{"as_of":"2026-08-08T06:20:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:0e930d9aba2b653b301c1cc34f52843bfeb089100841c2130d6a835f0918048f","coverage":[{"denominator":55,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":55,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T12:33:44.678373Z","state":"measured"},{"denominator":59,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":59,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-07T06:34:17.273281+00:00","state":"measured"},{"denominator":4,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":4,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T15:22:45.739186Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-07-03T02:37:34.195980Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.24353","snapshot_observed_at":"2026-08-06T15:22:45.739186Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning,","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.16871","last_updated":"2025-07-22T07:34:53Z","snapshot_observed_at":"2026-08-08T01:50:12.520512Z","submitted_at":"2025-07-22T07:34:53Z","title":"Navigation through Non-Compact Symmetric Spaces: a mathematical perspective on Cartan Neural Networks","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T15:22:45.739186Z"},"links":{"cited_paper":"/paper/2505.24353","citing_paper":"/paper/2507.16871"},"observation_digest":"sha256:98638f096325debe92877168ef713305a1cd82aadb371b98c2e0f210e4fcd00a","observation_id":"33322580-522a-401f-9f70-3ba39c535fc4","resolution":{"observed_at":"2026-08-06T15:22:45.739186Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.24353","snapshot_observed_at":"2026-08-03T15:35:34.827480Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning,","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.16772","last_updated":"2026-06-09T06:08:53Z","snapshot_observed_at":"2026-08-03T15:35:30.891252Z","submitted_at":"2025-12-18T17:04:43Z","title":"Thermodynamics a la Souriau on K\\\"ahler Non Compact Symmetric Spaces for Cartan Neural Networks","version":3},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-03T15:35:34.827480Z"},"links":{"cited_paper":"/paper/2505.24353","citing_paper":"/paper/2512.16772"},"observation_digest":"sha256:bffb428c4d048e7118720a5bde43fa829478cfeca7cce34819966ca8eef010c8","observation_id":"f091665a-4ade-44ef-b8f8-e12a1b9e4db4","resolution":{"observed_at":"2026-08-03T15:35:34.827480Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"cited_work":{"arxiv_id":"2505.24353","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2505.24353","snapshot_observed_at":"2026-07-03T02:37:34.195980Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning,","venue":null,"work_id":"ffb4ac6d-06ef-44ed-aad1-c91687d1f74b","year":2025},"citing_paper":{"arxiv_id":"2606.09438","last_updated":"2026-07-03T12:30:05Z","snapshot_observed_at":"2026-08-06T15:02:36.530896Z","submitted_at":"2026-06-08T12:48:27Z","title":"The macroscopic Kaehler metric of Geometric Thermodynamics versus the microscopic one on the Event Manifold: Exact Partition Functions on CV manifolds. Extended Souriau temperatures and spontaneous magnetizations","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-06-27T15:52:20.744263Z"},"links":{"cited_paper":"/paper/2505.24353","citing_paper":"/paper/2606.09438"},"observation_digest":"sha256:8cd5a3fca3cdb005d2d2d3e0a93bbb751dc42da39c66adb21f7789b0cb6f7d44","observation_id":"6d9ffe3d-54dc-47bd-8e2b-ecfb3e4a0f28","resolution":{"observed_at":"2026-07-03T02:37:34.197935Z","resolver_source":"arxiv_id","status":"verified_exact"},"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":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.24353","snapshot_observed_at":"2026-07-31T17:49:28.053791Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning,","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.24342","last_updated":"2026-07-27T12:19:39Z","snapshot_observed_at":"2026-08-07T00:12:08.711960Z","submitted_at":"2026-07-27T12:19:39Z","title":"General Properties of the Thermo-Metric for CV event manifolds and the magnetization combinatorial