{"as_of":"2026-08-07T15:34:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:93f29cd46348a16acc32336290930e4417e2f29406f9d4aca34ed78be96e003b","coverage":[{"denominator":40,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":40,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T23:11:55.907765Z","state":"measured"},{"denominator":40,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":40,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-07T06:34:17.273281+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2506.19482/citation-record","integrity":"/paper/2506.19482/integrity","json":"/paper/2506.19482/citation-record.json","paper":"/paper/2506.19482"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2104.13478","last_updated":"2021-05-02T16:16:03Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2021-04-27T21:09:51Z","title":"Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2104.13478","snapshot_observed_at":"2026-08-06T23:11:55.740635Z","title":"Geometric deep learning: Grids, groups, graphs, geodesics, and gauges,","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.740635Z"},"links":{"cited_paper":"/paper/2104.13478","citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:b1c832ba2389c1a6e52fdf1698a8b66b884730a7ca3eff0b0e799cebf3063f90","observation_id":"354bf1a5-03c5-4da0-b01f-ade6bd86e61c","resolution":{"observed_at":"2026-08-06T23:11:55.740635Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T23:11:57.060438Z","title":"A survey of geometric graph neural networks: data structures, models and applications,","venue":null,"work_id":"c3800dd8-f362-4329-b54b-38b49d67c7dd","year":2025},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.745823Z"},"links":{"citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:041e19c474b26409af0755c1d7aa175a241c8cef4a17281612e3509642b3d04c","observation_id":"29111ed2-9067-4685-8031-e1f12098d780","resolution":{"observed_at":"2026-08-06T23:11:57.063961Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2312.07511","last_updated":"2024-03-13T17:38:27Z","snapshot_observed_at":"2026-07-06T17:00:37.507046Z","submitted_at":"2023-12-12T18:44:19Z","title":"A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systems","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2312.07511","snapshot_observed_at":"2026-08-06T23:11:55.749791Z","title":"A hitchhiker’s guide to geometric gnns for 3d atomic systems,","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.749791Z"},"links":{"cited_paper":"/paper/2312.07511","citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:7ca6efeadff0235dd5739ed878e507f57b4bb832ceb9f7c7f407567cc9119937","observation_id":"82171e25-d9e1-4c2d-98e6-3d06474291c6","resolution":{"observed_at":"2026-08-06T23:11:55.749791Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2307.08423","last_updated":"2025-07-24T21:15:25Z","snapshot_observed_at":"2026-07-06T15:54:47.352645Z","submitted_at":"2023-07-17T12:14:14Z","title":"Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2307.08423","snapshot_observed_at":"2026-08-06T23:11:55.754422Z","title":"Artificial intelligence for science in quantum, atomistic, and continuum systems,","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.754422Z"},"links":{"cited_paper":"/paper/2307.08423","citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:62069c429a589146c4b43d18fe0368f3d86e777dfe85921dd32e5fb5dbafa524","observation_id":"1b6147aa-d5d1-481b-90ce-f0b814922b76","resolution":{"observed_at":"2026-08-06T23:11:55.754422Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T23:11:57.049413Z","title":"Equivariant spatio-temporal attentive graph networks to simulate physical dynamics,","venue":null,"work_id":"d49d9152-26b0-4416-a047-74b049aa998d","year":2023},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.759707Z"},"links":{"citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:8700d70a0647b8d31f70749e6fe6678e01493961ebda2971c22428989e23ffea","observation_id":"246c6168-a6c2-4278-bd26-ee6d736e5b5f","resolution":{"observed_at":"2026-08-06T23:11:57.052918Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T23:11:57.038571Z","title":"Equivariant graph neural operator for modeling 3d dynamics,","venue":null,"work_id":"1e17c1d9-3ad3-4243-a442-bb2c4a889725","year":2024},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.764341Z"},"links":{"citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:977fba19e0526d6e9add1a79ad0bf372e60db3b852706a328e27786b8a4a01ac","observation_id":"fff5cbf7-8368-446a-8313-61429b9e39da","resolution":{"observed_at":"2026-08-06T23:11:57.041963Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T23:11:57.027491Z","title":"De novo design of protein structure and function with