{"as_of":"2026-08-08T05:36:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:18ccc877b355fb6f97e5ac0daa617c5c8b7f5b281249d70ecce6636e4c8b3460","coverage":[{"denominator":24,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":24,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T15:23:34.371185Z","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":"2026-08-07T06:34:17.273281+00:00","state":"measured"},{"denominator":5,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":5,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T12:28:26.062143Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-25T04:45:20.322782Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2505.15507","last_updated":"2025-05-21T13:27:14Z","snapshot_observed_at":"2026-08-07T15:14:11.082266Z","submitted_at":"2025-05-21T13:27:14Z","title":"Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.15507","snapshot_observed_at":"2026-08-07T12:28:26.062143Z","title":"Directional Non-Commutative Monoidal Structures for Com- positional Embeddings in Machine Learning","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.24533","last_updated":"2025-05-30T12:40:01Z","snapshot_observed_at":"2026-08-07T12:16:50.340090Z","submitted_at":"2025-05-30T12:40:01Z","title":"Directional Non-Commutative Monoidal Structures with Interchange Law via Commutative Generators","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:26.062143Z"},"links":{"cited_paper":"/paper/2505.15507","citing_paper":"/paper/2505.24533"},"observation_digest":"sha256:86ff865e537b6b0e1b873f4bf35e4921e834c1a9a2bf695aa3344f804ef1a5ec","observation_id":"c88c17f0-29ea-40d7-98ae-e24f309d1f41","resolution":{"observed_at":"2026-08-07T12:28:26.062143Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.15507","last_updated":"2025-05-21T13:27:14Z","snapshot_observed_at":"2026-08-07T15:14:11.082266Z","submitted_at":"2025-05-21T13:27:14Z","title":"Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.15507","snapshot_observed_at":"2026-08-07T11:07:46.645351Z","title":"Godavarti, Directional Non-Commutative Monoidal Structures for Com- positional Embeddings in Machine Learning","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2506.03472","last_updated":"2025-06-04T01:07:51Z","snapshot_observed_at":"2026-08-07T10:59:59.898897Z","submitted_at":"2025-06-04T01:07:51Z","title":"Directional Non-Commutative Monoidal Embeddings for MNIST","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T11:07:46.645351Z"},"links":{"cited_paper":"/paper/2505.15507","citing_paper":"/paper/2506.03472"},"observation_digest":"sha256:ac7dc23e07ce733b66832712751f978acfd2e5e2022afea2ff3e86832efcbda8","observation_id":"6405777f-400b-4db7-b120-71e46f7bd831","resolution":{"observed_at":"2026-08-07T11:07:46.645351Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.15507","last_updated":"2025-05-21T13:27:14Z","snapshot_observed_at":"2026-08-07T15:14:11.082266Z","submitted_at":"2025-05-21T13:27:14Z","title":"Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.15507","snapshot_observed_at":"2026-08-07T05:10:50.642197Z","title":"Godavarti","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2506.08652","last_updated":"2025-06-10T10:05:29Z","snapshot_observed_at":"2026-08-07T05:02:54.566281Z","submitted_at":"2025-06-10T10:05:29Z","title":"JoFormer (Journey-based Transformer): Theory and Empirical Analysis on the Tiny Shakespeare