2a668988ae3b2de537e20e","coverage":[{"denominator":29,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":29,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T04:26:03.042061Z","state":"measured"},{"denominator":29,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":29,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-15T06:32:42.880941+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2608.08922/citation-record","integrity":"/paper/2608.08922/integrity","json":"/paper/2608.08922/citation-record.json","paper":"/paper/2608.08922"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T04:26:03.787649Z","title":"Vaswani, N","venue":null,"work_id":"9a388de4-f05e-43de-86b7-ee803662b1fa","year":2017},"citing_paper":{"arxiv_id":"2608.08922","last_updated":"2026-08-09T21:28:01Z","snapshot_observed_at":"2026-08-15T07:31:29.678107Z","submitted_at":"2026-08-09T21:28:01Z","title":"Clustered Attractor Manifolds and Dynamical Condensation in Self-Attention","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T04:26:02.819163Z"},"links":{"citing_paper":"/paper/2608.08922"},"observation_digest":"sha256:79090bc45aa83927bd5b0ed47e833e3b8efef648f2df5ad4394a2bd19e000a6c","observation_id":"94292014-c29a-4b56-90df-b680626aa180","resolution":{"observed_at":"2026-08-14T04:26:03.797470Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:26:03.753656Z","title":"Devlin, M.-W","venue":null,"work_id":"d4db5dc4-fecd-48e7-9082-e96252848bb2","year":2019},"citing_paper":{"arxiv_id":"2608.08922","last_updated":"2026-08-09T21:28:01Z","snapshot_observed_at":"2026-08-15T07:31:29.678107Z","submitted_at":"2026-08-09T21:28:01Z","title":"Clustered Attractor Manifolds and Dynamical Condensation in Self-Attention","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T04:26:02.826274Z"},"links":{"citing_paper":"/paper/2608.08922"},"observation_digest":"sha256:a9d17a0abd482a3b5b671f9abac2f349b75e11b35ccb0ecf477d397ee83fe82c","observation_id":"2c9dcba3-e5ee-4541-a124-5c1914d4a131","resolution":{"observed_at":"2026-08-14T04:26:03.765246Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:26:03.731534Z","title":null,"venue":null,"work_id":"0e00d15a-ffe6-4527-a497-7f43722f49f2","year":2020},"citing_paper":{"arxiv_id":"2608.08922","last_updated":"2026-08-09T21:28:01Z","snapshot_observed_at":"2026-08-15T07:31:29.678107Z","submitted_at":"2026-08-09T21:28:01Z","title":"Clustered Attractor Manifolds and Dynamical Condensation in Self-Attention","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T04:26:02.835177Z"},"links":{"citing_paper":"/paper/2608.08922"},"observation_digest":"sha256:110e9c2d4b6eaa9b121fdc76c670bc855e04a29734d294edab2cdac1e5a05773","observation_id":"1170a63d-ae14-4904-baff-9038e590a1b3","resolution":{"observed_at":"2026-08-14T04:26:03.736405Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:26:03.708962Z","title":"Dosovitskiy, L","venue":null,"work_id":"5cdd0c80-d676-4fb5-836b-4817d6cb5ffa","year":2021},"citing_paper":{"arxiv_id":"2608.08922","last_updated":"2026-08-09T21:28:01Z","snapshot_observed_at":"2026-08-15T07:31:29.678107Z","submitted_at":"2026-08-09T21:28:01Z","title":"Clustered Attractor Manifolds and Dynamical Condensation in Self-Attention","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T04:26:02.842203Z"},"links":{"citing_paper":"/paper/2608.08922"},"observation_digest":"sha256:0caafc3d41b0c3a1349f7cae1f14d9056a6d4179f72001b490f8c75cd0341362","observation_id":"00ec236e-01f1-45e1-b8b1-36bc3a52dbf4","resolution":{"observed_at":"2026-08-14T04:26:03.715396Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:26:03.671786Z","title":"Radford, J","venue":null,"work_id":"397e2cfc-a9f6-4375-bc0e-744eba82cf60","year":2021},"citing_paper":{"arxiv_id":"2608.08922","last_updated":"2026-08-09T21:28:01Z","snapshot_observed_at":"2026-08-15T07:31:29.678107Z","submitted_at":"2026-08-09T21:28:01Z","title":"Clustered