{"as_of":"2026-08-09T01:39:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c75997620d70916a29b713856af712d7e1f4eb6c361c2035e50f2fffdebe365c","coverage":[{"denominator":115,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":100,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-02T19:22:13.221384Z","state":"measured"},{"denominator":101,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":101,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+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":"2026-08-01T10:11:58.786716Z","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":[{"citation":{"cited_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2603.02645","snapshot_observed_at":"2026-08-01T10:11:58.786716Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.20339","last_updated":"2026-07-22T16:26:59Z","snapshot_observed_at":"2026-08-08T06:48:54.642568Z","submitted_at":"2026-07-22T16:26:59Z","title":"Interval and fuzzy physics-augmented neural networks (iPANN and fPANN) for uncertainty quantification and propagation in constitutive modeling","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-01T10:11:58.786716Z"},"links":{"cited_paper":"/paper/2603.02645","citing_paper":"/paper/2607.20339"},"observation_digest":"sha256:3c7f6e58a4e3438b860c0130dc9a7ec1dfd3b17ba6a1e4ac0b796c24249b2c67","observation_id":"6716a14b-fd41-4687-b2c0-e300e66d2a4a","resolution":{"observed_at":"2026-08-01T10:11:58.786716Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2603.02645/citation-record","integrity":"/paper/2603.02645/integrity","json":"/paper/2603.02645/citation-record.json","paper":"/paper/2603.02645"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T19:22:12.836186Z","title":null,"venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.836186Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:1a15635cee96bf5db5ba3d445bf7045f697420dd8c2d096c89e1a573cb089424","observation_id":"34e1f58e-e11c-4fe3-842b-b5dde3a86ba5","resolution":{"observed_at":"2026-08-02T19:22:12.836186Z","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":"2026-08-02T19:22:12.840889Z","title":"Model selection techniques: An overview.IEEE Signal Processing Magazine, 35(6):16–34, 2018","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.840889Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:3bf13cf32a6a83a179a2ef49aa7d139d2d7e95f06a2e03454ec22c7c9333b202","observation_id":"8e30802e-1e78-4872-87b4-882464cbd075","resolution":{"observed_at":"2026-08-02T19:22:12.840889Z","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":"2026-08-02T19:22:12.844839Z","title":"A review on data-driven constitutive laws for solids.Archives of Computational Methods in Engineering, 32(3):1841–1883, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.844839Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:369b069da68ec32199600c6db031fd3d9e377ea363c71761af46a663e684a27e","observation_id":"8f95d479-1542-48e8-a863-e9aa7b1d27be","resolution":{"observed_at":"2026-08-02T19:22:12.844839Z","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":"2026-08-02T19:22:12.849056Z","title":"Finite electro-elasticity with physics-augmented neural networks.Computer Methods in Applied Mechanics and Engineering, 400:115501, 2022","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.849056Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:387d211b4f83420639885784d2aaad7b507bec0200f5df5064f3665617dbf43f","observation_id":"32f86f84-65df-4868-9599-f1febf503e19","resolution":{"observed_at":"2026-08-02T19:22:12.849056Z","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":"2026-08-02T19:22:12.852996Z","title":"Viscoelasticty with physics-augmented neural networks: model formulation and training methods without prescribed internal vari- ables.Computational Mechanics, 74(6):1279–1301, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.852996Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:bd230789fe114744eac0f45060a6bb81e512dc8cab242e372e97506e46555d64","observation_id":"992b323f-e589-4033-92c3-a5191e648c3f","resolution":{"observed_at":"2026-08-02T19:22:12.852996Z","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":"2026-08-02T19:22:12.856968Z","title":"Extreme sparsification of physics-augmented neural networks for interpretable model discovery in mechanics.Computer Methods in Applied Mechanics and Engineering, 426:116973, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.856968Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:e3b6e18e045af420face4a553fe79c1e7367623ac8b24c5faf49a4fc1277452b","observation_id":"135f569e-54b0-48fd-91f0-ee1170388228","resolution":{"observed_at":"2026-08-02T19:22:12.856968Z","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":"2026-08-02T19:22:12.861248Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.861248Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:9f6356e81692f0e419bf46d1b5ea579e70c44f8082c70ebc44309fedaf568c14","observation_id":"63913270-2e1e-4f4e-8f8c-c2e0a75a93d6","resolution":{"observed_at":"2026-08-02T19:22:12.861248Z","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":"2026-08-02T19:22:12.864805Z","title":"Experimental learning of a hypere- lastic behavior with a physics-augmented neural network.Experimental Mechanics, 64(9):1465–1481, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.864805Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:40f06fcd9d7a706f44609cf9d36b2b9840d1f02bae3a9e9389a280fa20ca36c5","observation_id":"00d7ba7f-c1d1-4379-899f-b89a404f8de5","resolution":{"observed_at":"2026-08-02T19:22:12.864805Z","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":"2026-08-02T19:22:12.868421Z","title":"Inverse design of anisotropic microstructures using physics-augmented neural networks.Journal of the Mechanics and Physics of Solids, page 106161, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.868421Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:9a04158d497c8cdf2f3475a47b82460220dc30f460d543cb38be0342aab25580","observation_id":"aba5f2d8-aed9-476d-b773-bbfacad2ad20","resolution":{"observed_at":"2026-08-02T19:22:12.868421Z","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":"2026-08-02T19:22:12.872142Z","title":"Polyconvex physics- augmented neural network constitutive models in principal stretches.International Journal of Solids and Struc- tures, page 113469, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.872142Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:6a1680e00a564a37af6938768d5c8c6c9f146c70faef9f8b222f87bea81d624b","observation_id":"a865595a-5968-4510-93d4-f6958bb9f4f9","resolution":{"observed_at":"2026-08-02T19:22:12.872142Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2511.02959","last_updated":"2025-11-04T19:59:46Z","snapshot_observed_at":"2026-08-07T11:54:23.114483Z","submitted_at":"2025-11-04T19:59:46Z","title":"A