{"as_of":"2026-08-08T05:09:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:937d02d01b0f9d42926e0374fd689e87707b28d40bc9ca718e07e5b6e1855b5b","coverage":[{"denominator":31,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":31,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-02T08:02:57.868691Z","state":"measured"},{"denominator":31,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":31,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-07T06:34:17.273281+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/2607.20520/citation-record","integrity":"/paper/2607.20520/integrity","json":"/paper/2607.20520/citation-record.json","paper":"/paper/2607.20520"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T08:02:56.326935Z","title":"Current trends and future prospects of large -scale foundation model in K -12 education,","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.20520","last_updated":"2026-07-08T17:21:28Z","snapshot_observed_at":"2026-08-05T03:25:29.428394Z","submitted_at":"2026-07-08T17:21:28Z","title":"Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-02T08:02:56.326935Z"},"links":{"citing_paper":"/paper/2607.20520"},"observation_digest":"sha256:8dabd2713b1ccb0b7cb2c383cf448148ab33f5c6f91e857ce5b3fdac5697d40e","observation_id":"ee13f71c-14f4-43b4-beac-5974c4388a92","resolution":{"observed_at":"2026-08-02T08:02:56.326935Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2402.00157","last_updated":"2024-09-16T19:20:59Z","snapshot_observed_at":"2026-08-03T23:38:38.676420Z","submitted_at":"2024-01-31T20:26:32Z","title":"Large Language Models for Mathematical Reasoning: Progresses and Challenges","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.00157","snapshot_observed_at":"2026-08-02T08:02:56.456065Z","title":"Large language models for mathematical reasoning: Progresses and challenges,","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.20520","last_updated":"2026-07-08T17:21:28Z","snapshot_observed_at":"2026-08-05T03:25:29.428394Z","submitted_at":"2026-07-08T17:21:28Z","title":"Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-02T08:02:56.456065Z"},"links":{"cited_paper":"/paper/2402.00157","citing_paper":"/paper/2607.20520"},"observation_digest":"sha256:21d1d9aaf3153e9ddc102358956e22b5113c890c388a63cfd8afacd6789b55ea","observation_id":"3412a780-27cc-4607-a29d-79e7642dda2a","resolution":{"observed_at":"2026-08-02T08:02:56.456065Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2410.05229","last_updated":"2025-08-27T16:24:39Z","snapshot_observed_at":"2026-07-06T19:29:09.714725Z","submitted_at":"2024-10-07T17:36:37Z","title":"GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2410.05229","snapshot_observed_at":"2026-08-02T08:02:56.560521Z","title":"Gsm -symbolic: Understanding the limitations of mathematical reasoning in large language models,","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.20520","last_updated":"2026-07-08T17:21:28Z","snapshot_observed_at":"2026-08-05T03:25:29.428394Z","submitted_at":"2026-07-08T17:21:28Z","title":"Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-02T08:02:56.560521Z"},"links":{"cited_paper":"/paper/2410.05229","citing_paper":"/paper/2607.20520"},"observation_digest":"sha256:19b451c20449e8768f6f29f59f3b4cb56d533daae63c7dfb5676760a9523fc7e","observation_id":"fc38a537-dcc0-4344-a775-1ebc695aa187","resolution":{"observed_at":"2026-08-02T08:02:56.560521Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2404.11500","last_updated":"2024-04-17T15:53:49Z","snapshot_observed_at":"2026-07-06T18:01:40.563108Z","submitted_at":"2024-04-17T15:53:49Z","title":"Paraphrase and Solve: Exploring and Exploiting the Impact of Surface Form on Mathematical Reasoning in Large Language Models","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2404.11500","snapshot_observed_at":"2026-08-02T08:02:56.670895Z","title":"Paraphrase and solve: Exploring and exploiting the impact of surface form on mathematical reasoning in large language