Attractor Manifolds and Dynamical Condensation in Self-Attention","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T04:26:02.849536Z"},"links":{"citing_paper":"/paper/2608.08922"},"observation_digest":"sha256:c40562518e03e4c000691f7c8584c2555dc21c5b3217b9bb9a08478d1f541b32","observation_id":"3ae9a7fd-0a66-433c-8ac0-64a12ff14150","resolution":{"observed_at":"2026-08-14T04:26:03.689157Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:26:03.644650Z","title":"Jumper, R","venue":null,"work_id":"6af74ee7-015f-4f2f-83e6-4bd11b8372c6","year":2021},"citing_paper":{"arxiv_id":"2608.08922","last_updated":"2026-08-09T21:28:01Z","snapshot_observed_at":"2026-08-15T07:31:29.678107Z","submitted_at":"2026-08-09T21:28:01Z","title":"Clustered Attractor Manifolds and Dynamical Condensation in Self-Attention","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T04:26:02.855984Z"},"links":{"citing_paper":"/paper/2608.08922"},"observation_digest":"sha256:d8f49172f1933983155141c95ebabc48abe194b258b3a46719cf5359ccfbaefb","observation_id":"52125ebb-7000-440c-ae39-61165c9d6e34","resolution":{"observed_at":"2026-08-14T04:26:03.651835Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1906.02762","last_updated":"2019-06-06T18:10:08Z","snapshot_observed_at":"2026-08-15T04:58:57.466596Z","submitted_at":"2019-06-06T18:10:08Z","title":"Understanding and Improving Transformer From a Multi-Particle Dynamic System Point of View","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1906.02762","snapshot_observed_at":"2026-08-14T04:26:02.862311Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2608.08922","last_updated":"2026-08-09T21:28:01Z","snapshot_observed_at":"2026-08-15T07:31:29.678107Z","submitted_at":"2026-08-09T21:28:01Z","title":"Clustered Attractor Manifolds and Dynamical Condensation in Self-Attention","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T04:26:02.862311Z"},"links":{"cited_paper":"/paper/1906.02762","citing_paper":"/paper/2608.08922"},"observation_digest":"sha256:01732045cfb9e29224767b5513986a7292d2c5e10f38a7129e638d19883694c0","observation_id":"8aefd8b4-aa98-4708-a94c-18ef3e9719cb","resolution":{"observed_at":"2026-08-14T04:26:02.862311Z","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":"2026-08-14T04:26:03.625805Z","title":null,"venue":null,"work_id":"0ae8a83e-1433-40b6-9008-4ecf5ab7058d","year":2019},"citing_paper":{"arxiv_id":"2608.08922","last_updated":"2026-08-09T21:28:01Z","snapshot_observed_at":"2026-08-15T07:31:29.678107Z","submitted_at":"2026-08-09T21:28:01Z","title":"Clustered Attractor Manifolds and Dynamical Condensation in Self-Attention","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T04:26:02.868387Z"},"links":{"citing_paper":"/paper/2608.08922"},"observation_digest":"sha256:89e939f6c029a2247adcdeb8140de91f615da2c5b05b326ceeaad33374f48b8a","observation_id":"9aed5b64-bb82-47ea-bd86-a515f56dd646","resolution":{"observed_at":"2026-08-14T04:26:03.630801Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:26:03.607919Z","title":"Dong, J.-B","venue":null,"work_id":"1921ab27-508f-41c6-a9e8-ebb1f0e8c2a5","year":2021},"citing_paper":{"arxiv_id":"2608.08922","last_updated":"2026-08-09T21:28:01Z","snapshot_observed_at":"2026-08-15T07:31:29.678107Z","submitted_at":"2026-08-09T21:28:01Z","title":"Clustered Attractor Manifolds and Dynamical Condensation in Self-Attention","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T04:26:02.878062Z"},"links":{"citing_paper":"/paper/2608.08922"},"observation_digest":"sha256:b5665df9d3f290b22226c009fb66fe397142967e32b245e4cf33fd8267e7bfa2","observation_id":"0cb9a7aa-b6d8-453a-8c53-94e429337c91","resolution":{"observed_at":"2026-08-14T04:26:03.614183Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:26:03.583864Z","title":null,"venue":null,"work_id":"9e0f1db4-384b-4f49-9ac4-25ba0514aa98","year":2022},"citing_paper":{"arxiv_id":"2608.08922","last_updated":"2026-08-09T21:28:01Z","snapshot_observed_at":"2026-08-15T07:31:29.678107Z","submitted_at":"2026-08-09T21:28:01Z","title":"Clustered