{"as_of":"2026-08-07T15:37:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:1fb4bdcfcf34adf2664e6e2574d50cbc43919c0672247ed7615ffd612cb40571","coverage":[{"denominator":30,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":30,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-14T06:57:31.514910Z","state":"measured"},{"denominator":30,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":30,"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/2607.11116/citation-record","integrity":"/paper/2607.11116/integrity","json":"/paper/2607.11116/citation-record.json","paper":"/paper/2607.11116"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:57:31.514910Z","title":"Zico Kolter, and Vladlen Koltun","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.11116","last_updated":"2026-07-13T05:45:35Z","snapshot_observed_at":"2026-07-16T23:19:12.573935Z","submitted_at":"2026-07-13T05:45:35Z","title":"The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-07-14T06:57:31.514910Z"},"links":{"citing_paper":"/paper/2607.11116"},"observation_digest":"sha256:c81b505b25afafc52a360ab30ae7fd9e7b40709378ebb20e3c39ec76b44551a9","observation_id":"00f91019-3fde-420c-8e90-18d79f10cfd2","resolution":{"observed_at":"2026-07-14T06:57:31.514910Z","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":"2026-07-14T06:57:31.514910Z","title":"Uni- versal transformers","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.11116","last_updated":"2026-07-13T05:45:35Z","snapshot_observed_at":"2026-07-16T23:19:12.573935Z","submitted_at":"2026-07-13T05:45:35Z","title":"The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-07-14T06:57:31.514910Z"},"links":{"citing_paper":"/paper/2607.11116"},"observation_digest":"sha256:fb35718905394060a06d44cd4c07067129c88827543fc5e4ca124e628f9e17bc","observation_id":"1fcd05c0-a29c-46cf-9d89-3182ed94a82d","resolution":{"observed_at":"2026-07-14T06:57:31.514910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2502.05171","last_updated":"2025-02-17T17:14:04Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-02-07T18:55:02Z","title":"Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.05171","snapshot_observed_at":"2026-07-14T06:57:31.514910Z","title":"Scaling up test-time compute with latent reasoning: A recurrent depth approach.arXiv preprint arXiv:2502.05171, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.11116","last_updated":"2026-07-13T05:45:35Z","snapshot_observed_at":"2026-07-16T23:19:12.573935Z","submitted_at":"2026-07-13T05:45:35Z","title":"The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-07-14T06:57:31.514910Z"},"links":{"cited_paper":"/paper/2502.05171","citing_paper":"/paper/2607.11116"},"observation_digest":"sha256:d74ac4a2d78ddd9ccbbe9ed870a17e6ee57bf7029194573d3424fa2e7533a4e9","observation_id":"9de43db6-8111-4b94-92ee-fc4a05504d2a","resolution":{"observed_at":"2026-07-14T06:57:31.514910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1603.08983","last_updated":"2017-02-21T16:21:21Z","snapshot_observed_at":"2026-08-04T14:24:45.814840Z","submitted_at":"2016-03-29T22:09:00Z","title":"Adaptive Computation Time for Recurrent Neural Networks","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1603.08983","snapshot_observed_at":"2026-07-14T06:57:31.514910Z","title":"Adaptive computation time for recurrent neural networks.arXiv preprint arXiv:1603.08983, 2016","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.11116","last_updated":"2026-07-13T05:45:35Z","snapshot_observed_at":"2026-07-16T23:19:12.573935Z","submitted_at":"2026-07-13T05:45:35Z","title":"The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-07-14T06:57:31.514910Z"},"links":{"cited_paper":"/paper/1603.08983","citing_paper":"/paper/2607.11116"},"observation_digest":"sha256:fd4a9e75fcd7634841475dfdad3e946a30253bc2ea608a356a83cc0daf6bf9e8","observation_id":"e136c14d-ccb3-49c0-a6cd-1d8aab3e884d","resolution":{"observed_at":"2026-07-14T06:57:31.514910Z","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":"2026-07-14T06:57:31.514910Z","title":"Hamiltonian neural