{"as_of":"2026-08-18T08:38:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:b9cf7c1aa9707f41b13b3b0e7f24934e75ee0e567ce2c1a8ce2b8c1296e57080","coverage":[{"denominator":63,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":63,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-16T00:32:51.741884Z","state":"measured"},{"denominator":63,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":63,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-18T06:34:40.430872+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/2608.12010/citation-record","integrity":"/paper/2608.12010/integrity","json":"/paper/2608.12010/citation-record.json","paper":"/paper/2608.12010"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:32:51.153532Z","title":"Scaling Learning Algorithms Towards","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.153532Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:8d6262f044993326e8a3974350ed2925f8c6a9fd48cdb28db7a7f7aaeaa8e174","observation_id":"ef115073-4a95-42c0-a1ad-80ecfbcf3152","resolution":{"observed_at":"2026-08-16T00:32:51.153532Z","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":"2026-08-16T00:32:51.166873Z","title":"and Osindero, Simon and Teh, Yee Whye , journal =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.166873Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:c8f8b6b1ff499d67df83c6cdc9effbc8094fa9cf68d3a3ef7efe6641bf529dea","observation_id":"ea0525c2-7ddc-406f-bea5-c353241ce93c","resolution":{"observed_at":"2026-08-16T00:32:51.166873Z","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":"2026-08-16T00:32:51.174894Z","title":"2016 , publisher=","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.174894Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:7117ce5403de7659070f3b64d6590b6acd06cdfa4540bd52f5b34e8241b6b5bf","observation_id":"a38cd10d-c7da-4549-94f3-60da3266b77a","resolution":{"observed_at":"2026-08-16T00:32:51.174894Z","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":"2026-08-16T00:32:53.602375Z","title":"International conference on machine learning , pages=","venue":null,"work_id":"b7a1bba9-b780-49fa-8e7a-296d360f43f6","year":2023},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.180717Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:75558e86810844221ee4d385152312d84cd9393ffbc8cd39a1252c769e231fce","observation_id":"4b68a169-eba9-4a30-a12a-4b866977e7c5","resolution":{"observed_at":"2026-08-16T00:32:53.614168Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:32:53.575650Z","title":"Topology from the differentiable viewpoint , isbn =","venue":null,"work_id":"7a86d290-e347-4177-b926-675758e3f259","year":null},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.194822Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:d4304251738ce5078e1213c7f1b615b5db16a5eb974670e17e1db519eb52945c","observation_id":"b04cd9b0-e8cd-4bc9-a304-e70cc3229536","resolution":{"observed_at":"2026-08-16T00:32:53.586102Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:32:53.552815Z","title":", year =","venue":null,"work_id":"61724a1e-ff9c-4325-a9f9-4793233ca19f","year":null},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.204889Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:3c1c62ddcbd37183556e13f750d26aa8a57a1357360fb2e87bbc3df5de6673b9","observation_id":"07fba1d1-ecaf-471b-80cf-9d71e541737b","resolution":{"observed_at":"2026-08-16T00:32:53.559600Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:32:53.512140Z","title":"2007 , publisher=","venue":null,"work_id":"30c87c01-0dac-487f-b4bd-7271874e25cc","year":2007},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.212921Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:053e2c0c7d1f202f5215af80d423472b9fa516ad7aea90d4059e892ce66dd9dd","observation_id":"d0674f86-37b4-47fb-9472-e43ffa40392c","resolution":{"observed_at":"2026-08-16T00:32:53.525584Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:32:53.479790Z","title":"Symmetry defects and broken symmetry","venue":null,"work_id":"cd420271-15df-4997-ac12-5d37e262be48","year":null},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.220495Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:05efef3464b884ddb1ab405e84487880fee04fa2d0b9fd79e09f7c99db0d9efe","observation_id":"16b2e6b1-04ee-4370-80e1-822a5275292d","resolution":{"observed_at":"2026-08-16T00:32:53.492256Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:32:53.450563Z","title":"Pattern