Attractor Manifolds and Dynamical Condensation in Self-Attention","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T04:26:02.887310Z"},"links":{"citing_paper":"/paper/2608.08922"},"observation_digest":"sha256:86831ec992f2c4c42c8ea0dec269a02d717a9611d057dfa5239162ccee2ff41f","observation_id":"622f43ee-8abd-4de3-8fc1-0a0a4bd46dbb","resolution":{"observed_at":"2026-08-14T04:26:03.595456Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:26:03.561963Z","title":null,"venue":null,"work_id":"17943877-74f7-4bcf-8105-e53b6a8189d2","year":2023},"citing_paper":{"arxiv_id":"2608.08922","last_updated":"2026-08-09T21:28:01Z","snapshot_observed_at":"2026-08-15T07:31:29.678107Z","submitted_at":"2026-08-09T21:28:01Z","title":"Clustered Attractor Manifolds and Dynamical Condensation in Self-Attention","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-14T04:26:02.893131Z"},"links":{"citing_paper":"/paper/2608.08922"},"observation_digest":"sha256:084d6e008652a3e935ed83b1ce52803f64c613042d0cbd115beda4b15a5099b7","observation_id":"84fa5a4c-6e22-4bf8-9464-d8d08bac483f","resolution":{"observed_at":"2026-08-14T04:26:03.568048Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:26:03.543838Z","title":null,"venue":null,"work_id":"0777d295-c7f2-45e3-9d9a-5a15e0bcdf85","year":2024},"citing_paper":{"arxiv_id":"2608.08922","last_updated":"2026-08-09T21:28:01Z","snapshot_observed_at":"2026-08-15T07:31:29.678107Z","submitted_at":"2026-08-09T21:28:01Z","title":"Clustered Attractor Manifolds and Dynamical Condensation in Self-Attention","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-14T04:26:02.898720Z"},"links":{"citing_paper":"/paper/2608.08922"},"observation_digest":"sha256:129b395435a2ca3121ec888dfdc26e050ba64b073818233fda88d9118032b3ab","observation_id":"7f02655e-5161-40b0-bc96-4d9b102ac7f9","resolution":{"observed_at":"2026-08-14T04:26:03.548498Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2312.10794","last_updated":"2025-08-21T11:31:09Z","snapshot_observed_at":"2026-08-13T07:38:28.614683Z","submitted_at":"2023-12-17T19:06:29Z","title":"A mathematical perspective on Transformers","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2312.10794","snapshot_observed_at":"2026-08-14T04:26:02.912857Z","title":"Geshkovski, C","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.08922","last_updated":"2026-08-09T21:28:01Z","snapshot_observed_at":"2026-08-15T07:31:29.678107Z","submitted_at":"2026-08-09T21:28:01Z","title":"Clustered Attractor Manifolds and Dynamical Condensation in Self-Attention","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-14T04:26:02.912857Z"},"links":{"cited_paper":"/paper/2312.10794","citing_paper":"/paper/2608.08922"},"observation_digest":"sha256:7953cd3dd77d6f472f6064c7e9286dc062cc5b2a11db1e0749b8707fb689cf24","observation_id":"7b2ed2a7-d18e-4f0f-8a03-faf955a842ba","resolution":{"observed_at":"2026-08-14T04:26:02.912857Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2501.03096","last_updated":"2025-04-28T08:36:55Z","snapshot_observed_at":"2026-08-10T21:51:02.444976Z","submitted_at":"2025-01-06T15:53:29Z","title":"Analysis of mean-field models arising from self-attention dynamics in transformer architectures with layer normalization","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.03096","snapshot_observed_at":"2026-08-14T04:26:02.917918Z","title":"Burger, S","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.08922","last_updated":"2026-08-09T21:28:01Z","snapshot_observed_at":"2026-08-15T07:31:29.678107Z","submitted_at":"2026-08-09T21:28:01Z","title":"Clustered