{"as_of":"2026-08-10T04:17:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:b46317f2755aeddec076455c84409397a3d35b7b870f902b60119d4ba0e536ed","coverage":[{"denominator":73,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":73,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-30T14:51:29.700847Z","state":"measured"},{"denominator":73,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":73,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2607.26988/citation-record","integrity":"/paper/2607.26988/integrity","json":"/paper/2607.26988/citation-record.json","paper":"/paper/2607.26988"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:27.899927Z","title":"The Expressive Capacity of State Space Models:","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:27.899927Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:39176f48228b09d751a54faabd52cfae4e05705b263cc5b4afbaeef3927b8db9","observation_id":"d42f4803-ccc4-472e-afc6-822f097549ee","resolution":{"observed_at":"2026-07-30T14:51:27.899927Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:27.974646Z","title":"Unlocking State-Tracking in Linear","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:27.974646Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:d2c78a557b2f9d963df787e54a8799a4459c44f986d4758059ebb8e77befb635","observation_id":"e1dc7f5d-a1eb-442b-98d9-de0576d510d3","resolution":{"observed_at":"2026-07-30T14:51:27.974646Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:28.045097Z","title":"Finite Automata, Formal Logic, and Circuit Complexity , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:28.045097Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:70a0dbc861382facaecbe3d1db959e6b2bda1d21eeb9e17acfecd089df8d9538","observation_id":"e558cfa6-2314-4651-a793-785fc6385584","resolution":{"observed_at":"2026-07-30T14:51:28.045097Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:28.150037Z","title":"Algebraic Theory of Machines","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:28.150037Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:e299864e6ac6ccf3c036d7f4ffe0b0edd778f1c9aa181dd29f6fdc92aaabca2a","observation_id":"ab410adb-793b-49e5-89dc-1921c1bc0079","resolution":{"observed_at":"2026-07-30T14:51:28.150037Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1905.10901","last_updated":"2019-05-26T23:11:18Z","snapshot_observed_at":"2026-08-09T12:19:42.477146Z","submitted_at":"2019-05-26T23:11:18Z","title":"Seeing Convolution Through the Eyes of Finite Transformation Semigroup Theory: An Abstract Algebraic Interpretation of Convolutional Neural Networks","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1905.10901","snapshot_observed_at":"2026-07-30T14:51:28.283266Z","title":"Seeing Convolution Through the Eyes of Finite Transformation Semigroup Theory:","venue":null,"work_id":null,"year":1905},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:28.283266Z"},"links":{"cited_paper":"/paper/1905.10901","citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:dcf810486a163f8e63186d27cf2a0d471d97e72d8a89a684aab25f33ed584a95","observation_id":"8eb8798b-352d-4e9f-8027-182d98ac4f2d","resolution":{"observed_at":"2026-07-30T14:51:28.283266Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:28.399894Z","title":"and Sontag, Eduardo D","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:28.399894Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:d198271ca22a63a64dacc781aa21a4611340da641e08f6f5bc051624b51cd4ba","observation_id":"d108a253-4473-40c0-a3f7-1371d717df9e","resolution":{"observed_at":"2026-07-30T14:51:28.399894Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2310.12942","last_updated":"2024-05-30T14:49:25Z","snapshot_observed_at":"2026-08-09T11:27:05.002746Z","submitted_at":"2023-10-19T17:39:47Z","title":"On the Representational Capacity of Recurrent Neural Language Models","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2310.12942","snapshot_observed_at":"2026-07-30T14:51:28.495036Z","title":"arXiv preprint arXiv:2310.12942 , url=","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:28.495036Z"},"links":{"cited_paper":"/paper/2310.12942","citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:3af589a2d41638b8906ed7d1ad6393be7fe0dae41fdc62480a4196f169949706","observation_id":"f7f3be40-2d4c-45d9-a3e4-6793caecb20e","resolution":{"observed_at":"2026-07-30T14:51:28.495036Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:28.601479Z","title":"Proceedings of the 2024 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies (Volume 1: Long Papers) , month=","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:28.601479Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:ce346eac3adf3bccec37b011e4c3afa35b21726a4019e62176e184341841c286","observation_id":"9c921f9f-3fff-480d-b60d-bc20eb21319f","resolution":{"observed_at":"2026-07-30T14:51:28.601479Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:28.693780Z","title":"On the Practical Computational Power of Finite