selection with","venue":null,"work_id":"4ffa60e2-c020-494e-a86c-d1df42d3ee90","year":1984},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.227760Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:0e5f91ad213cf2a6aefe6731913ca9b8023261e1baf3483eb93086bcd7a91e71","observation_id":"0ee41d44-d671-490d-9e46-d6a7c1fbca7f","resolution":{"observed_at":"2026-08-16T00:32:53.457051Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:32:53.428476Z","title":null,"venue":null,"work_id":"527a4b07-a365-45f8-b582-e55e6ab58fcc","year":2001},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.235497Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:4b6877c7531332c0d19e2f70f7d8ebf4defb691231e18cd6cb71551ed88f6838","observation_id":"695747af-22a3-424b-b0d9-0df62eaa0da6","resolution":{"observed_at":"2026-08-16T00:32:53.435257Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:32:53.400872Z","title":"1972 , publisher=","venue":null,"work_id":"94f3ee55-0184-480a-be2c-035a6e74c386","year":1972},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.242423Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:4f1d5ae2542814e3f7e9fd2449e143a524cb871ed80ac9c89375affb3c862b60","observation_id":"3260b8ef-91b2-4ac5-a0d1-b0f2e7400aa4","resolution":{"observed_at":"2026-08-16T00:32:53.409422Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2301.08599","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:32:52.323391Z","title":"arXiv preprint arXiv:2301.08599v2 , year=","venue":null,"work_id":"f633226b-3d64-4c3b-b74e-34e7fb8a27a8","year":null},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.260791Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:d32f8364e58063aa96b487bc85fbb0eac74c1e5c4a7122619f064b1f3e9b22b6","observation_id":"11a2dd0f-b599-4245-9ac4-00c7432ac40a","resolution":{"observed_at":"2026-08-16T00:32:52.334929Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:32:51.268871Z","title":"The Annals of Mathematics , author =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.268871Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:508d64d5cbea08b75b60d75082117c41ea43e926030ef46ea4d9f5d429536d07","observation_id":"40fe9fce-3c25-4b44-b8b2-6d11fd7f60a4","resolution":{"observed_at":"2026-08-16T00:32:51.268871Z","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":"2026-08-16T00:32:53.373689Z","title":"2003 , url =","venue":null,"work_id":"3a6ec6bb-6f94-4c32-9cb2-2f30bad8f3f0","year":2003},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.276143Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:0298aead26136c3374ec3ad9ec1168a8bdce1df9c9ad30e5b8af1727afdb533a","observation_id":"606dfe53-91ee-4df3-a433-e384da4481f5","resolution":{"observed_at":"2026-08-16T00:32:53.381151Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:32:53.343972Z","title":"Group theory and its application to physical problems , publisher =","venue":null,"work_id":"b99cb7be-1f56-47d3-9315-32e129f85bf9","year":null},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.283711Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:ec701184356ba30572928445756c885d4c66cd892d60934bf0cfcf172e7e2b88","observation_id":"9ce72445-7815-4ecf-8eb4-6ded78ccfe1f","resolution":{"observed_at":"2026-08-16T00:32:53.357542Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:32:53.320911Z","title":", year =","venue":null,"work_id":"b62518d0-5fa7-4652-8904-ed86efb0a7d8","year":null},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.292500Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:b6b9a2eb1a5e12ec407a6f59034d6b46032f31d2834847d641c9efe59235b695","observation_id":"529063fc-8d0f-4d5b-8706-e0bef8d4d99c","resolution":{"observed_at":"2026-08-16T00:32:53.328989Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:32:53.295432Z","title":"Canadian Journal of Mathematics , volume=","venue":null,"work_id":"5d811c52-3a6d-49c7-b59e-8fc1ee99bf1b","year":1954},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.300561Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:06e6097b09ec064a6a4751faed67630db10d5b07c79a20278048165e16533af5","observation_id":"f327b06c-a161-4b3c-9764-105ab9497cce","resolution":{"observed_at":"2026-08-16T00:32:53.304529Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:32:53.270046Z","title":"Introduction