scheme","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-07-31T17:49:28.053791Z"},"links":{"cited_paper":"/paper/2505.24353","citing_paper":"/paper/2607.24342"},"observation_digest":"sha256:86102092942631ae42ec1cb8cd4b3bf8fe9283f87ea650c560f6cf1f2ca8c538","observation_id":"99f4d2c7-804b-4bf3-b103-b4d5b9116626","resolution":{"observed_at":"2026-07-31T17:49:28.053791Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2505.24353/citation-record","integrity":"/paper/2505.24353/integrity","json":"/paper/2505.24353/citation-record.json","paper":"/paper/2505.24353"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:33:54.315901Z","title":"Pattern Recognition and Machine Learning","venue":null,"work_id":"7aa55e69-d940-49c9-bd4f-3ba05890657a","year":2006},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:40.052024Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:0bcc4211587ea7ac29f2e4ca91d0e672e0fb17b86fe3dfdad769eb25a8b7e68f","observation_id":"70a9cfb1-4ccb-44b0-86fc-4b16700ef8a4","resolution":{"observed_at":"2026-08-07T12:33:54.389206Z","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":"2026-08-07T12:33:54.107533Z","title":"Poincaré embeddings for learning hierarchical represen- tations","venue":null,"work_id":"fbb8d164-dcb2-4384-a7de-52bcd79af3b4","year":2017},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:40.116060Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:068ea02ce82d8ad7270aeb3a1f3ba4cf1af6c3a53ae7032f54f32055532c025f","observation_id":"fc2f2664-698c-4fcf-9962-f4402040906e","resolution":{"observed_at":"2026-08-07T12:33:54.200682Z","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":"2026-08-07T12:33:53.920642Z","title":"Hyperbolic Neural Networks","venue":null,"work_id":"017b382f-180f-42cc-a709-87cac31d60af","year":2018},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:40.229224Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:2835cb26bcff5c260e3971d7203adef6d9b1e4d69b2dfa22aee666a0d87a928a","observation_id":"4ea5bb02-758e-4de1-a345-d56d4d8367b9","resolution":{"observed_at":"2026-08-07T12:33:54.003447Z","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":"2026-08-07T12:33:53.714953Z","title":"Hyperbolic neural networks++","venue":null,"work_id":"2387482a-dd37-4043-9eea-a100c5582227","year":2021},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:40.289303Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:fafb137842a347daf3763ad8c805943119874b6eddb45fc6cbd3c491890e34f8","observation_id":"738a10be-d8b2-4ed4-9c73-ef7870b9eb60","resolution":{"observed_at":"2026-08-07T12:33:53.791776Z","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":"2026-08-07T12:33:53.506869Z","title":"Fully hyperbolic neural networks","venue":null,"work_id":"1460dd55-ce53-4657-be54-3e8c484698b1","year":2022},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:40.344554Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:cc67697362a9090ccf6cc25e47ac159ec64c4b59345fa168b6a50d8a541431f1","observation_id":"85f7be8b-f835-4f6b-8578-b7f1f8ccb0ae","resolution":{"observed_at":"2026-08-07T12:33:53.601388Z","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":"2026-08-07T12:33:53.263927Z","title":"Fully hyperbolic convolutional neural networks for computer vision","venue":null,"work_id":"12792e29-55fc-428b-ba75-668a1c024597","year":2024},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:40.424949Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:1befcf4057c566c820e7f37db3b6ed0174ec74612068bc623c9cc0d190c41ad4","observation_id":"8e2b62f2-23b2-4102-b3fd-2de487a65386","resolution":{"observed_at":"2026-08-07T12:33:53.392330Z","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":"2026-08-07T12:33:53.077792Z","title":"Hyperbolic Graph Convolutional Neural Networks","venue":null,"work_id":"31537317-7992-48f3-9d1b-09a5d619641f","year":2019},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:40.533098Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:fb0559a3c137b7f8896e6c5ca3036976e01fe8d145f8b52ac4c5447842c1bc4c","observation_id":"54a6097c-755b-4c9b-964a-588b2dd7fc13","resolution":{"observed_at":"2026-08-07T12:33:53.148320Z","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":"2026-08-07T12:33:52.844457Z","title":"Hyperbolic attention networks","venue":null,"work_id":"7a46f6c3-6248-4f06-bccc-4f52c2730f5c","year":2019},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:40.604751Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:815a632b298cdeab9be66a16b3709506a3f26b512ea09a0063744cd9aa1935bd","observation_id":"b0559d70-14a8-4ebc-aafb-4580b0f35836","resolution":{"observed_at":"2026-08-07T12:33:52.941419Z","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":"2026-08-07T12:33:52.659479Z","title":"Hyperbolic