Precision","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:28.693780Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:22a49065fb1a1ff9cbd10abaf91c6fce9b940ba55963a0fbb6611c4c1fd8b3f9","observation_id":"087eef37-755c-4877-ac9b-2a8bee7874a4","resolution":{"observed_at":"2026-07-30T14:51:28.693780Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:28.796477Z","title":"Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing , month=","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:28.796477Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:a5018977f6fdd498ca383a1dcf4c4f2369f3230f276663cd65427455b34664c6","observation_id":"0c55e014-b726-4140-ae27-c652f0a9c29d","resolution":{"observed_at":"2026-07-30T14:51:28.796477Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:28.924398Z","title":", booktitle=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:28.924398Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:d21e70d83b20d071f7ac56fb6a0e7a82e65f593345f35d78da05e365a71708c4","observation_id":"60beb4d5-96b0-46c4-9975-0e6e66448072","resolution":{"observed_at":"2026-07-30T14:51:28.924398Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.055003Z","title":"Proceedings of the Workshop on Deep Learning and Formal Languages: Building Bridges , month=","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.055003Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:f68f5eab347cbdcda3433cf624414326ed49dd666d3e692a2c8eecd1334485b6","observation_id":"592d3973-76ac-4722-9b47-6872a342e353","resolution":{"observed_at":"2026-07-30T14:51:29.055003Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.122177Z","title":"Chain-of-Thought Prompting Elicits Reasoning in Large Language Models , url=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.122177Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:5a3ef922b6c86476b0e8bd3ef9b39ae8773bbb2c1c3c335734ba7a2a0e2ae42e","observation_id":"d4193c22-a30a-44e9-be1d-70d136abd379","resolution":{"observed_at":"2026-07-30T14:51:29.122177Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.171604Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.171604Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:d5d7ab1b837dc3e059c03c21893020976b1414f641380bb9fbeabc3312a873c5","observation_id":"05408d26-352e-45a4-b837-ae4ee7fdeef9","resolution":{"observed_at":"2026-07-30T14:51:29.171604Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.215452Z","title":"2021 , eprint=","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.215452Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:c7eb4a4716954e2a95f276f53698a124da10364e13ffd6c608fe4a05dae22e9e","observation_id":"63bbf48a-fcd0-4b01-8ad8-2c7a2abec51d","resolution":{"observed_at":"2026-07-30T14:51:29.215452Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2303.08774","last_updated":"2024-03-04T06:01:33Z","snapshot_observed_at":"2026-08-07T07:30:12.213965Z","submitted_at":"2023-03-15T17:15:04Z","title":"GPT-4 Technical Report","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2303.08774","snapshot_observed_at":"2026-07-30T14:51:29.244469Z","title":"2303.08774 , archiveprefix=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.244469Z"},"links":{"cited_paper":"/paper/2303.08774","citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:51369fd9e1045238dbde0f586a8974dc9d16b2c15557d13e179e09ddb7a9e36b","observation_id":"94015e14-8e6b-484d-a47d-840e711e5627","resolution":{"observed_at":"2026-07-30T14:51:29.244469Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.266561Z","title":"Advances in Neural Information Processing Systems , editor=","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.266561Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:9a752f239d2bbe0b98b8a916a86f9604b5cb2f351c39482e46e2aebb94030046","observation_id":"e175ed76-8974-43ca-a8ae-39c5c7705b7a","resolution":{"observed_at":"2026-07-30T14:51:29.266561Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.276124Z","title":"Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) , month=","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.276124Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:dad5d67a444a7d59a77342f7b4a4c6d90760a081e45fd5829f90756a4cf8621c","observation_id":"abeafd0b-0066-4895-99e2-25361d324802","resolution":{"observed_at":"2026-07-30T14:51:29.276124Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.289692Z","title":"Proceedings of the 41st International Conference on Machine Learning , articleno=","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.289692Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:828147d70513ed033a4b022eb4855ac8736506f8ae912daaaf1eec901c1a4036","observation_id":"2c1259d6-769c-496e-87ad-32e72385808c","resolution":{"observed_at":"2026-07-30T14:51:29.289692Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.299306Z","title":"Anderson and Amo Alonso, Carmen and Sejnowski, Terrence