{"as_of":"2026-08-07T22:13:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:07e7cfd09299d4fac50edf0ed3a07492897d20c858c38e4dc4aff95263707e55","coverage":[{"denominator":33,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":33,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T17:17:07.109039Z","state":"measured"},{"denominator":34,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":34,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-07T06:34:17.273281+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-28T06:37:37.832435Z","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":"2026-07-02T07:46:46.602182Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2507.11408","last_updated":"2026-01-19T08:53:46Z","snapshot_observed_at":"2026-08-07T19:50:49.876336Z","submitted_at":"2025-07-15T15:28:37Z","title":"KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?","version":2},"cited_work":{"arxiv_id":"2507.11408","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.11408","snapshot_observed_at":"2026-07-14T01:19:54.087576Z","title":null,"venue":null,"work_id":"9d4cc599-00a9-4cc7-86e0-7974756faa8f","year":2025},"citing_paper":{"arxiv_id":"2606.05106","last_updated":"2026-06-03T17:09:25Z","snapshot_observed_at":"2026-08-07T04:13:16.910304Z","submitted_at":"2026-06-03T17:09:25Z","title":"Arithmetic Pedagogy for Language Models","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-06-28T06:37:37.832435Z"},"links":{"cited_paper":"/paper/2507.11408","citing_paper":"/paper/2606.05106"},"observation_digest":"sha256:17c0c6a8f3a926eda14b9981d4a4599b482ad6edaf05e50bd5d4deec8cf05471","observation_id":"143fc381-3f3f-46bb-8cac-7d6ed9ba31cd","resolution":{"observed_at":"2026-07-14T01:19:54.087576Z","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/2507.11408/citation-record","integrity":"/paper/2507.11408/integrity","json":"/paper/2507.11408/citation-record.json","paper":"/paper/2507.11408"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:17:08.746481Z","title":null,"venue":null,"work_id":"743e7901-3978-42b2-bb13-a533fe6210df","year":2025},"citing_paper":{"arxiv_id":"2507.11408","last_updated":"2026-01-19T08:53:46Z","snapshot_observed_at":"2026-08-07T19:50:49.876336Z","submitted_at":"2025-07-15T15:28:37Z","title":"KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?","version":2},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-06T17:17:04.916366Z"},"links":{"citing_paper":"/paper/2507.11408"},"observation_digest":"sha256:7b70ce210c1dfd94fa6a6b0d6ce900e5c48c2c222f1f403ce3581e2350fbcc17","observation_id":"a5d830d8-3b33-4306-ba6e-ab3a6f0f7784","resolution":{"observed_at":"2026-08-06T17:17:08.834678Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:17:04.954835Z","title":"Bogdan, Uzay Macar, Neel Nanda, and Arthur Conmy","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.11408","last_updated":"2026-01-19T08:53:46Z","snapshot_observed_at":"2026-08-07T19:50:49.876336Z","submitted_at":"2025-07-15T15:28:37Z","title":"KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?","version":2},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-06T17:17:04.954835Z"},"links":{"citing_paper":"/paper/2507.11408"},"observation_digest":"sha256:aa976bde04799eb8ec3c76b076c0b79ad47e20acb738db32745c900a50a5b37f","observation_id":"889ec501-e012-416d-bedf-463b6d51c675","resolution":{"observed_at":"2026-08-06T17:17:04.954835Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2110.14168","last_updated":"2021-11-18T00:23:45Z","snapshot_observed_at":"2026-08-07T01:45:38.840969Z","submitted_at":"2021-10-27T04:49:45Z","title":"Training Verifiers to Solve Math Word Problems","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2110.14168","snapshot_observed_at":"2026-08-06T17:17:05.007332Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.11408","last_updated":"2026-01-19T08:53:46Z","snapshot_observed_at":"2026-08-07T19:50:49.876336Z","submitted_at":"2025-07-15T15:28:37Z","title":"KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?","version":2},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-06T17:17:05.007332Z"},"links":{"cited_paper":"/paper/2110.14168","citing_paper":"/paper/2507.11408"},"observation_digest":"sha256:0212259245a088b36016808889a836f8a583c066db157254ae17f34f93a67ac2","observation_id":"11d1682d