{"as_of":"2026-08-22T01:07:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:81fce8b31a6002dccdd4fe60fdb8c73ee980418f32ee5e564ca9941bd55d7b82","coverage":[{"denominator":0,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":10,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":10,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-21T06:32:19.484+00:00","state":"measured"},{"denominator":10,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":10,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-16T06:06:57.442994Z","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":"2026-07-03T04:27:36.920358Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2012.04728","last_updated":"2021-03-29T16:02:08Z","snapshot_observed_at":"2026-08-21T17:57:45.803363Z","submitted_at":"2020-12-08T20:33:30Z","title":"Neural Mechanics: Symmetry and Broken Conservation Laws in Deep Learning Dynamics","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2012.04728","snapshot_observed_at":"2026-08-16T06:06:57.442994Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2504.19274","last_updated":"2025-05-26T14:20:07Z","snapshot_observed_at":"2026-08-20T03:15:43.661490Z","submitted_at":"2025-04-27T15:14:09Z","title":"TeleSparse: Practical Privacy-Preserving Verification of Deep Neural Networks","version":2},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-16T06:06:57.442994Z"},"links":{"cited_paper":"/paper/2012.04728","citing_paper":"/paper/2504.19274"},"observation_digest":"sha256:ab041da60d603242dc04c710b9accac03a7c680ba0b7dfadaf1bd1a289bf2016","observation_id":"65df48c7-5d0f-4e6a-a05b-84f11d2b151a","resolution":{"observed_at":"2026-08-16T06:06:57.442994Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2012.04728","last_updated":"2021-03-29T16:02:08Z","snapshot_observed_at":"2026-08-21T17:57:45.803363Z","submitted_at":"2020-12-08T20:33:30Z","title":"Neural Mechanics: Symmetry and Broken Conservation Laws in Deep Learning Dynamics","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2012.04728","snapshot_observed_at":"2026-08-02T21:52:35.416538Z","title":"Kunin, J","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2602.18948","last_updated":"2026-07-21T16:06:23Z","snapshot_observed_at":"2026-08-20T05:30:21.786293Z","submitted_at":"2026-02-21T19:43:17Z","title":"Toward Manifest Relationality in Transformers via Symmetry Reduction","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-02T21:52:35.416538Z"},"links":{"cited_paper":"/paper/2012.04728","citing_paper":"/paper/2602.18948"},"observation_digest":"sha256:afdf3d8c5723ee9bf783c732d704a701a3db74a7019459f36bc6af43bfc791f0","observation_id":"93e00a5b-96c1-4402-a5f7-04cb1c2cb686","resolution":{"observed_at":"2026-08-02T21:52:35.416538Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2012.04728","last_updated":"2021-03-29T16:02:08Z","snapshot_observed_at":"2026-08-21T17:57:45.803363Z","submitted_at":"2020-12-08T20:33:30Z","title":"Neural Mechanics: Symmetry and Broken Conservation Laws in Deep Learning Dynamics","version":2},"cited_work":{"arxiv_id":"2012.04728","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2012.04728","snapshot_observed_at":"2026-07-03T04:27:36.920358Z","title":"Kunin, J","venue":null,"work_id":"66afffca-3609-4b3c-8e8a-6c37a64a87f1","year":2012},"citing_paper":{"arxiv_id":"2605.01288","last_updated":"2026-06-23T15:11:40Z","snapshot_observed_at":"2026-08-17T00:03:03.220431Z","submitted_at":"2026-05-02T06:55:15Z","title":"A Theory of Saddle Escape in Deep Nonlinear Networks","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-05-09T14:54:47.763122Z"},"links":{"cited_paper":"/paper/2012.04728","citing_paper":"/paper/2605.01288"},"observation_digest":"sha256:6f58a15852f9866c4b663e9e80c7b378cb59820cb5fc581fe4815e838985925e","observation_id":"17ce661d-991a-49f7-bbf9-e0aeb971c053","resolution":{"observed_at":"2026-05-11T16:51:05.717524Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2012.04728","last_updated":"2021-03-29T16:02:08Z","snapshot_observed_at":"2026-08-21T17:57:45.803363Z","submitted_at":"2020-12-08T20:33:30Z","title":"Neural Mechanics: Symmetry and Broken Conservation Laws in Deep Learning