J","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.299306Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:b85eccd702cbf87fbbaa2ad1bcac632c3869b400e1400f55556e7204508165de","observation_id":"ce659603-0f59-4834-9b6d-6d0d491b4a4c","resolution":{"observed_at":"2026-07-30T14:51:29.299306Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.320251Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.320251Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:d37ee887145fe085076ab0140a09acbfef01e43a497310cd9f175ae721eff6dc","observation_id":"54806b75-6527-4210-8210-7fcbdc6ff76d","resolution":{"observed_at":"2026-07-30T14:51:29.320251Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.329609Z","title":"Proceedings of the IEEE conference on computer vision and pattern recognition , pages=","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.329609Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:cd87ca74af43ab4a5703cf0f7c83d6da3a743c46630136430b1aa172d8411b57","observation_id":"1a27a4ab-7500-43c5-be3f-7cf9bdb2c49c","resolution":{"observed_at":"2026-07-30T14:51:29.329609Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.336255Z","title":"and Keutzer, Kurt , booktitle=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.336255Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:a3e576b8058dd0d654dbc23c0fa090183363fe55c43affbd626e93ce491bd3e9","observation_id":"40cf4524-113a-4789-8246-44922694a69e","resolution":{"observed_at":"2026-07-30T14:51:29.336255Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2109.09828","last_updated":"2022-02-14T19:41:09Z","snapshot_observed_at":"2026-08-09T17:47:28.566164Z","submitted_at":"2021-09-20T20:17:40Z","title":"iRNN: Integer-only Recurrent Neural Network","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2109.09828","snapshot_observed_at":"2026-07-30T14:51:29.344345Z","title":"arXiv preprint arXiv:2109.09828 , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.344345Z"},"links":{"cited_paper":"/paper/2109.09828","citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:d661eda796452aed1bd04402d570e9dbae05456f9cbc1129139945bf5db38783","observation_id":"8d67418d-cb32-4100-b616-8d2b73d837a7","resolution":{"observed_at":"2026-07-30T14:51:29.344345Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.352583Z","title":"Training Integer-Only Deep Recurrent Neural Networks , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.352583Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:8fa93c4b9abf25e4aa26aa265af7c4946dc980ebf8426421f0dc8de012030c86","observation_id":"35c6b26a-8616-4d4d-88b7-7aa11884cdd5","resolution":{"observed_at":"2026-07-30T14:51:29.352583Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.362050Z","title":"Transactions of the Association for Computational Linguistics , volume=","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.362050Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:a0e67797484a1b72debb524fab924a0e1c9a6e92d5cb21a36cc2526a4717f78c","observation_id":"66d5099c-6387-4d58-bbce-e01f6f4f10c0","resolution":{"observed_at":"2026-07-30T14:51:29.362050Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.369282Z","title":"Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) , month=","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.369282Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:560625764694c8bc7783c5f46334fa3a15ba57fe928de205ecc0e5426745b8f9","observation_id":"d56269f0-448a-4bd6-95c9-f3ed84399776","resolution":{"observed_at":"2026-07-30T14:51:29.369282Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.379876Z","title":"Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP) , month=","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.379876Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:1d840d76a20caa7de6b4aa05c1cc1315ff145aaa8a4cdbe4fc13fdd43d5808de","observation_id":"b5524333-c5b4-4d53-99f6-c9b961ee9986","resolution":{"observed_at":"2026-07-30T14:51:29.379876Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.390397Z","title":"Journal of Machine Learning Research , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.390397Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:62559e95f35d38dbf76e0a67a77b711d49be5fc42b41cc15bd743a2740734363","observation_id":"4a4d8a95-f0be-485c-8821-aa0875bf2922","resolution":{"observed_at":"2026-07-30T14:51:29.390397Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.402981Z","title":"Transactions of the Association for Computational Linguistics , volume=","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.402981Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:a06496020f3a4df4e84f9ede1e5210295c1de1c7f358772f1a8178877b8f1a8e","observation_id":"a861f9ac-e9d2-4709-96de-28921da4ddd5","resolution":{"observed_at":"2026-07-30T14:51:29.402981Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.409019Z","title":"What Formal Languages Can Transformers Express?","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.409019Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:4ccd9f0adcc47c14f6571edb9affc2ccc3ea406d8661326bc77e297fbbdc8e92","observation_id":"6d951341-3e67-42eb-ac12-efa10491e87e","resolution":{"observed_at":"2026-07-30T14:51:29.409019Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.414058Z","title":"Proceedings of the 2018 Conference of the