models,","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.20520","last_updated":"2026-07-08T17:21:28Z","snapshot_observed_at":"2026-08-05T03:25:29.428394Z","submitted_at":"2026-07-08T17:21:28Z","title":"Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-02T08:02:56.670895Z"},"links":{"cited_paper":"/paper/2404.11500","citing_paper":"/paper/2607.20520"},"observation_digest":"sha256:6cc2f9eb34bef52a1f87715e10b68a9b4167f9ed7282f07c94a4ba9e20a262a8","observation_id":"bb10508c-e78b-4b98-a39c-fdf11f3ffb83","resolution":{"observed_at":"2026-08-02T08:02:56.670895Z","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":"2026-08-02T08:02:56.778357Z","title":"The role of representation(s) in developing mathematical understanding,","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2607.20520","last_updated":"2026-07-08T17:21:28Z","snapshot_observed_at":"2026-08-05T03:25:29.428394Z","submitted_at":"2026-07-08T17:21:28Z","title":"Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-02T08:02:56.778357Z"},"links":{"citing_paper":"/paper/2607.20520"},"observation_digest":"sha256:7572b57e09a36c0fc378672e547830e595c7ee9e61dad46841752466fd69ec6e","observation_id":"e9e27747-a19a-4f4a-8578-a0ec4e98e91c","resolution":{"observed_at":"2026-08-02T08:02:56.778357Z","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":"2026-08-02T08:02:56.861733Z","title":"Have llms advanced enough? a challenging problem solving benchmark for large language models,","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.20520","last_updated":"2026-07-08T17:21:28Z","snapshot_observed_at":"2026-08-05T03:25:29.428394Z","submitted_at":"2026-07-08T17:21:28Z","title":"Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-02T08:02:56.861733Z"},"links":{"citing_paper":"/paper/2607.20520"},"observation_digest":"sha256:6e244eee1c46fa4a23fecfaa5f0b2d4bf603aba572c15482bcf7cc13f554112a","observation_id":"5d9ede92-347a-4c74-a1eb-05fc11af9245","resolution":{"observed_at":"2026-08-02T08:02:56.861733Z","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":"2026-08-02T08:02:56.917313Z","title":"Frequency norms and structural analysis of algebra story problems into families, categories, and templates,","venue":null,"work_id":null,"year":1981},"citing_paper":{"arxiv_id":"2607.20520","last_updated":"2026-07-08T17:21:28Z","snapshot_observed_at":"2026-08-05T03:25:29.428394Z","submitted_at":"2026-07-08T17:21:28Z","title":"Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-02T08:02:56.917313Z"},"links":{"citing_paper":"/paper/2607.20520"},"observation_digest":"sha256:2c3062e3ecb2e61d89e13fcb3da709e63a4e94f22a5d1b16d84cfaf7f03f5077","observation_id":"af19e6e1-7323-4660-8006-82046d4791b1","resolution":{"observed_at":"2026-08-02T08:02:56.917313Z","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":"2026-08-02T08:02:56.959048Z","title":"The real story behind story problems: Effects of representations on quantitative reasoning.,","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2607.20520","last_updated":"2026-07-08T17:21:28Z","snapshot_observed_at":"2026-08-05T03:25:29.428394Z","submitted_at":"2026-07-08T17:21:28Z","title":"Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-02T08:02:56.959048Z"},"links":{"citing_paper":"/paper/2607.20520"},"observation_digest":"sha256:16ea9a5524220d25fc77f3e68b5a4cacc91cfcc8cac8280b3ca70992205362e8","observation_id":"aa8a8196-d43f-4753-adcc-da8181d13e9e","resolution":{"observed_at":"2026-08-02T08:02:56.959048Z","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":"2026-08-02T08:02:57.029119Z","title":"Solving quantitative reasoning problems with language models,","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.20520","last_updated":"2026-07-08T17:21:28Z","snapshot_observed_at":"2026-08-05T03:25:29.428394Z","submitted_at":"2026-07-08T17:21:28Z","title":"Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-02T08:02:57.029119Z"},"links":{"citing_paper":"/paper/2607.20520"},"observation_digest":"sha256:9ecfc5159ec4467349548b3dafedf9470fed3e397db3a0068a8d6c3c19bcc013","observation_id":"265529ae-a665-4032-8114-5ffdfe4f852c","resolution":{"observed_at":"2026-08-02T08:02:57.029119Z","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":"2026-08-02T08:02:57.099020Z","title":"Stochastic LLMs do not understand language: towards symbolic, explainable and ontologically based