networks","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.11116","last_updated":"2026-07-13T05:45:35Z","snapshot_observed_at":"2026-07-16T23:19:12.573935Z","submitted_at":"2026-07-13T05:45:35Z","title":"The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-07-14T06:57:31.514910Z"},"links":{"citing_paper":"/paper/2607.11116"},"observation_digest":"sha256:f7200fefa6e7748b84ee753a628d02bcab7dd18995d493fbf4f5c8d4eeeb2a18","observation_id":"8710e4c9-399b-42c4-a135-8d7e8d79b8a6","resolution":{"observed_at":"2026-07-14T06:57:31.514910Z","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":"2026-07-14T06:57:31.514910Z","title":"SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems.Neural Networks, 132:166–179, 2020","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.11116","last_updated":"2026-07-13T05:45:35Z","snapshot_observed_at":"2026-07-16T23:19:12.573935Z","submitted_at":"2026-07-13T05:45:35Z","title":"The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-07-14T06:57:31.514910Z"},"links":{"citing_paper":"/paper/2607.11116"},"observation_digest":"sha256:3f4abae5edff66e1a6e49bf9a234f101cf42190ee5c2807f6dba6fd82554ce28","observation_id":"15f7d86b-346c-440a-8657-93b614160ca3","resolution":{"observed_at":"2026-07-14T06:57:31.514910Z","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":"2026-07-14T06:57:31.514910Z","title":"Desai, Marios Mattheakis, David Sondak, Pavlos Protopapas, and Stephen J","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.11116","last_updated":"2026-07-13T05:45:35Z","snapshot_observed_at":"2026-07-16T23:19:12.573935Z","submitted_at":"2026-07-13T05:45:35Z","title":"The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-07-14T06:57:31.514910Z"},"links":{"citing_paper":"/paper/2607.11116"},"observation_digest":"sha256:299f909e4c26753c809f73f8a6a5900ab34e474449b36480459b8a212e8e6d8d","observation_id":"08417bce-2d34-44cf-a764-dd53d121cc60","resolution":{"observed_at":"2026-07-14T06:57:31.514910Z","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":"2026-07-14T06:57:31.514910Z","title":"Zico Kolter","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.11116","last_updated":"2026-07-13T05:45:35Z","snapshot_observed_at":"2026-07-16T23:19:12.573935Z","submitted_at":"2026-07-13T05:45:35Z","title":"The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-07-14T06:57:31.514910Z"},"links":{"citing_paper":"/paper/2607.11116"},"observation_digest":"sha256:c5767034880bbbcd6be6ba3af138cf1e66eef76f0f33df0e6b23a163bd013d7b","observation_id":"c1839b3c-8b56-439c-a460-b102d9edfcfb","resolution":{"observed_at":"2026-07-14T06:57:31.514910Z","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":"2026-07-14T06:57:31.514910Z","title":"Implicit deep learning.SIAM Journal on Mathematics of Data Science, 3(3):930–958, 2021","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.11116","last_updated":"2026-07-13T05:45:35Z","snapshot_observed_at":"2026-07-16T23:19:12.573935Z","submitted_at":"2026-07-13T05:45:35Z","title":"The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-07-14T06:57:31.514910Z"},"links":{"citing_paper":"/paper/2607.11116"},"observation_digest":"sha256:6e0eb53feaab1539d138278efcd8727c6737454facf7fb6d1eb79464faec2a15","observation_id":"a0a750c5-918b-4e2e-b29e-4cfbea9f26ce","resolution":{"observed_at":"2026-07-14T06:57:31.514910Z","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":"2026-07-14T06:57:31.514910Z","title":"Zico Kolter","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.11116","last_updated":"2026-07-13T05:45:35Z","snapshot_observed_at":"2026-07-16T23:19:12.573935Z","submitted_at":"2026-07-13T05:45:35Z","title":"The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-07-14T06:57:31.514910Z"},"links":{"citing_paper":"/paper/2607.11116"},"observation_digest":"sha256:e68cea765c1ddf6a75b74d80964316e928f3e1a0e870b6d7205359173cfc3b26","observation_id":"348ddbf7-94a7-4b59-a437-68d9262818a7","resolution":{"observed_at":"2026-07-14T06:57:31.514910Z","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":"2026-07-14T06:57:31.514910Z","title":"Anderson","venue":null,"work_id":null,"year":1965},"citing_paper":{"arxiv_id":"2607.11116","last_updated":"2026-07-13T05:45:35Z","snapshot_observed_at":"2026-07-16T23:19:12.573935Z","submitted_at":"2026-07-13T05:45:35Z","title":"The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-07-14T06:57:31.514910Z"},"links":{"citing_paper":"/paper/2607.11116"},"observation_digest":"sha256:f6082d0739a6d1c4cd7a1032a4638c375e677f06936e78fabc098e578ca0e753","observation_id":"75c41a4d-7e48-4979-bd4f-5e3a136a6459","resolution":{"observed_at":"2026-07-14T06:57:31.514910Z","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":"2026-07-14T06:57:31.514910Z","title":"Zico