Deep Neural Networks: A Survey","venue":null,"work_id":"97f8e32e-cfd5-433f-8c3d-4930e173c371","year":2022},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:40.679655Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:3b9ed043dd8ad8328dd6cabeb5d4ad85d2ac93811cacf5ee2299d4f84fdad744","observation_id":"68baa510-5260-4653-a4b0-eb654c15e9f4","resolution":{"observed_at":"2026-08-07T12:33:52.756800Z","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":"2026-08-07T12:33:52.427391Z","title":"Poincaré embedding reveals edge-based func- tional networks of the brain","venue":null,"work_id":"ed9ee260-2206-401b-aa4b-e07287c1a4ab","year":2020},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:40.763214Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:dfdd8689288b4f7a7a5181cfd8fb4f5c510486998e9bc083f4bce5607dd3dec9","observation_id":"2dc94106-718b-4629-a649-7a4612653922","resolution":{"observed_at":"2026-08-07T12:33:52.507844Z","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":"2026-08-07T12:33:52.249376Z","title":"Poincaré maps for analyzing complex hierarchies in single-cell data","venue":null,"work_id":"e71ea73e-977d-4104-8e22-94a4537fb01c","year":2020},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:40.858942Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:bcc34dfdec38d10d62550104b8c42c5853cb3d48f26c73468ac0ac833a500e67","observation_id":"8f63f683-819b-4218-afb9-ffef98b5ab71","resolution":{"observed_at":"2026-08-07T12:33:52.341787Z","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":"1902.08648","last_updated":"2019-02-22T19:32:28Z","snapshot_observed_at":"2026-08-05T01:17:34.660337Z","submitted_at":"2019-02-22T19:32:28Z","title":"Scalable Hyperbolic Recommender Systems","version":1},"cited_work":{"arxiv_id":"1902.08648","doi":null,"metadata_source":"pith","pith_arxiv_id":"1902.08648","snapshot_observed_at":"2026-08-07T12:33:45.215111Z","title":"Scalable Hyperbolic Recommender Systems","venue":"cs.IR","work_id":"acac1584-2e78-4079-a13a-82a627a3d266","year":2019},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:40.983108Z"},"links":{"cited_paper":"/paper/1902.08648","citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:938541921e1e228f142dedd8ed48a4e573111d5902eb695db76af5bcc568b7de","observation_id":"64f32e6c-e0e9-41b4-a415-c47fd80cf319","resolution":{"observed_at":"2026-08-07T12:33:45.390124Z","resolver_source":"local_arxiv","status":"verified_exact"},"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":"2026-08-07T12:33:52.027393Z","title":"Sur une classe remarquable d’espaces de Riemann","venue":null,"work_id":"64e5a4b2-3ef4-4413-be37-1c7cdd655107","year":1926},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:41.060660Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:71533cb9eb0c4f03b44ba563dfc1cfe2b113305a62547487d10fb3f1dae032f6","observation_id":"6c1d2fff-db88-46ca-8a4e-b08eb57ede77","resolution":{"observed_at":"2026-08-07T12:33:52.134192Z","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":"2026-08-07T12:33:51.810473Z","title":"Differential geometry and symmetric spaces","venue":null,"work_id":"4b937ba5-723d-42c1-8fe0-485655358ff7","year":1962},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:41.117532Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:f0e137f52f5eefc7392b406e8f44044c39d4391ab3c59898196f9ffccf8c9cd6","observation_id":"c3e6273c-93a5-4ecf-a0da-c67104c5e699","resolution":{"observed_at":"2026-08-07T12:33:51.911411Z","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":"2026-08-07T12:33:51.506492Z","title":null,"venue":null,"work_id":"2a43a895-fa38-4d5e-a3ef-c3262f65f934","year":2023},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:41.186497Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:be8e34ad0abc39adb2f45385c614d0090de12e8de6eb5cda709db3d68bffe613","observation_id":"4788d0c0-bade-4b0f-ae93-4a5975c5f992","resolution":{"observed_at":"2026-08-07T12:33:51.578427Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"cond-mat/0205288","last_updated":"2002-05-14T13:17:02Z","snapshot_observed_at":"2026-07-07T01:50:59.014036Z","submitted_at":"2002-05-14T13:17:02Z","title":"An introduction to symmetric spaces","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"cond-mat/0205288","snapshot_observed_at":"2026-08-07T12:33:41.247776Z","title":"An