LLMs,","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.20520","last_updated":"2026-07-08T17:21:28Z","snapshot_observed_at":"2026-08-05T03:25:29.428394Z","submitted_at":"2026-07-08T17:21:28Z","title":"Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-02T08:02:57.099020Z"},"links":{"citing_paper":"/paper/2607.20520"},"observation_digest":"sha256:95adbf2074b683b3ac8a81b1b61bcbb194ef28ab3d5c00ab8fc19baff158b543","observation_id":"5f37974a-da4b-4276-b189-43f6b9f14bae","resolution":{"observed_at":"2026-08-02T08:02:57.099020Z","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":"2026-08-02T08:02:57.169161Z","title":"PAL: Program-aided Language Models,","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.20520","last_updated":"2026-07-08T17:21:28Z","snapshot_observed_at":"2026-08-05T03:25:29.428394Z","submitted_at":"2026-07-08T17:21:28Z","title":"Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-02T08:02:57.169161Z"},"links":{"citing_paper":"/paper/2607.20520"},"observation_digest":"sha256:7d018839749377f54003fcd86b88600dcad9ae7dab119e938ac43d6cf825f039","observation_id":"2daa1b60-d174-44c2-b0c5-63d7ea8a20e4","resolution":{"observed_at":"2026-08-02T08:02:57.169161Z","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":"2026-08-02T08:02:57.238383Z","title":"Toolformer: Language models can teach themselves to use tools.,","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.20520","last_updated":"2026-07-08T17:21:28Z","snapshot_observed_at":"2026-08-05T03:25:29.428394Z","submitted_at":"2026-07-08T17:21:28Z","title":"Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-02T08:02:57.238383Z"},"links":{"citing_paper":"/paper/2607.20520"},"observation_digest":"sha256:2ea2ffb039a1e4a4257d3696c55ac9a13cff4749e52686417c4c1ce25e7e2ec4","observation_id":"986c21b7-7f2f-4807-90bd-05ad698b1b1c","resolution":{"observed_at":"2026-08-02T08:02:57.238383Z","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":"2026-08-02T08:02:57.308476Z","title":"When LLMs hallucinate: Examining the effects of erroneous feedback in math tutoring systems,","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.20520","last_updated":"2026-07-08T17:21:28Z","snapshot_observed_at":"2026-08-05T03:25:29.428394Z","submitted_at":"2026-07-08T17:21:28Z","title":"Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-02T08:02:57.308476Z"},"links":{"citing_paper":"/paper/2607.20520"},"observation_digest":"sha256:2bbc5b213fb62732e9a9be04be3c495bca92c9957d38109e8f337e758e75dd30","observation_id":"6d869eca-ed62-4cdb-b761-ba78a0783602","resolution":{"observed_at":"2026-08-02T08:02:57.308476Z","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":"2026-08-02T08:02:57.354480Z","title":"Chain -of-thought prompting elicits reasoning in large language models,","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.20520","last_updated":"2026-07-08T17:21:28Z","snapshot_observed_at":"2026-08-05T03:25:29.428394Z","submitted_at":"2026-07-08T17:21:28Z","title":"Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-02T08:02:57.354480Z"},"links":{"citing_paper":"/paper/2607.20520"},"observation_digest":"sha256:d770e6c6235df24298d68d0c639e9a7e19ebdb8ee5d73b699f6e93c73e480f0b","observation_id":"2a4cd4a2-ce7d-4770-85be-58491bcb98f4","resolution":{"observed_at":"2026-08-02T08:02:57.354480Z","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":"2026-08-02T08:02:57.414076Z","title":"HCI 2026 dataset,","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.20520","last_updated":"2026-07-08T17:21:28Z","snapshot_observed_at":"2026-08-05T03:25:29.428394Z","submitted_at":"2026-07-08T17:21:28Z","title":"Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-02T08:02:57.414076Z"},"links":{"citing_paper":"/paper/2607.20520"},"observation_digest":"sha256:eb3b4acf3cf07e4453be9c4282af9cdb49e836df8eb0000ab3ff6e302b3eed3c","observation_id":"816ce390-e8b9-46b1-934e-74fac7324a55","resolution":{"observed_at":"2026-08-02T08:02:57.414076Z","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":"2026-08-02T08:02:57.518289Z","title":"The understanding process: Problem