Dataset","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T05:10:50.642197Z"},"links":{"cited_paper":"/paper/2505.15507","citing_paper":"/paper/2506.08652"},"observation_digest":"sha256:0080af93a80cb113dd71f4ecdbbf2dec2982ec25009a1cc55b468faff5b0f592","observation_id":"6bf5e5e2-cc82-420c-bfcb-58335dcb54c9","resolution":{"observed_at":"2026-08-07T05:10:50.642197Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.15507","last_updated":"2025-05-21T13:27:14Z","snapshot_observed_at":"2026-08-07T15:14:11.082266Z","submitted_at":"2025-05-21T13:27:14Z","title":"Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning","version":1},"cited_work":{"arxiv_id":"2505.15507","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2505.15507","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Directional non-commutative monoidal structures for compositional embeddings in machine learning","venue":null,"work_id":"4a9872fa-2764-49b5-8e90-bb649e4f3f68","year":2025},"citing_paper":{"arxiv_id":"2605.23449","last_updated":"2026-05-22T10:03:46Z","snapshot_observed_at":"2026-08-02T19:57:30.211113Z","submitted_at":"2026-05-22T10:03:46Z","title":"Commutator-Induced Uncertainty in VAEs","version":1},"reference_index":58,"source":"arxiv_source","source_observed_at":"2026-05-25T04:42:39.399803Z"},"links":{"cited_paper":"/paper/2505.15507","citing_paper":"/paper/2605.23449"},"observation_digest":"sha256:d506714593d1d2a2e58d4789c817e644feb474979c3536d9d0657b1fd6f601f1","observation_id":"d433bafd-1fbb-49bb-8054-9c5956afa970","resolution":{"observed_at":"2026-05-25T04:45:20.325909Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2505.15507","last_updated":"2025-05-21T13:27:14Z","snapshot_observed_at":"2026-08-07T15:14:11.082266Z","submitted_at":"2025-05-21T13:27:14Z","title":"Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.15507","snapshot_observed_at":"2026-07-30T21:28:26.173311Z","title":"arXiv preprint arXiv:2505.15507 , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.26775","last_updated":"2026-07-29T11:14:54Z","snapshot_observed_at":"2026-08-01T23:31:04.582002Z","submitted_at":"2026-07-29T11:14:54Z","title":"Journey Operators for Structured Multi-Axis Composition","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-07-30T21:28:26.173311Z"},"links":{"cited_paper":"/paper/2505.15507","citing_paper":"/paper/2607.26775"},"observation_digest":"sha256:3c7852ed029128fac6a4fe12543b6e5920464e6bee674f0501d2c7d1a0b24fea","observation_id":"ccb0602b-dcb4-4802-93b5-9f6737157389","resolution":{"observed_at":"2026-07-30T21:28:26.173311Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2505.15507/citation-record","integrity":"/paper/2505.15507/integrity","json":"/paper/2505.15507/citation-record.json","paper":"/paper/2505.15507"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:23:39.330353Z","title":"Mac Lane","venue":null,"work_id":"d09e12a2-63e4-455e-a85b-7c943c7055e1","year":1998},"citing_paper":{"arxiv_id":"2505.15507","last_updated":"2025-05-21T13:27:14Z","snapshot_observed_at":"2026-08-07T15:14:11.082266Z","submitted_at":"2025-05-21T13:27:14Z","title":"Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T15:23:31.950241Z"},"links":{"citing_paper":"/paper/2505.15507"},"observation_digest":"sha256:152e010b9bbded00ff9f25f4322007de254944cebc4becb6e21158cab41c1ae8","observation_id":"169ec391-eba8-4998-8ac1-1ffd11fda108","resolution":{"observed_at":"2026-08-07T15:23:39.417558Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T15:23:39.133912Z","title":"Mitchell and