to Number Theory , rights =","venue":null,"work_id":"2fe186a7-2d6c-48ff-bcf1-a8742bf48285","year":1982},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.310813Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:5946ced8460c2a1de37ea81e686ddbcd37a01978df8f6f99171103d533c85c9a","observation_id":"87881a5d-551d-46a3-8bfa-8ef79f0e209f","resolution":{"observed_at":"2026-08-16T00:32:53.276674Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:32:53.237324Z","title":"and Gusein-Zade, S.M","venue":null,"work_id":"c4a80006-058e-44c9-82b5-7ed64d309a14","year":null},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.319294Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:2793b14b9f8ac6285604c9a539cb4e4c926708b8271c6345b9cd6b5d3725f9cf","observation_id":"9dea223b-79b3-4a48-b857-d1ca578db4da","resolution":{"observed_at":"2026-08-16T00:32:53.246633Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:32:53.213056Z","title":"Transactions of the American Mathematical Society , volume=","venue":null,"work_id":"9d512f4a-ea70-412e-b73a-3d92109407ef","year":null},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.330767Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:a3efc21fe74b307d787a5e49d602448005833611eb51c59471a7f1397bc2b786","observation_id":"fa81526e-6534-435b-94b5-fb7b625dc9d7","resolution":{"observed_at":"2026-08-16T00:32:53.220323Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/978-1-4612-2972-8_33","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-17T11:03:46.409680Z","title":"Local Properties of Analytic Varieties , isbn =","venue":"Birkhäuser Boston eBooks","work_id":"79def997-470b-4a9d-8abb-3fcc0930c7f3","year":1992},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.338288Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:d63aac340aa55ccf7722b540b1688f82601cb5a2985b2972fa247d42e1803138","observation_id":"9d804d59-8642-4910-804a-c40e341168f5","resolution":{"observed_at":"2026-08-16T00:32:51.854461Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.2307/1994017","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:32:51.821556Z","title":null,"venue":null,"work_id":"4a0694c9-41bd-45e5-a0b7-ed68831f523b","year":1965},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.347629Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:08a67f839bfe767860debea8c35dec23d2f8c815fc5dc92b9043bc206c499ddb","observation_id":"1f12c3e5-06e9-4e84-a56a-51db053e6d92","resolution":{"observed_at":"2026-08-16T00:32:51.829189Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/bf01410081","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:32:51.798046Z","title":"Stability of transversality to a stratification implies Whitney (a)-regularity , volume =","venue":null,"work_id":"cdf48524-e830-4b91-9f84-6a45156bed16","year":null},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.362306Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:5e5309de32b138d9e1569ca4b2c5ad96e2e6e17bd23a0a4e04f88631719950f4","observation_id":"bc1fc153-06e8-47f7-904f-81518dbacff3","resolution":{"observed_at":"2026-08-16T00:32:51.806675Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:32:53.185577Z","title":"Real and complex singularities, Oslo , author=","venue":null,"work_id":"c48190a2-1e6f-43e7-85ce-eaae0305bca3","year":null},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.369818Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:cbfa05ce82120e6d74df1ec9e5c164cb2de48f330692b51f123e8f0ced790bef","observation_id":"6413d1d8-6baf-49c3-ad49-09f98f7cabe6","resolution":{"observed_at":"2026-08-16T00:32:53.193940Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:32:53.166177Z","title":", year =","venue":null,"work_id":"f4322a70-4618-455a-86b4-6a955c58e0ec","year":null},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.377687Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:961fd357566cb1ad554190e1f85120c781bdb2d6d25ea261186beccaf7df1bb2","observation_id":"5b64a75e-a3bf-45d2-9ab4-e0556c89d3af","resolution":{"observed_at":"2026-08-16T00:32:53.171977Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:32:53.143930Z","title":"Stable mappings and their singularities , isbn=","venue":null,"work_id":"2245499d-3b07-4870-83d7-a5662a5e9d0d","year":null},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.384685Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:3bbba93602019998887585375594aee906f5cd4412562a9ba86cc48cb6afcb50","observation_id":"d7b0ea35-d713-4b71-9432-a1b4c9e9dc83","resolution":{"observed_at":"2026-08-16T00:32:53.151938Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:32:51.406062Z","title":"Handbook of geometry and topology of singularities I , pages=","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.406062Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:0412a9e44cbbaf818816f2cd8ad1c8ab5372e15b95ed2e7cbe8e129ea3995046","observation_id":"ca9a49dc-ff5d-4399-b5f6-cde4e1f31914","resolution":{"observed_at":"2026-08-16T00:32:51.406062Z","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":"2026-08-16T00:32:53.100656Z","title":"Archiv der Mathematik , volume=","venue":null,"work_id":"a28804ca-2b50-4a99-8e32-616cfa7c54a3","year":2003},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.415981Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:dfd294aa9b7e55e62cdb412eadbeae5eb3651e615f408b4b6b51b2811d178198","observation_id":"16c2d810-0417-4216-84be-eddcdd08a218","resolution":{"observed_at":"2026-08-16T00:32:53.107233Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:32:53.079609Z","title":"Differential topology , isbn=","venue":null,"work_id":"f032c698-03ac-4d1d-812f-31369f110bed","year":null},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.423342Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:f8d4c5323b2f5092cc9f7e478f26626171052a840bd3cbd4d7b7f9194a5ad975","observation_id":"111ffd6d-4eb1-45af-86db-caef9678115b","resolution":{"observed_at":"2026-08-16T00:32:53.086641Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:32:53.046829Z","title":"Acta numerica , volume=","venue":null,"work_id":"9a0cdb27-6215-49ab-9bea-375d86d313a2","year":1999},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.431905Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:b79f3162460ccc185a2a2038b2f51fc0f3d15201640d03881db30f9e549ee610","observation_id":"9c4b3f3f-133b-47be-b7a8-6f769b1edf7d","resolution":{"observed_at":"2026-08-16T00:32:53.058036Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:32:53.021657Z","title":"On the Universality of Rotation Equivariant Point Cloud Networks , booktitle =","venue":null,"work_id":"21d9aeae-1809-4526-a6c1-0d4c363dd691","year":null},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.442819Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:b46ec7702cb2e5755dc06f579b0223fea2390dba1c7253994975077384245e32","observation_id":"a5068ecb-1525-4db4-81c5-06fe54ef8929","resolution":{"observed_at":"2026-08-16T00:32:53.029401Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:32:51.458421Z","title":"2007 , publisher=","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.458421Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:091f7b8c1f7246c0c5785676dc0bbd87065d8a67b18c2c4bdf6befa1ec8ad916","observation_id":"a276f870-f666-4e26-8eda-509faca7ffb1","resolution":{"observed_at":"2026-08-16T00:32:51.458421Z","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":"2026-08-16T00:32:52.971000Z","title":"Advances in Neural Information Processing Systems , author =","venue":null,"work_id":"869d90be-7f0b-4492-947f-1ea043bf6d4c","year":2024},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.467617Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:c9e6e1ea0a5e5f3912f5a0a51a86535697b88e7d127a3687d2d74c7a4af7e039","observation_id":"5b08b6fd-376a-42a8-aafc-11f5ac9450c5","resolution":{"observed_at":"2026-08-16T00:32:52.979897Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:32:52.939954Z","title":"Symmetry Breaking and Equivariant Neural Networks , booktitle =","venue":null,"work_id":"929094b7-5fd5-4334-9565-4127463a8b30","year":null},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.478872Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:6f5aa6758ecaf1e8563e1b7792e35a1ee88638e12853756465a0d4f6b24d3f09","observation_id":"43e749ed-2835-4524-abed-9db70253d2f5","resolution":{"observed_at":"2026-08-16T00:32:52.949101Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:32:52.914735Z","title":"Physical Review Research , volume=","venue":null,"work_id":"663ffa69-a80d-40c8-9209-41e9e9627f58","year":2021},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.486766Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:ffa704ea246c06e756d0ca12530c8279eb072b3e43a376fb36bef15167bc01ac","observation_id":"52a83b7a-b700-4c77-aead-2971656ab0b5","resolution":{"observed_at":"2026-08-16T00:32:52.923013Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1802.08219","last_updated":"2018-05-18T20:09:34Z","snapshot_observed_at":"2026-08-18T04:32:47.717269Z","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":"2026-08-16T00:32:51.493249Z","title":"arXiv preprint arXiv:1802.08219 , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.493249Z"},"links":{"cited_paper":"/paper/1802.08219","citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:faa592636cb70bfc0f7e6251198ff78017736895e96b6be6b0931bb7df0f2a0c","observation_id":"056eb359-0293-4d47-881f-5807f42a2ae4","resolution":{"observed_at":"2026-08-16T00:32:51.493249Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2207.09453","last_updated":"2022-07-18T21:19:40Z","snapshot_observed_at":"2026-08-16T16:45:00.963998Z","submitted_at":"2022-07-18T21:19:40Z","title":"e3nn: Euclidean Neural Networks","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2207.09453","snapshot_observed_at":"2026-08-16T00:32:51.503004Z","title":"arXiv preprint arXiv:2207.09453 , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.503004Z"},"links":{"cited_paper":"/paper/2207.09453","citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:68dbf45b967cc1d1ad1865a91273fa4be1dc605db7ac31844e2a4241999da542","observation_id":"e4beda23-7ac0-44d3-ad36-f2e10550b779","resolution":{"observed_at":"2026-08-16T00:32:51.503004Z","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":"2026-08-16T00:32:52.884862Z","title":null,"venue":null,"work_id":"3843a750-8325-42cf-94f9-98eb3e16491d","year":2016},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.511864Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:87cc22ae845b1015e145671568b4e6cdb27fc7ab9da9ea3aeec295d4ed83372d","observation_id":"18eb0d07-1b33-4d09-aba5-cc44740025fc","resolution":{"observed_at":"2026-08-16T00:32:52.893826Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:32:52.859596Z","title":null,"venue":null,"work_id":"ea98e33b-9569-4bde-8c1e-bf4230d6d4a6","year":2022},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.519264Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:ad60beff14de516ff0229cfe98722f09372c22b7885ec8185a00e021de913196","observation_id":"79084e3b-183d-42f8-8a97-205b5fd57889","resolution":{"observed_at":"2026-08-16T00:32:52.866702Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:32:52.832209Z","title":"1970 , location =","venue":null,"work_id":"1e6178b4-5ac9-44c4-9de3-78283d6ead45","year":1970},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.527314Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:926e4d2bca819c265aa23958b967ecb2d98a895e3612fc983c2b7d5ea25c7ba5","observation_id":"2aba6bb3-f676-4935-9998-a164da9dafda","resolution":{"observed_at":"2026-08-16T00:32:52.839036Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:32:51.536423Z","title":"Scientific data , volume=","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":42,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.536423Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:4e0044cd571cabb7516378c1666d79cb665140cb39006996d8c6fea26923df6c","observation_id":"b6482053-503a-43ab-abfd-a0baa39c367e","resolution":{"observed_at":"2026-08-16T00:32:51.536423Z","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":"2026-08-16T00:32:52.793720Z","title":"2025 , url =","venue":null,"work_id":"f9b974d9-0dfd-4df3-8c39-9e27882a644d","year":2025},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":43,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.544811Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:94b8d32dc40e16f4acc78349ec6909433858679acac58df9ec2fcc0f635b7a76","observation_id":"8eaaa01d-68fe-4fd9-8826-a8e329097b23","resolution":{"observed_at":"2026-08-16T00:32:52.800406Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1903.02428","last_updated":"2019-04-25T10:06:09Z","snapshot_observed_at":"2026-08-02T18:54:43.326912Z","submitted_at":"2019-03-06T14:50:02Z","title":"Fast Graph Representation Learning with PyTorch Geometric","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1903.02428","snapshot_observed_at":"2026-08-16T00:32:51.556224Z","title":"arXiv