{"as_of":"2026-08-09T16:30:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:954d4fb9442f2ca8a3196d1984e06063b2dc9b28124e0e87960618113dbfb2aa","coverage":[{"denominator":15,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":15,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-04T15:38:34.145477Z","state":"measured"},{"denominator":16,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":16,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+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":"2026-06-28T02:30:41.818145Z","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":"2026-07-02T12:06:55.950605Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2509.19710","last_updated":"2026-07-24T23:31:07Z","snapshot_observed_at":"2026-08-08T07:07:04.142549Z","submitted_at":"2025-09-24T02:42:25Z","title":"Probabilistic Symbolic Regression for Equation Discovery via Operator-induced and Regularized Symbolic Forests","version":2},"cited_work":{"arxiv_id":"2509.19710","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2509.19710","snapshot_observed_at":"2026-07-28T01:21:33.520974Z","title":"Hierarchical Bayesian Operator-induced Symbolic Regression Trees for Structural Learning of Scientific Expressions,","venue":null,"work_id":"9801f17f-d87f-4030-981b-5ae3ae73a15c","year":2025},"citing_paper":{"arxiv_id":"2606.06567","last_updated":"2026-06-04T17:29:56Z","snapshot_observed_at":"2026-08-03T06:40:35.784747Z","submitted_at":"2026-06-04T17:29:56Z","title":"Are you sure? A Comprehensive and Comprehensible Survey of Uncertainty Quantification in Symbolic Regression","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-06-28T02:30:41.818145Z"},"links":{"cited_paper":"/paper/2509.19710","citing_paper":"/paper/2606.06567"},"observation_digest":"sha256:216ab663777105db8c879fa5312dc8ebd6aa0a25ea28356996784195a384a75c","observation_id":"2020b16b-9731-4ff9-a798-152d9210f5b1","resolution":{"observed_at":"2026-07-28T01:21:33.520974Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2509.19710/citation-record","integrity":"/paper/2509.19710/integrity","json":"/paper/2509.19710/citation-record.json","paper":"/paper/2509.19710"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2104.05417","last_updated":"2021-04-12T12:50:50Z","snapshot_observed_at":"2026-07-06T10:58:41.121273Z","submitted_at":"2021-04-12T12:50:50Z","title":"An Approach to Symbolic Regression Using Feyn","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2104.05417","snapshot_observed_at":"2026-08-04T15:38:31.978584Z","title":null,"venue":null,"work_id":null,"year":1972},"citing_paper":{"arxiv_id":"2509.19710","last_updated":"2026-07-24T23:31:07Z","snapshot_observed_at":"2026-08-08T07:07:04.142549Z","submitted_at":"2025-09-24T02:42:25Z","title":"Probabilistic Symbolic Regression for Equation Discovery via Operator-induced and Regularized Symbolic Forests","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-04T15:38:31.978584Z"},"links":{"cited_paper":"/paper/2104.05417","citing_paper":"/paper/2509.19710"},"observation_digest":"sha256:445e3d691c8302e9264fe425ac292188d628e4a5279b5a9a8ba2412256e62c25","observation_id":"5c1b3c21-1447-4338-875e-68f07e9fb9c4","resolution":{"observed_at":"2026-08-04T15:38:31.978584Z","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":"2026-08-04T15:38:32.097325Z","title":"& Sedgewick, R","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2509.19710","last_updated":"2026-07-24T23:31:07Z","snapshot_observed_at":"2026-08-08T07:07:04.142549Z","submitted_at":"2025-09-24T02:42:25Z","title":"Probabilistic Symbolic Regression for Equation Discovery via Operator-induced and Regularized Symbolic