Kolter","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.11116","last_updated":"2026-07-13T05:45:35Z","snapshot_observed_at":"2026-07-16T23:19:12.573935Z","submitted_at":"2026-07-13T05:45:35Z","title":"The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-07-14T06:57:31.514910Z"},"links":{"citing_paper":"/paper/2607.11116"},"observation_digest":"sha256:fa95ff8d40a2f59a04967bdf07049139de12163eabc4a3a048ec20a2376829ab","observation_id":"707c4ab6-add1-4c9f-8bfa-bceb9f533964","resolution":{"observed_at":"2026-07-14T06:57:31.514910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2103.12803","last_updated":"2021-12-24T17:56:36Z","snapshot_observed_at":"2026-08-03T18:04:44.240946Z","submitted_at":"2021-03-23T19:20:33Z","title":"JFB: Jacobian-Free Backpropagation for Implicit Networks","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2103.12803","snapshot_observed_at":"2026-07-14T06:57:31.514910Z","title":"JFB: Jacobian-free backpropagation for implicit networks","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.11116","last_updated":"2026-07-13T05:45:35Z","snapshot_observed_at":"2026-07-16T23:19:12.573935Z","submitted_at":"2026-07-13T05:45:35Z","title":"The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-07-14T06:57:31.514910Z"},"links":{"cited_paper":"/paper/2103.12803","citing_paper":"/paper/2607.11116"},"observation_digest":"sha256:6d5971727267f52cb7d228be6955063b95500a7f7c9ada148f4fd8396e2d3e32","observation_id":"c04824cf-8bbb-4896-9656-0fda280b6ae1","resolution":{"observed_at":"2026-07-14T06:57:31.514910Z","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":"2026-07-14T06:57:31.514910Z","title":"Zico Kolter, and Roger B","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.11116","last_updated":"2026-07-13T05:45:35Z","snapshot_observed_at":"2026-07-16T23:19:12.573935Z","submitted_at":"2026-07-13T05:45:35Z","title":"The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-07-14T06:57:31.514910Z"},"links":{"citing_paper":"/paper/2607.11116"},"observation_digest":"sha256:1a3aba2a86125e01ca505764cb988c871890e8a8efd7de03270fde5b9bc43ea2","observation_id":"dd738453-b16d-405c-bedd-46145e7d5670","resolution":{"observed_at":"2026-07-14T06:57:31.514910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2003.04630","last_updated":"2020-07-30T05:22:58Z","snapshot_observed_at":"2026-08-04T10:05:44.957260Z","submitted_at":"2020-03-10T10:55:25Z","title":"Lagrangian Neural Networks","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2003.04630","snapshot_observed_at":"2026-07-14T06:57:31.514910Z","title":"Lagrangian neural networks.arXiv preprint arXiv:2003.04630, 2020","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2607.11116","last_updated":"2026-07-13T05:45:35Z","snapshot_observed_at":"2026-07-16T23:19:12.573935Z","submitted_at":"2026-07-13T05:45:35Z","title":"The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-07-14T06:57:31.514910Z"},"links":{"cited_paper":"/paper/2003.04630","citing_paper":"/paper/2607.11116"},"observation_digest":"sha256:a2953775880c3cb59c06d6f51e114059387ac14407246aec1ac4b6a2200e952a","observation_id":"bb3c5dfd-5fd9-4cc1-a13f-ec17984e2105","resolution":{"observed_at":"2026-07-14T06:57:31.514910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1806.07366","last_updated":"2019-12-14T02:01:18Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2018-06-19T17:50:12Z","title":"Neural Ordinary Differential