isomorphs,","venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2607.20520","last_updated":"2026-07-08T17:21:28Z","snapshot_observed_at":"2026-08-05T03:25:29.428394Z","submitted_at":"2026-07-08T17:21:28Z","title":"Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-02T08:02:57.518289Z"},"links":{"citing_paper":"/paper/2607.20520"},"observation_digest":"sha256:517d9a5c1d543d4dcd3607e2ce098ded33da715eb1cbe8193d804e40b57b0675","observation_id":"74d81430-816a-4fb2-81a5-68df548e3f42","resolution":{"observed_at":"2026-08-02T08:02:57.518289Z","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":"2026-08-02T08:02:57.609799Z","title":"Generative testing: From conception to implementation,","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.20520","last_updated":"2026-07-08T17:21:28Z","snapshot_observed_at":"2026-08-05T03:25:29.428394Z","submitted_at":"2026-07-08T17:21:28Z","title":"Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-02T08:02:57.609799Z"},"links":{"citing_paper":"/paper/2607.20520"},"observation_digest":"sha256:12fb2a25e83892fc8c69352374037daff1e00a953ecdf81e808b7b23d89e21e1","observation_id":"9b7e7463-edb4-4ecb-ad38-f4c04bd83cef","resolution":{"observed_at":"2026-08-02T08:02:57.609799Z","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":"2026-08-02T08:02:57.669651Z","title":"The role of isomorphisms in mathematical cognition,","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2607.20520","last_updated":"2026-07-08T17:21:28Z","snapshot_observed_at":"2026-08-05T03:25:29.428394Z","submitted_at":"2026-07-08T17:21:28Z","title":"Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-02T08:02:57.669651Z"},"links":{"citing_paper":"/paper/2607.20520"},"observation_digest":"sha256:7535748d1b63986db15a2445cabaa6f682ed2dabd1195dd09d508fee1fb9a161","observation_id":"d40847a3-12de-41f8-a89a-0544f4695fb5","resolution":{"observed_at":"2026-08-02T08:02:57.669651Z","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":"2026-08-02T08:02:57.777661Z","title":"The longitudinal study,","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.20520","last_updated":"2026-07-08T17:21:28Z","snapshot_observed_at":"2026-08-05T03:25:29.428394Z","submitted_at":"2026-07-08T17:21:28Z","title":"Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-02T08:02:57.777661Z"},"links":{"citing_paper":"/paper/2607.20520"},"observation_digest":"sha256:3adbec973021e6eeb8906c58040a899fa6c61842760081bc6d4d8fa4eae62f93","observation_id":"e400a555-4353-4c6c-af66-7665b331f1d0","resolution":{"observed_at":"2026-08-02T08:02:57.777661Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2411.04872","last_updated":"2025-12-23T02:23:47Z","snapshot_observed_at":"2026-08-04T15:54:46.196160Z","submitted_at":"2024-11-07T17:07:35Z","title":"FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI","version":7},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.04872","snapshot_observed_at":"2026-08-02T08:02:57.823644Z","title":"Frontiermath: A benchmark for evaluating advanced mathematical reasoning in AI,","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.20520","last_updated":"2026-07-08T17:21:28Z","snapshot_observed_at":"2026-08-05T03:25:29.428394Z","submitted_at":"2026-07-08T17:21:28Z","title":"Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-02T08:02:57.823644Z"},"links":{"cited_paper":"/paper/2411.04872","citing_paper":"/paper/2607.20520"},"observation_digest":"sha256:f4fd68c54ceefbbca7a84beb2a77f786574c085ce0d5198f47a98f2f41298d4a","observation_id":"581d2d67-2fbd-4e21-91d1-0a624c6b4c19","resolution":{"observed_at":"2026-08-02T08:02:57.823644Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2206.07682","last_updated":"2022-10-26T05:06:24Z","snapshot_observed_at":"2026-08-02T15:56:35.249569Z","submitted_at":"2022-06-15T17:32:01Z","title":"Emergent Abilities of Large Language Models","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2206.07682","snapshot_observed_at":"2026-08-02T08:02:57.827984Z","title":"Emergent abilities of large language