-2bea-4131-9d07-fcc93b6004ae","resolution":{"observed_at":"2026-08-06T17:17:05.007332Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:17:08.549622Z","title":null,"venue":null,"work_id":"e97cd7a9-5989-4a27-949a-1bdd701ee147","year":2025},"citing_paper":{"arxiv_id":"2507.11408","last_updated":"2026-01-19T08:53:46Z","snapshot_observed_at":"2026-08-07T19:50:49.876336Z","submitted_at":"2025-07-15T15:28:37Z","title":"KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?","version":2},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-06T17:17:05.110438Z"},"links":{"citing_paper":"/paper/2507.11408"},"observation_digest":"sha256:442efb37c8ec3465274b1b06218d6c916a12629c8afe9bdd322e5e350aaf591e","observation_id":"e45c6d40-2a9d-4557-9494-480e9890c62c","resolution":{"observed_at":"2026-08-06T17:17:08.640917Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2501.12948","last_updated":"2026-01-04T03:57:36Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-01-22T15:19:35Z","title":"DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.12948","snapshot_observed_at":"2026-08-06T17:17:05.253333Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.11408","last_updated":"2026-01-19T08:53:46Z","snapshot_observed_at":"2026-08-07T19:50:49.876336Z","submitted_at":"2025-07-15T15:28:37Z","title":"KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?","version":2},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-06T17:17:05.253333Z"},"links":{"cited_paper":"/paper/2501.12948","citing_paper":"/paper/2507.11408"},"observation_digest":"sha256:f2d5386ca5c0a8a305094f40cbc08d40395c37831f93a4df823946554c77355b","observation_id":"ad34e8fd-920c-42b4-9ea4-56e968b7c37a","resolution":{"observed_at":"2026-08-06T17:17:05.253333Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.21783","last_updated":"2024-11-23T23:27:33Z","snapshot_observed_at":"2026-07-06T18:55:11.576666Z","submitted_at":"2024-07-31T17:54:27Z","title":"The Llama 3 Herd of Models","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.21783","snapshot_observed_at":"2026-08-06T17:17:05.387275Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.11408","last_updated":"2026-01-19T08:53:46Z","snapshot_observed_at":"2026-08-07T19:50:49.876336Z","submitted_at":"2025-07-15T15:28:37Z","title":"KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?","version":2},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-06T17:17:05.387275Z"},"links":{"cited_paper":"/paper/2407.21783","citing_paper":"/paper/2507.11408"},"observation_digest":"sha256:b0535791ce22e52d2009b6d4824f7a71292ea0893c9bd41e75aaaefd21fa1313","observation_id":"d9663fea-2bb2-4c63-bf47-4ca03920ad49","resolution":{"observed_at":"2026-08-06T17:17:05.387275Z","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":"2026-08-06T17:17:05.495025Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.11408","last_updated":"2026-01-19T08:53:46Z","snapshot_observed_at":"2026-08-07T19:50:49.876336Z","submitted_at":"2025-07-15T15:28:37Z","title":"KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?","version":2},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-06T17:17:05.495025Z"},"links":{"citing_paper":"/paper/2507.11408"},"observation_digest":"sha256:2e882f228f586967b542600d760a0c6b20a3581f0d4089803a101e73b19d94fa","observation_id":"3554ae6e-77a8-41e8-8ed2-896199e7981a","resolution":{"observed_at":"2026-08-06T17:17:05.495025Z","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":"2026-08-06T17:17:05.592678Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.11408","last_updated":"2026-01-19T08:53:46Z","snapshot_observed_at":"2026-08-07T19:50:49.876336Z","submitted_at":"2025-07-15T15:28:37Z","title":"KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?","version":2},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-06T17:17:05.592678Z"},"links":{"citing_paper":"/paper/2507.11408"},"observation_digest":"sha256:736ea3fead00c0407c575a2737a8b619f4a560cb49db6218fa54698396757319","observation_id":"f14230b5-d459-4655-8e4e-fd1afe1841a0","resolution":{"observed_at":"2026-08-06T17:17:05.592678Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2307.13702","last_updated":"2023-07-17T01:08:39Z","snapshot_observed_at":"2026-07-31T04:21:27.501709Z","submitted_at":"2023-07-17T01:08:39Z","title":"Measuring Faithfulness in