{"as_of":"2026-08-14T14:51:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:51755e6b10a402812a6bfbb860b53fd28029554fdc9b6065d366cbfb69c9de59","coverage":[{"denominator":29,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":29,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-04T17:48:37.444438Z","state":"measured"},{"denominator":30,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":30,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-14T06:32:32.682623+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":"2026-07-31T23:24:55.938007Z","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":"2509.10659","last_updated":"2025-09-12T19:38:38Z","snapshot_observed_at":"2026-08-07T20:08:35.955158Z","submitted_at":"2025-09-12T19:38:38Z","title":"M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2509.10659","snapshot_observed_at":"2026-07-31T23:24:55.938007Z","title":"M4gn: Mesh-based multi-segment hierarchical graph network for dynamic simulations.arXiv preprint arXiv:2509.10659, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.27901","last_updated":"2026-07-30T09:17:03Z","snapshot_observed_at":"2026-08-10T18:22:05.979291Z","submitted_at":"2026-07-30T09:17:03Z","title":"Data-free neural PDE solvers based on Graph Neural Networks and weak forms","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-07-31T23:24:55.938007Z"},"links":{"cited_paper":"/paper/2509.10659","citing_paper":"/paper/2607.27901"},"observation_digest":"sha256:9e7309ac452aef192e13c8ccbeb31aeb6a3be673b3058f61c67727ca46d6f15f","observation_id":"cb0fd642-5bdf-4ec9-ba89-1b597ee7e7f7","resolution":{"observed_at":"2026-07-31T23:24:55.938007Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2509.10659/citation-record","integrity":"/paper/2509.10659/integrity","json":"/paper/2509.10659/citation-record.json","paper":"/paper/2509.10659"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T17:48:37.109827Z","title":"At this segmentation level, the model achieves the lowest RMSE and Chamfer Distance, indicating high prediction accuracy and precise shape representation","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.10659","last_updated":"2025-09-12T19:38:38Z","snapshot_observed_at":"2026-08-07T20:08:35.955158Z","submitted_at":"2025-09-12T19:38:38Z","title":"M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-04T17:48:37.109827Z"},"links":{"citing_paper":"/paper/2509.10659"},"observation_digest":"sha256:f30f8a9ff59f58c3d6bd476dcd6f4170fd69283382678cba08eaed2e11742181","observation_id":"b92f9e35-9347-44e5-a75b-25c8af77d479","resolution":{"observed_at":"2026-08-04T17:48:37.109827Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1609.02907","last_updated":"2017-02-22T09:55:36Z","snapshot_observed_at":"2026-08-13T11:38:10.906031Z","submitted_at":"2016-09-09T19:48:41Z","title":"Semi-Supervised Classification with Graph Convolutional Networks","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1609.02907","snapshot_observed_at":"2026-08-04T17:48:35.062580Z","title":"Semi-supervised classification with graph convolutional networks.arXiv preprint arXiv:1609.02907,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.10659","last_updated":"2025-09-12T19:38:38Z","snapshot_observed_at":"2026-08-07T20:08:35.955158Z","submitted_at":"2025-09-12T19:38:38Z","title":"M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-04T17:48:35.062580Z"},"links":{"cited_paper":"/paper/1609.02907","citing_paper":"/paper/2509.10659"},"observation_digest":"sha256:41f7f55adb1fec432ea33160b1f60d2f9e7f053b86e42b69ca3eff063ab650c9","observation_id":"b574385c-0d27-47aa-8956-58bb7135b7c7","resolution":{"observed_at":"2026-08-04T17:48:35.062580Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2205.02637","last_updated":"2022-05-05T13:33:03Z","snapshot_observed_at":"2026-08-13T15:49:34.827084Z","submitted_at":"2022-05-05T13:33:03Z","title":"Towards Fast Simulation of Environmental Fluid Mechanics with Multi-Scale Graph Neural Networks","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2205.02637","snapshot_observed_at":"2026-08-04T17:48:35.326706Z","title":"Towards fast simulation of environmental fluid mechanics with multi-scale graph neural networks.arXiv preprint