North","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.414058Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:3091e7b10136b68210df8079d692e8fc4d822b52b29aa0575b00a45e1891a4be","observation_id":"3f8c3636-0da7-4220-bb33-10f81e31b255","resolution":{"observed_at":"2026-07-30T14:51:29.414058Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.422042Z","title":"The Parallelism Tradeoff:","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.422042Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:de8390d10201dc72bfd92424dcf9cc83c8bcc4324587ee7c0f5e9510c1c4045e","observation_id":"0cded9ee-bb7c-47ff-beb0-397c8452d258","resolution":{"observed_at":"2026-07-30T14:51:29.422042Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.428461Z","title":"Proceedings of the 38th International Conference on Machine Learning , series=","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.428461Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:bd60e48ef5397fa829d3c57a7ff414e0db26eb4d4e462ad601d471cbfd44f65b","observation_id":"a6337f9f-2867-428e-9c81-39ce5776dcdd","resolution":{"observed_at":"2026-07-30T14:51:29.428461Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.436255Z","title":"International Conference on Learning Representations , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.436255Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:dbd1c918d93d46a79cf432f3ffb29bea31aa6cf0c5810de1119772c73c0750f0","observation_id":"07bcda0b-7c20-403d-8daf-56a02473cf56","resolution":{"observed_at":"2026-07-30T14:51:29.436255Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.443957Z","title":"International Conference on Learning Representations , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.443957Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:259fd4d1d78395153530905a5af5ba505b2b5b49e45ed16676455c037f33e47f","observation_id":"bf177b14-27b5-4fca-b59e-6fc9d1d12c8f","resolution":{"observed_at":"2026-07-30T14:51:29.443957Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.465493Z","title":"First Conference on Language Modeling , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.465493Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:2871d855820015cae4508e1a2f1abd3bb4bf217effa28654f92479d1e1880f48","observation_id":"069b3402-dcea-4d63-ae24-206b5265f5d3","resolution":{"observed_at":"2026-07-30T14:51:29.465493Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.475052Z","title":"Findings of the Association for Computational Linguistics: EMNLP 2023 , month=","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.475052Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:64a1a73f85d909df64892efdac0dd67625dc43aa3b741180a87ab65f62d7dbac","observation_id":"e6e91791-994d-4b62-82c4-55124a268508","resolution":{"observed_at":"2026-07-30T14:51:29.475052Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2503.14456","last_updated":"2025-03-30T13:46:44Z","snapshot_observed_at":"2026-08-07T16:54:15.957609Z","submitted_at":"2025-03-18T17:31:05Z","title":"RWKV-7 \"Goose\" with Expressive Dynamic State Evolution","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2503.14456","snapshot_observed_at":"2026-07-30T14:51:29.480937Z","title":"and Wu, Tianyi and Wuttke, Daniel and Zhou-Zheng, Christian , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.480937Z"},"links":{"cited_paper":"/paper/2503.14456","citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:ac44e3417df4f203e1c0f230408a68120afcd282cbb65066b0db2e509d1dea7a","observation_id":"790260d5-6586-4c48-84e7-b19bbbbd16de","resolution":{"observed_at":"2026-07-30T14:51:29.480937Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.486939Z","title":"Transformers are","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.486939Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:ac7a59b80f4e35b63a6ea45ed51edb98955dcd5ae483c049e27cc5ee12b46d4d","observation_id":"f5c1b820-b38d-44e2-9a77-be456b98f7c8","resolution":{"observed_at":"2026-07-30T14:51:29.486939Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.493029Z","title":"2023 , publisher=","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.493029Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:f8751baeb413b4b8bea23e75688857c0a47ced7e4d8897ec236974ab29f7c942","observation_id":"90efbadb-ccda-446a-91e7-e00ce794521a","resolution":{"observed_at":"2026-07-30T14:51:29.493029Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.501216Z","title":"2025 , eprint=","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":42,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.501216Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:a4a383ee265029d88292c7a5ec771472ce1ffcdbcc45bcc7499d4cd3598d939c","observation_id":"1d69b185-7cb3-4049-a2a9-4916d82dd09f","resolution":{"observed_at":"2026-07-30T14:51:29.501216Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.507238Z","title":"1976 , publisher=","venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":43,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.507238Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:364aea2f3307bc771dcd9bbdf790fa2ff6a3c03b180e7bcb9e082edcc223803f","observation_id":"f4243920-ed99-4408-9fdf-229288c2d958","resolution":{"observed_at":"2026-07-30T14:51:29.507238Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.512836Z","title":"Moore , title =","venue":null,"work_id":null,"year":1956},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":44,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.512836Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:e3ec6d2deb504d453a73bfd693316ea48c4d76df395f4427417ce5d417f820f0","observation_id":"1ebf068b-759a-445f-9561-e47ffa177192","resolution":{"observed_at":"2026-07-30T14:51:29.512836Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.518297Z","title":"Mealy , title =","venue":null,"work_id":null,"year":1955},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.518297Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:0fdffd8edc8535ee524b34bd0e1a5b9e627151a30821af87d0e68ae35be6a0a9","observation_id":"688fe865-59a2-401d-a4f8-d7a0cf68c016","resolution":{"observed_at":"2026-07-30T14:51:29.518297Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.523899Z","title":null,"venue":null,"work_id":null,"year":1955},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":46,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.523899Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:b4a5f17bf102f3bd0e3eee6fdc88444dba1b63cf355b4d88125b2b09126edee5","observation_id":"223f83f8-1ca0-4e2b-ac36-24bfd016f546","resolution":{"observed_at":"2026-07-30T14:51:29.523899Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.532212Z","title":"ACM computing surveys (CSUR) , volume=","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":47,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.532212Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:636d2b4aa86eccc9b808f66e4ffd5e2d2fa2dcf6083f88206b36a92bded7cb1b","observation_id":"4dcac37e-1c7d-423e-afd6-fd7ba688c0af","resolution":{"observed_at":"2026-07-30T14:51:29.532212Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.538109Z","title":"Neural computation , volume=","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":48,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.538109Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:8d21a823c1a102e569e7626434141b4366ab5649823fbb0dbdecef38b0d5d021","observation_id":"2efa9021-6825-4e55-9bfa-8e55d1ffc1a3","resolution":{"observed_at":"2026-07-30T14:51:29.538109Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.543548Z","title":"Cognitive science , volume=","venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":49,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.543548Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:709e674762a223d8b476f3f030037524855bf8294a122bb79e501228f9ce0018","observation_id":"6f339e53-7e42-45c2-9cff-dc68a237f123","resolution":{"observed_at":"2026-07-30T14:51:29.543548Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1406.1078","last_updated":"2014-09-03T00:25:02Z","snapshot_observed_at":"2026-07-06T03:45:28.546418Z","submitted_at":"2014-06-03T17:47:08Z","title":"Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1406.1078","snapshot_observed_at":"2026-07-30T14:51:29.550399Z","title":"Learning phrase representations using","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":50,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.550399Z"},"links":{"cited_paper":"/paper/1406.1078","citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:9d0cd3d92ec5c9aaca28231c632b8b6ae260849beb5edfd612fcc839a0fe679e","observation_id":"22b219fb-aef4-40d7-bfdd-606273f4e427","resolution":{"observed_at":"2026-07-30T14:51:29.550399Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.560716Z","title":"IEEE Transactions on Computers , volume=","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":51,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.560716Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:fe85778f2b65e5ec6845d52cb43698cd055881699c1b64768f41505e2116535c","observation_id":"419190f6-d522-4212-8954-029091437252","resolution":{"observed_at":"2026-07-30T14:51:29.560716Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.570936Z","title":"Lecture notes LIAFA, Universit","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":52,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.570936Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:b4c04eb43de9e4419d2bb908ac67dd3884e3bb71d8048913f793d76f88878b00","observation_id":"0faaeb63-1436-4849-976a-6ce3f7c8fa9d","resolution":{"observed_at":"2026-07-30T14:51:29.570936Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1906.06349","last_updated":"2019-06-19T02:04:08Z","snapshot_observed_at":"2026-08-09T23:23:43.692966Z","submitted_at":"2019-06-14T18:04:39Z","title":"On the Computational Power of RNNs","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1906.06349","snapshot_observed_at":"2026-07-30T14:51:29.577568Z","title":"Korsky and Robert C","venue":null,"work_id":null,"year":1906},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":53,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.577568Z"},"links":{"cited_paper":"/paper/1906.06349","citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:6c74fef81f70c86ec5521b58de7da092b9b35a2844b703fccda721a8fa41e17b","observation_id":"47134af1-86a9-405d-a3d5-975132a0f458","resolution":{"observed_at":"2026-07-30T14:51:29.577568Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.584285Z","title":"Lee