Dynamics","version":2},"cited_work":{"arxiv_id":"2012.04728","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2012.04728","snapshot_observed_at":"2026-07-03T04:27:36.920358Z","title":"Kunin, J","venue":null,"work_id":"66afffca-3609-4b3c-8e8a-6c37a64a87f1","year":2012},"citing_paper":{"arxiv_id":"2605.01288","last_updated":"2026-06-23T15:11:40Z","snapshot_observed_at":"2026-08-17T00:03:03.220431Z","submitted_at":"2026-05-02T06:55:15Z","title":"A Theory of Saddle Escape in Deep Nonlinear Networks","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-05-11T02:22:38.751375Z"},"links":{"cited_paper":"/paper/2012.04728","citing_paper":"/paper/2605.01288"},"observation_digest":"sha256:7415cf9f64d197f5ba06a71085f300e0caa8b227aef87af1471b12254af81a5e","observation_id":"b12013a8-6950-4565-aaeb-ee34d7e703c7","resolution":{"observed_at":"2026-05-11T02:25:54.510205Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2012.04728","last_updated":"2021-03-29T16:02:08Z","snapshot_observed_at":"2026-08-21T17:57:45.803363Z","submitted_at":"2020-12-08T20:33:30Z","title":"Neural Mechanics: Symmetry and Broken Conservation Laws in Deep Learning Dynamics","version":2},"cited_work":{"arxiv_id":"2012.04728","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2012.04728","snapshot_observed_at":"2026-07-03T04:27:36.920358Z","title":"Kunin, J","venue":null,"work_id":"66afffca-3609-4b3c-8e8a-6c37a64a87f1","year":2012},"citing_paper":{"arxiv_id":"2605.01288","last_updated":"2026-06-23T15:11:40Z","snapshot_observed_at":"2026-08-17T00:03:03.220431Z","submitted_at":"2026-05-02T06:55:15Z","title":"A Theory of Saddle Escape in Deep Nonlinear Networks","version":3},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-07-01T00:37:16.364388Z"},"links":{"cited_paper":"/paper/2012.04728","citing_paper":"/paper/2605.01288"},"observation_digest":"sha256:f2428ad6c44050aa411c7f5a3098c26fe13c35c61899a200072dc6cedbe116c9","observation_id":"4c8d2ccd-53fa-4f53-8129-ac2a3b3831a8","resolution":{"observed_at":"2026-07-01T00:45:12.007531Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2012.04728","last_updated":"2021-03-29T16:02:08Z","snapshot_observed_at":"2026-08-21T17:57:45.803363Z","submitted_at":"2020-12-08T20:33:30Z","title":"Neural Mechanics: Symmetry and Broken Conservation Laws in Deep Learning Dynamics","version":2},"cited_work":{"arxiv_id":"2012.04728","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2012.04728","snapshot_observed_at":"2026-07-03T04:27:36.920358Z","title":"Kunin, J","venue":null,"work_id":"66afffca-3609-4b3c-8e8a-6c37a64a87f1","year":2012},"citing_paper":{"arxiv_id":"2605.04115","last_updated":"2026-05-05T07:41:15Z","snapshot_observed_at":"2026-08-15T04:44:40.526328Z","submitted_at":"2026-05-05T07:41:15Z","title":"Learning reveals invisible structure in low-rank RNNs","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-05-08T18:38:44.820013Z"},"links":{"cited_paper":"/paper/2012.04728","citing_paper":"/paper/2605.04115"},"observation_digest":"sha256:d34fa783b9e8c51450449cb547113a013e01353d2ab0223ab820fe7723bc7aff","observation_id":"806b4588-7239-43d2-b5b3-0b18ee09f4e8","resolution":{"observed_at":"2026-05-09T06:15:39.625604Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2012.04728","last_updated":"2021-03-29T16:02:08Z","snapshot_observed_at":"2026-08-21T17:57:45.803363Z","submitted_at":"2020-12-08T20:33:30Z","title":"Neural Mechanics: Symmetry and Broken Conservation Laws in Deep Learning Dynamics","version":2},"cited_work":{"arxiv_id":"2012.04728","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2012.04728","snapshot_observed_at":"2026-07-03T04:27:36.920358Z","title":"Kunin, J","venue":null,"work_id":"66afffca-3609-4b3c-8e8a-6c37a64a87f1","year":2012},"citing_paper":{"arxiv_id":"2605.20189","last_updated":"2026-03-23T07:18:02Z","snapshot_observed_at":"2026-08-16T16:24:07.331889Z","submitted_at":"2026-03-23T07:18:02Z","title":"SOLAR: A Self-Optimizing Open-Ended Autonomous Agent for Lifelong Learning and Continual Adaptation","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-05-21T11:21:30.867480Z"},"links":{"cited_paper":"/paper/2012.04728","citing_paper":"/paper/2605.20189"},"observation_digest":"sha256:9b94e851aab091db4a2ddcd4cb6fbb432932de8259565e518a65d4576c0a01d0","observation_id":"15937e6f-3936-4566-bfb7-14e57a82d55f","resolution":{"observed_at":"2026-05-21T11:24:08.626851Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2012.04728","last_updated":"2021-03-29T16:02:08Z","snapshot_observed_at":"2026-08-21T17:57:45.803363Z","submitted_at":"2020-12-08T20:33:30Z","title":"Neural