physics-augmented neural network framework for finite strain incompressible viscoelasticity","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2511.02959","snapshot_observed_at":"2026-08-02T19:22:12.875861Z","title":"A physics-augmented neural network framework for finite strain incompressible viscoelasticity.arXiv preprint arXiv:2511.02959, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.875861Z"},"links":{"cited_paper":"/paper/2511.02959","citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:69318ccb293ee0eee216c9d31c18a5d3b18fd9c0f69fbce6f269f3fe40df956d","observation_id":"aed63338-f072-479d-8efa-293c8bfe0b86","resolution":{"observed_at":"2026-08-02T19:22:12.875861Z","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":"2026-08-02T19:22:12.879790Z","title":"Recovering mullins damage hyperelastic behaviour with physics augmented neural networks.Journal of the Mechanics and Physics of Solids, 193:105839, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.879790Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:cc4699c2a2efe6de3162191d5e1ed046b3c8c43c4064b31b4bb8fd2071d4bf1b","observation_id":"da9f2e32-80a7-4d6c-8fdc-6b52f10b9717","resolution":{"observed_at":"2026-08-02T19:22:12.879790Z","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":"2026-08-02T19:22:12.883448Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.883448Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:0e884674b372e1679faa32b1fb5d8c20f2aa411fef59b78fe016b61112511533","observation_id":"57caeee7-9dcf-444d-a108-8823ff04c628","resolution":{"observed_at":"2026-08-02T19:22:12.883448Z","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":"2026-08-02T19:22:12.887177Z","title":"A new family of constitutive artificial neural networks towards automated model discovery.Computer Methods in Applied Mechanics and Engineering, 403:115731, 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.887177Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:0e2b0124a5a4d9ce0c3c213c862b0498961b8fb217683277bf026bb9dd4ba389","observation_id":"8cbdf96a-f7e6-4be4-b4ac-43f73d6c9eb3","resolution":{"observed_at":"2026-08-02T19:22:12.887177Z","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":"2026-08-02T19:22:12.890791Z","title":"Theory and implementation of inelastic constitutive artificial neural networks.Computer Methods in Applied Mechanics and Engineering, 428:117063, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.890791Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:e4405d6866e57f3021072f3c7cacd958c31dd7da4a87463a69876d7891d5109f","observation_id":"b8b82815-72b2-45ff-90af-4568b8408fd0","resolution":{"observed_at":"2026-08-02T19:22:12.890791Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.19326","last_updated":"2025-06-07T06:08:04Z","snapshot_observed_at":"2026-07-06T18:52:51.827101Z","submitted_at":"2024-07-27T19:19:42Z","title":"Accounting for plasticity: An extension of inelastic Constitutive Artificial Neural Networks","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.19326","snapshot_observed_at":"2026-08-02T19:22:12.894514Z","title":"Accounting for plasticity: An extension of inelastic constitutive artificial neural networks.arXiv preprint arXiv:2407.19326, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.894514Z"},"links":{"cited_paper":"/paper/2407.19326","citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:64158a9d7d3b171147f93fd42c4d0b61a107feba8f46193579de7167bd01b994","observation_id":"4cdb03e1-125a-4b94-90ee-55186c38c02d","resolution":{"observed_at":"2026-08-02T19:22:12.894514Z","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":"2026-08-02T19:22:12.898602Z","title":"Polyconvex inelastic constitutive artificial neural networks.PAMM, 24(3):e202400032, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.898602Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:81ed47a36eacefd80e873fc5d5f1e52717d34f9c9a6f4d9c17579a4a31de7bce","observation_id":"b33465a4-bf68-49cf-ba9f-f6f0cbb6026f","resolution":{"observed_at":"2026-08-02T19:22:12.898602Z","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":"2026-08-02T19:22:12.902582Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.902582Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:d3f97361c4b238a1ecb47deab897a3ff136b651fef316bf23251728b540fe1e6","observation_id":"2bfa4b8b-da5b-43fa-b59a-5774022863c7","resolution":{"observed_at":"2026-08-02T19:22:12.902582Z","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":"2026-08-02T19:22:12.906929Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.906929Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:1a8ebc73116fdf3ae116f2c77af59881555af81bbd796d3469b8c5bfc29de193","observation_id":"32bfa5d9-e136-4594-93ac-1d1e77fca6b9","resolution":{"observed_at":"2026-08-02T19:22:12.906929Z","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":"2026-08-02T19:22:12.910720Z","title":"Hamiltonian neural networks.Advances in neural information processing systems, 32, 2019","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.910720Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:4f77fd508620465aee71f1889874dba90fedc0ae001a9770778d1a28ba141ebc","observation_id":"e237470d-e187-4c03-af91-f3401a4aa4ce","resolution":{"observed_at":"2026-08-02T19:22:12.910720Z","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":"2026-08-02T19:22:12.914719Z","title":"Lagrangian neural networks.arXiv preprint arXiv:2003.04630, 2020","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.914719Z"},"links":{"cited_paper":"/paper/2003.04630","citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:6f20526502dc092bd70372f9e35d44dcd6dce0a3bfd9655580f64286cb4e3d3c","observation_id":"355aceaf-33af-4e7d-b6bf-b0d4345d23bd","resolution":{"observed_at":"2026-08-02T19:22:12.914719Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1909.13334","last_updated":"2020-04-25T16:32:53Z","snapshot_observed_at":"2026-08-08T04:57:50.001903Z","submitted_at":"2019-09-29T18:04:07Z","title":"Symplectic Recurrent Neural Networks","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1909.13334","snapshot_observed_at":"2026-08-02T19:22:12.919302Z","title":"Symplectic recurrent neural networks.arXiv preprint arXiv:1909.13334, 2019","venue":null,"work_id":null,"year":1909},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.919302Z"},"links":{"cited_paper":"/paper/1909.13334","citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:47172ed801b095f171a81066bbcd4f09f21e65b60ddb1231eed560e7e2c388c6","observation_id":"61606698-368b-4aed-8f17-b38e26cf2128","resolution":{"observed_at":"2026-08-02T19:22:12.919302Z","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":"2026-08-02T19:22:12.923474Z","title":"Thermodynamically consistent data-driven computa- tional mechanics.Continuum Mechanics