arXiv:2205.02637,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.10659","last_updated":"2025-09-12T19:38:38Z","snapshot_observed_at":"2026-08-07T20:08:35.955158Z","submitted_at":"2025-09-12T19:38:38Z","title":"M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-04T17:48:35.326706Z"},"links":{"cited_paper":"/paper/2205.02637","citing_paper":"/paper/2509.10659"},"observation_digest":"sha256:4cf6739e688593fb0cc4d8ed64ef8a8a8d6c4fc991c2c378e35c46e9fde1ed6a","observation_id":"3fef70c9-6e37-40ab-b564-538f65fa10b8","resolution":{"observed_at":"2026-08-04T17:48:35.326706Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2010.03409","last_updated":"2021-06-18T16:32:43Z","snapshot_observed_at":"2026-08-13T21:24:13.171027Z","submitted_at":"2020-10-07T13:34:49Z","title":"Learning Mesh-Based Simulation with Graph Networks","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2010.03409","snapshot_observed_at":"2026-08-04T17:48:35.444207Z","title":"Learning mesh-based simulation with graph networks.arXiv preprint arXiv:2010.03409,","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2509.10659","last_updated":"2025-09-12T19:38:38Z","snapshot_observed_at":"2026-08-07T20:08:35.955158Z","submitted_at":"2025-09-12T19:38:38Z","title":"M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-04T17:48:35.444207Z"},"links":{"cited_paper":"/paper/2010.03409","citing_paper":"/paper/2509.10659"},"observation_digest":"sha256:a783f45e2205129b42e0f4af2f2a17db9526fef040a52bf1976e3b4bdb4a3c56","observation_id":"e02dc04e-9e51-49dc-85bc-563c96b084d4","resolution":{"observed_at":"2026-08-04T17:48:35.444207Z","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":"2026-08-04T17:48:35.586655Z","title":"U-net: Convolutional networks for biomedical image segmentation","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.10659","last_updated":"2025-09-12T19:38:38Z","snapshot_observed_at":"2026-08-07T20:08:35.955158Z","submitted_at":"2025-09-12T19:38:38Z","title":"M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-04T17:48:35.586655Z"},"links":{"citing_paper":"/paper/2509.10659"},"observation_digest":"sha256:568526d101596379afbab722b7f12a86ed80e5f000024bb44272201f8c236023","observation_id":"2f66556a-142c-4984-8fcd-413d4da1a0f0","resolution":{"observed_at":"2026-08-04T17:48:35.586655Z","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":"2026-08-04T17:48:35.708332Z","title":"Superpixels and supervoxels in an energy optimization framework","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2509.10659","last_updated":"2025-09-12T19:38:38Z","snapshot_observed_at":"2026-08-07T20:08:35.955158Z","submitted_at":"2025-09-12T19:38:38Z","title":"M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-04T17:48:35.708332Z"},"links":{"citing_paper":"/paper/2509.10659"},"observation_digest":"sha256:fa9d545c23917dd5f5c6bbcd79baab882205a2157fc325dd2999013fb0ff6f7f","observation_id":"e997e517-df68-4966-9e46-387dbd6522e2","resolution":{"observed_at":"2026-08-04T17:48:35.708332Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2408.12171","last_updated":"2024-08-22T07:33:11Z","snapshot_observed_at":"2026-08-12T22:59:30.835344Z","submitted_at":"2024-08-22T07:33:11Z","title":"Recent Advances on Machine Learning for Computational Fluid Dynamics: A Survey","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2408.12171","snapshot_observed_at":"2026-08-04T17:48:35.939705Z","title":"Recent advances on machine learning for computational fluid dynamics: A survey","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.10659","last_updated":"2025-09-12T19:38:38Z","snapshot_observed_at":"2026-08-07T20:08:35.955158Z","submitted_at":"2025-09-12T19:38:38Z","title":"M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-04T17:48:35.939705Z"},"links":{"cited_paper":"/paper/2408.12171","citing_paper":"/paper/2509.10659"},"observation_digest":"sha256:5c498bc6653bfc8cae1009b0dc693af2a5667da4d8f2b0db8f0c1617a676b68e","observation_id":"1df73cd0-1cd9-438d-ad12-cc2761c3ade5","resolution":{"observed_at":"2026-08-04T17:48:35.939705Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2003.13663","last_updated":"2020-06-17T21:45:09Z","snapshot_observed_at":"2026-08-10T10:41:42.604795Z","submitted_at":"2020-03-30T17:48:04Z","title":"Revisiting