rfdiffusion,","venue":null,"work_id":"bdbb37b9-6622-4add-b14c-3a7b8849c1c9","year":2023},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.768936Z"},"links":{"citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:d2c1dea84f81e16802a015e937174b1c8ebf9c9846b37fd6a98ea1899dfb7994","observation_id":"6d771464-8685-48cc-84c8-7c33b2cf7364","resolution":{"observed_at":"2026-08-06T23:11:57.031297Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T23:11:57.015944Z","title":"Illuminating protein space with a programmable generative model,","venue":null,"work_id":"eaf7e43a-55de-4663-a527-bdfb8488c975","year":2023},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.773478Z"},"links":{"citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:cd49d39d170e5d89809d3ff566d23706ec012bd235f077c89fed46aa8d56e784","observation_id":"b4143cde-3a66-4626-b1c8-f0c0bfad2644","resolution":{"observed_at":"2026-08-06T23:11:57.019524Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T23:11:57.004396Z","title":"E (n) equiv- ariant graph neural networks,","venue":null,"work_id":"db1223e0-e2ac-4448-b625-7e73d005dbc8","year":2021},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.777273Z"},"links":{"citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:d457d41e1afaa1ffa3310e2b4ed74f47261408641441164b0459393597489655","observation_id":"bfff3790-fa88-4bcb-96c3-de20dfaff704","resolution":{"observed_at":"2026-08-06T23:11:57.008340Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T23:11:56.991382Z","title":"The fast multipole method: numerical implementa- tion,","venue":null,"work_id":"3182498e-912e-45d3-ad0e-1fec69731c93","year":2000},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.780965Z"},"links":{"citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:ed37308c16f57113be9b2b83ba350e2c31b8bad69998e68ca50142a85f97bd53","observation_id":"8a83b316-b19f-43a9-9f42-64984cbcc039","resolution":{"observed_at":"2026-08-06T23:11:56.995904Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T23:11:56.888580Z","title":"Improving equivariant graph neural networks on large geometric graphs via virtual nodes learning,","venue":null,"work_id":"caa018ca-ffd7-419f-8570-7106a8f94a12","year":2024},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.785001Z"},"links":{"citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:3cbb6034c0262f6403121e11efc606ac99018ad47e2e92b05f1230b3ceb2a901","observation_id":"24664167-f5f2-41e5-9cfb-aaa6925c4edb","resolution":{"observed_at":"2026-08-06T23:11:56.962809Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T23:11:56.725032Z","title":"Integrating structured biological data by kernel maximum mean discrepancy,","venue":null,"work_id":"8af030bd-c28c-4bde-b088-4ab8de865012","year":2006},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.788761Z"},"links":{"citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:5919bed69ec4ac73ebc39bc601b771be200653ca09c8b8939324946ec48c948c","observation_id":"6f2a5bb5-0dc8-4f65-bc4b-c72234de04da","resolution":{"observed_at":"2026-08-06T23:11:56.795456Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T23:11:56.578212Z","title":"Schnet–a deep learning architecture for molecules and materials,","venue":null,"work_id":"fb8aabd3-051c-4051-865f-45f79e238a39","year":2018},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.792534Z"},"links":{"citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:36aa8d5905e1d54bcdf72140c164098b2dcb9c519848d3161b315313f0c62add","observation_id":"fd96545f-03c7-40ac-90f0-d1f6c2df0472","resolution":{"observed_at":"2026-08-06T23:11:56.639954Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T23:11:56.448833Z","title":"Directional message passing for molecular graphs,","venue":null,"work_id":"bb48df76-db6c-4076-9322-95dab32cb242","year":2020},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.796388Z"},"links":{"citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:91c496193305d0cc7b1913466d08e596d850439fd51c412dd9e382d43d44b0f3","observation_id":"6b8c390e-0939-4451-948b-2b1fd943aca7","resolution":{"observed_at":"2026-08-06T23:11:56.488987Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1802.08219","last_updated":"2018-05-18T20:09:34Z","snapshot_observed_at":"2026-07-06T06:24:51.822169Z","submitted_at":"2018-02-22T18:17:31Z","title":"Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1802.08219","snapshot_observed_at":"2026-08-06T23:11:55.800785Z","title":"Tensor field networks: Rotation-and translation- equivariant neural networks for 3d point clouds,","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.800785Z"},"links":{"cited_paper":"/paper/1802.08219","citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:4ff8a149105ad7f94cb609336715c9ac13aa40706e9364421ac30735a2d7254a","observation_id":"061e9cf1-80a8-42db-b4bc-cb61a5f774f1","resolution":{"observed_at":"2026-08-06T23:11:55.800785Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T23:11:56.424511Z","title":"Geometric