{"as_of":"2026-08-08T11:37:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:5387d8bd60ada4b173ac69b368bbb8a3fb1f2022639ebeca049a9570e02492ea","coverage":[{"denominator":41,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":41,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-28T03:50:38.792407Z","state":"measured"},{"denominator":42,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":42,"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":"2026-08-01T10:28:15.662505Z","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":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2606.04447","snapshot_observed_at":"2026-08-01T10:28:15.662505Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.20235","last_updated":"2026-07-22T14:56:15Z","snapshot_observed_at":"2026-08-06T21:56:48.814200Z","submitted_at":"2026-07-22T14:56:15Z","title":"Dynamical and Optimization Trade-offs of Levi--Civita Coordinates for Learned Close-Encounter Dynamics","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-01T10:28:15.662505Z"},"links":{"cited_paper":"/paper/2606.04447","citing_paper":"/paper/2607.20235"},"observation_digest":"sha256:ca1251fe36f24107b0b94e9840a97f8707b23274e26b1cc0591b0dc906116a5c","observation_id":"6896ff5b-2166-4411-84f8-e0ee009f2b53","resolution":{"observed_at":"2026-08-01T10:28:15.662505Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2606.04447/citation-record","integrity":"/paper/2606.04447/integrity","json":"/paper/2606.04447/citation-record.json","paper":"/paper/2606.04447"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T03:50:38.792407Z","title":"Machine learning and the physical sciences.Reviews of Modern Physics, 91(4):045002, 2019","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:b0369d1a34cd868af9456432c68b5dab851cf86f820fe9b4c17e7e0bd92e9552","observation_id":"7ec40d49-d6aa-402b-8c32-554e527a0f14","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":"Physics- informed neural networks (pinns) for fluid mechanics: A review.Acta Mechanica Sinica, 37(12):1727– 1738, 2021","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:e3a04eef8fbb3845f27ec06fc93a76dd4ca42b1e1d93363792cf41dad54f4ecf","observation_id":"351b1749-35d3-4b77-a521-aefa9b7d57e9","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":"Learning nonlinear operators via deeponet based on the universal approximation theorem of operators.Nature machine intelligence, 3(3):218–229, 2021","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:4c485d9e336eac5e8068ae36eb4ddcbe106320b33510a59dc1a85057e8e2d7bb","observation_id":"34a68277-156e-4ede-803e-1933893deb78","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":"Fourier neural operator for parametric partial differential equations","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:0dc4a356022278845ffe38a5b215fa24b4799f09194917a7847634b1c90b318f","observation_id":"05322682-446b-4c0b-8127-b284a5a50d85","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:9ae97f1d7d7aef51846c06cfb3ed5243a90c391203e424b1605741b47ac26a58","observation_id":"b7552d05-3082-4e0f-aeb3-7d5e9855fd19","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":"Scientific machine learning benchmarks.Nature Reviews Physics, 4(6):413–420, 2022","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:e82a931c6cccf62b06556e47b55717330ad54bbe4af0d886f585c6a5c962ee02","observation_id":"4a7b8c11-c508-4853-bf65-e09d25e2852e","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":"Universal differential equations for scientific machine learning.CoRR, 2020","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:deaa02bebcc32899cf425b1b0b5f5820d4331e9a86dced306b433d1f5a2a2cc5","observation_id":"a2557762-ab8a-4b06-860b-bc3e5b7e25bb","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":"Neural ordinary differ- ential equations.Advances in neural information processing systems, 31, 2018","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:e62a06e2db22941592ade26e7f74c919db8d83f160f6327fc8e78f061575138f","observation_id":"b29bd5f3-b68f-4db2-9031-4fecf89ece4d","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":"Neural ode control for classification, approximation, and transport.SIAM Review, 65(3):735–773, 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:a66fe6eb88ef5aa992c6d639315d7aca308bf04bbc8a7c211e2cb6ac30ccf737","observation_id":"601f2666-3426-4b9e-a193-e1961d79fc06","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":"Hamiltonian systems and transformation in hilbert space.Proceedings of the National Academy of Sciences, 17(5):315–318, 1931","venue":null,"work_id":null,"year":1931},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:30101d4feebfaa6dacbe826f5fc4a29ddb746d4684e45529f44686e491f3d5a4","observation_id":"8b87647f-09c6-4798-90e1-34b02f5a2427","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":"Marsden.Foundations of Mechanics","venue":null,"work_id":null,"year":1978},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:4beef6229050be2fca2bd48b50e687752b26d81db5113b112e3c76e6d95681b2","observation_id":"cf2a3d91-e9dc-4134-8a9f-e2eee891a492","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":"Springer Science & Business Media, 2013","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:32b3e296128eb4e3cd9e43ec428bc6810c931e93ef84c24d7149eba18f140b5b","observation_id":"dcac6d69-62bb-4bf9-9ddc-bf35c546283b","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":"Pearson