{"as_of":"2026-08-08T04:43:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:e1ea8fee6d631e4ff1731ec0f4d4b79536d3fc5c14dc2be65b3583d593ff2ae7","coverage":[{"denominator":0,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":8,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":8,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-07T06:34:17.273281+00:00","state":"measured"},{"denominator":8,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":8,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T14:13:06.748375Z","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":"2026-06-29T14:33:30.564243Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2502.21212","last_updated":"2025-02-28T16:40:38Z","snapshot_observed_at":"2026-08-07T17:39:12.775789Z","submitted_at":"2025-02-28T16:40:38Z","title":"Transformers Learn to Implement Multi-step Gradient Descent with Chain of Thought","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.21212","snapshot_observed_at":"2026-08-07T14:13:06.748375Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.19815","last_updated":"2025-05-26T10:52:17Z","snapshot_observed_at":"2026-08-07T21:55:42.875455Z","submitted_at":"2025-05-26T10:52:17Z","title":"Deciphering Trajectory-Aided LLM Reasoning: An Optimization Perspective","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-07T14:13:06.748375Z"},"links":{"cited_paper":"/paper/2502.21212","citing_paper":"/paper/2505.19815"},"observation_digest":"sha256:e4627a8d3a71406d00f852c088cbea279bb6d00959363cafef124be0d1eb86ca","observation_id":"04a28cdf-1d77-4bec-8a79-869984e94306","resolution":{"observed_at":"2026-08-07T14:13:06.748375Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2502.21212","last_updated":"2025-02-28T16:40:38Z","snapshot_observed_at":"2026-08-07T17:39:12.775789Z","submitted_at":"2025-02-28T16:40:38Z","title":"Transformers Learn to Implement Multi-step Gradient Descent with Chain of Thought","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.21212","snapshot_observed_at":"2026-08-07T12:46:35.648813Z","title":"Transformers learn to implement multi-step gradient descent with chain of thought.arXiv preprint arXiv:2502.21212, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.23683","last_updated":"2025-05-29T17:22:00Z","snapshot_observed_at":"2026-08-07T21:59:35.039840Z","submitted_at":"2025-05-29T17:22:00Z","title":"Learning Compositional Functions with Transformers from Easy-to-Hard Data","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T12:46:35.648813Z"},"links":{"cited_paper":"/paper/2502.21212","citing_paper":"/paper/2505.23683"},"observation_digest":"sha256:1e09ac59f398ead03f70d9fa7ffe20568770da743a8b49e6104e4226aa1725b2","observation_id":"9fb45c7f-1a84-423b-a32d-f6bf87f6f129","resolution":{"observed_at":"2026-08-07T12:46:35.648813Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2502.21212","last_updated":"2025-02-28T16:40:38Z","snapshot_observed_at":"2026-08-07T17:39:12.775789Z","submitted_at":"2025-02-28T16:40:38Z","title":"Transformers Learn to Implement Multi-step Gradient Descent with Chain of Thought","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.21212","snapshot_observed_at":"2026-08-07T10:42:39.805726Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2506.04611","last_updated":"2025-06-05T04:02:17Z","snapshot_observed_at":"2026-08-07T13:54:09.003484Z","submitted_at":"2025-06-05T04:02:17Z","title":"Revisiting Test-Time Scaling: A Survey and a Diversity-Aware Method for Efficient Reasoning","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-07T10:42:39.805726Z"},"links":{"cited_paper":"/paper/2502.21212","citing_paper":"/paper/2506.04611"},"observation_digest":"sha256:8c7c64d004d4e95c843adf117a69e98b3b6c2857b88ddab34dd42e5cfa5dd5a7","observation_id":"2c0353aa-28ea-4756-a534-246b4d84a5bd","resolution":{"observed_at":"2026-08-07T10:42:39.805726Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2502.21212","last_updated":"2025-02-28T16:40:38Z","snapshot_observed_at":"2026-08-07T17:39:12.775789Z","submitted_at":"2025-02-28T16:40:38Z","title":"Transformers Learn to Implement Multi-step Gradient Descent with Chain of Thought","version":1},"cited_work":{"arxiv_id":"2502.21212","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2502.21212","snapshot_observed_at":"2026-06-29T14:33:30.564243Z","title":"Transformers learn to implement multi-step gradient descent with chain of thought","venue":null,"work_id":"ece1b22d-af1a-4da0-9adc-1da598db3cc9","year":2025},"citing_paper":{"arxiv_id":"2510.25741","last_updated":"2026-07-01T23:25:58Z","snapshot_observed_at":"2026-08-04T07:30:51.188041Z","submitted_at":"2025-10-29T17:45:42Z","title":"Scaling Latent Reasoning via Looped Language Models","version":4},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-05-15T07:43:11.620446Z"},"links":{"cited_paper":"/paper/2502.21212","citing_paper":"/paper/2510.25741"},"observation_digest":"sha256:80e36a901d3706ab74e0a34497b76ec38ffe10fd63c3abea09b0d8ff9231690e","observation_id":"20322a7a-6bb9-45f5-b225-73b09a4fd085","resolution":{"observed_at":"2026-05-15T07:43:11.868463Z","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":"2502.21212","last_updated":"2025-02-28T16:40:38Z","snapshot_observed_at":"2026-08-07T17:39:12.775789Z","submitted_at":"2025-02-28T16:40:38Z","title":"Transformers