Over-smoothing in Deep GCNs","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2003.13663","snapshot_observed_at":"2026-08-04T17:48:36.103634Z","title":"Revisiting over-smoothing in deep gcns.arXiv preprint arXiv:2003.13663,","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2509.10659","last_updated":"2025-09-12T19:38:38Z","snapshot_observed_at":"2026-08-07T20:08:35.955158Z","submitted_at":"2025-09-12T19:38:38Z","title":"M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-04T17:48:36.103634Z"},"links":{"cited_paper":"/paper/2003.13663","citing_paper":"/paper/2509.10659"},"observation_digest":"sha256:6770523d05a5d91f9969bfb22902158a519788d50e0b7c2a9e18fb151db2db9f","observation_id":"03c5dca1-2388-47cc-86e2-142250a8aac3","resolution":{"observed_at":"2026-08-04T17:48:36.103634Z","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":"2026-08-04T17:48:36.705084Z","title":"For example, for triangular meshes, the aspect ratio is defined asLmax 2 √√ 3A , whereLmax is the longest edge length, A is the area of the triangle","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.10659","last_updated":"2025-09-12T19:38:38Z","snapshot_observed_at":"2026-08-07T20:08:35.955158Z","submitted_at":"2025-09-12T19:38:38Z","title":"M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-04T17:48:36.705084Z"},"links":{"citing_paper":"/paper/2509.10659"},"observation_digest":"sha256:2e484bc2e953be4a1da40a28f70bde28494aa248c3f649f5511eb3d6de220f0b","observation_id":"6b0c9afc-dbb3-4360-961e-80689d001f81","resolution":{"observed_at":"2026-08-04T17:48:36.705084Z","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":"2026-08-04T17:48:36.793004Z","title":"Segment overlap (δ) δ = 0(none), δ = 1(one -ring) Helps Eulerian or directional meshes at highNseg (smoothertransitions); canadd redundancy and hurt Lagrangian cases","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.10659","last_updated":"2025-09-12T19:38:38Z","snapshot_observed_at":"2026-08-07T20:08:35.955158Z","submitted_at":"2025-09-12T19:38:38Z","title":"M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-04T17:48:36.793004Z"},"links":{"citing_paper":"/paper/2509.10659"},"observation_digest":"sha256:fdc1df0f85b4da04845dbefaf2a98ff0dd6b761f1a77b7c886d11445c0de3c68","observation_id":"c87e84b8-9f0c-497e-b4dd-147529d33344","resolution":{"observed_at":"2026-08-04T17:48:36.793004Z","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":"2026-08-04T17:48:37.293855Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.10659","last_updated":"2025-09-12T19:38:38Z","snapshot_observed_at":"2026-08-07T20:08:35.955158Z","submitted_at":"2025-09-12T19:38:38Z","title":"M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-04T17:48:37.293855Z"},"links":{"citing_paper":"/paper/2509.10659"},"observation_digest":"sha256:31f51ee272776dfc21c3212df533e5b81d6a4597e53641360e2171070bf37beb","observation_id":"29a62fdb-6520-4b4d-82d6-0615051e0c48","resolution":{"observed_at":"2026-08-04T17:48:37.293855Z","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":"2026-08-04T17:48:37.444438Z","title":"The time of our model tours is computed by adding the time used for segmentation and inference on a single NVIDIA Tesla P100 GPU","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.10659","last_updated":"2025-09-12T19:38:38Z","snapshot_observed_at":"2026-08-07T20:08:35.955158Z","submitted_at":"2025-09-12T19:38:38Z","title":"M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-04T17:48:37.444438Z"},"links":{"citing_paper":"/paper/2509.10659"},"observation_digest":"sha256:a5163e8db1b51bcddf6d6d3f0a1280ebc4a821d171ea67c1010806238860c044","observation_id":"8bd85019-c2cd-4084-add2-a0802e11284c","resolution":{"observed_at":"2026-08-04T17:48:37.444438Z","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":"2026-08-04T17:48:36.930622Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.10659","last_updated":"2025-09-12T19:38:38Z","snapshot_observed_at":"2026-08-07T20:08:35.955158Z","submitted_at":"2025-09-12T19:38:38Z","title":"M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-04T17:48:36.930622Z"},"links":{"citing_paper":"/paper/2509.10659"},"observation_digest":"sha256:393b1d2bcbbd4695dc3a817afc1f10603717c22e6d9ac1b6f46688b6f7ce1197","observation_id":"6986691a-9c11-4d66-8385-15fe427abc4b","resolution":{"observed_at":"2026-08-04T17:48:36.930622Z","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":"2026-08-04T17:48:36.478687Z","title":"Node