Attractor Manifolds and Dynamical Condensation in Self-Attention","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-14T04:26:02.917918Z"},"links":{"cited_paper":"/paper/2501.03096","citing_paper":"/paper/2608.08922"},"observation_digest":"sha256:6179c52c809c95529090dcd7a78bde9a0775e310b8be23b3e5109235b3f90230","observation_id":"cfd8cbd1-781f-4c24-aa11-2cb1fdf34e75","resolution":{"observed_at":"2026-08-14T04:26:02.917918Z","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":"2026-08-14T04:26:03.524860Z","title":"Rigollet, The mean-field dynamics of transformers, in Proceedings of the International Congress of Mathemati- cians 2026—Volume 7: Invited Lectures (Sections 15–20), edited by S","venue":null,"work_id":"d22330b8-fab2-4d84-b9c7-90576f92066b","year":2026},"citing_paper":{"arxiv_id":"2608.08922","last_updated":"2026-08-09T21:28:01Z","snapshot_observed_at":"2026-08-15T07:31:29.678107Z","submitted_at":"2026-08-09T21:28:01Z","title":"Clustered Attractor Manifolds and Dynamical Condensation in Self-Attention","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-14T04:26:02.923619Z"},"links":{"citing_paper":"/paper/2608.08922"},"observation_digest":"sha256:1d7091e72cbec521d434aaa3e181aba81db83514487f42e8ecf2b45782de0f80","observation_id":"224f8f8b-a13e-4c5a-9851-218326053dd8","resolution":{"observed_at":"2026-08-14T04:26:03.531704Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:26:02.929861Z","title":"Altafini, Multistability of self-attention dynamics in transformers, arXiv preprint arXiv:2511.11553 (2025), arXiv:2511.11553 [cs.LG]","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.08922","last_updated":"2026-08-09T21:28:01Z","snapshot_observed_at":"2026-08-15T07:31:29.678107Z","submitted_at":"2026-08-09T21:28:01Z","title":"Clustered Attractor Manifolds and Dynamical Condensation in Self-Attention","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-14T04:26:02.929861Z"},"links":{"citing_paper":"/paper/2608.08922"},"observation_digest":"sha256:a26a6d73305b32a482429e285d016ca3e93d850f05ecee3ffc0c9f1fd4b7ca97","observation_id":"53111042-d571-4b7c-9d25-92653687c7f7","resolution":{"observed_at":"2026-08-14T04:26:02.929861Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2402.11180","last_updated":"2024-02-17T03:29:20Z","snapshot_observed_at":"2026-08-13T04:17:09.481201Z","submitted_at":"2024-02-17T03:29:20Z","title":"PureNav: A Personalized Navigation Service for Environmental Justice Communities Impacted by Planned Disruptions","version":1},"cited_work":{"arxiv_id":"2402.11180","doi":null,"metadata_source":"pith","pith_arxiv_id":"2402.11180","snapshot_observed_at":"2026-08-14T04:26:03.249295Z","title":"PureNav: A Personalized Navigation Service for Environmental Justice Communities Impacted by Planned Disruptions","venue":"cs.SI","work_id":"4ef7c2eb-13a2-4727-8b14-5ef4775a6ad2","year":2024},"citing_paper":{"arxiv_id":"2608.08922","last_updated":"2026-08-09T21:28:01Z","snapshot_observed_at":"2026-08-15T07:31:29.678107Z","submitted_at":"2026-08-09T21:28:01Z","title":"Clustered Attractor Manifolds and Dynamical Condensation in Self-Attention","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-14T04:26:02.934854Z"},"links":{"cited_paper":"/paper/2402.11180","citing_paper":"/paper/2608.08922"},"observation_digest":"sha256:ba32b4ca65332d5d3899db5dcdcc64fff9b74793c3b53d52e53aa8cf79760024","observation_id":"742fe03d-e8d5-4ecb-9359-376daaa27f56","resolution":{"observed_at":"2026-08-14T04:26:03.256555Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2505.15290","last_updated":"2026-06-25T14:49:43Z","snapshot_observed_at":"2026-08-13T00:39:29.014517Z","submitted_at":"2025-05-21T09:20:46Z","title":"Robust Probabilistic Bisimilarity for Labelled