Chain-of-Thought Reasoning","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2307.13702","snapshot_observed_at":"2026-08-06T17:17:05.673632Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.11408","last_updated":"2026-01-19T08:53:46Z","snapshot_observed_at":"2026-08-07T19:50:49.876336Z","submitted_at":"2025-07-15T15:28:37Z","title":"KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?","version":2},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-06T17:17:05.673632Z"},"links":{"cited_paper":"/paper/2307.13702","citing_paper":"/paper/2507.11408"},"observation_digest":"sha256:b8247597664301979d6b203487d024a320cbfd82bee1241cfc9da6965d7a2717","observation_id":"1b1b603f-09f4-40a5-9641-6bf998291991","resolution":{"observed_at":"2026-08-06T17:17:05.673632Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2506.02532","last_updated":"2025-06-03T07:11:34Z","snapshot_observed_at":"2026-08-07T17:40:58.834761Z","submitted_at":"2025-06-03T07:11:34Z","title":"ReasoningFlow: Semantic Structure of Complex Reasoning Traces","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.02532","snapshot_observed_at":"2026-08-06T17:17:05.769550Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.11408","last_updated":"2026-01-19T08:53:46Z","snapshot_observed_at":"2026-08-07T19:50:49.876336Z","submitted_at":"2025-07-15T15:28:37Z","title":"KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?","version":2},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-06T17:17:05.769550Z"},"links":{"cited_paper":"/paper/2506.02532","citing_paper":"/paper/2507.11408"},"observation_digest":"sha256:109a144dea811411eb72347962b3af9c8b4fff27f6bab8ce657d8d033011258d","observation_id":"0e1672ca-eb2b-4662-893f-62aa20d00ed9","resolution":{"observed_at":"2026-08-06T17:17:05.769550Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2502.07374","last_updated":"2025-02-18T05:20:33Z","snapshot_observed_at":"2026-08-07T21:53:35.875689Z","submitted_at":"2025-02-11T08:48:48Z","title":"LLMs Can Easily Learn to Reason from Demonstrations Structure, not content, is what matters!","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.07374","snapshot_observed_at":"2026-08-06T17:17:05.905312Z","title":"Patil, Matei Zaharia, Joseph E","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.11408","last_updated":"2026-01-19T08:53:46Z","snapshot_observed_at":"2026-08-07T19:50:49.876336Z","submitted_at":"2025-07-15T15:28:37Z","title":"KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?","version":2},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-06T17:17:05.905312Z"},"links":{"cited_paper":"/paper/2502.07374","citing_paper":"/paper/2507.11408"},"observation_digest":"sha256:1ab2b529b7c03d78dc2734833aca68f64037564bc39c7528b7cfcdbdbc9cb0af","observation_id":"11949cf2-eac1-4506-805d-9f8473787bbd","resolution":{"observed_at":"2026-08-06T17:17:05.905312Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2305.20050","last_updated":"2023-05-31T17:24:00Z","snapshot_observed_at":"2026-08-05T13:11:04.104454Z","submitted_at":"2023-05-31T17:24:00Z","title":"Let's Verify Step by Step","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2305.20050","snapshot_observed_at":"2026-08-06T17:17:05.984780Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.11408","last_updated":"2026-01-19T08:53:46Z","snapshot_observed_at":"2026-08-07T19:50:49.876336Z","submitted_at":"2025-07-15T15:28:37Z","title":"KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?","version":2},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-06T17:17:05.984780Z"},"links":{"cited_paper":"/paper/2305.20050","citing_paper":"/paper/2507.11408"},"observation_digest":"sha256:6c84e8b7eb0321ec59a770054de6c5e46294c24ca4822b6afff312757d02fe7b","observation_id":"2e3dc360-929b-426e-8d21-3c379425d7a3","resolution":{"observed_at":"2026-08-06T17:17:05.984780Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:17:08.408231Z","title":null,"venue":null,"work_id":"75acaff5-f761-412b-8da9-40b71c2be677","year":2024},"citing_paper":{"arxiv_id":"2507.11408","last_updated":"2026-01-19T08:53:46Z","snapshot_observed_at":"2026-08-07T19:50:49.876336Z","submitted_at":"2025-07-15T15:28:37Z","title":"KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?","version":2},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-06T17