Forests","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-04T15:38:32.097325Z"},"links":{"citing_paper":"/paper/2509.19710"},"observation_digest":"sha256:4efe0c500d5cf63fa138c9bff2958947111450f9bb2578bc7f81800f098bfede","observation_id":"07058d30-5b20-48d6-ae19-3ad459a87ddf","resolution":{"observed_at":"2026-08-04T15:38:32.097325Z","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":"2026-08-04T15:38:32.413329Z","title":"& Rubin, D","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2509.19710","last_updated":"2026-07-24T23:31:07Z","snapshot_observed_at":"2026-08-08T07:07:04.142549Z","submitted_at":"2025-09-24T02:42:25Z","title":"Probabilistic Symbolic Regression for Equation Discovery via Operator-induced and Regularized Symbolic Forests","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-04T15:38:32.413329Z"},"links":{"citing_paper":"/paper/2509.19710"},"observation_digest":"sha256:0e5625bc5b93ccc2c9d9f57d30726706a63f8ef264ae45879020c7c3b33f46af","observation_id":"da3c9c92-218e-4766-9702-56653720163c","resolution":{"observed_at":"2026-08-04T15:38:32.413329Z","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":"2026-08-04T15:38:32.591808Z","title":"(1992), Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments, in ‘Bayesian Statistics’, Vol","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2509.19710","last_updated":"2026-07-24T23:31:07Z","snapshot_observed_at":"2026-08-08T07:07:04.142549Z","submitted_at":"2025-09-24T02:42:25Z","title":"Probabilistic Symbolic Regression for Equation Discovery via Operator-induced and Regularized Symbolic Forests","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-04T15:38:32.591808Z"},"links":{"citing_paper":"/paper/2509.19710"},"observation_digest":"sha256:1619844d2ec07f0e1acb2cbc5b2a6e05ddae4b09e7d27a8f955f403f103ba948","observation_id":"925f7538-e823-4fab-a481-27b5569850eb","resolution":{"observed_at":"2026-08-04T15:38:32.591808Z","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":"2026-08-04T15:38:32.715318Z","title":"& van der Vaart, A","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2509.19710","last_updated":"2026-07-24T23:31:07Z","snapshot_observed_at":"2026-08-08T07:07:04.142549Z","submitted_at":"2025-09-24T02:42:25Z","title":"Probabilistic Symbolic Regression for Equation Discovery via Operator-induced and Regularized Symbolic Forests","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-04T15:38:32.715318Z"},"links":{"citing_paper":"/paper/2509.19710"},"observation_digest":"sha256:e3f28e38a201ca7b3e28ddccd6cd26e88d6ea71af09f5f9a1d2484e0ab321fa1","observation_id":"b922c9c2-82f1-463f-99e9-73961e011f7e","resolution":{"observed_at":"2026-08-04T15:38:32.715318Z","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":"2026-08-04T15:38:32.823883Z","title":null,"venue":null,"work_id":null,"year":1963},"citing_paper":{"arxiv_id":"2509.19710","last_updated":"2026-07-24T23:31:07Z","snapshot_observed_at":"2026-08-08T07:07:04.142549Z","submitted_at":"2025-09-24T02:42:25Z","title":"Probabilistic Symbolic Regression for Equation Discovery via Operator-induced and Regularized Symbolic Forests","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-04T15:38:32.823883Z"},"links":{"citing_paper":"/paper/2509.19710"},"observation_digest":"sha256:c726b4d9c5ee359073998eae3a22587d21e2754828a906cad78dff03a1a29f3b","observation_id":"3a35ea91-e411-466a-99df-83696377402e","resolution":{"observed_at":"2026-08-04T15:38:32.823883Z","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":"2026-08-04T15:38:32.953355Z","title":null,"venue":null,"work_id":null,"year":1970},"citing_paper":{"arxiv_id":"2509.19710","last_updated":"2026-07-24T23:31:07Z","snapshot_observed_at":"2026-08-08T07:07:04.142549Z","submitted_at":"2025-09-24T02:42:25Z","title":"Probabilistic Symbolic Regression for Equation Discovery via Operator-induced and Regularized Symbolic