introduction to symmetric spaces","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:41.247776Z"},"links":{"cited_paper":"/paper/cond-mat/0205288","citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:b446cb1762acca2e0ae0e33d02e5cc0efb746044faf0c677b893efc5d93b0ba9","observation_id":"d986e8c1-2215-492f-8f56-bbfffadd8980","resolution":{"observed_at":"2026-08-07T12:33:41.247776Z","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":"2026-08-07T12:33:51.307935Z","title":"Fré, and Mario Trigiante","venue":null,"work_id":"600ecb35-11d7-40f7-8598-fa8d041e2d3f","year":1997},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:41.325150Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:537cdf893a08d7a4a965e50cb0d57d44a5833079d77969415276c2acf2a112b5","observation_id":"5dbf7eaa-4b76-45a0-b7e8-ae9705e539fb","resolution":{"observed_at":"2026-08-07T12:33:51.372458Z","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":"2026-08-07T12:33:51.103461Z","title":"Fré, Ruben Minasian, and Mario Trigiante","venue":null,"work_id":"809fb0c4-59bc-44c9-82cc-726810f460a0","year":1997},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:41.406102Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:ee90ae724ec490724c7a3135ccacf40152f5811fd37f237c4c9f00a4b48a8a5f","observation_id":"5397833e-089a-4758-ab7e-e647f096fd3e","resolution":{"observed_at":"2026-08-07T12:33:51.228347Z","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":"2026-08-07T12:33:50.951741Z","title":"Fré, Floriana Gargiulo, Jan Rosseel, Ksenya Rulik, Mario Trigiante, and Antoine Van Proeyen","venue":null,"work_id":"c71c920f-5b7f-4d21-a229-57cb7c06664f","year":2007},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:41.495825Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:33e0c4129988aca67ebbf3b189184fba98f50a79e499f62e71b2a3ec2bde8f25","observation_id":"9d053b2a-1b23-4c81-a972-22e0db131ff6","resolution":{"observed_at":"2026-08-07T12:33:51.023051Z","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":"2026-08-07T12:33:50.782264Z","title":"Alekseevsky","venue":null,"work_id":"e1c82af0-ff49-4b0f-ac08-cde9f8622a23","year":1975},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:41.581817Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:89b425b8b2fa3866937c9f3792fce0c111a752073f9fff94cc7437a0453145ee","observation_id":"718d3e4e-a39c-49fd-9345-23c0f61b8c30","resolution":{"observed_at":"2026-08-07T12:33:50.862033Z","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":"2026-08-07T12:33:50.609499Z","title":"Alekseevskian spaces.Differential Geometry and its Applications, 6(2):129–168, 1996","venue":null,"work_id":"a7c470e4-f731-4723-8917-86f622b4187a","year":1996},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:41.661860Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:9a2dd356648e4cbaf02b547d4a0f5f043a44cca1b8419771bc23fa77d80894fd","observation_id":"aba471e3-123c-4a09-8419-4845ec106183","resolution":{"observed_at":"2026-08-07T12:33:50.704681Z","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":"2026-08-07T12:33:50.388212Z","title":"Alekseevsky, Vicente Cortés, Chandrashekar Devchand, and Antoine Van Proeyen","venue":null,"work_id":"cbbb8b9e-ea9c-4b00-a032-d42576751ee3","year":2004},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:41.696120Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:8d93acd1f2c07cb2519529d5e02f6a7f3e27b3d83e595553eb5d495a19ad68f5","observation_id":"d48637de-b400-48ca-9f15-23eab2903c38","resolution":{"observed_at":"2026-08-07T12:33:50.505221Z","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":"2503.07626","last_updated":"2026-07-08T11:58:20Z","snapshot_observed_at":"2026-08-08T00:16:18.266533Z","submitted_at":"2025-02-28T16:39:33Z","title":"The paint group Tits Satake theory of hyperbolic symmetric spaces: the distance function, paint invariants and discrete subgroups","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2503.07626","snapshot_observed_at":"2026-08-07T12:33:41.779943Z","title":"Fré, and Mario Trigiante","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:41.779943Z"},"links":{"cited_paper":"/paper/2503.07626","citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:579b406f52a8ee5528f771e7c3b483ed1eff6b29a1eb59f368d51b62ad5b144d","observation_id":"f12a20bc-7845-4d0e-b465-f690b004b3a3","resolution":{"observed_at":"2026-08-07T12:33:41.779943Z","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":"2026-08-07T12:33:50.172730Z","title":"Navigation