:17:06.025691Z"},"links":{"citing_paper":"/paper/2507.11408"},"observation_digest":"sha256:da4b0dface6409a24e69f9f2f0afbade75d2b2d682c7bd7e039bf9d22072a5bc","observation_id":"d319a2b3-3120-4f18-b630-97519837cab4","resolution":{"observed_at":"2026-08-06T17:17:08.485327Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:17:08.218631Z","title":null,"venue":null,"work_id":"8d45a532-32f4-4876-9b16-ee8da354e141","year":2024},"citing_paper":{"arxiv_id":"2507.11408","last_updated":"2026-01-19T08:53:46Z","snapshot_observed_at":"2026-08-07T19:50:49.876336Z","submitted_at":"2025-07-15T15:28:37Z","title":"KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?","version":2},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-06T17:17:06.100531Z"},"links":{"citing_paper":"/paper/2507.11408"},"observation_digest":"sha256:e6e5f3b822c5ba2832dfb11d2a4a849efd2233e0c1ebbd6bb4312ab2f7afd811","observation_id":"4d0e86f2-69d9-4298-9d3f-23a9aff7df12","resolution":{"observed_at":"2026-08-06T17:17:08.315326Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.16720","last_updated":"2026-04-30T02:46:40Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2024-12-21T18:04:31Z","title":"OpenAI o1 System Card","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.16720","snapshot_observed_at":"2026-08-06T17:17:06.112529Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.11408","last_updated":"2026-01-19T08:53:46Z","snapshot_observed_at":"2026-08-07T19:50:49.876336Z","submitted_at":"2025-07-15T15:28:37Z","title":"KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?","version":2},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-06T17:17:06.112529Z"},"links":{"cited_paper":"/paper/2412.16720","citing_paper":"/paper/2507.11408"},"observation_digest":"sha256:66a1bac288a49db65a71b332ab46c0c5180b5997bfa122a50bcfc9892bba2012","observation_id":"93d4aab3-98e9-4271-9aca-01f82aa4554b","resolution":{"observed_at":"2026-08-06T17:17:06.112529Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:17:07.999912Z","title":null,"venue":null,"work_id":"3151cef9-fc43-418c-99ef-3dcf9508ff90","year":2025},"citing_paper":{"arxiv_id":"2507.11408","last_updated":"2026-01-19T08:53:46Z","snapshot_observed_at":"2026-08-07T19:50:49.876336Z","submitted_at":"2025-07-15T15:28:37Z","title":"KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?","version":2},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-06T17:17:06.147795Z"},"links":{"citing_paper":"/paper/2507.11408"},"observation_digest":"sha256:856b105fabaf1200cdf98615133096d913bb76d4d23415f6aa11ff3e97ea87fe","observation_id":"2d36bcbd-a5b0-40d3-9ad9-ed6a0a8fc70f","resolution":{"observed_at":"2026-08-06T17:17:08.119153Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:17:06.188426Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.11408","last_updated":"2026-01-19T08:53:46Z","snapshot_observed_at":"2026-08-07T19:50:49.876336Z","submitted_at":"2025-07-15T15:28:37Z","title":"KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?","version":2},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-06T17:17:06.188426Z"},"links":{"citing_paper":"/paper/2507.11408"},"observation_digest":"sha256:9188bb82761422762f834c397533c2052fa1339bb1fe586bf195fc33478609bf","observation_id":"d252b394-8a88-4e1d-ab18-a7d8d51740c2","resolution":{"observed_at":"2026-08-06T17:17:06.188426Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.15115","last_updated":"2025-01-03T02:18:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2024-12-19T17:56:09Z","title":"Qwen2.5 Technical Report","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.15115","snapshot_observed_at":"2026-08-06T17:17:06.239435Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.11408","last_updated":"2026-01-19T08:53:46Z","snapshot_observed_at":"2026-08-07T19:50:49.876336Z","submitted_at":"2025-07-15T15:28:37Z","title":"KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?","version":2},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-06T17:17:06.239435Z"},"links":{"cited_paper":"/paper/2412.15115","citing_paper":"/paper/2507.11408"},"observation_digest":"sha256:a7c2e2085ac677f35d062466c0c23d6ceddf82f48b30616c15a5c7076ea8805a","observation_id":"f7926c33-c618-48e1-9c30-86cb108a7a69","resolution":{"observed_at":"2026-08-06T17:17:06.239435Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2506.10947","last_updated":"2026-02-25T01:06:05Z","snapshot_observed_at":"2026-07-30T09:54:40.100382Z","submitted_at":"2025-06-12T17:49:55Z","title":"Spurious