and Thermodynamics, 31(1):239–253, 2019","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.923474Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:c136bf7ab90565c2c42d4e9d8d4f07becbc21e14159ac0b998b7378289987537","observation_id":"e1a2bdba-4673-49bc-b2a0-2b952ebc8825","resolution":{"observed_at":"2026-08-02T19:22:12.923474Z","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":"2026-08-02T19:22:12.927401Z","title":"Efficiently parameterized neural metriplectic systems","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.927401Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:0baac6ee5cefee5846a9e429e5d94f538bc4bc97e9ac1309103992a9456a5ac7","observation_id":"0e8a5742-7c6d-4d5d-aa3d-7ae9e8c76ca6","resolution":{"observed_at":"2026-08-02T19:22:12.927401Z","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":"2026-08-02T19:22:12.931090Z","title":"Thermodynamics with internal state variables.The journal of chemical physics, 47(2):597–613, 1967","venue":null,"work_id":null,"year":1967},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.931090Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:c006bccaa5aa848e9000bbb5d1cbd5ee774ac897077bde8623acf1f4608a5b1e","observation_id":"8e9d6096-31c1-4d00-b369-75a54f2fe70c","resolution":{"observed_at":"2026-08-02T19:22:12.931090Z","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":"2026-08-02T19:22:12.934645Z","title":"Cambridge university press, 1994","venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.934645Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:f7e1adc4c60219d9825382f97bfd0910d6486cff0fe8148fa3d21adf4edca056","observation_id":"e28de63d-ba81-4a1c-a31b-595a26be36f0","resolution":{"observed_at":"2026-08-02T19:22:12.934645Z","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":"2026-08-02T19:22:12.938605Z","title":"Sur les matériaux standard généralisés.Journal de mécanique, 14(1):39–63, 1975","venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.938605Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:000ff6e50e193208768f589b591d4da3d3cdb5d729c99ce6e811e0c2f7b51705","observation_id":"7e5b67a2-874c-4cd2-806e-a262068645f0","resolution":{"observed_at":"2026-08-02T19:22:12.938605Z","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":"2026-08-02T19:22:12.942369Z","title":"Bracket formulation for irreversible classical fields.Physics Letters A, 100(8):423–427, 1984","venue":null,"work_id":null,"year":1984},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.942369Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:fd752fe7d9a58b5c5221503743548de18bb4ed5d84bc778ac2ca7ea4a88982e5","observation_id":"1fe2b359-1e15-495e-8362-c2c476feda57","resolution":{"observed_at":"2026-08-02T19:22:12.942369Z","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":"2026-08-02T19:22:12.945995Z","title":"Dynamics and thermodynamics of complex fluids","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.945995Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:2f417d449ec78f02b6c7d0959306a1a184e072b49bdd67c8a2bfb53782000257","observation_id":"1a92301d-5a0a-4bef-b4ca-329a3720fd5c","resolution":{"observed_at":"2026-08-02T19:22:12.945995Z","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":"2026-08-02T19:22:12.949728Z","title":"A review on data-driven constitutive laws for solids.Archives of Computational Methods in Engineering, pages 1–43, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.949728Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:d70fdabeb9aa70323ba6d85e9423b36e05527b1838e99417d64108c20c59c6d2","observation_id":"30b41ccc-5b15-4bfb-be3d-5a6f479535ae","resolution":{"observed_at":"2026-08-02T19:22:12.949728Z","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":"2026-08-02T19:22:12.953483Z","title":"Reflections on the motive power of fire, and on machines fitted to develop that power.Paris: Bachelier, 108(1824):1824, 1824","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.953483Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:4cb90e34dc99a3725bdf9290c757147c062201758aefe690fe96c4449b98d8a4","observation_id":"01ee573f-e2d2-4691-8e69-0c9558b36bff","resolution":{"observed_at":"2026-08-02T19:22:12.953483Z","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":"2026-08-02T19:22:12.957793Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.957793Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:b33b2fd220e7233096d8a63edd640caf8d9d50de57999cf5bed6852d92861e3b","observation_id":"2d369137-7d36-4124-8864-0e054dc8e093","resolution":{"observed_at":"2026-08-02T19:22:12.957793Z","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":"2026-08-02T19:22:12.961832Z","title":"Ueber die bewegende kraft der wärme und die gesetze, welche sich daraus für die wärmelehre selbst ableiten lassen.Annalen der Physik, 155(3):368–397, 1850","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.961832Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:54c52a246ce9cfcdaa8f23f4156be4bec0d1cd5586503ffa507f078e320d96ea","observation_id":"33949028-85b1-4843-9136-3fd798dcbe33","resolution":{"observed_at":"2026-08-02T19:22:12.961832Z","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":"2026-08-02T19:22:12.965914Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.965914Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:f2b1c264710c4989b7e67a54bea46e4ea30789e72c303776a9f37ecd86fa406e","observation_id":"f761090b-aa5c-44a2-9dcf-deeed340d13b","resolution":{"observed_at":"2026-08-02T19:22:12.965914Z","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":"2026-08-02T19:22:12.970502Z","title":"Xv.—on the dynamical theory of heat, with numerical results deduced from mr joule’s equivalent of a thermal unit, and m","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.970502Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:951e3ba68765b449d3bbc7d3e0d625b780ae7159de25ad01776d6b22615a0a1c","observation_id":"4a0be43c-e899-44ee-a887-853de0001433","resolution":{"observed_at":"2026-08-02T19:22:12.970502Z","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":"2026-08-02T19:22:12.974369Z","title":"Xxii.