input includes mesh positionxi for CylinderFlow","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2509.10659","last_updated":"2025-09-12T19:38:38Z","snapshot_observed_at":"2026-08-07T20:08:35.955158Z","submitted_at":"2025-09-12T19:38:38Z","title":"M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations","version":1},"reference_index":128,"source":"pdf_text","source_observed_at":"2026-08-04T17:48:36.478687Z"},"links":{"citing_paper":"/paper/2509.10659"},"observation_digest":"sha256:df35390d21bf8c11b859c07a35fae990fc7df585d3501a14bffbb6b2ca3889ec","observation_id":"e26214ff-af9e-4b6b-8e41-0d6bd6acd4c2","resolution":{"observed_at":"2026-08-04T17:48:36.478687Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2302.10803","last_updated":"2023-03-17T08:38:35Z","snapshot_observed_at":"2026-08-13T16:18:35.132387Z","submitted_at":"2023-02-16T12:59:08Z","title":"Eagle: Large-Scale Learning of Turbulent Fluid Dynamics with Mesh Transformers","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2302.10803","snapshot_observed_at":"2026-08-04T17:48:34.950332Z","title":"Eagle: Large-scale learning of turbulent fluid dynamics with mesh transformers.arXiv preprint arXiv:2302.10803,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.10659","last_updated":"2025-09-12T19:38:38Z","snapshot_observed_at":"2026-08-07T20:08:35.955158Z","submitted_at":"2025-09-12T19:38:38Z","title":"M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations","version":1},"reference_index":1993,"source":"pdf_text","source_observed_at":"2026-08-04T17:48:34.950332Z"},"links":{"cited_paper":"/paper/2302.10803","citing_paper":"/paper/2509.10659"},"observation_digest":"sha256:125c30c4d946d09aaa690fd926cee584caa938fba74ff3ed680a2f53d752ca37","observation_id":"08e77182-826e-4212-a115-5ec82d7e7a2a","resolution":{"observed_at":"2026-08-04T17:48:34.950332Z","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":"2026-08-04T17:48:34.049835Z","title":"Propagation of ocean waves in discrete spectral wave models.Journal of Computational Physics, 68(2):307–326,","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.10659","last_updated":"2025-09-12T19:38:38Z","snapshot_observed_at":"2026-08-07T20:08:35.955158Z","submitted_at":"2025-09-12T19:38:38Z","title":"M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations","version":1},"reference_index":1998,"source":"pdf_text","source_observed_at":"2026-08-04T17:48:34.049835Z"},"links":{"citing_paper":"/paper/2509.10659"},"observation_digest":"sha256:b951f49fd979ceb6cba1d34ac4a5c666d44abca1cac558601f52e50d66bf6c70","observation_id":"7b331ee8-3e9a-4b2d-be70-550bf30675e8","resolution":{"observed_at":"2026-08-04T17:48:34.049835Z","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":"2026-08-04T17:48:36.337414Z","title":"18 B Model Details 18 B.1 M4GN Configurations","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.10659","last_updated":"2025-09-12T19:38:38Z","snapshot_observed_at":"2026-08-07T20:08:35.955158Z","submitted_at":"2025-09-12T19:38:38Z","title":"M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations","version":1},"reference_index":2005,"source":"pdf_text","source_observed_at":"2026-08-04T17:48:36.337414Z"},"links":{"citing_paper":"/paper/2509.10659"},"observation_digest":"sha256:1dba1034a9c373bbe2fd9d49cd24ea25f5ec4c4160c7ea5740e1571d3df22a91","observation_id":"de604f09-23bd-4a3d-bf12-2af0066150da","resolution":{"observed_at":"2026-08-04T17:48:36.337414Z","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":"2026-08-04T17:48:34.493104Z","title":"Multiscale