Markov Chains","version":2},"cited_work":{"arxiv_id":"2505.15290","doi":null,"metadata_source":"pith","pith_arxiv_id":"2505.15290","snapshot_observed_at":"2026-08-14T04:26:03.225927Z","title":"Robust Probabilistic Bisimilarity for Labelled Markov Chains","venue":"cs.LO","work_id":"4131dec8-8adc-4ecd-bf44-c9ce188a0ccb","year":2025},"citing_paper":{"arxiv_id":"2608.08922","last_updated":"2026-08-09T21:28:01Z","snapshot_observed_at":"2026-08-15T07:31:29.678107Z","submitted_at":"2026-08-09T21:28:01Z","title":"Clustered Attractor Manifolds and Dynamical Condensation in Self-Attention","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-14T04:26:02.944496Z"},"links":{"cited_paper":"/paper/2505.15290","citing_paper":"/paper/2608.08922"},"observation_digest":"sha256:f815a6a9867b53ed204b052c16fe0a8b9b1064de8f3edddd95703e248d310b2e","observation_id":"f427e7f8-d8da-4714-a889-0d0b41930445","resolution":{"observed_at":"2026-08-14T04:26:03.232583Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:26:02.955996Z","title":"Bruno, F","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.08922","last_updated":"2026-08-09T21:28:01Z","snapshot_observed_at":"2026-08-15T07:31:29.678107Z","submitted_at":"2026-08-09T21:28:01Z","title":"Clustered Attractor Manifolds and Dynamical Condensation in Self-Attention","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-14T04:26:02.955996Z"},"links":{"citing_paper":"/paper/2608.08922"},"observation_digest":"sha256:0edca6c73eb641b8685656cf3b3dad3d2f1821207c58ebf88b489277763deea5","observation_id":"71ccedfd-9132-4d5f-bb5d-838fc34ac2c4","resolution":{"observed_at":"2026-08-14T04:26:02.955996Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.24333","last_updated":"2026-02-09T14:17:44Z","snapshot_observed_at":"2026-08-09T18:45:01.721579Z","submitted_at":"2025-05-30T08:18:23Z","title":"Two failure modes of deep transformers and how to avoid them: a unified theory of signal propagation at initialisation","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.24333","snapshot_observed_at":"2026-08-14T04:26:02.963314Z","title":"Giorlandino and S","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2608.08922","last_updated":"2026-08-09T21:28:01Z","snapshot_observed_at":"2026-08-15T07:31:29.678107Z","submitted_at":"2026-08-09T21:28:01Z","title":"Clustered Attractor Manifolds and Dynamical Condensation in Self-Attention","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-14T04:26:02.963314Z"},"links":{"cited_paper":"/paper/2505.24333","citing_paper":"/paper/2608.08922"},"observation_digest":"sha256:399f5375e55ae2d33b54ae783bc84fce4004b8fd9e169776eb0d5b1dfe24bf4a","observation_id":"ba52068f-0ec0-4607-8bcc-803ad8e15152","resolution":{"observed_at":"2026-08-14T04:26:02.963314Z","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":"2026-08-14T04:26:03.482109Z","title":null,"venue":null,"work_id":"c3aed0e4-aa57-4595-ba15-c8a19d9dbb7f","year":null},"citing_paper":{"arxiv_id":"2608.08922","last_updated":"2026-08-09T21:28:01Z","snapshot_observed_at":"2026-08-15T07:31:29.678107Z","submitted_at":"2026-08-09T21:28:01Z","title":"Clustered Attractor Manifolds and Dynamical Condensation in Self-Attention","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-14T04:26:02.981808Z"},"links":{"citing_paper":"/paper/2608.08922"},"observation_digest":"sha256:74f273ccda8d2baa87e9d7aeeb500fd246af33a3d13cd0a10d4e555999fb9346","observation_id":"52579474-3b1e-494b-9e97-4031a1537c9b","resolution":{"observed_at":"2026-08-14T04:26:03.488168Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:26:03.438294Z","title":"Katharopoulos, A","venue":null,"work_id":"16840a92-102c-47bc-b545-30b160c5dee9","year":2020},"citing_paper":{"arxiv_id":"2608.08922","last_updated":"2026-08-09T21:28:01Z","snapshot_observed_at":"2026-08-15T07:31:29.678107Z","submitted_at":"2026-08-09T21:28:01Z","title":"Clustered