M","venue":null,"work_id":"3a18c52c-af1c-4a79-8298-a36c99bb5fab","year":2010},"citing_paper":{"arxiv_id":"2505.15507","last_updated":"2025-05-21T13:27:14Z","snapshot_observed_at":"2026-08-07T15:14:11.082266Z","submitted_at":"2025-05-21T13:27:14Z","title":"Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T15:23:31.988940Z"},"links":{"citing_paper":"/paper/2505.15507"},"observation_digest":"sha256:5f6f4f6ea5725feeebbc2fdff2ae48be01a775237ef3b8c32ae19aa2ae5cadb0","observation_id":"d6acc554-12a8-44d3-9176-391d6cfd6528","resolution":{"observed_at":"2026-08-07T15:23:39.204051Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T15:23:38.934486Z","title":"Sabour, N","venue":null,"work_id":"f349ce09-ebe8-43b0-ad86-1e02ca57124f","year":2017},"citing_paper":{"arxiv_id":"2505.15507","last_updated":"2025-05-21T13:27:14Z","snapshot_observed_at":"2026-08-07T15:14:11.082266Z","submitted_at":"2025-05-21T13:27:14Z","title":"Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T15:23:32.042170Z"},"links":{"citing_paper":"/paper/2505.15507"},"observation_digest":"sha256:fbe7e5e80a66cdecd9a8b5ef08029413939926b3bd2de7c3e4847a6f5906b037","observation_id":"62fda000-0372-44ea-a3fa-7ed0e84c6457","resolution":{"observed_at":"2026-08-07T15:23:39.033706Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T15:23:38.651608Z","title":"Gilmer, S","venue":null,"work_id":"5422e499-eed5-42d6-bec9-9bbc0bc637d3","year":2017},"citing_paper":{"arxiv_id":"2505.15507","last_updated":"2025-05-21T13:27:14Z","snapshot_observed_at":"2026-08-07T15:14:11.082266Z","submitted_at":"2025-05-21T13:27:14Z","title":"Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T15:23:32.140701Z"},"links":{"citing_paper":"/paper/2505.15507"},"observation_digest":"sha256:b15be367f8c5ca77a45f88e209bd9279101f1e615f7e6fa3a047c52fff3531ae","observation_id":"53a09cdf-6592-46bc-8325-6a74a23f4e55","resolution":{"observed_at":"2026-08-07T15:23:38.788912Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T15:23:38.317794Z","title":"Coecke, M","venue":null,"work_id":"0b9d6bc3-8bc3-4e13-abab-9ebc510389ad","year":2010},"citing_paper":{"arxiv_id":"2505.15507","last_updated":"2025-05-21T13:27:14Z","snapshot_observed_at":"2026-08-07T15:14:11.082266Z","submitted_at":"2025-05-21T13:27:14Z","title":"Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T15:23:32.200406Z"},"links":{"citing_paper":"/paper/2505.15507"},"observation_digest":"sha256:f59859a49f7b8766194e878b9a136acb90a51c452eaaaeba2de6800f27ebc565","observation_id":"d7caaca9-9ed3-471f-8979-5b2ff73f5a82","resolution":{"observed_at":"2026-08-07T15:23:38.483863Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T15:23:38.007119Z","title":"Baroni and R","venue":null,"work_id":"7aa7b3b5-b30d-4e5a-a0ae-b375eabfdf2f","year":2010},"citing_paper":{"arxiv_id":"2505.15507","last_updated":"2025-05-21T13:27:14Z","snapshot_observed_at":"2026-08-07T15:14:11.082266Z","submitted_at":"2025-05-21T13:27:14Z","title":"Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T15:23:32.240047Z"},"links":{"citing_paper":"/paper/2505.15507"},"observation_digest":"sha256:9f6cccec37d553e6778ca5f40ce093e28dfc49e2b47fcd02c0a451159cb2e4c8","observation_id":"2112df82-4d81-400c-83a2-73a0532b7a9e","resolution":{"observed_at":"2026-08-07T15:23:38.161331Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T15:23:37.737575Z","title":"Rudolph and