through Non Compact Symmetric Spaces, that is Cartan Neural Networks","venue":null,"work_id":"ddaaaed3-91ce-43ef-98e0-f59d591db70d","year":2025},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:41.858967Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:ce290dd18bb5360682f3bf12cd1e3b2c87bc26b1785d836725ca042a647dc8b5","observation_id":"4259ca09-630f-47ed-9308-de93635836ba","resolution":{"observed_at":"2026-08-07T12:33:50.261495Z","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":"2026-08-07T12:33:49.959219Z","title":"A Gyrovector Space Approach to Hyperbolic Geometry","venue":null,"work_id":"78921f46-7d48-4e3a-b35b-04ba5ee2ad5c","year":2009},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:41.939003Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:4cc76c5666b20a19634c2d405c25ae8aeb5d8828a1d357f64fb05c73d22fd48f","observation_id":"dbdfd891-a007-4122-bc1c-6813c32cca02","resolution":{"observed_at":"2026-08-07T12:33:50.074226Z","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":"2308.15639","last_updated":"2023-08-29T21:20:16Z","snapshot_observed_at":"2026-07-06T16:12:02.944409Z","submitted_at":"2023-08-29T21:20:16Z","title":"Hyperbolic Convolutional Neural Networks","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2308.15639","snapshot_observed_at":"2026-08-07T12:33:42.004127Z","title":"Hyperbolic Convolutional Neural Networks","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:42.004127Z"},"links":{"cited_paper":"/paper/2308.15639","citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:9b709a47b334817334e91df864b5747153d430cba0320000786d1a01c137b007","observation_id":"2fa4bba1-212b-4e28-a3b4-584e7f0daca4","resolution":{"observed_at":"2026-08-07T12:33:42.004127Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2411.10128","last_updated":"2024-11-15T12:01:03Z","snapshot_observed_at":"2026-08-03T14:17:57.018729Z","submitted_at":"2024-11-15T12:01:03Z","title":"On the Universal Statistical Consistency of Expansive Hyperbolic Deep Convolutional Neural Networks","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.10128","snapshot_observed_at":"2026-08-07T12:33:42.063005Z","title":"On the universal statistical consistency of expansive hyperbolic deep convolutional neural networks","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:42.063005Z"},"links":{"cited_paper":"/paper/2411.10128","citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:fc69ae46976550d3b86f7ee282f26497552c66f24f127ed88853304aa3b389a2","observation_id":"78fc9447-c31c-4592-a732-f6f5b678ecb6","resolution":{"observed_at":"2026-08-07T12:33:42.063005Z","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":"2026-08-07T12:33:49.780171Z","title":"Cohen, Mario Geiger, and Maurice Weiler","venue":null,"work_id":"3c360e3f-f908-4a04-9d09-723d27e16922","year":2019},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:42.135576Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:bf12047afd24f05d67a6130b7b9fa7706f3cb9511cba24fbed1a8cc032892b7f","observation_id":"fb8bed0f-9746-4c8e-b7f2-1eed2b4f371a","resolution":{"observed_at":"2026-08-07T12:33:49.858325Z","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":"2026-08-07T12:33:49.604590Z","title":null,"venue":null,"work_id":"e2e9171a-635a-4016-81e6-297e0b681937","year":2020},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:42.198033Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:29c6f437523e64295b5a294415477e74c0cdf5069e3f93546f8039125dca6ff6","observation_id":"7f686fb8-ecfd-4f66-acfe-39c144390f78","resolution":{"observed_at":"2026-08-07T12:33:49.684648Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"2311.00212","last_updated":"2025-06-11T18:48:38Z","snapshot_observed_at":"2026-08-03T20:29:59.292525Z","submitted_at":"2023-11-01T01:19:54Z","title":"A Unified Framework to Enforce, Discover, and Promote Symmetry in Machine Learning","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2311.00212","snapshot_observed_at":"2026-08-07T12:33:42.267272Z","title":"Otto, Nicholas Zolman, J","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:42.267272Z"},"links":{"cited_paper":"/paper/2311.00212","citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:41ab2c990f8c3985845df3580fb79651e0204ab1909864582cabb05c38a7c614","observation_id":"38978b12-e068-4bfb-a8d4-e884e8eb0c09","resolution":{"observed_at":"2026-08-07T12:33:42.267272Z","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":"2026-08-07T12:33:49.401478Z","title":"Lie