Equations","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1806.07366","snapshot_observed_at":"2026-07-14T06:57:31.514910Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.11116","last_updated":"2026-07-13T05:45:35Z","snapshot_observed_at":"2026-07-16T23:19:12.573935Z","submitted_at":"2026-07-13T05:45:35Z","title":"The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-07-14T06:57:31.514910Z"},"links":{"cited_paper":"/paper/1806.07366","citing_paper":"/paper/2607.11116"},"observation_digest":"sha256:e276027f2a9bc5847c4ae8edda1ad8551d3c64be29a26e4bed4aa4f75b9a8d67","observation_id":"b5e372b2-2d18-4d05-9d92-b8ddd71542f1","resolution":{"observed_at":"2026-07-14T06:57:31.514910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2107.05407","last_updated":"2021-09-02T08:48:41Z","snapshot_observed_at":"2026-07-06T11:28:17.810519Z","submitted_at":"2021-07-12T13:24:03Z","title":"PonderNet: Learning to Ponder","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2107.05407","snapshot_observed_at":"2026-07-14T06:57:31.514910Z","title":"PonderNet: Learning to ponder.arXiv preprint arXiv:2107.05407, 2021","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.11116","last_updated":"2026-07-13T05:45:35Z","snapshot_observed_at":"2026-07-16T23:19:12.573935Z","submitted_at":"2026-07-13T05:45:35Z","title":"The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-07-14T06:57:31.514910Z"},"links":{"cited_paper":"/paper/2107.05407","citing_paper":"/paper/2607.11116"},"observation_digest":"sha256:cdd27afc01572fe2431c5d13b99d9451474cc0565c0107da84a8f761abd8f846","observation_id":"b6f7a5b9-75b6-4985-8d5c-754b090c43a7","resolution":{"observed_at":"2026-07-14T06:57:31.514910Z","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":"2026-07-14T06:57:31.514910Z","title":"Can you learn an algorithm? Generalizing from easy to hard problems with recurrent networks","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.11116","last_updated":"2026-07-13T05:45:35Z","snapshot_observed_at":"2026-07-16T23:19:12.573935Z","submitted_at":"2026-07-13T05:45:35Z","title":"The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-07-14T06:57:31.514910Z"},"links":{"citing_paper":"/paper/2607.11116"},"observation_digest":"sha256:a7cbc676ad65aee80b165759424aaf4a8951a49c42f14c5cfbbc49d15856a8a0","observation_id":"5d2266d9-5771-4583-b4b3-fe2f90dba5e7","resolution":{"observed_at":"2026-07-14T06:57:31.514910Z","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":"2026-07-14T06:57:31.514910Z","title":"End-to-end algorithm synthesis with recurrent networks: Extrapolation without overthinking","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.11116","last_updated":"2026-07-13T05:45:35Z","snapshot_observed_at":"2026-07-16T23:19:12.573935Z","submitted_at":"2026-07-13T05:45:35Z","title":"The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-07-14T06:57:31.514910Z"},"links":{"citing_paper":"/paper/2607.11116"},"observation_digest":"sha256:804cd51d672e10dfd686d2efafe2ad9bea3074a4df372700eca201f057d744a9","observation_id":"ee59ea79-b184-4f2b-b39d-53b9d8437e59","resolution":{"observed_at":"2026-07-14T06:57:31.514910Z","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":"2026-07-14T06:57:31.514910Z","title":"Nowak, and Dimitris Papailiopoulos","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.11116","last_updated":"2026-07-13T05:45:35Z","snapshot_observed_at":"2026-07-16T23:19:12.573935Z","submitted_at":"2026-07-13T05:45:35Z","title":"The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-07-14T06:57:31.514910Z"},"links":{"citing_paper":"/paper/2607.11116"},"observation_digest":"sha256:8c5078a635a0b46ad2197bb369adb14ea7d9ba6212259f443b0f0432c05673f9","observation_id":"89b7a40e-9868-483b-8447-9b303b98d6a2","resolution":{"observed_at":"2026-07-14T06:57:31.514910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2506.21734","last_updated":"2025-08-04T08:45:08Z","snapshot_observed_at":"2026-08-06T13:55:12.607273Z","submitted_at":"2025-06-26T19:39:54Z","title":"Hierarchical Reasoning Model","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.21734","snapshot_observed_at":"2026-07-14T06:57:31.514910Z","title":"Hierarchical reasoning model.arXiv preprint