Mechanics: Symmetry and Broken Conservation Laws in Deep Learning Dynamics","version":2},"cited_work":{"arxiv_id":"2012.04728","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2012.04728","snapshot_observed_at":"2026-07-03T04:27:36.920358Z","title":"Kunin, J","venue":null,"work_id":"66afffca-3609-4b3c-8e8a-6c37a64a87f1","year":2012},"citing_paper":{"arxiv_id":"2606.05957","last_updated":"2026-06-04T09:54:08Z","snapshot_observed_at":"2026-08-14T05:17:37.167621Z","submitted_at":"2026-06-04T09:54:08Z","title":"Dead Directions: Geometric Singular Learning","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-06-28T03:20:09.365073Z"},"links":{"cited_paper":"/paper/2012.04728","citing_paper":"/paper/2606.05957"},"observation_digest":"sha256:3fc2f65d732544cef20d782742056f3cc3627956bac7bb0aa400f898999a031a","observation_id":"d312d5a4-ceb6-4458-91dd-0aed16155d1c","resolution":{"observed_at":"2026-07-02T11:36:55.214326Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2012.04728","last_updated":"2021-03-29T16:02:08Z","snapshot_observed_at":"2026-08-21T17:57:45.803363Z","submitted_at":"2020-12-08T20:33:30Z","title":"Neural Mechanics: Symmetry and Broken Conservation Laws in Deep Learning Dynamics","version":2},"cited_work":{"arxiv_id":"2012.04728","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2012.04728","snapshot_observed_at":"2026-07-03T04:27:36.920358Z","title":"Kunin, J","venue":null,"work_id":"66afffca-3609-4b3c-8e8a-6c37a64a87f1","year":2012},"citing_paper":{"arxiv_id":"2606.07495","last_updated":"2026-06-05T17:49:19Z","snapshot_observed_at":"2026-08-12T13:13:58.855746Z","submitted_at":"2026-06-05T17:49:19Z","title":"Second-Order Path Kernel Interpolation Formulas in Machine Learning","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-06-27T22:20:15.074286Z"},"links":{"cited_paper":"/paper/2012.04728","citing_paper":"/paper/2606.07495"},"observation_digest":"sha256:200bb083a1514689e7667e2566b1ff4513a3853b0b540df07d052b1087d9326c","observation_id":"fe9ba437-3ea4-4217-9cdb-3cee0a70641f","resolution":{"observed_at":"2026-07-02T16:47:10.358792Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2012.04728","last_updated":"2021-03-29T16:02:08Z","snapshot_observed_at":"2026-08-21T17:57:45.803363Z","submitted_at":"2020-12-08T20:33:30Z","title":"Neural Mechanics: Symmetry and Broken Conservation Laws in Deep Learning Dynamics","version":2},"cited_work":{"arxiv_id":"2012.04728","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2012.04728","snapshot_observed_at":"2026-07-03T04:27:36.920358Z","title":"Kunin, J","venue":null,"work_id":"66afffca-3609-4b3c-8e8a-6c37a64a87f1","year":2012},"citing_paper":{"arxiv_id":"2606.10913","last_updated":"2026-06-09T14:23:34Z","snapshot_observed_at":"2026-07-06T23:50:01.838569Z","submitted_at":"2026-06-09T14:23:34Z","title":"Conservation Laws from Data Symmetry in Neural Networks","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-06-27T13:53:48.656780Z"},"links":{"cited_paper":"/paper/2012.04728","citing_paper":"/paper/2606.10913"},"observation_digest":"sha256:3df812d4c2d989e4264bdc5b06efe774db7b1db61da12894c82ef4688ac7674b","observation_id":"984c6536-f890-4d2c-8a13-2f5012ab0002","resolution":{"observed_at":"2026-07-03T04:27:36.921807Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2012.04728/citation-record","integrity":"/paper/2012.04728/integrity","json":"/paper/2012.04728/citation-record.json","paper":"/paper/2012.04728"},"outbound":[],"paper":{"arxiv_id":"2012.04728","last_updated":"2021-03-29T16:02:08Z","latest_version":2,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-21T17:57:45.803363Z","submitted_at":"2020-12-08T20:33:30Z","title":"Neural Mechanics: Symmetry and Broken Conservation Laws in Deep Learning Dynamics"},"reference_resolution":{"displayed":0,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":0},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"thesis":"As of 22 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 10 inbound Pith citation observations for arXiv:2012.04728."}