models,","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.20520","last_updated":"2026-07-08T17:21:28Z","snapshot_observed_at":"2026-08-05T03:25:29.428394Z","submitted_at":"2026-07-08T17:21:28Z","title":"Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-02T08:02:57.827984Z"},"links":{"cited_paper":"/paper/2206.07682","citing_paper":"/paper/2607.20520"},"observation_digest":"sha256:585e7ea8371e9d1eb36d2a7f10c00e16327b0145b67a5141f198094296400d91","observation_id":"b6be4590-ea96-4ee8-aa32-46dfd10bee17","resolution":{"observed_at":"2026-08-02T08:02:57.827984Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2001.08361","last_updated":"2020-01-23T03:59:20Z","snapshot_observed_at":"2026-07-06T08:52:12.656082Z","submitted_at":"2020-01-23T03:59:20Z","title":"Scaling Laws for Neural Language Models","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2001.08361","snapshot_observed_at":"2026-08-02T08:02:57.832397Z","title":"Scaling laws for neural language models,","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2607.20520","last_updated":"2026-07-08T17:21:28Z","snapshot_observed_at":"2026-08-05T03:25:29.428394Z","submitted_at":"2026-07-08T17:21:28Z","title":"Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-02T08:02:57.832397Z"},"links":{"cited_paper":"/paper/2001.08361","citing_paper":"/paper/2607.20520"},"observation_digest":"sha256:78173b1bd066537641a258f8392f6f80a296803bbe9bf030092507a9642ad029","observation_id":"d1bb3d71-e082-4e4e-9583-254d8de6d249","resolution":{"observed_at":"2026-08-02T08:02:57.832397Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2503.14227","last_updated":"2025-03-18T13:04:55Z","snapshot_observed_at":"2026-08-07T16:54:57.772961Z","submitted_at":"2025-03-18T13:04:55Z","title":"Benchmarking Failures in Tool-Augmented Language Models","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2503.14227","snapshot_observed_at":"2026-08-02T08:02:57.836797Z","title":"Benchmarking failures in tool -augmented language models,","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.20520","last_updated":"2026-07-08T17:21:28Z","snapshot_observed_at":"2026-08-05T03:25:29.428394Z","submitted_at":"2026-07-08T17:21:28Z","title":"Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-02T08:02:57.836797Z"},"links":{"cited_paper":"/paper/2503.14227","citing_paper":"/paper/2607.20520"},"observation_digest":"sha256:d9e8243ac0f02da8c22817e13877231487a962855abe3b964f051d608e9af503","observation_id":"3544ef28-7c0d-411e-8762-a2a1c9f2f53c","resolution":{"observed_at":"2026-08-02T08:02:57.836797Z","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":"2026-08-02T08:02:57.840882Z","title":"Evaluating the Intelligence of large language models: A comparative study using verbal and visual IQ tests,","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.20520","last_updated":"2026-07-08T17:21:28Z","snapshot_observed_at":"2026-08-05T03:25:29.428394Z","submitted_at":"2026-07-08T17:21:28Z","title":"Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-02T08:02:57.840882Z"},"links":{"citing_paper":"/paper/2607.20520"},"observation_digest":"sha256:0667d3cd9ace6b4faab6b3f13ec357c35033ada7c1c4d356f2b1cd3e8fb7f1c1","observation_id":"a76c6cea-8f9c-4e21-88be-f67796b211af","resolution":{"observed_at":"2026-08-02T08:02:57.840882Z","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":"2026-08-02T08:02:57.844684Z","title":"WIP: Beyond Code: Evaluating ChatGPT, Gemini, Claude, and Meta AI as AI Tutors in Computer Science and Engineering Education,","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.20520","last_updated":"2026-07-08T17:21:28Z","snapshot_observed_at":"2026-08-05T03:25:29.428394Z","submitted_at":"2026-07-08T17:21:28Z","title":"Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-02T08:02:57.844684Z"},"links":{"citing_paper":"/paper/2607.20520"},"observation_digest":"sha256:74a618230027b57f2f397ae7bde06ff2fceee7856cf421e082094072d3a2c6a4","observation_id":"052da4c1-cd95-4387-a7de-87afbfdd9069","resolution":{"observed_at":"2026-08-02T08:02:57.844684Z","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":"2026-08-02T08:02:57.848638Z","title":"OpenRouter,","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.20520","last_updated":"2026-07-08T17:21:28Z","snapshot_observed_at":"2026-08-05T03:25:29.428394Z","submitted_at":"2026-07-08T17:21:28Z","title":"Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-02T08:02:57.848638Z"},"links":{"citing_paper":"/paper/2607.20520"},"observation_digest":"sha256:7a51910a13e21361d21cf740c79dd672c8d35d7c6df7ea71087cb50c182c8c8b","observation_id":"5d4c6c7a-7e7e-4d3f-95ae-b6a7597ca3c0","resolution":{"observed_at":"2026-08-02T08:02:57.848638Z","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":"2026-08-02T08:02:57.852223Z","title":"Statistical