Rewards: Rethinking Training Signals in RLVR","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.10947","snapshot_observed_at":"2026-08-06T17:17:06.284535Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.11408","last_updated":"2026-01-19T08:53:46Z","snapshot_observed_at":"2026-08-07T19:50:49.876336Z","submitted_at":"2025-07-15T15:28:37Z","title":"KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?","version":2},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-06T17:17:06.284535Z"},"links":{"cited_paper":"/paper/2506.10947","citing_paper":"/paper/2507.11408"},"observation_digest":"sha256:8a57d2d366da69bb582fa2f13535ba95b571658a21964b379def04a04ff9ce29","observation_id":"9ebc9ced-6798-441c-9ce9-e5b486c46400","resolution":{"observed_at":"2026-08-06T17:17:06.284535Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.13775","last_updated":"2026-05-25T19:08:50Z","snapshot_observed_at":"2026-08-07T15:42:47.674672Z","submitted_at":"2025-05-19T23:29:23Z","title":"Beyond Semantics: The Unreasonable Effectiveness of Reasonless Intermediate Tokens","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.13775","snapshot_observed_at":"2026-08-06T17:17:06.328065Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.11408","last_updated":"2026-01-19T08:53:46Z","snapshot_observed_at":"2026-08-07T19:50:49.876336Z","submitted_at":"2025-07-15T15:28:37Z","title":"KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?","version":2},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-06T17:17:06.328065Z"},"links":{"cited_paper":"/paper/2505.13775","citing_paper":"/paper/2507.11408"},"observation_digest":"sha256:778311cf94ecaa7755a65a736554df3f74d3889bd004eb406020cfebb0781b82","observation_id":"ac9def3b-4c90-4447-a0cd-a989c99d49c2","resolution":{"observed_at":"2026-08-06T17:17:06.328065Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:17:07.811469Z","title":null,"venue":null,"work_id":"6e311c9c-af44-4199-980f-9410374f2f0f","year":2024},"citing_paper":{"arxiv_id":"2507.11408","last_updated":"2026-01-19T08:53:46Z","snapshot_observed_at":"2026-08-07T19:50:49.876336Z","submitted_at":"2025-07-15T15:28:37Z","title":"KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?","version":2},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-06T17:17:06.370164Z"},"links":{"citing_paper":"/paper/2507.11408"},"observation_digest":"sha256:160be7e96b03a4daa70872f31bbdc9b64c5c1a96caaa39201a79711df4269a3f","observation_id":"9c528f80-d571-4196-9d09-981d99b4fcb0","resolution":{"observed_at":"2026-08-06T17:17:07.903709Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.18653/v1/2023.blackboxnlp-1.12","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:17:07.237012Z","title":null,"venue":null,"work_id":"fa9ea644-95f9-4238-b324-af62b6000e72","year":2023},"citing_paper":{"arxiv_id":"2507.11408","last_updated":"2026-01-19T08:53:46Z","snapshot_observed_at":"2026-08-07T19:50:49.876336Z","submitted_at":"2025-07-15T15:28:37Z","title":"KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?","version":2},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-06T17:17:06.413900Z"},"links":{"citing_paper":"/paper/2507.11408"},"observation_digest":"sha256:08df8357d0a832412b7a35539175ca03b1cd057f81cfe925f7c5001f35c779eb","observation_id":"f1bfda2c-2b04-44a2-b8f3-58e8579e74db","resolution":{"observed_at":"2026-08-06T17:17:07.297748Z","resolver_source":"doi","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":"2503.19786","last_updated":"2025-03-25T15:52:34Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-03-25T15:52:34Z","title":"Gemma 3 Technical