Attractor Manifolds and Dynamical Condensation in Self-Attention","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-14T04:26:03.004298Z"},"links":{"citing_paper":"/paper/2608.08922"},"observation_digest":"sha256:808aed3b759a244262b4e230dbb3df69ba0af041f087160a362d36f95b646aba","observation_id":"7c134f52-5cd5-4499-966a-20f1a8551297","resolution":{"observed_at":"2026-08-14T04:26:03.447071Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:26:03.503115Z","title":"Derrida, Random-energy model: An exactly solvable model of disordered systems, Physical Review B24, 2613 (1981)","venue":null,"work_id":"74d9ed6c-44f3-4605-9b51-b5b1750b1186","year":1981},"citing_paper":{"arxiv_id":"2608.08922","last_updated":"2026-08-09T21:28:01Z","snapshot_observed_at":"2026-08-15T07:31:29.678107Z","submitted_at":"2026-08-09T21:28:01Z","title":"Clustered Attractor Manifolds and Dynamical Condensation in Self-Attention","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-14T04:26:03.014922Z"},"links":{"citing_paper":"/paper/2608.08922"},"observation_digest":"sha256:565be09b9936b72e14205a41720f9d75745d00bb16b8f6536f0e2d5ff83ccf79","observation_id":"f68e6883-fcfd-46ed-8fd8-a4c307d56612","resolution":{"observed_at":"2026-08-14T04:26:03.509723Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2305.05465","last_updated":"2024-02-12T10:21:08Z","snapshot_observed_at":"2026-08-13T11:45:52.746896Z","submitted_at":"2023-05-09T14:04:42Z","title":"The emergence of clusters in self-attention dynamics","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2305.05465","snapshot_observed_at":"2026-08-14T04:26:03.020086Z","title":"Geshkovski, C","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2608.08922","last_updated":"2026-08-09T21:28:01Z","snapshot_observed_at":"2026-08-15T07:31:29.678107Z","submitted_at":"2026-08-09T21:28:01Z","title":"Clustered Attractor Manifolds and Dynamical Condensation in Self-Attention","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-14T04:26:03.020086Z"},"links":{"cited_paper":"/paper/2305.05465","citing_paper":"/paper/2608.08922"},"observation_digest":"sha256:07714e8fbb7a2af7bc1d4be80b80367e0418183854b867119d03a1ec21537945","observation_id":"3adf5708-a035-491c-b71e-927566f225da","resolution":{"observed_at":"2026-08-14T04:26:03.020086Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2410.06833","last_updated":"2024-10-09T12:50:50Z","snapshot_observed_at":"2026-08-13T06:39:04.803010Z","submitted_at":"2024-10-09T12:50:50Z","title":"Dynamic metastability in the self-attention model","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2410.06833","snapshot_observed_at":"2026-08-14T04:26:03.024523Z","title":"Geshkovski, H","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.08922","last_updated":"2026-08-09T21:28:01Z","snapshot_observed_at":"2026-08-15T07:31:29.678107Z","submitted_at":"2026-08-09T21:28:01Z","title":"Clustered Attractor Manifolds and Dynamical Condensation in Self-Attention","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-14T04:26:03.024523Z"},"links":{"cited_paper":"/paper/2410.06833","citing_paper":"/paper/2608.08922"},"observation_digest":"sha256:7a81bf5320cba1970f1bda7462265459565ffee86d73781dedc9857783037f37","observation_id":"8b9bd1c6-52eb-47d5-ab75-526b2b683d14","resolution":{"observed_at":"2026-08-14T04:26:03.024523Z","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":"2026-08-14T04:26:03.458917Z","title":"Bruno, F","venue":null,"work_id":"a083ce79-1311-465c-9a17-222d04342edf","year":2025},"citing_paper":{"arxiv_id":"2608.08922","last_updated":"2026-08-09T21:28:01Z","snapshot_observed_at":"2026-08-15T07:31:29.678107Z","submitted_at":"2026-08-09T21:28:01Z","title":"Clustered Attractor Manifolds and Dynamical Condensation in