—on the dynamical evidence of the molecular constitution of bodies.Journal of the Chemical Society, 28:493–508, 1875","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.974369Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:2818bf11dc84bbaa16789917f8ee357177def5414bdc631c2e9a57b652b6d2e1","observation_id":"66b8992a-a594-4ef6-921d-f7c5edf3af63","resolution":{"observed_at":"2026-08-02T19:22:12.974369Z","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":"2026-08-02T19:22:12.978698Z","title":"Graphical methods in the thermodynamics of fluids.Transactions of the Connecticut Academy of Arts and Sciences, 1:309–342, 1873","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.978698Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:88ed3c91f43318fcde17abbef894234cdcceb136f21b6e4512c8e10c099201d5","observation_id":"613e7543-f95b-4366-82e0-dc3f47be140a","resolution":{"observed_at":"2026-08-02T19:22:12.978698Z","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":"2026-08-02T19:22:12.982431Z","title":"Reciprocal relations in irreversible processes","venue":null,"work_id":null,"year":1931},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.982431Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:60def7bef0705e29d6def57c22f47712df489a0d2d8d8d59d576ea0620cab9fa","observation_id":"0ce434bb-b182-47a8-ad3f-339b5752c9a9","resolution":{"observed_at":"2026-08-02T19:22:12.982431Z","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":"2026-08-02T19:22:12.986337Z","title":"Reciprocal relations in irreversible processes","venue":null,"work_id":null,"year":1931},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.986337Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:7f4026945ff61746f8cdeee3b773ba384b12e58695927f0f7d85cee79138714b","observation_id":"61d3b30b-0469-48bc-99f1-5f986078045a","resolution":{"observed_at":"2026-08-02T19:22:12.986337Z","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":"2026-08-02T19:22:12.990733Z","title":"Introduction to thermodynamics of irreversible processes.Journal of The Electrochemical Society, 110(4):97C, 1963","venue":null,"work_id":null,"year":1963},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.990733Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:42cefd14910741842d7a01f54749efc9e6644fd513e38a33ce51ada6a25d9635","observation_id":"26afe57e-e647-4d27-aa0f-9e5d08841ab6","resolution":{"observed_at":"2026-08-02T19:22:12.990733Z","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":"2026-08-02T19:22:12.994743Z","title":"Courier Corporation, 2013","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.994743Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:30c9a20ecb6625d345373b9a60f86728fdb4ec09bb1b838dd7dc03d4abedc307","observation_id":"e6e6bb84-a30c-4cd0-ad0c-d4851187daf4","resolution":{"observed_at":"2026-08-02T19:22:12.994743Z","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":"2026-08-02T19:22:12.998331Z","title":"Springer, 2008","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:12.998331Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:b59c72ef4d7f92486eb0a924d0e3b9e6f8317fff58389a661a49be4d3832a012","observation_id":"640aa93e-da89-4dce-9888-46d73b79939d","resolution":{"observed_at":"2026-08-02T19:22:12.998331Z","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":"2026-08-02T19:22:13.002410Z","title":"Quelques réflexions au sujet de la physique expérimentale","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.002410Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:fcffeedf4d8f7f37a245d1b6a6aa1f266d93788435e19dd435c69e2a228bbfce","observation_id":"5ca40b02-3046-4038-9d6e-2374c1db8af4","resolution":{"observed_at":"2026-08-02T19:22:13.002410Z","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":"2026-08-02T19:22:13.006059Z","title":"The thermal conductivity of liquids under pressure","venue":null,"work_id":null,"year":1923},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.006059Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:ce577073c58c11259929c1025c345dd6f15aaf635abe9293165e704b3806ca9c","observation_id":"c1b9c790-f9e6-486d-ba89-9088872da582","resolution":{"observed_at":"2026-08-02T19:22:13.006059Z","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":"2026-08-02T19:22:13.009851Z","title":"Historical review of internal state variable theory for inelasticity","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.009851Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:793c356ced04a3344caca688fbb698d207952e20bcd8e80ad481e23a3d4b4d71","observation_id":"eae1fd48-c218-466b-9bdd-99be1aeb5503","resolution":{"observed_at":"2026-08-02T19:22:13.009851Z","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":"2026-08-02T19:22:13.013604Z","title":"The thermodynamics of irreversible processes","venue":null,"work_id":null,"year":1940},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.013604Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:c6cfef83d92dc9c38da6ce2519dd44157b9d0c675cf208809ac594acfede4461","observation_id":"7e87d1e9-eac1-4717-bb18-cdf0ff0061b0","resolution":{"observed_at":"2026-08-02T19:22:13.013604Z","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":"2026-08-02T19:22:13.017322Z","title":"How the internal state of a plastically deformed body is to be described in a continuum theory","venue":null,"work_id":null,"year":1965},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.017322Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:303cb4ab48fa077fda9a6be64643d25c0ff7ef2fe713eef17928166af80c35be","observation_id":"82619b38-ab07-4e7a-a194-3bb85bfcc307","resolution":{"observed_at":"2026-08-02T19:22:13.017322Z","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":"2026-08-02T19:22:13.021097Z","title":"Thermodynamics with internal variables","venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.021097Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:e5ec5ce0813ceb7ddaab43d60c955e4f94fc2adb9e2f155b07b70acbc883634b","observation_id":"d4f54187-c472-46b7-bf99-20e7e4bf566b","resolution":{"observed_at":"2026-08-02T19:22:13.021097Z","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":"2026-08-02T19:22:13.024775Z","title":"A theory of finite viscoelasticity and numerical aspects.International journal of solids and structures, 35(26-27):3455–3482, 1998","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.024775Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:b95584d7e5168e93a04e42e3c30dae99f8c269b2a6444c8a9ae0a1d86a6d1492","observation_id":"aeb68099-67bf-4d37-85c6-c0643ba91fca","resolution":{"observed_at":"2026-08-02T19:22:13.024775Z","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":"2026-08-02T19:22:13.028457Z","title":"Continuum thermodynamics.Journal of applied mechan- ics, 50:1010–1020, 1983","venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.028457Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:b8506328696206d7542dd2f3ee2b264b6acfa1b12b0a048a6ca175da7ca3f528","observation_id":"788a7573-ac65-4064-b453-140200694f8c","resolution":{"observed_at":"2026-08-02T19:22:13.028457Z","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":"2026-08-02T19:22:13.032554Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.032554Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:8e539f179c7ac548eaeae2915b073f4c15b92781cf63bde7f51ed77fc7fcdb33","observation_id":"66b69be0-af81-411f-8202-4ad33f30eb21","resolution":{"observed_at":"2026-08-02T19:22:13.032554Z","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":"2026-08-02T19:22:13.036216Z","title":"Neural