Report","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2503.19786","snapshot_observed_at":"2026-08-06T17:17:06.459419Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.11408","last_updated":"2026-01-19T08:53:46Z","snapshot_observed_at":"2026-08-07T19:50:49.876336Z","submitted_at":"2025-07-15T15:28:37Z","title":"KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?","version":2},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-06T17:17:06.459419Z"},"links":{"cited_paper":"/paper/2503.19786","citing_paper":"/paper/2507.11408"},"observation_digest":"sha256:cd78e7e644e68d080a62ef83cc09fffb2e781e8f0e7aed6f385e89e5db17f630","observation_id":"f1ad7c41-4c8b-4db2-8d08-bee946a9c411","resolution":{"observed_at":"2026-08-06T17:17:06.459419Z","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":"2026-08-06T17:17:06.524439Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.11408","last_updated":"2026-01-19T08:53:46Z","snapshot_observed_at":"2026-08-07T19:50:49.876336Z","submitted_at":"2025-07-15T15:28:37Z","title":"KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?","version":2},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-06T17:17:06.524439Z"},"links":{"citing_paper":"/paper/2507.11408"},"observation_digest":"sha256:0f0df453026f8c83f3b6c37bf52f7b029ea076a30d9d35c312f7072fd4d19348","observation_id":"3646dda1-cccf-4f8d-8ff8-8fac6981ff50","resolution":{"observed_at":"2026-08-06T17:17:06.524439Z","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":"2026-08-06T17:17:06.592472Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.11408","last_updated":"2026-01-19T08:53:46Z","snapshot_observed_at":"2026-08-07T19:50:49.876336Z","submitted_at":"2025-07-15T15:28:37Z","title":"KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?","version":2},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-06T17:17:06.592472Z"},"links":{"citing_paper":"/paper/2507.11408"},"observation_digest":"sha256:03b4f67c6c9ffef2e868a40bf4ed72b284764b52905e6c2641bc612ee830a7cc","observation_id":"7ea3e9e9-a3e9-41e7-9d59-27846b1a03ca","resolution":{"observed_at":"2026-08-06T17:17:06.592472Z","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":"2026-08-06T17:17:06.632777Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.11408","last_updated":"2026-01-19T08:53:46Z","snapshot_observed_at":"2026-08-07T19:50:49.876336Z","submitted_at":"2025-07-15T15:28:37Z","title":"KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?","version":2},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-06T17:17:06.632777Z"},"links":{"citing_paper":"/paper/2507.11408"},"observation_digest":"sha256:2c68dca4a275caf82058d8a16823448335da584a36d77f4a3467988f8ca1161e","observation_id":"51092e78-e80e-4545-8f9a-ff0a2bc1cdb3","resolution":{"observed_at":"2026-08-06T17:17:06.632777Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2506.01939","last_updated":"2025-11-13T10:08:29Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-06-02T17:54:39Z","title":"Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.01939","snapshot_observed_at":"2026-08-06T17:17:06.695466Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.11408","last_updated":"2026-01-19T08:53:46Z","snapshot_observed_at":"2026-08-07T19:50:49.876336Z","submitted_at":"2025-07-15T15:28:37Z","title":"KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?","version":2},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-06T17:17:06.695466Z"},"links":{"cited_paper":"/paper/2506.01939","citing_paper":"/paper/2507.11408"},"observation_digest":"sha256:a8f904ac343d7b6988acfaa123c22193c11cfec73a249d7e2b95e08076986672","observation_id":"02853bf4-463f-428f-ba57-2c2d8260d6e1","resolution":{"observed_at":"2026-08-06T17:17:06.695466Z","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":"2026-08-06T17:17:06.751275Z","title":"Chi, Quoc V Le, and Denny Zhou","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.11408","last_updated":"2026-01-19T08:53:46Z","snapshot_observed_at":"2026-08-07T19:50:49.876336Z","submitted_at":"2025-07-15T15:28:37Z","title":"KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?","version":2},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-06T17:17:06.751275Z"},"links":{"citing_paper":"/paper/2507.11408"},"observation_digest":"sha256:414a1427c55b129e0d6eb85dd4733b5d4310af51df9dc49142fd7c53c08cb588","observation_id":"ab874204-f249-495b-8819-57d26956f0af","resolution":{"observed_at":"2026-08-06T17:17:06.751275Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.09388","last_updated":"2025-05-14T13:41:34Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-05-14T13:41:34Z","title":"Qwen3 Technical