E","venue":null,"work_id":"d920f632-1503-44db-9130-4a35d3ca633d","year":2010},"citing_paper":{"arxiv_id":"2505.15507","last_updated":"2025-05-21T13:27:14Z","snapshot_observed_at":"2026-08-07T15:14:11.082266Z","submitted_at":"2025-05-21T13:27:14Z","title":"Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T15:23:32.275902Z"},"links":{"citing_paper":"/paper/2505.15507"},"observation_digest":"sha256:9b2442ece69bf29742a755eeec9b9ef5839b13083bc5762fee1226973d8bfc6b","observation_id":"af5f5cd0-37e5-414e-9380-3e12b7bf175b","resolution":{"observed_at":"2026-08-07T15:23:37.860004Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T15:23:37.386094Z","title":"Socher, B","venue":null,"work_id":"2fd43375-3d59-4554-9d73-1fd814de2619","year":2012},"citing_paper":{"arxiv_id":"2505.15507","last_updated":"2025-05-21T13:27:14Z","snapshot_observed_at":"2026-08-07T15:14:11.082266Z","submitted_at":"2025-05-21T13:27:14Z","title":"Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T15:23:32.318356Z"},"links":{"citing_paper":"/paper/2505.15507"},"observation_digest":"sha256:8d5ddeda3ae1e94aa754feaf62e20e72fbd69542c0fea632aadd1940aa4ecf3c","observation_id":"3e2019f2-3245-463b-aa71-66767c44f072","resolution":{"observed_at":"2026-08-07T15:23:37.555877Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T15:23:37.056283Z","title":"V aswani, N","venue":null,"work_id":"26a01042-ead1-4112-ad65-56aa6d57c8cb","year":2017},"citing_paper":{"arxiv_id":"2505.15507","last_updated":"2025-05-21T13:27:14Z","snapshot_observed_at":"2026-08-07T15:14:11.082266Z","submitted_at":"2025-05-21T13:27:14Z","title":"Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T15:23:32.351697Z"},"links":{"citing_paper":"/paper/2505.15507"},"observation_digest":"sha256:007bf8a31f22e29f2064406f0336e6945fb1fd1c8cd1c73a81f694ab076978d2","observation_id":"55b52bb0-d3b6-42db-84c3-9542e8e72968","resolution":{"observed_at":"2026-08-07T15:23:37.160483Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T15:23:36.735392Z","title":null,"venue":null,"work_id":"e4b3b005-eb31-4993-bccf-921a9067aaae","year":2018},"citing_paper":{"arxiv_id":"2505.15507","last_updated":"2025-05-21T13:27:14Z","snapshot_observed_at":"2026-08-07T15:14:11.082266Z","submitted_at":"2025-05-21T13:27:14Z","title":"Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T15:23:32.426415Z"},"links":{"citing_paper":"/paper/2505.15507"},"observation_digest":"sha256:5dd65c4ebdb150c2dae4389634871dacfddbfce65d0f94ccab32a55b0c7b22b2","observation_id":"7a467c97-4c7e-4cf6-a5c9-c67fdad4363f","resolution":{"observed_at":"2026-08-07T15:23:36.885955Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T15:23:36.399728Z","title":null,"venue":null,"work_id":"0eae9e3d-6ab9-4f77-a126-496fac0862e6","year":2019},"citing_paper":{"arxiv_id":"2505.15507","last_updated":"2025-05-21T13:27:14Z","snapshot_observed_at":"2026-08-07T15:14:11.082266Z","submitted_at":"2025-05-21T13:27:14Z","title":"Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T15:23:32.514929Z"},"links":{"citing_paper":"/paper/2505.15507"},"observation_digest":"sha256:e54883e81f73d4dc194bb6488a01b8a99c6e6fdd00b98c9334b9bcce04268763","observation_id":"b90e8319-3ce7-43f4-8a65-476fd5b713cb","resolution":{"observed_at":"2026-08-07T15:23:36.615267Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1910.10683","last_updated":"2023-09-19T15:14:48Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2019-10-23T17:37:36Z","title":"Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1910.10683","snapshot_observed_at":"2026-08-07T15:23:32.655174Z","title":"Raffel, N","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2505.15507","last_updated":"2025-05-21T13:27:14Z","snapshot_observed_at":"2026-08-07T15:14:11.082266Z","submitted_at":"2025-05-21T13:27:14Z","title":"Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T15:23:32.655174Z"},"links":{"cited_paper":"/paper/1910.10683","citing_paper":"/paper/2505.15507"},"observation_digest":"sha256:2116f3690005ad636e5d3aa214550e2f33ddacb97a73a4c2dcc44eceb8706b22","observation_id":"70259861-069e-412b-b531-6084f86eaf7d","resolution":{"observed_at":"2026-08-07T15:23:32.655174Z","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":"2026-08-07T15:23:36.048172Z","title":"Aguiar