Education India, 2011","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:dd6c102eea6f5651db5f128cb8a06fb50d36fed62fe9cc6e18457ba0f247f514","observation_id":"1ccc231a-9bcb-4a24-833c-6c12cb858a24","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":"Hamiltonian operator inference: Physics-preserving learning of reduced-order models for canonical hamiltonian systems.Physica D: Nonlinear Phenomena, 431:133122, 2022","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:47b1d7bfa9855f318409e801d7f2788109ef1eb986bf20ff5bcbe487f32454fb","observation_id":"30099f1b-09b9-46ed-a0d6-7f1d932f48e6","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":"Symplectic integrators: An introduction.American Journal of Physics, 73(10):938–945, 2005","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:0ffe685c6534e174d86a27738c4b8bbf10810891a1237b08b4cb8bbc18d13bca","observation_id":"b29a47c5-1efa-486f-955c-e437b9f6df00","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":"Number 14","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:b85e014eef23e8a4a3d580069d5801f8e032dcb5d187b6590b59df0ed87980c6","observation_id":"7395d034-9711-4d84-9158-527c1fb6cc83","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":"Structure-preserving algorithms for ordinary differential equations.Geometric numerical integration, 31, 2006","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:90de742aa9591a06180c6617800e198b7b07e866af7f78d1e0a9552040ff718b","observation_id":"9c2c00e5-79ba-4f35-89ed-547679e55ad7","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":"The symplectic methods for the computation of hamiltonian equations","venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:ce2c740f798b12192621d4051a26c6bcc3fa85f7128f15555d15bece4204e12f","observation_id":"945c7167-eda5-438c-9656-39f33c7557da","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":"A new look at finite elements in time: a variational interpretation of runge-kutta methods.Applied Numerical Mathematics, 25(4):355–368, 1997","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:aa7f285161ac85479c5d466546b759f94b6f8d3579dbd82eace6cd4dc48d6d61","observation_id":"aef9ecad-2754-4c98-b1c2-60ed0543e59b","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":"Hamiltonian neural networks.Advances in neural information processing systems, 32, 2019","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:74064b1d68bdbc391b53784ca8f654a98e523f75267072b497f386afb20d4d34","observation_id":"d330f3e3-fa3e-4b49-ad24-ac1b7e71b674","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":"Hamiltonian neural networks for solving equations of motion.Physical Review E, 105(6):065305, 2022","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:6986844c1853bf6f19707a0842aa4f8e9301507ded0222b4eac614d6327fd65d","observation_id":"da0ef99a-852e-4b30-99e6-068003b3a19f","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:79bdbdd31b195cfabb82e1556813aa31b256d5b5a2b8e1e7164d49b6fc34b4f0","observation_id":"7b18a6f0-5326-4d0d-9a62-cc5f755c8395","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":"Port- hamiltonian neural networks for learning explicit time-dependent dynamical systems.Physical Review E, 104(3):034312, 2021","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:1e5712b3fe3f196b04e03ca52f241d8a86db19c2077d878c47319c5cb44e343d","observation_id":"7cfd7092-676e-4272-a8d8-fc7492937e79","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2211.00214","last_updated":"2022-11-01T01:50:00Z","snapshot_observed_at":"2026-07-06T14:12:53.672775Z","submitted_at":"2022-11-01T01:50:00Z","title":"Transfer Learning with Physics-Informed Neural Networks for Efficient Simulation of Branched Flows","version":1},"cited_work":{"arxiv_id":"2211.00214","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2211.00214","snapshot_observed_at":"2026-07-02T11:26:54.526957Z","title":"Transfer learn- ing with physics-informed neural networks for efficient simulation of branched flows.arXiv preprint arXiv:2211.00214, 2022","venue":null,"work_id":"6a036f4e-c68b-4bc3-b37d-43b67b0fa187","year":2022},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"cited_paper":"/paper/2211.00214","citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:5e69660402f55c38b2914a2c74a58dec9c973df13ed60fa728272990f12ae764","observation_id":"b5dcaa19-12e7-4aae-bcdf-5f06be5f52af","resolution":{"observed_at":"2026-07-02T11:26:54.528766Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T03:50:38.792407Z","title":"Springer, 2003","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:dab44928ad8c0958cd4194815464b6dcb3989e69e783725d32d8942d6e266c0f","observation_id":"e1ef5771-1d7c-434a-971c-25320f196bb2","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":"Addison-wesley Reading, MA, 1950","venue":null,"work_id":null,"year":1950},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:53187148bbddc3a31932820eb384ee1cd19138c3560598cbbe896dd92d5b0047","observation_id":"7d45df33-663b-419b-85aa-057c6f705894","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":"Cambridge University Press, 2020","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:d9d2092002dd795f23665972289bc02133a87863b8468c074ccfb312570f5aa8","observation_id":"2c81a8de-9489-4045-9835-f66cf78ed051","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":"John Wiley & Sons, 