Forests","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-04T15:38:32.953355Z"},"links":{"citing_paper":"/paper/2509.19710"},"observation_digest":"sha256:fe6a4cf0226f0f73f7d10542f6408705ead3f2ea5d426c1cd8d0050f5e6d7d22","observation_id":"1e62a44d-07dd-44aa-8a09-67b54e3362ca","resolution":{"observed_at":"2026-08-04T15:38:32.953355Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1910.08892","last_updated":"2020-01-16T02:11:21Z","snapshot_observed_at":"2026-07-06T08:30:47.148345Z","submitted_at":"2019-10-20T04:28:50Z","title":"Bayesian Symbolic Regression","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1910.08892","snapshot_observed_at":"2026-08-04T15:38:33.145011Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2509.19710","last_updated":"2026-07-24T23:31:07Z","snapshot_observed_at":"2026-08-08T07:07:04.142549Z","submitted_at":"2025-09-24T02:42:25Z","title":"Probabilistic Symbolic Regression for Equation Discovery via Operator-induced and Regularized Symbolic Forests","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-04T15:38:33.145011Z"},"links":{"cited_paper":"/paper/1910.08892","citing_paper":"/paper/2509.19710"},"observation_digest":"sha256:36c77dee02e73386330ae0f8778d004c47ac181ddd7501fc5c7f9169494e6d75","observation_id":"db6c4f34-7ffc-4cd6-a050-ac1a4196af79","resolution":{"observed_at":"2026-08-04T15:38:33.145011Z","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":"2026-08-04T15:38:33.251174Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2509.19710","last_updated":"2026-07-24T23:31:07Z","snapshot_observed_at":"2026-08-08T07:07:04.142549Z","submitted_at":"2025-09-24T02:42:25Z","title":"Probabilistic Symbolic Regression for Equation Discovery via Operator-induced and Regularized Symbolic Forests","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-04T15:38:33.251174Z"},"links":{"citing_paper":"/paper/2509.19710"},"observation_digest":"sha256:720bbd9941938be1477ff9624faa3d4daaa9d6b63e128076a33e3b0242273c66","observation_id":"caa6fc42-867d-4731-9ccf-a14f3c7322dd","resolution":{"observed_at":"2026-08-04T15:38:33.251174Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1805.12495","last_updated":"2021-02-11T20:44:04Z","snapshot_observed_at":"2026-08-09T03:46:57.821130Z","submitted_at":"2018-05-29T22:48:59Z","title":"Invariant Representation of Mathematical Expressions","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1805.12495","snapshot_observed_at":"2026-08-04T15:38:33.354538Z","title":"(2021), ‘Invariant Representation of Mathematical Expressions’, arXiv:1805.12495","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2509.19710","last_updated":"2026-07-24T23:31:07Z","snapshot_observed_at":"2026-08-08T07:07:04.142549Z","submitted_at":"2025-09-24T02:42:25Z","title":"Probabilistic Symbolic Regression for Equation Discovery via Operator-induced and Regularized Symbolic Forests","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-04T15:38:33.354538Z"},"links":{"cited_paper":"/paper/1805.12495","citing_paper":"/paper/2509.19710"},"observation_digest":"sha256:8925706578ba74a4527f0c1cc1546396c3a11cd5539aa87e7f32a9d0d9cfe742","observation_id":"67566189-dd6f-4366-a808-9472fd9bb875","resolution":{"observed_at":"2026-08-04T15:38:33.354538Z","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":"2026-08-04T15:38:33.555792Z","title":"(1994), ‘Markov Chains for Exploring Posterior Distributions’, The Annals of Statistics 22(4)","venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2509.19710","last_updated":"2026-07-24T23:31:07Z","snapshot_observed_at":"2026-08-08T07:07:04.142549Z","submitted_at":"2025-09-24T02:42:25Z","title":"Probabilistic Symbolic Regression for Equation Discovery via Operator-induced and Regularized Symbolic