ordinary differential equations.Advances in neural information processing systems, 31, 2018","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.036216Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:350d2f0f595799e6dc26368214225ec0571443e97a6806e48efb388cc1d0ee06","observation_id":"57fa7ccb-37bd-4dd2-b3b0-e7f09f0cee40","resolution":{"observed_at":"2026-08-02T19:22:13.036216Z","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":"2026-08-02T19:22:13.040195Z","title":"Augmented neural odes.Advances in neural information processing systems, 32, 2019","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.040195Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:b99d8f320c217c298e54d5fc640c0c0f00b85d75c09a13890b036953b7568488","observation_id":"9d98c682-5e33-463f-af12-15bace0f9b31","resolution":{"observed_at":"2026-08-02T19:22:13.040195Z","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":"2026-08-02T19:22:13.044116Z","title":"Automated discovery of generalized standard mate- rial models with euclid.Computer Methods in Applied Mechanics and Engineering, 405:115867, 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.044116Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:1f7fa5a91581c76fd62b9fca7aedca709ae530f4aacff6a2a6162c7737185fac","observation_id":"c52c2036-bffb-4849-bb7e-f892c39db027","resolution":{"observed_at":"2026-08-02T19:22:13.044116Z","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":"2026-08-02T19:22:13.047927Z","title":"Convex neural networks learn generalized standard material models.Journal of the Mechanics and Physics of Solids, 200:106103, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.047927Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:9eacadec25a29522e7c269f4d0821424711be67885a793d296ade5059f67cfae","observation_id":"875fa63a-ca18-48fb-a37c-c8352e0825e9","resolution":{"observed_at":"2026-08-02T19:22:13.047927Z","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":"2026-08-02T19:22:13.051734Z","title":"Data-driven anisotropic finite viscoelasticity using neural ordinary differential equations.Computer methods in applied mechanics and engineering, 411:116046, 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.051734Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:d46e055f656c10a959f9f160c5e8418d0fc8fb8a93a2aaf4c475b7ab13e59d93","observation_id":"57b464ee-ebd9-40e4-a032-4e9f515240fd","resolution":{"observed_at":"2026-08-02T19:22:13.051734Z","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":"2026-08-02T19:22:13.055680Z","title":"A physics-augmented neural network frame- work for modeling and detecting thermo-visco-plastic behavior.arXiv preprint arXiv:2512.09284, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.055680Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:0d919959335b1d9da1d983d37e95e6909bd759c1ca9721fa16a0481a669225cf","observation_id":"7ab658f5-f617-488d-808a-88d98002b302","resolution":{"observed_at":"2026-08-02T19:22:13.055680Z","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":"2026-08-02T19:22:13.059512Z","title":"A complement to neural networks for anisotropic inelasticity at finite strains","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.059512Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:cdd2c715d8dce272fca941d39e0a2a20cc64397836d430df59a3326a49add849","observation_id":"091a9f72-5887-40ca-963c-583b4d191b28","resolution":{"observed_at":"2026-08-02T19:22:13.059512Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2409.07545","last_updated":"2024-09-11T18:08:16Z","snapshot_observed_at":"2026-07-06T19:13:59.780393Z","submitted_at":"2024-09-11T18:08:16Z","title":"Hammering at the entropy: A GENERIC-guided approach to learning polymeric rheological constitutive equations using PINNs","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2409.07545","snapshot_observed_at":"2026-08-02T19:22:13.063766Z","title":"Ham- mering at the entropy: A generic-guided approach to learning polymeric rheological constitutive equations using pinns.arXiv preprint arXiv:2409.07545, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.063766Z"},"links":{"cited_paper":"/paper/2409.07545","citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:3f62733dd0bd677ad07b31df9eb9871813074582544e0946df04b0584291460a","observation_id":"e35384a4-58ae-4963-93a4-e18c4f29f5e6","resolution":{"observed_at":"2026-08-02T19:22:13.063766Z","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":"2026-08-02T19:22:13.068446Z","title":"Port-metriplectic neural net- works: thermodynamics-informed machine learning of complex physical systems.Computational Mechanics, 72(3):553–561, 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.068446Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:91779564d4eaff80722f77cfa39a9c859079bbd9f18c66716db0cc583e14a821","observation_id":"5f99a26b-4c7c-4e2c-a688-8472c9264c62","resolution":{"observed_at":"2026-08-02T19:22:13.068446Z","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":"2026-08-02T19:22:13.072197Z","title":"Formulation of thermoelastic dissipative material behavior using generic.Continuum Me- chanics and Thermodynamics, 23(3):233–256, 2011","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.072197Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:0afd7db204c1202c770ff742991d31e2709c2d8b68883412c890f7b7ed6510b1","observation_id":"3f6e6bba-2e85-4bba-8553-6c0e8bb0ffc0","resolution":{"observed_at":"2026-08-02T19:22:13.072197Z","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":"2026-08-02T19:22:13.076166Z","title":"Data-driven generic modeling of poroviscoelastic materials.Entropy, 21(12):1165, 2019","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.076166Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:8e910bf79efa17d0b75b9117439ca528bea9aea2011e8916b182324b3c37cdd9","observation_id":"9b39b321-726a-411a-8988-1d0660e105e6","resolution":{"observed_at":"2026-08-02T19:22:13.076166Z","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":"2026-08-02T19:22:13.079947Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.079947Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:93576c6cad016bba5bddd5722d6f45078433f22b0ed2898fe00e1f87dca3195e","observation_id":"ad70a8e9-f769-4d78-93fd-0791f36237e9","resolution":{"observed_at":"2026-08-02T19:22:13.079947Z","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":"2026-08-02T19:22:13.083729Z","title":null,"venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.083729Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:5db441b90dab069e9227b83245e62d97eb1cb3f71dbf3f6e8c2575d83749b4da","observation_id":"c2beb999-7e6e-4d89-bbc1-dec26b52f040","resolution":{"observed_at":"2026-08-02T19:22:13.083729Z","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":"2026-08-02T19:22:13.087617Z","title":"Continuum