meshgraphnets","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2509.10659","last_updated":"2025-09-12T19:38:38Z","snapshot_observed_at":"2026-08-07T20:08:35.955158Z","submitted_at":"2025-09-12T19:38:38Z","title":"M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations","version":1},"reference_index":2007,"source":"pdf_text","source_observed_at":"2026-08-04T17:48:34.493104Z"},"links":{"citing_paper":"/paper/2509.10659"},"observation_digest":"sha256:03eb662fd2fcaa299f4929945ada14f8592a5e4b8e15752e6f0a4d90b55df86e","observation_id":"4ab8f03c-8e21-4128-9aa9-3bf954727b98","resolution":{"observed_at":"2026-08-04T17:48:34.493104Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1810.01566","last_updated":"2019-04-18T00:37:03Z","snapshot_observed_at":"2026-08-02T02:17:27.273861Z","submitted_at":"2018-10-03T02:10:16Z","title":"Learning Particle Dynamics for Manipulating Rigid Bodies, Deformable Objects, and Fluids","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1810.01566","snapshot_observed_at":"2026-08-04T17:48:35.136017Z","title":"Deeper insights into graph convolutional networks for semi- supervised learning","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.10659","last_updated":"2025-09-12T19:38:38Z","snapshot_observed_at":"2026-08-07T20:08:35.955158Z","submitted_at":"2025-09-12T19:38:38Z","title":"M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations","version":1},"reference_index":2009,"source":"pdf_text","source_observed_at":"2026-08-04T17:48:35.136017Z"},"links":{"cited_paper":"/paper/1810.01566","citing_paper":"/paper/2509.10659"},"observation_digest":"sha256:31af264349bbaa377fd6d02e20df07b68931a69793f2fe62a32ca121c968f134","observation_id":"065dc008-6018-4c07-b8d8-cbb4c7f6eb96","resolution":{"observed_at":"2026-08-04T17:48:35.136017Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1511.06391","last_updated":"2016-02-23T22:25:12Z","snapshot_observed_at":"2026-08-11T23:24:32.551602Z","submitted_at":"2015-11-19T21:31:26Z","title":"Order Matters: Sequence to sequence for sets","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1511.06391","snapshot_observed_at":"2026-08-04T17:48:35.854280Z","title":"Order matters: Sequence to sequence for sets.arXiv preprint arXiv:1511.06391,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.10659","last_updated":"2025-09-12T19:38:38Z","snapshot_observed_at":"2026-08-07T20:08:35.955158Z","submitted_at":"2025-09-12T19:38:38Z","title":"M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations","version":1},"reference_index":2010,"source":"pdf_text","source_observed_at":"2026-08-04T17:48:35.854280Z"},"links":{"cited_paper":"/paper/1511.06391","citing_paper":"/paper/2509.10659"},"observation_digest":"sha256:0f54d8928f5c0fc7c7d8cfae93184d5afffc9fdf1265b2969b924afeea3ef2ad","observation_id":"a66dd874-cd70-4ffe-b3b8-6f212b351513","resolution":{"observed_at":"2026-08-04T17:48:35.854280Z","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":"2026-08-04T17:48:36.597973Z","title":"In our approach, we adapt SLIC to segment the mesh based on physics- informed features","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.10659","last_updated":"2025-09-12T19:38:38Z","snapshot_observed_at":"2026-08-07T20:08:35.955158Z","submitted_at":"2025-09-12T19:38:38Z","title":"M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations","version":1},"reference_index":2012,"source":"pdf_text","source_observed_at":"2026-08-04T17:48:36.597973Z"},"links":{"citing_paper":"/paper/2509.10659"},"observation_digest":"sha256:0a2a791e107c2a7c4b2b3a6caaf4d8c6130ca0fb33ffaf8f37106cd43a0c90eb","observation_id":"4181d7b1-5054-4170-8053-0a908a44611f","resolution":{"observed_at":"2026-08-04T17:48:36.597973Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2201.09113","last_updated":"2022-05-26T17:14:04Z","snapshot_observed_at":"2026-08-10T10:41:43.785929Z","submitted_at":"2022-01-22T18:32:54Z","title":"Predicting Physics in Mesh-reduced Space with Temporal Attention","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2201.09113","snapshot_observed_at":"2026-08-04T17:48:34.902571Z","title":"Predicting physics in mesh-reduced space with temporal attention.arXiv preprint