notes for clinical researchers: Chi -squared test and Fisher's exact test,","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.20520","last_updated":"2026-07-08T17:21:28Z","snapshot_observed_at":"2026-08-05T03:25:29.428394Z","submitted_at":"2026-07-08T17:21:28Z","title":"Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-02T08:02:57.852223Z"},"links":{"citing_paper":"/paper/2607.20520"},"observation_digest":"sha256:fedbd1ffc8d10ac79b16208eec762b83a694a4d6f09acd65f3916e92b7f26271","observation_id":"545e4a30-1bdd-4774-94a7-d41eb08250ca","resolution":{"observed_at":"2026-08-02T08:02:57.852223Z","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":"2026-08-02T08:02:57.856300Z","title":"Structured outputs,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.20520","last_updated":"2026-07-08T17:21:28Z","snapshot_observed_at":"2026-08-05T03:25:29.428394Z","submitted_at":"2026-07-08T17:21:28Z","title":"Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-02T08:02:57.856300Z"},"links":{"citing_paper":"/paper/2607.20520"},"observation_digest":"sha256:01934b1a0894e0ac18523c4bcc937b400be5dd04c4bd7f0b8cab4b0fe16662f2","observation_id":"c9b63a28-ced7-4a30-98bd-20670b15236d","resolution":{"observed_at":"2026-08-02T08:02:57.856300Z","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":"2026-08-02T08:02:57.860338Z","title":"Structured output support for the Prompt API,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.20520","last_updated":"2026-07-08T17:21:28Z","snapshot_observed_at":"2026-08-05T03:25:29.428394Z","submitted_at":"2026-07-08T17:21:28Z","title":"Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-02T08:02:57.860338Z"},"links":{"citing_paper":"/paper/2607.20520"},"observation_digest":"sha256:bc3739b5f80afa283f30dde92f026e1d3864b83fd9f1d919bd488f93befab546","observation_id":"0e71f033-54b7-4ed4-953b-b353f6ce7b44","resolution":{"observed_at":"2026-08-02T08:02:57.860338Z","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":"2026-08-02T08:02:57.864481Z","title":"The good, the bad, and the ugly of Gemini’s structured outputs,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.20520","last_updated":"2026-07-08T17:21:28Z","snapshot_observed_at":"2026-08-05T03:25:29.428394Z","submitted_at":"2026-07-08T17:21:28Z","title":"Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-02T08:02:57.864481Z"},"links":{"citing_paper":"/paper/2607.20520"},"observation_digest":"sha256:f512df3d555dc0a8757084ddfaacee112d3f9ceb0d909da08626deec53791b30","observation_id":"a028917f-499b-488f-9f54-36671385e67e","resolution":{"observed_at":"2026-08-02T08:02:57.864481Z","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":"2026-08-02T08:02:57.868691Z","title":"Reasoning or Reciting? Exploring the Capabilities and Limitations of Language Models Through Counterfactual Tasks,","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.20520","last_updated":"2026-07-08T17:21:28Z","snapshot_observed_at":"2026-08-05T03:25:29.428394Z","submitted_at":"2026-07-08T17:21:28Z","title":"Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-02T08:02:57.868691Z"},"links":{"citing_paper":"/paper/2607.20520"},"observation_digest":"sha256:fb7927e5d5ee4ec9b47547e48ea25df2e0160c6cceb1f4b95cc45081907b4711","observation_id":"aebbbdeb-751c-4ec5-bfa1-e2b74f2887d9","resolution":{"observed_at":"2026-08-02T08:02:57.868691Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.20520","last_updated":"2026-07-08T17:21:28Z","latest_version":1,"primary_category":"cs.AI","snapshot_observed_at":"2026-08-05T03:25:29.428394Z","submitted_at":"2026-07-08T17:21:28Z","title":"Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving"},"reference_resolution":{"displayed":31,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":31,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":31},"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 31 of 31 outbound references and 0 inbound Pith citation observations for arXiv:2607.20520."}