and S","venue":null,"work_id":"7c4d7518-473a-489a-bd7f-d72ba032d7cf","year":2010},"citing_paper":{"arxiv_id":"2505.15507","last_updated":"2025-05-21T13:27:14Z","snapshot_observed_at":"2026-08-07T15:14:11.082266Z","submitted_at":"2025-05-21T13:27:14Z","title":"Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T15:23:32.791304Z"},"links":{"citing_paper":"/paper/2505.15507"},"observation_digest":"sha256:3ec94a063942b7ddab088ae32f2e11ebf54a77e332547a9116385b28886882db","observation_id":"85bbe20f-c6b7-472b-914d-35e1b4a16d5f","resolution":{"observed_at":"2026-08-07T15:23:36.216311Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T15:23:35.777092Z","title":null,"venue":null,"work_id":"d7d658c5-7cdb-4895-81d0-461337b5987b","year":2017},"citing_paper":{"arxiv_id":"2505.15507","last_updated":"2025-05-21T13:27:14Z","snapshot_observed_at":"2026-08-07T15:14:11.082266Z","submitted_at":"2025-05-21T13:27:14Z","title":"Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T15:23:33.001293Z"},"links":{"citing_paper":"/paper/2505.15507"},"observation_digest":"sha256:f1406ce874cc2fbe9935fda72b13aa0736eed50b48b8a4d9f794dc2bac792472","observation_id":"e34019b8-d9ba-40f0-a4ad-93ed65d5aa46","resolution":{"observed_at":"2026-08-07T15:23:35.906851Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T15:23:35.421173Z","title":"Balteanu, Z","venue":null,"work_id":"a936049a-46e5-48a3-aeb8-2e00ab17c396","year":2003},"citing_paper":{"arxiv_id":"2505.15507","last_updated":"2025-05-21T13:27:14Z","snapshot_observed_at":"2026-08-07T15:14:11.082266Z","submitted_at":"2025-05-21T13:27:14Z","title":"Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T15:23:33.134083Z"},"links":{"citing_paper":"/paper/2505.15507"},"observation_digest":"sha256:e1aa4bf9a7cf5bf016eb117879eff82f3ec2fb4f2e5eadf7705b47d0b255797e","observation_id":"fae5d155-19a5-48a2-a24c-b6e12fed6ff7","resolution":{"observed_at":"2026-08-07T15:23:35.582689Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T15:23:35.122446Z","title":"Cichocki, N","venue":null,"work_id":"26798293-08b4-4e23-b345-820d2ffabfa8","year":2016},"citing_paper":{"arxiv_id":"2505.15507","last_updated":"2025-05-21T13:27:14Z","snapshot_observed_at":"2026-08-07T15:14:11.082266Z","submitted_at":"2025-05-21T13:27:14Z","title":"Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T15:23:33.271086Z"},"links":{"citing_paper":"/paper/2505.15507"},"observation_digest":"sha256:b636e106f6368ed15fcba8b1a311220e24e1c7a9f75c1de829c7f741ec139805","observation_id":"cc7b863c-515f-42fd-b7ed-c7d7ba7b3912","resolution":{"observed_at":"2026-08-07T15:23:35.287382Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2104.09864","last_updated":"2023-11-08T13:36:32Z","snapshot_observed_at":"2026-07-06T11:01:58.137141Z","submitted_at":"2021-04-20T09:54:06Z","title":"RoFormer: Enhanced Transformer with Rotary Position Embedding","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2104.09864","snapshot_observed_at":"2026-08-07T15:23:33.390015Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2505.15507","last_updated":"2025-05-21T13:27:14Z","snapshot_observed_at":"2026-08-07T15:14:11.082266Z","submitted_at":"2025-05-21T13:27:14Z","title":"Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T15:23:33.390015Z"},"links":{"cited_paper":"/paper/2104.09864","citing_paper":"/paper/2505.15507"},"observation_digest":"sha256:8567ae66adb6547ed83a91054c7e675637c8d903fc71e2a035f8eb0ae7f020ca","observation_id":"815400c3-384c-445b-b7d7-a56b01cfb48b","resolution":{"observed_at":"2026-08-07T15:23:33.390015Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2403.13298","last_updated":"2024-07-16T04:54:56Z","snapshot_observed_at":"2026-07-06T17:47:30.518562Z","submitted_at":"2024-03-20T04:47:13Z","title":"Rotary