arXiv:2201.09113,","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.10659","last_updated":"2025-09-12T19:38:38Z","snapshot_observed_at":"2026-08-07T20:08:35.955158Z","submitted_at":"2025-09-12T19:38:38Z","title":"M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations","version":1},"reference_index":2013,"source":"pdf_text","source_observed_at":"2026-08-04T17:48:34.902571Z"},"links":{"cited_paper":"/paper/2201.09113","citing_paper":"/paper/2509.10659"},"observation_digest":"sha256:299cf71cee8c227ff45e8d0bd8c4bbf4071904685c0eaf6162227e96133ec739","observation_id":"fbcf5ed5-96aa-42c1-8b68-8d9d235e0419","resolution":{"observed_at":"2026-08-04T17:48:34.902571Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1412.3555","last_updated":"2014-12-11T06:46:53Z","snapshot_observed_at":"2026-08-13T10:35:27.214652Z","submitted_at":"2014-12-11T06:46:53Z","title":"Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1412.3555","snapshot_observed_at":"2026-08-04T17:48:34.298032Z","title":"Empirical evaluation of gated recurrent neural networks on sequence modeling.arXiv preprint arXiv:1412.3555,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.10659","last_updated":"2025-09-12T19:38:38Z","snapshot_observed_at":"2026-08-07T20:08:35.955158Z","submitted_at":"2025-09-12T19:38:38Z","title":"M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations","version":1},"reference_index":2014,"source":"pdf_text","source_observed_at":"2026-08-04T17:48:34.298032Z"},"links":{"cited_paper":"/paper/1412.3555","citing_paper":"/paper/2509.10659"},"observation_digest":"sha256:936c49ae1defb483918afafa8d23ee16038d338946366b6ff98dcf9a8884e02f","observation_id":"a6652a81-f167-451a-9752-1792ba81f6fb","resolution":{"observed_at":"2026-08-04T17:48:34.298032Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2110.07875","last_updated":"2022-02-10T07:56:13Z","snapshot_observed_at":"2026-08-14T07:59:21.924155Z","submitted_at":"2021-10-15T05:59:15Z","title":"Graph Neural Networks with Learnable Structural and Positional Representations","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2110.07875","snapshot_observed_at":"2026-08-04T17:48:34.403907Z","title":"Graph neural networks with learnable structural and positional representations.arXiv preprint arXiv:2110.07875,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.10659","last_updated":"2025-09-12T19:38:38Z","snapshot_observed_at":"2026-08-07T20:08:35.955158Z","submitted_at":"2025-09-12T19:38:38Z","title":"M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations","version":1},"reference_index":2015,"source":"pdf_text","source_observed_at":"2026-08-04T17:48:34.403907Z"},"links":{"cited_paper":"/paper/2110.07875","citing_paper":"/paper/2509.10659"},"observation_digest":"sha256:fcf472a0051fdf14dc24611948d54cfc8160cd5ce1493e67077ead3172296738","observation_id":"c2855bef-b5ea-4b75-aebe-a51043d163d9","resolution":{"observed_at":"2026-08-04T17:48:34.403907Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2312.12467","last_updated":"2024-03-26T01:50:54Z","snapshot_observed_at":"2026-08-13T04:58:55.727205Z","submitted_at":"2023-12-19T05:30:08Z","title":"Learning Flexible Body Collision Dynamics with Hierarchical Contact Mesh Transformer","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2312.12467","snapshot_observed_at":"2026-08-04T17:48:36.236797Z","title":"Learning flexible body collision dynamics with hierarchical contact mesh transformer.arXiv preprint arXiv:2312.12467,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.10659","last_updated":"2025-09-12T19:38:38Z","snapshot_observed_at":"2026-08-07T20:08:35.955158Z","submitted_at":"2025-09-12T19:38:38Z","title":"M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations","version":1},"reference_index":2016,"source":"pdf_text","source_observed_at":"2026-08-04T17:48:36.236797Z"},"links":{"cited_paper":"/paper/2312.12467","citing_paper":"/paper/2509.10659"},"observation_digest":"sha256:57b2e133f15aecc34c45831f427ad9c55174a086b1824868f3064ff2b7601a10","observation_id":"84c3610a-4990-4729-a9a5-338f2b980973","resolution":{"observed_at":"2026-08-04T17:48:36.236797Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2106.07971","last_updated":"2022-03-15T16:16:29Z","snapshot_observed_at":"2026-08-13T19:03:38.799686Z","submitted_at":"2021-06-15T08:50:10Z","title":"Simple GNN Regularisation for 3D Molecular Property Prediction & Beyond","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2106.07971","snapshot_observed_at":"2026-08-04T17:48:34.760996Z","title":"Simple gnn regularisation for 3d molecular property prediction & beyond.arXiv preprint