2016","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:8ce493dcebabb83422adcfecbae96feddd7635c04218a02688df5fa571df974f","observation_id":"4f9b26aa-53e2-418d-b42a-161aa9330e6a","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":"Springer, 1998","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:fdebce7cbff3192b3195984c9ef26a485f79bc6ee115baf6ae59cf60bbe7c542","observation_id":"6865a8c9-1ed2-4ae8-aebf-2e6520fc3fac","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":"A survey of transfer learning.Journal of Big data, 3(1):9, 2016","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:b21b5d113c45d21bce9d8f0ee7efbc0147675763b8f130356320fd440d02dfeb","observation_id":"4ac0023f-bf64-4275-8647-4c08e69e7caa","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":"Transfer learning","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:ee093dc557e12c2e6542379b4b2b1b075d01d75b36990ca4165b22c6b3883141","observation_id":"61575e61-5e8a-4d6f-9746-b538ff18d09d","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":"A comprehensive survey on transfer learning.Proceedings of the IEEE, 109(1):43–76, 2020","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:6e000316f3029cea1090dd61719a5274bf23a8a56f6302a54f08fc776e33a5fd","observation_id":"8af25f67-cdee-4df2-9e5f-ce0544e5421a","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":"Anharmonic oscillator.Physical Review, 184(5):1231, 1969","venue":null,"work_id":null,"year":1969},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:aa25237af5f8a629c048b0b100211ae3192375ff955b63ef7a6d969674427ec2","observation_id":"6011175b-7ef4-4ddc-91fa-34b74f220b6d","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":"An efficient data-driven multiscale stochastic reduced order modeling framework for complex systems.Journal of Computational Physics, 493:112450, 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:1891e89a7ef5dc3160aad2c95edf37598677c20b949ba8e23280a63ab1df3750","observation_id":"28f4d78b-c12a-4f4b-a0b9-e58120b596c0","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":"Springer, 2016","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:a2845012af535ecb746e441f910b325b69dd4ebed99987ceb38bf3519a181639","observation_id":"b373adeb-b2c1-40d2-b451-fc65d66f596e","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":"Using machine learning to predict extreme events in complex systems","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:5fdfc8f1d87d1c21fc175898a06d9faff479751b3ff7e94739733cde973bfacb","observation_id":"6d4938ef-407f-42d3-981b-bf178af06f05","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":"A stochastic precipitating quasi- geostrophic model.Physics of Fluids, 36(11), 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:31fdcfd1246be5bbc302a3f3f528463e9b7e1cdff5677fb257d4241a7cb7dd69","observation_id":"21f9afa1-db63-4ea7-a997-d948da4ac92e","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:8af2459892c0154ba83a8d184281359793731dcb9f4c6bcf949ae657a06e1390","observation_id":"624b8472-c275-493f-9e8b-944b2f05971c","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2026-06-28T03:50:38.792407Z","title":"Fast-wave averaging with phase changes: asymptotics and application to moist atmospheric dynamics.Journal of Nonlinear Science, 31(2):38, 2021","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:bf7c475d0c59a7ff499829fb1029d30191e352829b9786ec6ef0cde35ff2d10b","observation_id":"f31f27da-1a28-407e-8a65-8044c73f0d5b","resolution":{"observed_at":"2026-06-28T03:50:38.792407Z","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":"2511.14925","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-02T11:26:54.531159Z","title":"PAS-Net: Physics-informed adaptive scale deep operator network","venue":null,"work_id":"f718d16a-9b17-4549-8266-470783ee1109","year":2025},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:e8c0a287511872972c5779ae4406b5ec229e8d4c6ddcca573d24e5cd1bd8ed88","observation_id":"63b1ddcd-b0c9-47d3-86e8-506f91f6e7b3","resolution":{"observed_at":"2026-07-02T11:26:54.532856Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2512.15086","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-02T11:26:54.533465Z","title":"Pip2 net: Physics-informed partition penalty deep operator network.arXiv preprint arXiv:2512.15086, 2025","venue":null,"work_id":"8b61dd57-07da-45bc-b09c-cfc00e4b678c","year":2025},"citing_paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-06-28T03:50:38.792407Z"},"links":{"citing_paper":"/paper/2606.04447"},"observation_digest":"sha256:7c4cc714895e71bdce492ce19c9b68a18da28584686984b4ffebb4287f93a918","observation_id":"546392b8-9e36-4eca-afbf-3b87934bd2c9","resolution":{"observed_at":"2026-07-02T11:26:54.535235Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}}],"paper":{"arxiv_id":"2606.04447","last_updated":"2026-06-03T04:48:05Z","latest_version":1,"primary_category":"physics.comp-ph","snapshot_observed_at":"2026-07-06T23:44:33.095008Z","submitted_at":"2026-06-03T04:48:05Z","title":"ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics"},"reference_resolution":{"displayed":41,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":38,"verified_exact":3,"verified_fuzzy":0},"total_outbound_references":41},"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 8 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 1 inbound Pith citation observation for arXiv:2606.04447."}