Learn to Implement Multi-step Gradient Descent with Chain of Thought","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.21212","snapshot_observed_at":"2026-08-04T07:31:11.198585Z","title":"Transformers learn to implement multi-step gradient descent with chain of thought.arXiv preprint arXiv:2502.21212, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2510.25741","last_updated":"2026-07-01T23:25:58Z","snapshot_observed_at":"2026-08-04T07:30:51.188041Z","submitted_at":"2025-10-29T17:45:42Z","title":"Scaling Latent Reasoning via Looped Language Models","version":5},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-04T07:31:11.198585Z"},"links":{"cited_paper":"/paper/2502.21212","citing_paper":"/paper/2510.25741"},"observation_digest":"sha256:c52677ec99f28ed28f1f5a1de929d169eabe6c215904cd0ec80e1f35e673d00b","observation_id":"9f3afce4-bad0-40fd-816b-e86b429d8a5c","resolution":{"observed_at":"2026-08-04T07:31:11.198585Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2502.21212","last_updated":"2025-02-28T16:40:38Z","snapshot_observed_at":"2026-08-07T17:39:12.775789Z","submitted_at":"2025-02-28T16:40:38Z","title":"Transformers Learn to Implement Multi-step Gradient Descent with Chain of Thought","version":1},"cited_work":{"arxiv_id":"2502.21212","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2502.21212","snapshot_observed_at":"2026-06-29T14:33:30.564243Z","title":"Transformers learn to implement multi-step gradient descent with chain of thought","venue":null,"work_id":"ece1b22d-af1a-4da0-9adc-1da598db3cc9","year":2025},"citing_paper":{"arxiv_id":"2604.22951","last_updated":"2026-07-08T19:29:03Z","snapshot_observed_at":"2026-07-12T23:17:30.297545Z","submitted_at":"2026-04-24T18:49:08Z","title":"The Power of Power Law: Asymmetry Enables Compositional Reasoning","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-05-08T11:49:49.787123Z"},"links":{"cited_paper":"/paper/2502.21212","citing_paper":"/paper/2604.22951"},"observation_digest":"sha256:b78f98e49d34aba7ae2800fc584ad014ebc0e009d922a7054c1f0859dbd43164","observation_id":"d4bc93b8-17f3-4004-af50-aa0d241b74ba","resolution":{"observed_at":"2026-05-11T19:31:08.209336Z","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":"2502.21212","last_updated":"2025-02-28T16:40:38Z","snapshot_observed_at":"2026-08-07T17:39:12.775789Z","submitted_at":"2025-02-28T16:40:38Z","title":"Transformers Learn to Implement Multi-step Gradient Descent with Chain of Thought","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.21212","snapshot_observed_at":"2026-07-12T18:26:05.728364Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2604.22951","last_updated":"2026-07-08T19:29:03Z","snapshot_observed_at":"2026-07-12T23:17:30.297545Z","submitted_at":"2026-04-24T18:49:08Z","title":"The Power of Power Law: Asymmetry Enables Compositional Reasoning","version":2},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-07-12T18:26:05.728364Z"},"links":{"cited_paper":"/paper/2502.21212","citing_paper":"/paper/2604.22951"},"observation_digest":"sha256:0a9a7f4b405867eda03dae082670e4c9599fd4a6d83b31b5d5fcedd5c57f7550","observation_id":"1a30b7a3-8988-4d53-8a5f-c0c3e2cbcef5","resolution":{"observed_at":"2026-07-12T18:26:05.728364Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2502.21212","last_updated":"2025-02-28T16:40:38Z","snapshot_observed_at":"2026-08-07T17:39:12.775789Z","submitted_at":"2025-02-28T16:40:38Z","title":"Transformers Learn to Implement Multi-step Gradient Descent with Chain of Thought","version":1},"cited_work":{"arxiv_id":"2502.21212","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2502.21212","snapshot_observed_at":"2026-06-29T14:33:30.564243Z","title":"Transformers learn to implement multi-step gradient descent with chain of thought","venue":null,"work_id":"ece1b22d-af1a-4da0-9adc-1da598db3cc9","year":2025},"citing_paper":{"arxiv_id":"2605.28600","last_updated":"2026-05-27T15:17:06Z","snapshot_observed_at":"2026-08-05T23:04:48.328422Z","submitted_at":"2026-05-27T15:17:06Z","title":"Transformers Provably Learn to Internalize Chain-of-Thought","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-06-29T14:29:10.010212Z"},"links":{"cited_paper":"/paper/2502.21212","citing_paper":"/paper/2605.28600"},"observation_digest":"sha256:c4435c9c4f97908425d4328af1da674ebf195cd7dd90633b568ed296aab361fa","observation_id":"fca0c2da-bbf3-459b-86dd-bad78171dcfe","resolution":{"observed_at":"2026-06-29T14:33:30.565722Z","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"}}],"links":{"evidence":"/evidence","html":"/paper/2502.21212/citation-record","integrity":"/paper/2502.21212/integrity","json":"/paper/2502.21212/citation-record.json","paper":"/paper/2502.21212"},"outbound":[],"paper":{"arxiv_id":"2502.21212","last_updated":"2025-02-28T16:40:38Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-07T17:39:12.775789Z","submitted_at":"2025-02-28T16:40:38Z","title":"Transformers Learn to Implement Multi-step Gradient Descent with Chain of Thought"},"reference_resolution":{"displayed":0,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":0},"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 0 of 0 outbound references and 8 inbound Pith citation observations for arXiv:2502.21212."}