neurons: Adjoint-equivariant neural networks for semisimple lie algebras","venue":null,"work_id":"b8f0ed67-50d9-49f8-9b18-d6b7333e84bc","year":2024},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:42.330372Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:fda5de595b2135ec3984282d25069015f41b12424b2acae3e3f014d6c9bf0c5e","observation_id":"ba2dda84-6853-4c48-8e63-dd915b2329c5","resolution":{"observed_at":"2026-08-07T12:33:49.513845Z","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":"2501.06934","last_updated":"2025-01-12T21:06:38Z","snapshot_observed_at":"2026-07-06T20:20:00.374482Z","submitted_at":"2025-01-12T21:06:38Z","title":"A group-theoretic framework for machine learning in hyperbolic spaces","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.06934","snapshot_observed_at":"2026-08-07T12:33:42.416839Z","title":"A group-theoretic framework for machine learning in hyperbolic spaces","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:42.416839Z"},"links":{"cited_paper":"/paper/2501.06934","citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:22bc1d416adc8c0b053f7503ccf4928bd56383d12ba6b103cfca84e4e89008fc","observation_id":"0eaa8f54-7c6b-4663-a793-6d56d9c72ebd","resolution":{"observed_at":"2026-08-07T12:33:42.416839Z","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":"2026-08-07T12:33:49.224696Z","title":"Humphreys","venue":null,"work_id":"0208eb31-0e25-472a-884d-bb76a85d42a8","year":1972},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:42.484662Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:83deff8bb9c6e883929ccee6084b959ed129013d2fe192d02ba50474545bcdf0","observation_id":"16864901-3d28-4a15-bec9-23b44f34d4ca","resolution":{"observed_at":"2026-08-07T12:33:49.300068Z","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":"2026-08-07T12:33:49.054604Z","title":"The Numerical Stability of Hyperbolic Representation Learning","venue":null,"work_id":"e4be19dd-2ff7-4858-83f7-3071773ea75d","year":2023},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:42.561807Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:7706dc644c38eb8eba8e0cf8e5740e28d24219bcf6c8335f32eb8d0093b6bd66","observation_id":"c77a7402-ba8c-484f-9f3c-6402a24810ff","resolution":{"observed_at":"2026-08-07T12:33:49.143379Z","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":"2501.19247","last_updated":"2025-01-31T16:03:06Z","snapshot_observed_at":"2026-08-05T12:19:05.918523Z","submitted_at":"2025-01-31T16:03:06Z","title":"Clustering in hyperbolic balls","version":1},"cited_work":{"arxiv_id":"2501.19247","doi":null,"metadata_source":"pith","pith_arxiv_id":"2501.19247","snapshot_observed_at":"2026-08-07T12:33:44.836457Z","title":"Clustering in hyperbolic balls","venue":"cs.LG","work_id":"e398fdcf-6ea1-4b87-8295-3c21ebbf5d6c","year":2025},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:42.653519Z"},"links":{"cited_paper":"/paper/2501.19247","citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:d030f3622923611eb73af9c9446b472bbbb79bb9f13105ddf68aeccc2f5f5abf","observation_id":"71fe5345-349e-4155-a888-7e95d850a3cd","resolution":{"observed_at":"2026-08-07T12:33:44.952246Z","resolver_source":"local_arxiv","status":"verified_exact"},"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":"2026-08-07T12:33:48.872873Z","title":"Compact manifolds of nonpositive curvature","venue":null,"work_id":"1b71fd03-b3ed-4dd3-96dc-a83d5fc6f121","year":1975},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:42.738672Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:468cc7dd99621c0ad495b3650e64030bbe840f54888b11ee847164d6ae5e5564","observation_id":"3e07debb-8b81-4f27-a3ab-bdbeeb78c442","resolution":{"observed_at":"2026-08-07T12:33:48.960595Z","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":"2026-08-07T12:33:48.727036Z","title":"Nguyen, and Christopher Re","venue":null,"work_id":"11e3bdf8-5f9a-4528-819e-08a721c1dd16","year":2021},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:42.804565Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:a834539ffd14e7e089695e2ee54b6350d38798897eac02b70fe2cf84b049219d","observation_id":"278d249f-1743-4e9d-8883-a235ecbe045f","resolution":{"observed_at":"2026-08-07T12:33:48.794831Z","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":"2026-08-07T12:33:48.591937Z","title":"Stochastic