and physical quantities improve e(3) equivariant message passing,","venue":null,"work_id":"40f90c6c-ad96-4447-92db-a6bb1b9b82e7","year":2022},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.805354Z"},"links":{"citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:4325602ae3dd50483eaccba7c6401806cd8640f7636775417c936a804dfc202e","observation_id":"df51d24b-56f0-4d68-87d7-af94f0a5ac8a","resolution":{"observed_at":"2026-08-06T23:11:56.435440Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T23:11:56.405343Z","title":"Se(3)- transformers: 3d roto-translation equivariant attention networks,","venue":null,"work_id":"d3f31a20-c05d-4215-9b5b-a01c94ac33e4","year":2020},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.809770Z"},"links":{"citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:06ca1da227fd21858c6b87f6cc5e36aea11b3814309f1eb8297dc83235109a67","observation_id":"5cba3f8d-5886-4189-b3ed-9a8db9dd6610","resolution":{"observed_at":"2026-08-06T23:11:56.413001Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1910.00753","last_updated":"2019-10-02T02:42:34Z","snapshot_observed_at":"2026-07-06T08:26:17.265696Z","submitted_at":"2019-10-02T02:42:34Z","title":"Equivariant Flows: sampling configurations for multi-body systems with symmetric energies","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1910.00753","snapshot_observed_at":"2026-08-06T23:11:55.814068Z","title":"Equivariant flows: sampling configurations for multi-body systems with symmetric energies,","venue":null,"work_id":null,"year":1910},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.814068Z"},"links":{"cited_paper":"/paper/1910.00753","citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:aa6767a4f1683d2506bd8f8f91b8b681a34beef688ea0f793b4f6f278bdd36b9","observation_id":"47db26da-a02c-448a-af51-e22d9f63753b","resolution":{"observed_at":"2026-08-06T23:11:55.814068Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T23:11:56.385895Z","title":"Learning from protein structure with geometric vector perceptrons,","venue":null,"work_id":"85849d12-fc81-4e76-b524-8673a242d104","year":2021},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.818190Z"},"links":{"citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:73b6191b8f4ce2429cb74bd8c89087b7df1a5b0a8d4fa0f373d5aee9d80bb3ac","observation_id":"79b99fb7-50da-4b50-bc59-626ceb25ba94","resolution":{"observed_at":"2026-08-06T23:11:56.393939Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T23:11:56.362911Z","title":"Are high- degree representations really unnecessary in equivariant graph neural networks?","venue":null,"work_id":"dadaf830-d96b-47cd-90ed-97972655da70","year":2024},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.822629Z"},"links":{"citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:d60a1b3d83a421798d32b224e3d87845a7ccc8036ef47241d235e92c7d706345","observation_id":"2f1f67f6-4d77-47b4-8df8-a0b939ec8d4e","resolution":{"observed_at":"2026-08-06T23:11:56.373066Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T23:11:56.339781Z","title":"Neural message passing for quantum chemistry,","venue":null,"work_id":"2b5d5dec-2dd8-4271-ba97-e74ab5d37d68","year":2017},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.826649Z"},"links":{"citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:8f3f4f71409016d502210cbb52e35794b223ab8597ab53d0740ff4e66bd9ed2c","observation_id":"e9027f56-3f82-43a9-9a16-e4690bdca4d9","resolution":{"observed_at":"2026-08-06T23:11:56.348595Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1708.04357","last_updated":"2017-08-14T23:47:02Z","snapshot_observed_at":"2026-07-06T05:55:18.328353Z","submitted_at":"2017-08-14T23:47:02Z","title":"Graph Classification via Deep Learning with Virtual Nodes","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1708.04357","snapshot_observed_at":"2026-08-06T23:11:55.830579Z","title":"Graph classi- fication via deep learning with virtual nodes,","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.830579Z"},"links":{"cited_paper":"/paper/1708.04357","citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:4694e62aee31c41e9c5d3c22f513da26796629bb393937d952d324d27e015d98","observation_id":"8a86d18a-8ade-4339-9790-cbba542d3a4f","resolution":{"observed_at":"2026-08-06T23:11:55.830579Z","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":"2026-08-06T23:11:55.834960Z","title":"An analysis of virtual nodes in graph neural networks for link prediction,","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.834960Z"},"links":{"citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:b35985369dff135723d946b4b9c3363d3a1c81a4de31ddc7a28bf78e060520f3","observation_id":"97f08c77-9659-46ce-a12a-397e4fd0d9cb","resolution":{"observed_at":"2026-08-06T23:11:55.834960Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T23:11:56.304374Z","title":"Learning