Giles , doi =","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":54,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.584285Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:b5c59369edb2859bc48c271552bf9672e41eb60e65912d6ffdca6f53bcddffa8","observation_id":"632952a7-63e2-4a43-89ab-68de1cac8c19","resolution":{"observed_at":"2026-07-30T14:51:29.584285Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.595878Z","title":"and Giles, C","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":55,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.595878Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:5dd6a729a502e81d2e40193c701a2cc6c306755134984f08fe83e19990b32e6a","observation_id":"ff1bd7f3-fb90-4819-b58c-5cdaff849342","resolution":{"observed_at":"2026-07-30T14:51:29.595878Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.603313Z","title":"On pseudovarieties , url =","venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":56,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.603313Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:2ad6b8e1ffb9c416fb28afe87cdf449e0f004fcf7966342a663621b39a90bc93","observation_id":"abb4cc45-63bf-44af-b763-4a0321d352ef","resolution":{"observed_at":"2026-07-30T14:51:29.603313Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.609200Z","title":"and Yahav, Eran","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":57,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.609200Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:7ae84696467ae6bce8ace4b00d1744f66751203270c3fe6c663b1ac75dd72589","observation_id":"f9aa9e4f-fa08-4b26-a16b-fe109682bc58","resolution":{"observed_at":"2026-07-30T14:51:29.609200Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.615020Z","title":", title =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":58,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.615020Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:0aee587cfca05700ae55f3b365dc05851fef706ec7b93cc8393e42674652fd93","observation_id":"9a7d4e50-07b4-4568-b5c3-80e4710221a9","resolution":{"observed_at":"2026-07-30T14:51:29.615020Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.622999Z","title":"1954 , publisher=","venue":null,"work_id":null,"year":1954},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":59,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.622999Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:62b77c220c9b4d1ed227a393d61ebbbbbbbacae8879c9c6acb36adf94731cb2f","observation_id":"83f7a069-992e-4f00-a11c-7fc16515db23","resolution":{"observed_at":"2026-07-30T14:51:29.622999Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.628475Z","title":"Proceedings of the 38th International Conference on Machine Learning , pages =","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":60,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.628475Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:f61c97888f09a2395b849959ff4aaf465caca7b00a5e56703f58499d6fc9db60","observation_id":"c1d88cfb-f9ba-4e19-a955-3dcb4ee5db69","resolution":{"observed_at":"2026-07-30T14:51:29.628475Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.634433Z","title":"Masked Hard-Attention Transformers Recognize Exactly the Star-Free Languages , url =","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":61,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.634433Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:aa8c934258aaa00c6effae614f2715e790137ff5c01a8ff19fd850d811138c0c","observation_id":"1e1c6879-4ec9-4864-b57e-76dab255b540","resolution":{"observed_at":"2026-07-30T14:51:29.634433Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.640726Z","title":"2021 , isbn =","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":62,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.640726Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:9b8119f9a1be73d8b690a11e00e3f776ff1cb058af407557c0086264ab976cbc","observation_id":"bd2d2e86-a16a-435b-ab8f-58fb0471c98f","resolution":{"observed_at":"2026-07-30T14:51:29.640726Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.646101Z","title":"ArXiv , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":63,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.646101Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:acba33597cf3ce6699c594205aab3fff41e7e6d1dd10e34f4f0e1f6ce8eaff59","observation_id":"b0b18055-1453-4cc7-b70f-606177563e4e","resolution":{"observed_at":"2026-07-30T14:51:29.646101Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.652468Z","title":"39th Annual Conference on Neural Information Processing Systems (NeurIPS 2025) , year=","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":64,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.652468Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:309312daddb2cd5259fdef1902ce9afcb6d5e8d05fa876707aa5354fd9dfd540","observation_id":"04aee737-57ef-4e41-ab35-a7c9bf8186c1","resolution":{"observed_at":"2026-07-30T14:51:29.652468Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.657699Z","title":"Forty-third