Report","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.09388","snapshot_observed_at":"2026-08-06T17:17:06.809622Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.11408","last_updated":"2026-01-19T08:53:46Z","snapshot_observed_at":"2026-08-07T19:50:49.876336Z","submitted_at":"2025-07-15T15:28:37Z","title":"KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?","version":2},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-06T17:17:06.809622Z"},"links":{"cited_paper":"/paper/2505.09388","citing_paper":"/paper/2507.11408"},"observation_digest":"sha256:55030d87aa2abd643166703dc30652b493c64b11fb7afb96a73dc9f1c88e05e6","observation_id":"04a2ea36-eeb6-4d13-8db7-38f09ccc94ce","resolution":{"observed_at":"2026-08-06T17:17:06.809622Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2504.13837","last_updated":"2025-11-24T06:11:04Z","snapshot_observed_at":"2026-07-06T21:11:34.701779Z","submitted_at":"2025-04-18T17:59:56Z","title":"Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2504.13837","snapshot_observed_at":"2026-08-06T17:17:06.887900Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.11408","last_updated":"2026-01-19T08:53:46Z","snapshot_observed_at":"2026-08-07T19:50:49.876336Z","submitted_at":"2025-07-15T15:28:37Z","title":"KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?","version":2},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-06T17:17:06.887900Z"},"links":{"cited_paper":"/paper/2504.13837","citing_paper":"/paper/2507.11408"},"observation_digest":"sha256:f8af5a2a2e5a0f992194d842bd9eaccfa78f2c30bb644171c9706a99fce9dd35","observation_id":"a293c8df-f488-4445-90df-9786c672dfe0","resolution":{"observed_at":"2026-08-06T17:17:06.887900Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:17:07.623978Z","title":null,"venue":null,"work_id":"a024d453-e47f-4ebd-8707-76d1d934719c","year":2023},"citing_paper":{"arxiv_id":"2507.11408","last_updated":"2026-01-19T08:53:46Z","snapshot_observed_at":"2026-08-07T19:50:49.876336Z","submitted_at":"2025-07-15T15:28:37Z","title":"KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?","version":2},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-06T17:17:06.963849Z"},"links":{"citing_paper":"/paper/2507.11408"},"observation_digest":"sha256:84f5ed7fe0f6fcc4b5c6c7e5d6125035ffe04d78c85273e79f000d2346a34c1a","observation_id":"656446af-f648-4668-8d11-c00d2a3b77c6","resolution":{"observed_at":"2026-08-06T17:17:07.697841Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:17:07.034919Z","title":"online\" 'onlinestring :=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.11408","last_updated":"2026-01-19T08:53:46Z","snapshot_observed_at":"2026-08-07T19:50:49.876336Z","submitted_at":"2025-07-15T15:28:37Z","title":"KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?","version":2},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-06T17:17:07.034919Z"},"links":{"citing_paper":"/paper/2507.11408"},"observation_digest":"sha256:54d968b838f0cd080a4fce036a8526bfac91e015cd9ac557ef9e9dc3d3d4b91d","observation_id":"b5eea71e-131a-4861-8e2d-6acd97c11460","resolution":{"observed_at":"2026-08-06T17:17:07.034919Z","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":"2026-08-06T17:17:07.109039Z","title":"write newline","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.11408","last_updated":"2026-01-19T08:53:46Z","snapshot_observed_at":"2026-08-07T19:50:49.876336Z","submitted_at":"2025-07-15T15:28:37Z","title":"KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?","version":2},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-06T17:17:07.109039Z"},"links":{"citing_paper":"/paper/2507.11408"},"observation_digest":"sha256:72ef6becc2f7b615be58eab6b111620ffeccd28de6b0b852d652761272bf6a35","observation_id":"ef09ca13-9a8c-4c9f-8071-7228026493f5","resolution":{"observed_at":"2026-08-06T17:17:07.109039Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2507.11408","last_updated":"2026-01-19T08:53:46Z","latest_version":2,"primary_category":"cs.CL","snapshot_observed_at":"2026-08-07T19:50:49.876336Z","submitted_at":"2025-07-15T15:28:37Z","title":"KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?"},"reference_resolution":{"displayed":33,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":32,"verified_exact":1,"verified_fuzzy":0},"total_outbound_references":33},"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 7 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 1 inbound Pith citation observation for arXiv:2507.11408."}