Position Embedding for Vision Transformer","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.13298","snapshot_observed_at":"2026-08-07T15:23:33.614694Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.15507","last_updated":"2025-05-21T13:27:14Z","snapshot_observed_at":"2026-08-07T15:14:11.082266Z","submitted_at":"2025-05-21T13:27:14Z","title":"Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T15:23:33.614694Z"},"links":{"cited_paper":"/paper/2403.13298","citing_paper":"/paper/2505.15507"},"observation_digest":"sha256:f9c556a2071e2705c158b98c5dcaa533330435128dcc9f9a549e3b1392c13df9","observation_id":"8843e37b-8c22-4118-ba7c-26ceab61d659","resolution":{"observed_at":"2026-08-07T15:23:33.614694Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2006.03654","last_updated":"2021-10-06T21:02:00Z","snapshot_observed_at":"2026-07-06T09:26:29.068023Z","submitted_at":"2020-06-05T19:54:34Z","title":"DeBERTa: Decoding-enhanced BERT with Disentangled Attention","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2006.03654","snapshot_observed_at":"2026-08-07T15:23:33.742269Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2505.15507","last_updated":"2025-05-21T13:27:14Z","snapshot_observed_at":"2026-08-07T15:14:11.082266Z","submitted_at":"2025-05-21T13:27:14Z","title":"Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T15:23:33.742269Z"},"links":{"cited_paper":"/paper/2006.03654","citing_paper":"/paper/2505.15507"},"observation_digest":"sha256:ac8e7ef825896a5dbcdabde83e0558b290c22e34a057ef07a6223685274f5e62","observation_id":"14e2d092-5ddd-48b9-86b6-7ee05dc72463","resolution":{"observed_at":"2026-08-07T15:23:33.742269Z","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":"2210.1232","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:23:34.771018Z","title":"Neelakantan, K","venue":null,"work_id":"7480d495-4358-4004-b2c5-15dd9e0d9993","year":2022},"citing_paper":{"arxiv_id":"2505.15507","last_updated":"2025-05-21T13:27:14Z","snapshot_observed_at":"2026-08-07T15:14:11.082266Z","submitted_at":"2025-05-21T13:27:14Z","title":"Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T15:23:33.882931Z"},"links":{"citing_paper":"/paper/2505.15507"},"observation_digest":"sha256:c8b3ce92318ef332828db51faf4863114a7e0082a4aa60837129542d40fbb460","observation_id":"eac20ea5-6869-4e26-9879-491a42618d25","resolution":{"observed_at":"2026-08-07T15:23:34.895926Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2111.00396","last_updated":"2022-08-05T17:54:38Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2021-10-31T03:32:18Z","title":"Efficiently Modeling Long Sequences with Structured State Spaces","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2111.00396","snapshot_observed_at":"2026-08-07T15:23:33.992490Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2505.15507","last_updated":"2025-05-21T13:27:14Z","snapshot_observed_at":"2026-08-07T15:14:11.082266Z","submitted_at":"2025-05-21T13:27:14Z","title":"Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T15:23:33.992490Z"},"links":{"cited_paper":"/paper/2111.00396","citing_paper":"/paper/2505.15507"},"observation_digest":"sha256:9b9ca15fd4de5e2c18a79f6e8c4e60b622a4bf4493e4cdf03f200cf3d362d200","observation_id":"460733f2-f682-4b7b-910c-74f9ecd56756","resolution":{"observed_at":"2026-08-07T15:23:33.992490Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2302.10866","last_updated":"2023-04-19T20:08:39Z","snapshot_observed_at":"2026-07-06T14:54:15.390552Z","submitted_at":"2023-02-21T18:29:25Z","title":"Hyena