damage mechanics: combining thermodynamics with a thoughtful characterization of the microstructure.Acta mechanica, 201(1):297–312, 2008","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.087617Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:53403f6e9c1cdc9208c528866d8d31505906dcb034adca9999b66b9d71ccce6f","observation_id":"a479fdbe-c2a4-433a-a399-62bc100282c3","resolution":{"observed_at":"2026-08-02T19:22:13.087617Z","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":"2026-08-02T19:22:13.091282Z","title":"Finite anisotropic elasticity and material frame indifference from a nonequilibrium thermodynamics perspective.Journal of Non-Newtonian Fluid Mechanics, 152(1-3):45–52, 2008","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.091282Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:dd61590e7fca68cb9fa792f4f53ddd26b7fcf3e0208a30795ffe58064d2764e1","observation_id":"bfc1102b-b33f-459a-badf-30ca41ac8f1f","resolution":{"observed_at":"2026-08-02T19:22:13.091282Z","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":"2026-08-02T19:22:13.095754Z","title":"Statistical-mechanics based modeling of anisotropic viscoplastic defor- mation.Mechanics of Materials, 80:37–51, 2015","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.095754Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:3c38ca0b63c57993461e8b95fcb7b12145da603cac44e38ad32168ebe1afed0e","observation_id":"7c286cf5-725f-42a6-b2ac-355acbd6bdbc","resolution":{"observed_at":"2026-08-02T19:22:13.095754Z","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":"2026-08-02T19:22:13.099611Z","title":"Why generic?Journal of non-newtonian fluid mechanics, 165(17-18):980–986, 2010","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.099611Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:a9c219a57ff935cc7b35ca585bec40b75fbae6feb057b938660fd4bcb0e8ef1a","observation_id":"3b85cb12-254f-4c37-9cb0-0aa78c6c1929","resolution":{"observed_at":"2026-08-02T19:22:13.099611Z","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":"2026-08-02T19:22:13.103533Z","title":"The principle of fading memory.Archive for Rational Mechanics and Analysis, 18(5):343–366, 1965","venue":null,"work_id":null,"year":1965},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.103533Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:864f6d9ce8d69d22e1eb4c32434ab766eb6cf2520070c687580c8281a539d278","observation_id":"b845172c-b6b0-488e-9da6-43a82c493eb3","resolution":{"observed_at":"2026-08-02T19:22:13.103533Z","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":"2026-08-02T19:22:13.107267Z","title":"The non-linear field theories of mechanics","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.107267Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:19bc78b299beaff200e4cfd63f09cb0899a1d1e74fcb13821a35b2ab15c29ac9","observation_id":"88520981-e7d8-4c6e-adaa-16adecf1e009","resolution":{"observed_at":"2026-08-02T19:22:13.107267Z","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":"2026-08-02T19:22:13.110781Z","title":"The thermodynamics of elastic materials with heat conduction and viscosity","venue":null,"work_id":null,"year":1974},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.110781Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:695b43c844c92e1765f6e4544294557040114b88cb6a989a43d37d54ae2bd15a","observation_id":"530ab516-60ac-424f-9181-063ba75c916a","resolution":{"observed_at":"2026-08-02T19:22:13.110781Z","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":"2026-08-02T19:22:13.114961Z","title":"Polyconvex neural network models of thermoelasticity.Journal of the Mechanics and Physics of Solids, 192:105837, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":72,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.114961Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:2947d419074b25fa0d8f936b94f6c3b4e8d1fa803ed59128f1ba56b0218d32ea","observation_id":"ea4ab7c8-efbb-4163-aa74-4f83b7d56a1c","resolution":{"observed_at":"2026-08-02T19:22:13.114961Z","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":"2026-08-02T19:22:13.118577Z","title":"A new mathematical theory of simple materials.Archive for Rational Mechanics and Analysis, 48(1):1–50, 1972","venue":null,"work_id":null,"year":1972},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":73,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.118577Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:4d0957d7f8d19ff4db0880e6f051edc7c47ea05bd6461c54387cc7420bc53f90","observation_id":"3f203d8c-9908-4ad0-b310-a6aff3d457c6","resolution":{"observed_at":"2026-08-02T19:22:13.118577Z","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":"2026-08-02T19:22:13.122331Z","title":"Springer Science & Business Media, 1993","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":74,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.122331Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:a96b74e7065b6a794154a3cc0a5d31b8c4ed37af9d055fa5e2f88e0f4a4a8e79","observation_id":"e489969a-047a-4688-88c6-21b5590de429","resolution":{"observed_at":"2026-08-02T19:22:13.122331Z","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":"2026-08-02T19:22:13.126193Z","title":null,"venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":75,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.126193Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:2dfef7778f4ef73d391281bc9c94fbe2759120aff3a690809eb5ae117f7f6cb4","observation_id":"ae5bdcfa-307a-4d74-bc72-ccbf73d2aace","resolution":{"observed_at":"2026-08-02T19:22:13.126193Z","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":"2026-08-02T19:22:13.130313Z","title":"Extended irreversible thermodynamics.Reports on Progress in Physics, 51(8):1105, 1988","venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":76,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.130313Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:a0018ea0ca1a365262219049b22f78144abf2c43964c75b40b654e46e176d1c6","observation_id":"97519776-97b6-4f97-bf58-a027f6a36dae","resolution":{"observed_at":"2026-08-02T19:22:13.130313Z","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":"2026-08-02T19:22:13.134188Z","title":"Extended irreversible thermodynamics revisited (1988-98)","venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":77,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.134188Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:14bb4269f3802ffb0a04f9c83546770795324ce67fa093776f656239ad1d0004","observation_id":"4c72867f-8421-4d38-8b06-0e66bb80acbc","resolution":{"observed_at":"2026-08-02T19:22:13.134188Z","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":"2026-08-02T19:22:13.138051Z","title":"Thermodynamics of elastic-plastic materials as a theory with internal state variables.Journal of Applied Physics, 