preprint arXiv:1903.02428 , year=","venue":null,"work_id":null,"year":1903},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":44,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.556224Z"},"links":{"cited_paper":"/paper/1903.02428","citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:b2766eba4034ae421ea73ff18ae2cd575d6ac3a85297915f648987e0754e9597","observation_id":"358dbb9d-1e04-4370-9257-a3cae2468c38","resolution":{"observed_at":"2026-08-16T00:32:51.556224Z","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":"2026-08-16T00:32:52.767425Z","title":"Artificial Intelligence Chemistry , pages=","venue":null,"work_id":"be905b73-46dd-403e-8bd2-6a531ebb03dd","year":2025},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.564022Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:ecfa483ac660d5406611b2f2192f3bd42a3a47fb7448b71bc2d69aa7fc05de49","observation_id":"e25061ff-81eb-499b-b445-30f97be97ab1","resolution":{"observed_at":"2026-08-16T00:32:52.773822Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2207.02862","last_updated":"2023-03-02T19:00:00Z","snapshot_observed_at":"2026-08-16T16:47:51.985920Z","submitted_at":"2022-07-06T18:00:00Z","title":"Verifying the Union of Manifolds Hypothesis for Image Data","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2207.02862","snapshot_observed_at":"2026-08-16T00:32:51.576355Z","title":"arXiv preprint arXiv:2207.02862 , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":46,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.576355Z"},"links":{"cited_paper":"/paper/2207.02862","citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:e62e8d3dfc14ffc32e1791ab06b5dc3e45cf0e5e9360b7be8312387cbd8928ff","observation_id":"af0190cd-303f-4ac0-b179-cca1a0c846d4","resolution":{"observed_at":"2026-08-16T00:32:51.576355Z","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":"2026-08-16T00:32:51.584552Z","title":"2021 , eprint=","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":47,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.584552Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:051cabf8582e1cd0157041818f4d46e4d07c48d3623616496b6323eeab546133","observation_id":"d0fe0d06-b6ac-4126-bc8e-0ab28bf77de6","resolution":{"observed_at":"2026-08-16T00:32:51.584552Z","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":"2026-08-16T00:32:52.709221Z","title":"Deep Learning in Drug Design , pages=","venue":null,"work_id":"b7334fc1-428f-429c-a895-2696e7f1c300","year":2026},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":48,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.593090Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:d870357f8bb258470273b5dfeec25c88cbfc0ed9c25e499824a16395ce935132","observation_id":"1cfb025d-d987-488a-8dc0-5c14a4ed5193","resolution":{"observed_at":"2026-08-16T00:32:52.723734Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:32:52.684065Z","title":"Universally Invariant Learning in Equivariant","venue":null,"work_id":"58105d93-f696-438b-87b0-8c09a16c1990","year":null},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":49,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.600041Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:96da01be0979d85fb07b700a56f59a351cdd0a3d04ddc29ca64dcafe0f0b7207","observation_id":"68715f2a-7cf9-4953-ad6d-87d9dc069415","resolution":{"observed_at":"2026-08-16T00:32:52.689808Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:32:52.666623Z","title":"Forty-first International Conference on Machine Learning , year=","venue":null,"work_id":"e19a1385-640f-4cd7-a65a-605cb14cf05c","year":null},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":50,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.616799Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:856a964abbe4cbf0e6f7d4983ee803dff564abc703df972517670c6f4867b9c0","observation_id":"86a83632-aeb0-4e9d-b33e-84e0a3d4b3b2","resolution":{"observed_at":"2026-08-16T00:32:52.672225Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2506.19482","last_updated":"2025-06-24T10:17:38Z","snapshot_observed_at":"2026-08-18T03:29:30.836741Z","submitted_at":"2025-06-24T10:17:38Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","version":1},"cited_work":{"arxiv_id":"2506.19482","doi":null,"metadata_source":"pith","pith_arxiv_id":"2506.19482","snapshot_observed_