International Conference on Machine Learning , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":65,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.657699Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:73f7c29c3c28a6f1676503375e84c5b0ea0586c11de625a1c41168792b82ec46","observation_id":"f4ba49c3-f36a-464d-a025-a6ea6ad2e231","resolution":{"observed_at":"2026-07-30T14:51:29.657699Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.663974Z","title":"ArXiv , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":66,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.663974Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:b2e83ec74d4a70c2ad258034cc78663c0012d4b2a3d48e7d45a7a65ba793b72f","observation_id":"4ce4bf5e-94ea-42bb-8ff6-d5b3d93b4372","resolution":{"observed_at":"2026-07-30T14:51:29.663974Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.669343Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":67,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.669343Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:6642e209dda0b29e50eefe75b428fafc45303695b86e2be6a5baa54d3e7a2120","observation_id":"de6a8985-c50f-45ba-a761-ac328cadd357","resolution":{"observed_at":"2026-07-30T14:51:29.669343Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.675330Z","title":"Chapter 1","venue":null,"work_id":null,"year":1973},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":68,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.675330Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:41722727dfc256d8eb6ff0a69b339d102524927b5ec9f65e62d56c50dcea201b","observation_id":"3e8eea6b-61cb-4b5c-90a8-a354887d3fde","resolution":{"observed_at":"2026-07-30T14:51:29.675330Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.681229Z","title":"Brzozowski and Faith E","venue":null,"work_id":null,"year":1980},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":69,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.681229Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:c9071753f0f3265c1e7dd1e0d7338823ffc583ae49a9df4e48bfcf73995c870b","observation_id":"d3130d57-440a-4e83-84b8-af0a76e0fc6e","resolution":{"observed_at":"2026-07-30T14:51:29.681229Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.686145Z","title":"Methods of the algebraic theory of machines: I","venue":null,"work_id":null,"year":1967},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":70,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.686145Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:a55165cec8d31c669a614c2295a3be08e74dbb46c18386f8859c860e2de7a873","observation_id":"187f5bb0-1206-4c31-94e1-19ac2a0b3ae5","resolution":{"observed_at":"2026-07-30T14:51:29.686145Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.690930Z","title":"The Eleventh International Conference on Learning Representations , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":71,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.690930Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:6cfb8a083d7f1aab2559c5abbbe3353f97777b3dd107faabbcf03e10a43c8418","observation_id":"84a4c80d-b31b-4c49-8d3a-1421930979ab","resolution":{"observed_at":"2026-07-30T14:51:29.690930Z","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":"10.18653/v1/2026.acl-long.1739","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:56:30.931767Z","title":"Characterizing the Expressivity of Local Attention in Transformers","venue":null,"work_id":"30050eec-7bd8-46cb-a0d5-8a7f0c565b68","year":2026},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":72,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.695678Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:8e597d40457340dcf1d116b89c79d44993c1d80b9a3755c3f29fddf7a8a49983","observation_id":"3719db33-7315-4fc4-a726-5fa36923f7eb","resolution":{"observed_at":"2026-07-30T14:56:30.942477Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T14:51:29.700847Z","title":"2021 , MONTH = Sep, DOI =","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers","version":1},"reference_index":73,"source":"arxiv_source","source_observed_at":"2026-07-30T14:51:29.700847Z"},"links":{"citing_paper":"/paper/2607.26988"},"observation_digest":"sha256:06613d0a0d7326f3fca74883620a29d2a8aea2ff0159619789442b900212158b","observation_id":"6bbd46d2-fcc1-4c9d-9e2d-9a056358fd76","resolution":{"observed_at":"2026-07-30T14:51:29.700847Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.26988","last_updated":"2026-07-29T14:47:19Z","latest_version":1,"primary_category":"cs.FL","snapshot_observed_at":"2026-08-09T16:30:25.899595Z","submitted_at":"2026-07-29T14:47:19Z","title":"A Compositional Theory of Causally Masked Transformers"},"reference_resolution":{"displayed":73,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":72,"verified_exact":1,"verified_fuzzy":0},"total_outbound_references":73},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 73 of 73 outbound references and 0 inbound Pith citation observations for arXiv:2607.26988."}