40(8):3207–3218, 1969","venue":null,"work_id":null,"year":1969},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":78,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.138051Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:285411855f546632756229ad69ff7458e287b3a17a9d51220b9258774d375a18","observation_id":"b3fa53bc-d681-46e4-b44b-74d524913bf6","resolution":{"observed_at":"2026-08-02T19:22:13.138051Z","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":"2026-08-02T19:22:13.141658Z","title":"Internal state variable theory","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":79,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.141658Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:b257cac0c8abf7dde669f0d2abc70c6377d3efcb8578ceb307616d369bb5a0bc","observation_id":"bbd2bea7-9efa-4177-8d06-18fd491d33e7","resolution":{"observed_at":"2026-08-02T19:22:13.141658Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2502.10633","last_updated":"2025-02-15T02:09:49Z","snapshot_observed_at":"2026-08-07T18:16:30.508513Z","submitted_at":"2025-02-15T02:09:49Z","title":"An attention-based neural ordinary differential equation framework for modeling inelastic processes","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.10633","snapshot_observed_at":"2026-08-02T19:22:13.145424Z","title":"An attention-based neural ordinary differential equation framework for modeling inelastic processes.arXiv preprint arXiv:2502.10633, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":80,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.145424Z"},"links":{"cited_paper":"/paper/2502.10633","citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:3134e7a6b9e182d2dfbdb6bb4edd53c15ae1446c5232f908a5d0944ef193f8b2","observation_id":"115e1897-4b9a-44e3-9bb6-11096e9ab462","resolution":{"observed_at":"2026-08-02T19:22:13.145424Z","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":"2026-08-02T19:22:13.149547Z","title":"Some extremum principles in irreversible thermodynamics, with application to continuum me- chanics.Progress in solid mechanics, vol","venue":null,"work_id":null,"year":1963},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":81,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.149547Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:c40c28ccced78e59d869db4e61cb7949c3ccd1589a1a2b89e883aac2c5b221d1","observation_id":"a58a7108-9379-4ade-bf8c-a2cc95d718c4","resolution":{"observed_at":"2026-08-02T19:22:13.149547Z","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":"2026-08-02T19:22:13.153365Z","title":"Sur les lois de frottement, de viscosité et de plasticité.CR Acad","venue":null,"work_id":null,"year":1970},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":82,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.153365Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:d22d13111b87c56ce6615c4157ce0443926cc073537c4edfdc8e6b7315be8d03","observation_id":"283db503-cc38-46b0-bc11-462d9ba627c3","resolution":{"observed_at":"2026-08-02T19:22:13.153365Z","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":"2026-08-02T19:22:13.157303Z","title":"Elsevier, 2005","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":83,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.157303Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:143f4c847d9eb6415f250a83409303b7ddfa8904b3ad5a64917002e8e42241e3","observation_id":"5bb2e431-9b95-4333-ae78-24ce96b8026c","resolution":{"observed_at":"2026-08-02T19:22:13.157303Z","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":"2026-08-02T19:22:13.161079Z","title":"Mechanical modelling of anelasticity.Revue de Physique Appliquée, 23(4):325–330, 1988","venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":84,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.161079Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:e6a74378fa937ec13c3c0e0e7f55660757e37a4833c4a65075fc67fcde6eba9b","observation_id":"c8aa67b7-5202-4df0-afbc-59c3ecc54220","resolution":{"observed_at":"2026-08-02T19:22:13.161079Z","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":"2026-08-02T19:22:13.164871Z","title":"Dissipation-consistent modelling and classification of ex- tended plasticity formulations.Journal of the Mechanics and Physics of Solids, 119:118–139, 2018","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":85,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.164871Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:85ef3f4d77ab61f93ef333292a79596e8a31528e030159512f4ef86e1e2637f2","observation_id":"547005fb-1ceb-42b0-9daa-475b8abccbc6","resolution":{"observed_at":"2026-08-02T19:22:13.164871Z","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":"2026-08-02T19:22:13.168978Z","title":"Theory of stress-strain relations in anisotropic viscoelasticity and relaxation phenomena","venue":null,"work_id":null,"year":1954},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":86,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.168978Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:8a36d7e0cc981278690ca6aa838b560097da8ba25178c6e8edbd59e2894df2fb","observation_id":"1ff4bb9f-e59d-4cab-a8da-738e71ae33eb","resolution":{"observed_at":"2026-08-02T19:22:13.168978Z","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":"2026-08-02T19:22:13.172798Z","title":"A variational approach to modeling coupled thermo-mechanical nonlinear dissipative behav- iors.Advances in Applied Mechanics, 46:69–126, 2013","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":87,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.172798Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:b2b650ea8cd5fed0543edf0e3779a19cc1e536f5fb76b722273acfda605258ac","observation_id":"b3238dd8-00cf-43eb-bb37-4a3720e3198c","resolution":{"observed_at":"2026-08-02T19:22:13.172798Z","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":"2026-08-02T19:22:13.176472Z","title":"A paradigm for joined hamiltonian and dissipative systems.Physica D: Nonlinear Phenom- ena, 18(1-3):410–419, 1986","venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":88,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.176472Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:044220587979bec2241cf48f26037ca9940d3e8b763c3b25302c467dd4f3d30a","observation_id":"17653e7d-cb48-4ffb-8883-890f1b6c65ab","resolution":{"observed_at":"2026-08-02T19:22:13.176472Z","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":"2026-08-02T19:22:13.180183Z","title":"Dynamics and thermodynamics of complex fluids","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":89,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.180183Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:f523ec85180c950ba7330a5234fd6c5ee2e74f613d28bfeb0bcbeccf88b80c40","observation_id":"91f9ecfc-2ed2-499b-9858-47b200b115fa","resolution":{"observed_at":"2026-08-02T19:22:13.180183Z","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":"2026-08-02T19:22:13.183644Z","title":"Rheological