physical dynamics with subequivariant graph neural networks,","venue":null,"work_id":"039cce96-7652-43da-9ee9-0c512cc7038a","year":2022},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.839043Z"},"links":{"citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:097cfb6fa916b26dc3c0e3156b048abc3c435bb191051f91eb04d8df2843878b","observation_id":"655cdac9-45ce-4c3d-8862-71eaa4134757","resolution":{"observed_at":"2026-08-06T23:11:56.319048Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T23:11:56.277086Z","title":"Conditional antibody design as 3d equivariant graph translation,","venue":null,"work_id":"42805e7c-c382-47f8-a375-0807da779659","year":2023},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.842864Z"},"links":{"citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:25591c864d39db9b09ffbf87da2f82417647cc6237fcfd499396e5a459b3a6ad","observation_id":"ee89221e-ddef-4d4c-9ca1-3e5356d0d666","resolution":{"observed_at":"2026-08-06T23:11:56.287741Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T23:11:56.250279Z","title":"Graph neural networks: Scalability,","venue":null,"work_id":"a20635ab-c691-44d0-9152-126cfed32c4d","year":2022},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.847497Z"},"links":{"citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:cea9152c5fb4e06b17f4e35ce02c73e5c68ce90e96bcc8beba715fa69e5aa818","observation_id":"9054ea29-bf5c-42f5-b374-4cb5ee050550","resolution":{"observed_at":"2026-08-06T23:11:56.260759Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T23:11:56.222733Z","title":"Scalable and effective graph neural networks via trainable random walk sampling,","venue":null,"work_id":"849e7842-48dc-4a67-b29e-f81ae281d088","year":2025},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.851665Z"},"links":{"citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:1476e79c4d0be65712b19aa28dc97ea463fb46f1d53190382a2e163dd70750e8","observation_id":"da25675d-349f-44c9-bd27-783eee847916","resolution":{"observed_at":"2026-08-06T23:11:56.233149Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T23:11:56.198656Z","title":"Distgnn: Scalable distributed training for large-scale graph neural networks,","venue":null,"work_id":"2ab71c19-b49b-47c9-b498-60735f9a78f0","year":2021},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.856003Z"},"links":{"citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:48a6916378248826172d24b93310222f940006d3162edbc6d1d06f4574f6795f","observation_id":"febebfec-4143-4f0b-aecd-36917dcb4d20","resolution":{"observed_at":"2026-08-06T23:11:56.207985Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T23:11:56.181947Z","title":"Equivariant graph mechanics networks with constraints,","venue":null,"work_id":"091a73d9-24e5-46bd-96b8-106e4f5169c0","year":2022},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.859887Z"},"links":{"citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:26c952cc820287764d353a4aece2d4e754393c99cbcc71f7e5816305d5337614","observation_id":"3913fcdb-11f5-44c1-bd67-cd6909807a19","resolution":{"observed_at":"2026-08-06T23:11:56.186476Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T23:11:56.168818Z","title":"Scalars are universal: Equivariant machine learning, structured like classical physics,","venue":null,"work_id":"256d10ed-1ef7-4b45-8a19-2b48e07b11dc","year":2021},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.863869Z"},"links":{"citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:d78efc3cd9d535c5adb1bcebc054daa918393138dd887179361cf5f90ab6dd79","observation_id":"6e7d6d15-9142-4581-b7c7-194218549549","resolution":{"observed_at":"2026-08-06T23:11:56.173001Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T23:11:56.154247Z","title":"Metis—a software package for parti- tioning unstructured graphs, partitioning meshes and computing fill-reducing ordering of sparse matrices,","venue":null,"work_id":"f5a6fc8a-5464-4054-a7ac-7c3c196b1e6b","year":1997},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.868275Z"},"links":{"citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:2185c088a3e890c43984deff70403f9bf3d3af178603bd4f4ea388003d53fa4f","observation_id":"c209b2de-6ae0-472d-a1bd-0d9f6b993bc6","resolution":{"observed_at":"2026-08-06T23:11:56.159579Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T23:11:56.139873Z","title":"Neu- ral relational inference for interacting systems,","venue":null,"work_id":"8644e0b8-063b-4a8e-b5e7-58075a29f22d","year":2018},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.872170Z"},"links":{"citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:016b6ea10d9580c54957ee6a7e1a4dcd3124fd21534370373d6c21eb458d68df","observation_id":"0b6d6f15-0a1b-455f-80c2-b212c3a92721","resolution":{"observed_at":"2026-08-06T23:11:56.144944Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T23:11:56.124845Z","title":"Equivariant