arXiv:2106.07971,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.10659","last_updated":"2025-09-12T19:38:38Z","snapshot_observed_at":"2026-08-07T20:08:35.955158Z","submitted_at":"2025-09-12T19:38:38Z","title":"M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations","version":1},"reference_index":2019,"source":"pdf_text","source_observed_at":"2026-08-04T17:48:34.760996Z"},"links":{"cited_paper":"/paper/2106.07971","citing_paper":"/paper/2509.10659"},"observation_digest":"sha256:e519ea82819a27cd961945ff6830569e9d15e747c14bfde76dcc07bd949ff4c2","observation_id":"70febe48-7f76-406a-bbb1-f708be72209e","resolution":{"observed_at":"2026-08-04T17:48:34.760996Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1406.1078","last_updated":"2014-09-03T00:25:02Z","snapshot_observed_at":"2026-07-06T03:45:28.546418Z","submitted_at":"2014-06-03T17:47:08Z","title":"Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1406.1078","snapshot_observed_at":"2026-08-04T17:48:34.234465Z","title":"Learning phrase representations using rnn encoder-decoder for statistical machine translation.arXiv preprint arXiv:1406.1078,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.10659","last_updated":"2025-09-12T19:38:38Z","snapshot_observed_at":"2026-08-07T20:08:35.955158Z","submitted_at":"2025-09-12T19:38:38Z","title":"M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations","version":1},"reference_index":2020,"source":"pdf_text","source_observed_at":"2026-08-04T17:48:34.234465Z"},"links":{"cited_paper":"/paper/1406.1078","citing_paper":"/paper/2509.10659"},"observation_digest":"sha256:cf04498ea270a151b431ba43794a4ffeb48c3691eaea2cfbbdb8c194ebab2929","observation_id":"a856a8d9-1293-4620-bb45-e0094fea62e6","resolution":{"observed_at":"2026-08-04T17:48:34.234465Z","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":"2026-08-04T17:48:34.554832Z","title":"Graph u-nets","venue":null,"work_id":null,"year":2083},"citing_paper":{"arxiv_id":"2509.10659","last_updated":"2025-09-12T19:38:38Z","snapshot_observed_at":"2026-08-07T20:08:35.955158Z","submitted_at":"2025-09-12T19:38:38Z","title":"M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations","version":1},"reference_index":2022,"source":"pdf_text","source_observed_at":"2026-08-04T17:48:34.554832Z"},"links":{"citing_paper":"/paper/2509.10659"},"observation_digest":"sha256:d1ba854fbaee828f41d660666c1898041a0fddb0034439cebbcc6be78f85463d","observation_id":"c9b53a11-4390-4662-8f23-59d7ca24e968","resolution":{"observed_at":"2026-08-04T17:48:34.554832Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1612.00341","last_updated":"2017-03-04T17:44:06Z","snapshot_observed_at":"2026-08-07T20:39:45.840252Z","submitted_at":"2016-12-01T16:39:04Z","title":"A Compositional Object-Based Approach to Learning Physical Dynamics","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1612.00341","snapshot_observed_at":"2026-08-04T17:48:34.146731Z","title":"A compositional object-based approach to learning physical dynamics.arXiv preprint arXiv:1612.00341,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.10659","last_updated":"2025-09-12T19:38:38Z","snapshot_observed_at":"2026-08-07T20:08:35.955158Z","submitted_at":"2025-09-12T19:38:38Z","title":"M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations","version":1},"reference_index":2023,"source":"pdf_text","source_observed_at":"2026-08-04T17:48:34.146731Z"},"links":{"cited_paper":"/paper/1612.00341","citing_paper":"/paper/2509.10659"},"observation_digest":"sha256:1bddf78ae307debd6351451e5ab963f523cb0160be04c62ed2dd13bd6b41077f","observation_id":"3fc1467e-c516-478d-a574-511fe6a9fe98","resolution":{"observed_at":"2026-08-04T17:48:34.146731Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2509.10659","last_updated":"2025-09-12T19:38:38Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-07T20:08:35.955158Z","submitted_at":"2025-09-12T19:38:38Z","title":"M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations"},"reference_resolution":{"displayed":29,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":29,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":29},"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":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 1 inbound Pith citation observation for arXiv:2509.10659."}