arXiv:2506.21734, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.11116","last_updated":"2026-07-13T05:45:35Z","snapshot_observed_at":"2026-07-16T23:19:12.573935Z","submitted_at":"2026-07-13T05:45:35Z","title":"The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-07-14T06:57:31.514910Z"},"links":{"cited_paper":"/paper/2506.21734","citing_paper":"/paper/2607.11116"},"observation_digest":"sha256:7f2bd9469ca6ce6cd8f5c1f3b81cee4662aa4221c9cb6f746e17b7577ba1c5c3","observation_id":"a133d40c-c127-42da-973b-c08bf391a49b","resolution":{"observed_at":"2026-07-14T06:57:31.514910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2510.04871","last_updated":"2025-10-06T14:58:08Z","snapshot_observed_at":"2026-07-06T22:31:49.574184Z","submitted_at":"2025-10-06T14:58:08Z","title":"Less is More: Recursive Reasoning with Tiny Networks","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2510.04871","snapshot_observed_at":"2026-07-14T06:57:31.514910Z","title":"Less is more: Recursive reasoning with tiny networks.arXiv preprint arXiv:2510.04871, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.11116","last_updated":"2026-07-13T05:45:35Z","snapshot_observed_at":"2026-07-16T23:19:12.573935Z","submitted_at":"2026-07-13T05:45:35Z","title":"The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-07-14T06:57:31.514910Z"},"links":{"cited_paper":"/paper/2510.04871","citing_paper":"/paper/2607.11116"},"observation_digest":"sha256:dc02393b051140789c533b8398485e9d9b1c87e07dec7b8265da1a9ce166898f","observation_id":"c101359a-fc11-4a1e-9025-ba73f4314cbc","resolution":{"observed_at":"2026-07-14T06:57:31.514910Z","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":"2026-07-14T06:57:31.514910Z","title":"The CLRS algorithmic reasoning benchmark","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.11116","last_updated":"2026-07-13T05:45:35Z","snapshot_observed_at":"2026-07-16T23:19:12.573935Z","submitted_at":"2026-07-13T05:45:35Z","title":"The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-07-14T06:57:31.514910Z"},"links":{"citing_paper":"/paper/2607.11116"},"observation_digest":"sha256:2c3c806b24b685b1f3d87bafc412577ca6fcf15fb07be977eaeb74c90bb3e121","observation_id":"abc6c49d-e214-40f7-b5d0-0319baedfc72","resolution":{"observed_at":"2026-07-14T06:57:31.514910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1610.01644","last_updated":"2018-11-22T23:40:00Z","snapshot_observed_at":"2026-07-06T05:13:30.860932Z","submitted_at":"2016-10-05T20:59:01Z","title":"Understanding intermediate layers using linear classifier probes","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1610.01644","snapshot_observed_at":"2026-07-14T06:57:31.514910Z","title":"Understanding intermediate layers using linear classifier probes.arXiv preprint arXiv:1610.01644, 2016","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.11116","last_updated":"2026-07-13T05:45:35Z","snapshot_observed_at":"2026-07-16T23:19:12.573935Z","submitted_at":"2026-07-13T05:45:35Z","title":"The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-07-14T06:57:31.514910Z"},"links":{"cited_paper":"/paper/1610.01644","citing_paper":"/paper/2607.11116"},"observation_digest":"sha256:3a3340e7b9a05f1fa8341ed9e6d4d73ab628a27b4a585c1fc6815c4707bc804b","observation_id":"676e7afb-a257-4998-b62e-682040756b6a","resolution":{"observed_at":"2026-07-14T06:57:31.514910Z","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":"2026-07-14T06:57:31.514910Z","title":"Designing and interpreting probes with control tasks","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.11116","last_updated":"2026-07-13T05:45:35Z","snapshot_observed_at":"2026-07-16T23:19:12.573935Z","submitted_at":"2026-07-13T05:45:35Z","title":"The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-07-14T06:57:31.514910Z"},"links":{"citing_paper":"/paper/2607.11116"},"observation_digest":"sha256:858b312ab410338415127fb81aefd4b985348bb1384651ed25b6d26da14c7bb5","observation_id":"c7fd43e2-1b6f-46ce-b49d-5bb6736a0182","resolution":{"observed_at":"2026-07-14T06:57:31.514910Z","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":"2026-07-14T06:57:31.514910Z","title":"Gradient starvation: A learning proclivity in neural