gradient descent on riemannian manifolds","venue":null,"work_id":"b38e8b33-3fbd-43dc-a2f5-5db5416d433b","year":2013},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:42.876272Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:38226c12f025357d9114ed72d56d191687531f6a7417d8f7fe85f1a1f665cd7f","observation_id":"41a72d22-5842-4128-a28d-9d2283587726","resolution":{"observed_at":"2026-08-07T12:33:48.645181Z","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":"2026-08-07T12:33:48.424371Z","title":"Riemannian adaptive optimization methods","venue":null,"work_id":"1fc03317-cbb7-4821-ae37-fdb53cdd90e8","year":2019},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:42.992922Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:66de0b133210b98beb72f9e728dcf1da90f86eb5495bdd6604817f3a19f65a58","observation_id":"e8c4d023-ebf0-4d4e-81b4-2c45fe7e897a","resolution":{"observed_at":"2026-08-07T12:33:48.483344Z","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":"2026-08-07T12:33:48.283317Z","title":"Fast and accurate deep net- work learning by exponential linear units (elus)","venue":null,"work_id":"3979a76f-dca4-41d9-b9ce-09ace655f010","year":2016},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:43.118263Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:275b16c813ee95786619a65e8bf5a80ea6984c79614c724abfe48381ee376d35","observation_id":"00ab652a-c557-448e-9fb1-3f338b82e5ae","resolution":{"observed_at":"2026-08-07T12:33:48.350382Z","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":"2026-08-07T12:33:48.035492Z","title":"PyTorch: An Imperative Style, High-Performance Deep Learning Library","venue":null,"work_id":"a60eb913-504f-4c1c-8e73-bbdc8d86cc4f","year":2019},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:43.233302Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:bcad295699c6b0de3a52c3c46f56cc2bebd4cbaac23c9e12de70f42fce939b56","observation_id":"83f6646e-2630-4465-85ed-24d5321b36fa","resolution":{"observed_at":"2026-08-07T12:33:48.172978Z","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":"2026-08-07T12:33:47.798092Z","title":"Lie groups, Lie algebras, and some of their applications","venue":null,"work_id":"fe0bdaa5-0c40-4bfd-a1f7-ed80051bec52","year":2016},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:43.320464Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:4a2969439fb8be472bb6eb58e1af40aad74f5a166d8475aae2f571152801c28f","observation_id":"4c491a75-c558-4ce6-92b2-6bb7334fc140","resolution":{"observed_at":"2026-08-07T12:33:47.915129Z","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":"2026-08-07T12:33:47.516494Z","title":null,"venue":null,"work_id":"e5c062c8-cc6b-44db-a790-980d365a216b","year":2012},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:43.444307Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:dd2e250f2dba17d87cfd1bb5e4c1279e9efd4849cda0c2733e96df4179f47954","observation_id":"b15110af-498c-482e-bf2a-c4636bf67d2f","resolution":{"observed_at":"2026-08-07T12:33:47.640105Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"2026-08-07T12:33:47.283475Z","title":"do Carmo","venue":null,"work_id":"d1476630-273a-4f5d-91fb-e66662eb3457","year":1992},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:43.613400Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:8b8b8c18a68fe290b3d7d0b2ff8abf13da9d1f361b80c17cd66a892e7ba50a5c","observation_id":"dc6173bb-c8ed-480c-9680-fe296b53b41d","resolution":{"observed_at":"2026-08-07T12:33:47.395903Z","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":"2026-08-07T12:33:46.999141Z","title":"Fré, Floriana Gargiulo, and Ksenya Rulik","venue":null,"work_id":"107e40ed-f779-4fbb-8e44-d497ab8efcbe","year":2006},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:43.743186Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:7b67be22ecdf12d6a27b6f9a37fc9fe1683d5ae642933f0f3eee9fc2fadee67d","observation_id":"b4b15a55-bd1e-4f93-8775-6c1822dc4df9","resolution":{"observed_at":"2026-08-07T12:33:47.155024Z","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":"2026-08-07T12:33:46.600384Z","title":null,"venue":null,"work_id":"4ba7f2c5-da7d-4e6b-ba90-102e685d4350","year":2015},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:43.860536Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:0530612d4005e80fad285b7bfb08ad7a72aa5a2b0c170daf8009d4c33ce12d03","observation_id":"ebe76caa-eadd-4958-abca-887750e45fed","resolution":{"observed_at":"2026-08-07T12:33:46.824590Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"2026-08-07T12:33:46.340445Z","title":"Foundations