Self-Attention","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-14T04:26:03.028817Z"},"links":{"citing_paper":"/paper/2608.08922"},"observation_digest":"sha256:9da218a8cbc85ffccf209f15678e549efd881c58bad69e592c8c963cc86de5ab","observation_id":"8272dced-e9cb-40da-b973-eaf80a0fc5a3","resolution":{"observed_at":"2026-08-14T04:26:03.465197Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:26:03.421462Z","title":"Katharopoulos, A","venue":null,"work_id":"343a5e33-2ca0-4db8-873c-b99f89791990","year":2020},"citing_paper":{"arxiv_id":"2608.08922","last_updated":"2026-08-09T21:28:01Z","snapshot_observed_at":"2026-08-15T07:31:29.678107Z","submitted_at":"2026-08-09T21:28:01Z","title":"Clustered Attractor Manifolds and Dynamical Condensation in Self-Attention","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-14T04:26:03.033191Z"},"links":{"citing_paper":"/paper/2608.08922"},"observation_digest":"sha256:d39248aac1389d34219975bab632a59619cd02da3f170b6b48b2cbc9847ee1fd","observation_id":"ee687e00-c14a-4de0-a0c7-7d017712ad24","resolution":{"observed_at":"2026-08-14T04:26:03.427006Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2009.14794","last_updated":"2022-11-19T12:45:21Z","snapshot_observed_at":"2026-08-12T04:58:34.201421Z","submitted_at":"2020-09-30T17:09:09Z","title":"Rethinking Attention with Performers","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2009.14794","snapshot_observed_at":"2026-08-14T04:26:03.037934Z","title":"Choromanski, V","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2608.08922","last_updated":"2026-08-09T21:28:01Z","snapshot_observed_at":"2026-08-15T07:31:29.678107Z","submitted_at":"2026-08-09T21:28:01Z","title":"Clustered Attractor Manifolds and Dynamical Condensation in Self-Attention","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-14T04:26:03.037934Z"},"links":{"cited_paper":"/paper/2009.14794","citing_paper":"/paper/2608.08922"},"observation_digest":"sha256:a218d8f452028487c8891d68026b0b9edc9962c7fdfed1c8ffa9796220ee4fe9","observation_id":"f992af93-8416-47d3-bf59-5129bd90549e","resolution":{"observed_at":"2026-08-14T04:26:03.037934Z","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":"2026-08-14T04:26:03.404785Z","title":"Rigollet, The mean-field dynamics of transformers, inProceedings of the International Congress of Mathematicians 2026—Volume 7: Invited Lectures (Sections 15–20), edited by S","venue":null,"work_id":"821924b6-e6dd-4227-ae57-1f9040cd5328","year":2026},"citing_paper":{"arxiv_id":"2608.08922","last_updated":"2026-08-09T21:28:01Z","snapshot_observed_at":"2026-08-15T07:31:29.678107Z","submitted_at":"2026-08-09T21:28:01Z","title":"Clustered Attractor Manifolds and Dynamical Condensation in Self-Attention","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-14T04:26:03.042061Z"},"links":{"citing_paper":"/paper/2608.08922"},"observation_digest":"sha256:56ed522e77ecb4e49fabfcecf7cf166584123bb81aeb2c354fdeeb831d32d249","observation_id":"4c1194e2-7d13-4590-972b-0458df408171","resolution":{"observed_at":"2026-08-14T04:26:03.411345Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2608.08922","last_updated":"2026-08-09T21:28:01Z","latest_version":1,"primary_category":"cond-mat.dis-nn","snapshot_observed_at":"2026-08-15T07:31:29.678107Z","submitted_at":"2026-08-09T21:28:01Z","title":"Clustered Attractor Manifolds and Dynamical Condensation in Self-Attention"},"reference_resolution":{"displayed":29,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":15,"verified_exact":2,"verified_fuzzy":12},"total_outbound_references":29},"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":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"thesis":"As of 15 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 0 inbound Pith citation observations for arXiv:2608.08922."}