Hierarchy: Towards Larger Convolutional Language Models","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2302.10866","snapshot_observed_at":"2026-08-07T15:23:34.109068Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2505.15507","last_updated":"2025-05-21T13:27:14Z","snapshot_observed_at":"2026-08-07T15:14:11.082266Z","submitted_at":"2025-05-21T13:27:14Z","title":"Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T15:23:34.109068Z"},"links":{"cited_paper":"/paper/2302.10866","citing_paper":"/paper/2505.15507"},"observation_digest":"sha256:669997fd43c8315a3c651ab60c62b6f2fc5ac7432bad76976ac1626342c9317c","observation_id":"996648a7-754d-4887-a0b5-ec61406fcea1","resolution":{"observed_at":"2026-08-07T15:23:34.109068Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2312.00752","last_updated":"2024-05-31T17:55:27Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2023-12-01T18:01:34Z","title":"Mamba: Linear-Time Sequence Modeling with Selective State Spaces","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2312.00752","snapshot_observed_at":"2026-08-07T15:23:34.223253Z","title":"Gu and T","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2505.15507","last_updated":"2025-05-21T13:27:14Z","snapshot_observed_at":"2026-08-07T15:14:11.082266Z","submitted_at":"2025-05-21T13:27:14Z","title":"Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T15:23:34.223253Z"},"links":{"cited_paper":"/paper/2312.00752","citing_paper":"/paper/2505.15507"},"observation_digest":"sha256:35ba4b3ba177dbe6e9d9a963eb7410ac189a3b356b290bce30e7e152120f80a3","observation_id":"9998e6ce-5f45-445a-9187-5e56665e4be0","resolution":{"observed_at":"2026-08-07T15:23:34.223253Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2312.00756","last_updated":"2023-12-01T18:20:16Z","snapshot_observed_at":"2026-07-06T16:55:45.402426Z","submitted_at":"2023-12-01T18:20:16Z","title":"Operadic categories and 2-Segal sets","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2312.00756","snapshot_observed_at":"2026-08-07T15:23:34.371185Z","title":"Mehta, T","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2505.15507","last_updated":"2025-05-21T13:27:14Z","snapshot_observed_at":"2026-08-07T15:14:11.082266Z","submitted_at":"2025-05-21T13:27:14Z","title":"Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T15:23:34.371185Z"},"links":{"cited_paper":"/paper/2312.00756","citing_paper":"/paper/2505.15507"},"observation_digest":"sha256:985ca97dcfe80d4244c9732c673e446836b2267756cf40b88f033886a8570d7a","observation_id":"5592d445-b953-4432-9af4-55e3ef3ac710","resolution":{"observed_at":"2026-08-07T15:23:34.371185Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2505.15507","last_updated":"2025-05-21T13:27:14Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-07T15:14:11.082266Z","submitted_at":"2025-05-21T13:27:14Z","title":"Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning"},"reference_resolution":{"displayed":24,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":11,"verified_exact":1,"verified_fuzzy":12},"total_outbound_references":24},"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":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 5 inbound Pith citation observations for arXiv:2505.15507."}