Forests","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-04T15:38:33.555792Z"},"links":{"citing_paper":"/paper/2509.19710"},"observation_digest":"sha256:970d786a8d4d59feeabe3cb869ea33cd563213ac431dc583f32a6244d51d7b3b","observation_id":"aa87a79c-b967-4b08-b377-ea44340705f4","resolution":{"observed_at":"2026-08-04T15:38:33.555792Z","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":"2026-08-04T15:38:33.725942Z","title":"& Tegmark, M","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2509.19710","last_updated":"2026-07-24T23:31:07Z","snapshot_observed_at":"2026-08-08T07:07:04.142549Z","submitted_at":"2025-09-24T02:42:25Z","title":"Probabilistic Symbolic Regression for Equation Discovery via Operator-induced and Regularized Symbolic Forests","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-04T15:38:33.725942Z"},"links":{"citing_paper":"/paper/2509.19710"},"observation_digest":"sha256:2168b534a9ec33f0ca1e5c95bea33a83dd7dc00e731c8612efdc1d49c68c0260","observation_id":"d1b0c508-715d-4ac0-8d8d-d54491d52224","resolution":{"observed_at":"2026-08-04T15:38:33.725942Z","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":"2026-08-04T15:38:33.887466Z","title":"(2018), High-Dimensional Probability: An Introduction with Applications in Data Science , Cambridge University Press","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2509.19710","last_updated":"2026-07-24T23:31:07Z","snapshot_observed_at":"2026-08-08T07:07:04.142549Z","submitted_at":"2025-09-24T02:42:25Z","title":"Probabilistic Symbolic Regression for Equation Discovery via Operator-induced and Regularized Symbolic Forests","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-04T15:38:33.887466Z"},"links":{"citing_paper":"/paper/2509.19710"},"observation_digest":"sha256:14aa771d5cf1a8e32165f1447d57da164b2597f04b39c7ee1e640a131d24239f","observation_id":"49ba5ae2-5b7b-4ef7-824a-6e5510aa29a8","resolution":{"observed_at":"2026-08-04T15:38:33.887466Z","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":"2026-08-04T15:38:34.023675Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.19710","last_updated":"2026-07-24T23:31:07Z","snapshot_observed_at":"2026-08-08T07:07:04.142549Z","submitted_at":"2025-09-24T02:42:25Z","title":"Probabilistic Symbolic Regression for Equation Discovery via Operator-induced and Regularized Symbolic Forests","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-04T15:38:34.023675Z"},"links":{"citing_paper":"/paper/2509.19710"},"observation_digest":"sha256:efaa28de031c47d0aa15288c5a68fe0554a0ec6707dac33ca1918e80f64aa072","observation_id":"d7e5e632-8e1a-4a2c-9a41-dc4f14257b21","resolution":{"observed_at":"2026-08-04T15:38:34.023675Z","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":"2026-08-04T15:38:34.145477Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.19710","last_updated":"2026-07-24T23:31:07Z","snapshot_observed_at":"2026-08-08T07:07:04.142549Z","submitted_at":"2025-09-24T02:42:25Z","title":"Probabilistic Symbolic Regression for Equation Discovery via Operator-induced and Regularized Symbolic Forests","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-04T15:38:34.145477Z"},"links":{"citing_paper":"/paper/2509.19710"},"observation_digest":"sha256:79a5884a75197e2fffa4d477f58bc260f63c8b39f0eeafe8343ce7206b39de2f","observation_id":"bdf8d71b-146c-4f2e-b7bf-a05ccf20d6f5","resolution":{"observed_at":"2026-08-04T15:38:34.145477Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2509.19710","last_updated":"2026-07-24T23:31:07Z","latest_version":2,"primary_category":"stat.ME","snapshot_observed_at":"2026-08-08T07:07:04.142549Z","submitted_at":"2025-09-24T02:42:25Z","title":"Probabilistic Symbolic Regression for Equation Discovery via Operator-induced and Regularized Symbolic Forests"},"reference_resolution":{"displayed":15,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":15,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":15},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 15 of 15 outbound references and 1 inbound Pith citation observation for arXiv:2509.19710."}