networks","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.11116","last_updated":"2026-07-13T05:45:35Z","snapshot_observed_at":"2026-07-16T23:19:12.573935Z","submitted_at":"2026-07-13T05:45:35Z","title":"The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-07-14T06:57:31.514910Z"},"links":{"citing_paper":"/paper/2607.11116"},"observation_digest":"sha256:463e68c425255db4beba847426baeb57d863001bc5ba76b7417b1d093826ac7d","observation_id":"1b1fb8d4-6aa2-445c-8604-37bc93a9368a","resolution":{"observed_at":"2026-07-14T06:57:31.514910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2004.07780","last_updated":"2023-11-21T15:22:43Z","snapshot_observed_at":"2026-07-06T09:12:52.864215Z","submitted_at":"2020-04-16T17:18:49Z","title":"Shortcut Learning in Deep Neural Networks","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2004.07780","snapshot_observed_at":"2026-07-14T06:57:31.514910Z","title":"Wichmann","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.11116","last_updated":"2026-07-13T05:45:35Z","snapshot_observed_at":"2026-07-16T23:19:12.573935Z","submitted_at":"2026-07-13T05:45:35Z","title":"The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-07-14T06:57:31.514910Z"},"links":{"cited_paper":"/paper/2004.07780","citing_paper":"/paper/2607.11116"},"observation_digest":"sha256:f846f0d7e2e236693d6cc4c9d88992241c9d5614a6eae28eeaffe275cd6c0ce0","observation_id":"20bd1a1f-ebd7-4e6e-897f-506204470a16","resolution":{"observed_at":"2026-07-14T06:57:31.514910Z","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":"2026-07-14T06:57:31.514910Z","title":"ProofWriter: Generating implications, proofs, and abductive statements over natural language","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.11116","last_updated":"2026-07-13T05:45:35Z","snapshot_observed_at":"2026-07-16T23:19:12.573935Z","submitted_at":"2026-07-13T05:45:35Z","title":"The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-07-14T06:57:31.514910Z"},"links":{"citing_paper":"/paper/2607.11116"},"observation_digest":"sha256:5e3879ac3cb016a034d5db5d1f0b3837bf20fbea11c924c99fa8495e2657a047","observation_id":"0603fc2b-213a-435c-ae18-97bd74c426f4","resolution":{"observed_at":"2026-07-14T06:57:31.514910Z","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":"2026-07-14T06:57:31.514910Z","title":"DeBERTaV3: Improving DeBERTa using ELECTRA-style pre-training with gradient-disentangled embedding sharing","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.11116","last_updated":"2026-07-13T05:45:35Z","snapshot_observed_at":"2026-07-16T23:19:12.573935Z","submitted_at":"2026-07-13T05:45:35Z","title":"The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-07-14T06:57:31.514910Z"},"links":{"citing_paper":"/paper/2607.11116"},"observation_digest":"sha256:246934aa0a54320b00c5041eef97dc63a6aaac509c31b3552fe90fb02ff30932","observation_id":"a5a46cfa-bbdb-4bdc-93d5-18dba150a4b9","resolution":{"observed_at":"2026-07-14T06:57:31.514910Z","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":"2026-07-14T06:57:31.514910Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.11116","last_updated":"2026-07-13T05:45:35Z","snapshot_observed_at":"2026-07-16T23:19:12.573935Z","submitted_at":"2026-07-13T05:45:35Z","title":"The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-07-14T06:57:31.514910Z"},"links":{"citing_paper":"/paper/2607.11116"},"observation_digest":"sha256:9ccda2fe0b178272e0d45f0cdb29f7e02f485900e413201861dda4ed98f79b24","observation_id":"d522053a-9dd7-4ea5-bbf8-a79889df019e","resolution":{"observed_at":"2026-07-14T06:57:31.514910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.11116","last_updated":"2026-07-13T05:45:35Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-07-16T23:19:12.573935Z","submitted_at":"2026-07-13T05:45:35Z","title":"The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning"},"reference_resolution":{"displayed":30,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":30,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":30},"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 30 of 30 outbound references and 0 inbound Pith citation observations for arXiv:2607.11116."}