graph hierarchy-based neural networks,","venue":null,"work_id":"b845ec54-ab91-493e-ba89-2b4ebda80b62","year":2022},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.877112Z"},"links":{"citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:367b23be1b0b4e4f0f2e9f1097b4b28ae383526f43baad7f40f9c3b0baddd659","observation_id":"b18e4e26-3dd7-478d-b928-f79ab3775f8d","resolution":{"observed_at":"2026-08-06T23:11:56.130162Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T23:11:56.111566Z","title":"MDAnalysis: A Python Package for the Rapid Analysis of Molecular Dynamics Simulations,","venue":null,"work_id":"771cc5e7-6047-4576-b3fd-f7651c09ab32","year":2016},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.881088Z"},"links":{"citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:6940767ea50332b48f6a6167c173da9f6c0ec1c0e5475c700eae88e788a0fdf3","observation_id":"805d1739-2512-427e-9664-b49b9c13389a","resolution":{"observed_at":"2026-08-06T23:11:56.116405Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T23:11:56.096761Z","title":"Molecular dynamics trajectory for benchmarking mdanalysis,","venue":null,"work_id":"813097c1-704c-43ce-8e9f-36a011b00191","year":2017},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.884895Z"},"links":{"citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:41efc4c612a38c9d36da1ac571e3ccfd79969179c5e0026d2c3c889d1632c894","observation_id":"955d4570-1206-40b1-93a8-97dc3def7630","resolution":{"observed_at":"2026-08-06T23:11:56.101703Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T23:11:56.082356Z","title":"Learning to simulate complex physics with graph networks,","venue":null,"work_id":"1f12c713-2cff-4307-8e6c-a181c89e489a","year":2020},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.889231Z"},"links":{"citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:ccd2f06e58fca699691ea30b2edc49e8c3c2921e6cbc6cfc7d72929194eaf82f","observation_id":"c78c45f5-a7e7-46d2-9406-1ee7d9e744b6","resolution":{"observed_at":"2026-08-06T23:11:56.086587Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T23:11:56.067197Z","title":"La- grangian fluid simulation with continuous convolutions,","venue":null,"work_id":"d373bdd0-826d-4b80-82f6-372244ec78bb","year":2020},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.893948Z"},"links":{"citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:b17912150b741746198bb8927ea7308f099018fbc3df2e8bdb82041394e632cf","observation_id":"2c3ce3c2-03a5-4be4-bec4-425007a974ea","resolution":{"observed_at":"2026-08-06T23:11:56.072702Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T23:11:56.053506Z","title":"SPlisHSPlasH Library","venue":null,"work_id":"8a4c92b3-c05f-46be-8fcc-7da3b8905789","year":null},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.898319Z"},"links":{"citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:b3558926f01be679791b76d89b4593ece07072084b29b9c5d214993d09a2e2ee","observation_id":"55db67dd-b3ff-4868-96d9-bb85cd67e4ff","resolution":{"observed_at":"2026-08-06T23:11:56.057896Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T23:11:56.039924Z","title":"AMONG THEM , F LUID 113K IS OUR GENERATED LARGE -SCALE FLUID SIMULATION DATASET , WHERE EACH GRAPH CONTAINS OVER 100K NODES AND AN AVERAGE OF 1.7M EDGES","venue":null,"work_id":"b2b8492f-627c-4310-98bf-a97cc2432a28","year":null},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.903325Z"},"links":{"citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:4e2172697446696457dda306922c5920097c4d8b7c40e466879257d430fcf0a5","observation_id":"5842ed2f-b19f-4041-bdee-71faae872cd7","resolution":{"observed_at":"2026-08-06T23:11:56.044635Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T23:11:56.023324Z","title":"(10) 1.5 1 .0 1 .5 3 .0 Balancing factor λ in Eq","venue":null,"work_id":"e3ca454d-c4e4-4554-9377-ed16e3ae59d7","year":2000},"citing_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-06T23:11:55.907765Z"},"links":{"citing_paper":"/paper/2506.19482"},"observation_digest":"sha256:3e6c3734d4549214ea96ce0e068fa4b1a985c6c9949d43bb0e5450299ddc157f","observation_id":"9f8e0f90-53f1-402f-8d04-a99948ba6cc3","resolution":{"observed_at":"2026-08-06T23:11:56.029808Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-06T23:04:34.586817Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning"},"reference_resolution":{"displayed":40,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":7,"verified_exact":0,"verified_fuzzy":33},"total_outbound_references":40},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"thesis":"As of 7 August 2026, this Paper Citation Record lists 40 of 40 outbound references and 0 inbound Pith citation observations for arXiv:2506.19482."}