modeling with generic and with the onsager principle.arXiv preprint arXiv:2507.22144, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":90,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.183644Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:8726db10c3bcdc0d01e81060cb92fd3a7a8176ad1c3ff4de104412b39ae78bb8","observation_id":"ac99dd2e-63ea-4ea4-9f35-4879348e9ab7","resolution":{"observed_at":"2026-08-02T19:22:13.183644Z","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":"2026-08-02T19:22:13.187452Z","title":"Generic guide to the multiscale dynamics and thermodynamics.Journal of Physics Commu- nications, 2(3):032001, 2018","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":91,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.187452Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:efc20a993c1c1a1371fd665b884e2c96b7d881b01db0a633aacd1639eb7f9c18","observation_id":"efc788bb-9d57-4e61-ab7a-1c942149ebe9","resolution":{"observed_at":"2026-08-02T19:22:13.187452Z","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":"2026-08-02T19:22:13.191375Z","title":"Thermomechanics.Quarterly of Applied Mathematics, 30(1):91–107, 1972","venue":null,"work_id":null,"year":1972},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":92,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.191375Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:82790f9004fdec4046efa20524fc5187dfc141eddc6106d4f2cac149ae81ce51","observation_id":"1a1cd5a1-4f9a-43d6-a42e-e673aafe1f4f","resolution":{"observed_at":"2026-08-02T19:22:13.191375Z","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":"2026-08-02T19:22:13.194952Z","title":"Thermodynamics and an introduction to thermostatistics.John Wiley& Sons, 2, 1993","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":93,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.194952Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:075643881ca128cff2bac506c782875bfbd2961be805f709197f3120b701f13e","observation_id":"2e19d76c-1544-476e-a9d7-bdbb5ea7a214","resolution":{"observed_at":"2026-08-02T19:22:13.194952Z","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":"2026-08-02T19:22:13.198664Z","title":"Une généralisation de l’inégalité de fenchel et ses applications aux lois constitutives.Comptes rendus de l’Académie des sciences","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":94,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.198664Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:18a63dca4a6a284889b9340de64b3cb6b63484898de1740cc0f0ae67e1414036","observation_id":"e9b935f3-e7c1-4665-b695-3a7612092951","resolution":{"observed_at":"2026-08-02T19:22:13.198664Z","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":"2026-08-02T19:22:13.202338Z","title":"The implicit standard material theory for modelling the nonassociative behaviour of metals","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":95,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.202338Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:50a0b50b708c77d948d20089f591dd0f89c8343a594730be26ffab12c36b0fd5","observation_id":"4a877fe9-778a-46e1-9d05-2c34ae88b7e3","resolution":{"observed_at":"2026-08-02T19:22:13.202338Z","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":"2026-08-02T19:22:13.205995Z","title":"Input specific neural networks.Computa- tional Mechanics, pages 1–23, 2026","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":96,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.205995Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:8e02f939a7352d06897f50e361dcdc61e0fda21d56e8efc66e5e748597f26b31","observation_id":"2227109f-80ef-4a7b-a4f8-e3ade2f865e8","resolution":{"observed_at":"2026-08-02T19:22:13.205995Z","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":"2026-08-02T19:22:13.209837Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":97,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.209837Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:7ab0f92506d5fe6b9ecd4c968f9d1ce207ebdb2fe3b9f7760ea578db51470d08","observation_id":"054d8358-9972-4e68-9f9f-202d362037c7","resolution":{"observed_at":"2026-08-02T19:22:13.209837Z","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":"2026-08-02T19:22:13.213574Z","title":"Learning hyperelastic anisotropy from data via a tensor basis neural network.Journal of the Mechanics and Physics of Solids, 168:105022, 2022","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":98,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.213574Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:4c5d2e2cd12682fe0a7bf81d04d19ab54f0014aa2f0aeb0c2a46de7cfcacb5c4","observation_id":"34c4f438-52bb-48c7-9fbd-c56f7a0106af","resolution":{"observed_at":"2026-08-02T19:22:13.213574Z","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":"2026-08-02T19:22:13.217546Z","title":"Convexity conditions and existence theorems in nonlinear elasticity.Archive for rational mechan- ics and Analysis, 63(4):337–403, 1976","venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":99,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.217546Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:1b137ddd2cc0f6add500ec92149085587202385faf5448510a4383256a130bf0","observation_id":"0db9ac60-0afc-48a2-a7ba-66b8b00f711a","resolution":{"observed_at":"2026-08-02T19:22:13.217546Z","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":"2026-08-02T19:22:13.221384Z","title":"Invariant formulation of hyperelastic transverse isotropy based on polyconvex free energy functions.International journal of solids and structures, 40(2):401–445, 2003","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling","version":2},"reference_index":100,"source":"pdf_text","source_observed_at":"2026-08-02T19:22:13.221384Z"},"links":{"citing_paper":"/paper/2603.02645"},"observation_digest":"sha256:9f11b1ef5bb457150e0d645bae4f6da29a5981b0ee61a24de0e642881381947b","observation_id":"633a7f9b-596d-45cf-b667-d688b5087199","resolution":{"observed_at":"2026-08-02T19:22:13.221384Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2603.02645","last_updated":"2026-05-26T23:16:26Z","latest_version":2,"primary_category":"cond-mat.mtrl-sci","snapshot_observed_at":"2026-08-07T11:54:50.210654Z","submitted_at":"2026-03-03T06:22:02Z","title":"A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling"},"reference_resolution":{"displayed":100,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":100,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":115},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 100 of 115 outbound references and 1 inbound Pith citation observation for arXiv:2603.02645."}