at":"2026-08-16T00:32:52.124009Z","title":"Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning","venue":"cs.LG","work_id":"a0b30575-7dda-480d-8b60-624be93fe342","year":2025},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":51,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.623263Z"},"links":{"cited_paper":"/paper/2506.19482","citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:eaf016e7d43d48a05cc2830717ae478a230d4f980629d2d04e396bff6e14aace","observation_id":"ad43975f-eb4a-4c31-9182-a2becd6bb379","resolution":{"observed_at":"2026-08-16T00:32:52.131588Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:32:52.624978Z","title":"International Conference on Learning Representations , year=","venue":null,"work_id":"1fd45601-50f3-4ad6-b1de-2c30c4014289","year":null},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":52,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.629707Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:612dc197ef73fd89056641d5291645a53f08fed926a80ad554569e79abc2ef04","observation_id":"ae359b28-fecc-44ca-b739-8c2ce334e9d7","resolution":{"observed_at":"2026-08-16T00:32:52.632966Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:32:51.642514Z","title":"International Conference on Machine Learning , pages=","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":53,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.642514Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:ec17e2649ae0061b8934fcd2b174a2029941efdc9cee3ee69c53132fda0796b0","observation_id":"c64e1ab9-98d3-4317-8338-c8409c4bfa8f","resolution":{"observed_at":"2026-08-16T00:32:51.642514Z","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":"2026-08-16T00:32:51.648869Z","title":"2025 , title =","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":54,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.648869Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:dd6d43a625cab2307b3ffa99d67e3a2e9f58df481b8994f742fec42d61abe79e","observation_id":"85272284-90ef-48db-af86-194d9fdf0e91","resolution":{"observed_at":"2026-08-16T00:32:51.648869Z","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":"2026-08-16T00:32:52.547510Z","title":"International Conference on Machine Learning , year=","venue":null,"work_id":"9d7019f9-0bb9-488f-9ea7-beb97bddc9fb","year":null},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":55,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.657510Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:783cea7162e1fe5acd5787c099351f3102e1ca72d76d56206af16a8eaa596830","observation_id":"59d015ee-29db-4123-98f8-17c602cbb848","resolution":{"observed_at":"2026-08-16T00:32:52.554563Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:32:52.523902Z","title":null,"venue":null,"work_id":"85de4368-136a-41ea-9c07-a14cb8c7638b","year":null},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":56,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.665006Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:fad26a74951c2342e6c256f7aa69a362a5c69a889ce7e9483bafab151c9c8b18","observation_id":"3a5dd046-10dc-4140-a8be-6240118e249e","resolution":{"observed_at":"2026-08-16T00:32:52.530599Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:32:52.503741Z","title":"The Fourteenth International Conference on Learning Representations , year=","venue":null,"work_id":"9fea2dc3-4a44-4fda-a672-0ce5c3c6c7be","year":null},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":57,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.674979Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:8e368be82a9144fae06ed7ea18a7faa72da11dd1a8b29c0e624277b987683506","observation_id":"b157f350-b95f-4f26-aba3-077c2d3dc20f","resolution":{"observed_at":"2026-08-16T00:32:52.510659Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:32:52.476420Z","title":"Size-Generalizable","venue":null,"work_id":"f3d3d357-4a85-46be-ad87-e1d1e44356e2","year":null},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":58,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.685351Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:d9708a08c9b1929678c494d4213dc52016cebdc683ec78327c0ccbc009d3e381","observation_id":"974c0a1c-8c2a-4f57-b74f-ec7bfaef77c0","resolution":{"observed_at":"2026-08-16T00:32:52.482070Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:32:52.437582Z","title":"Advances in Neural Information Processing Systems , volume=","venue":null,"work_id":"6fb9caad-5800-4883-ab8a-1a871d362f00","year":null},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":59,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.698033Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:39fe482beb4f0f5794d359847b3db96a53b42308d1863cbda4b4533eb3d7b68d","observation_id":"ae0cb7af-c8af-49a5-beb5-9843f0ac0b38","resolution":{"observed_at":"2026-08-16T00:32:52.445407Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:32:52.413724Z","title":"The Thirty-ninth Annual Conference on Neural Information Processing Systems , year=","venue":null,"work_id":"dc8ee59d-6455-450b-89aa-5782498d101a","year":null},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":60,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.708771Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:c37c6649a4a9c07f1c4339de92ed8bade1d715df8a486909c6bb32300e0be495","observation_id":"c804aac1-ed40-493b-86b0-2e4e37e4ac03","resolution":{"observed_at":"2026-08-16T00:32:52.420783Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:32:52.384345Z","title":"Nature Communications , volume=","venue":null,"work_id":"6c6a2f8d-362c-4a5c-8c6c-e0bcb74d993d","year":2025},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":61,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.718651Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:012ac81524521507e3329f3130491ba3998840a9d26054f5c3a3ff995a2ca2c8","observation_id":"2aef8091-706c-4a7a-82f9-090f5b726cec","resolution":{"observed_at":"2026-08-16T00:32:52.394102Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2503.10471","last_updated":"2026-04-14T03:47:25Z","snapshot_observed_at":"2026-08-15T11:35:54.301117Z","submitted_at":"2025-03-13T15:44:16Z","title":"Siamese Foundation Models for Crystal Structure Prediction","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2503.10471","snapshot_observed_at":"2026-08-16T00:32:51.725036Z","title":"arXiv preprint arXiv:2503.10471 , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":62,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.725036Z"},"links":{"cited_paper":"/paper/2503.10471","citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:a0b018a40625193a95044d78d06d4565cb0058d286a6252ccd837fde9359f282","observation_id":"0691f0a9-0d75-47df-9fbf-6d99b1e2aef5","resolution":{"observed_at":"2026-08-16T00:32:51.725036Z","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":"2026-08-16T00:32:51.732151Z","title":"arXiv preprint arXiv:2602.04734 , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":63,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.732151Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:beec9c08c8bbb2f61a9457a357a3707caf6962f9d905c238f372f387e5ff611b","observation_id":"f1126b4d-4e10-4e0e-81f7-902eea61fc94","resolution":{"observed_at":"2026-08-16T00:32:51.732151Z","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":"2026-08-16T00:32:52.358773Z","title":"Frontiers of Computer Science , volume=","venue":null,"work_id":"e575bfc7-cb05-4fcd-8c63-ca1526c8cc73","year":2025},"citing_paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks","version":1},"reference_index":64,"source":"arxiv_source","source_observed_at":"2026-08-16T00:32:51.741884Z"},"links":{"citing_paper":"/paper/2608.12010"},"observation_digest":"sha256:cce3eac02c7dbe18efdc405ccfa70b191bd9d1fd12f8a88c966b5dfd30f7c2da","observation_id":"35c4489b-575f-4eb9-9c21-69f05b72e719","resolution":{"observed_at":"2026-08-16T00:32:52.365950Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2608.12010","last_updated":"2026-08-12T12:46:25Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-16T05:44:13.799868Z","submitted_at":"2026-08-12T12:46:25Z","title":"Reducing Symmetry Increase in Equivariant Neural Networks"},"reference_resolution":{"displayed":63,"state_counts":{"malformed_identifier":0,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":20,"verified_exact":4,"verified_fuzzy":38},"total_outbound_references":63},"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":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"thesis":"As of 18 August 2026, this Paper Citation Record lists 63 of 63 outbound references and 0 inbound Pith citation observations for arXiv:2608.12010."}