of Differential Geometry, volume 2","venue":null,"work_id":"1f6afa17-f649-4698-9a03-1d16e8b8ad90","year":1963},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:43.957976Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:5fb01de4f16ba426f7ffef09b4a69cc1932ebf66131ad76ca18e7c3f53c68398","observation_id":"d6ce4830-f024-4618-ace8-abe1dd17e441","resolution":{"observed_at":"2026-08-07T12:33:46.432736Z","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":"2005.02819","last_updated":"2020-07-17T16:42:53Z","snapshot_observed_at":"2026-07-06T09:18:07.000011Z","submitted_at":"2020-05-06T13:39:30Z","title":"Geoopt: Riemannian Optimization in PyTorch","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2005.02819","snapshot_observed_at":"2026-08-07T12:33:44.070146Z","title":"Geoopt: Riemannian optimization in pytorch","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:44.070146Z"},"links":{"cited_paper":"/paper/2005.02819","citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:823d3c3ba3c677dab1f8b16591b3af1bb345ac0e588ca8d2482ff41f063981cb","observation_id":"26a8c247-a476-4ac2-a517-405a3a2ca7a4","resolution":{"observed_at":"2026-08-07T12:33:44.070146Z","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":"2026-08-07T12:33:46.156229Z","title":"The merged-staircase prop- erty: a necessary and nearly sufficient condition for sgd learning of sparse functions on two-layer neural networks","venue":null,"work_id":"b45da69d-973b-468b-850b-4e114a004df6","year":2022},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:44.187267Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:7e84d6b179b26efbee7a68f6c53590a88c0640cb240fd86619d458b67f2f4a63","observation_id":"adf9239e-2413-48c7-9f85-5c13f046ec96","resolution":{"observed_at":"2026-08-07T12:33:46.254198Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:33:44.339261Z","title":"Gradient-based learning applied to document recognition","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:44.339261Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:e44e3d97250a1dcabc0c6ac0d1591eed2af97da89986264022c5c9e3efdef56e","observation_id":"16d94bee-8073-471b-8037-bed35de8ed0e","resolution":{"observed_at":"2026-08-07T12:33:44.339261Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1708.07747","last_updated":"2017-09-15T21:29:49Z","snapshot_observed_at":"2026-07-06T05:56:41.814255Z","submitted_at":"2017-08-25T14:01:29Z","title":"Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1708.07747","snapshot_observed_at":"2026-08-07T12:33:44.474942Z","title":"Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:44.474942Z"},"links":{"cited_paper":"/paper/1708.07747","citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:f0ea236590519012ddc359291bc0ed6043293912e380a395cc75c7c344410f9a","observation_id":"a49e5085-2a3a-44f5-b078-0dc5d767e545","resolution":{"observed_at":"2026-08-07T12:33:44.474942Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1812.01718","last_updated":"2018-12-03T12:37:31Z","snapshot_observed_at":"2026-07-06T07:19:11.957225Z","submitted_at":"2018-12-03T12:37:31Z","title":"Deep Learning for Classical Japanese Literature","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1812.01718","snapshot_observed_at":"2026-08-07T12:33:44.534910Z","title":"Deep learning for classical japanese literature","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:44.534910Z"},"links":{"cited_paper":"/paper/1812.01718","citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:d063e2549d7d6a9c0d1dcbd3a8c82f29f09b83fb9f8228176573dc4368ff48aa","observation_id":"2bc9146c-4a96-4031-b5d4-7ae8c3bcc360","resolution":{"observed_at":"2026-08-07T12:33:44.534910Z","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":"2026-08-07T12:33:45.989447Z","title":"Learning multiple layers of features from tiny images","venue":null,"work_id":"ef73c834-28d8-4901-b228-ec083e8f92f8","year":2009},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:44.599561Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:6e91bb54f93743ca81a1b76976b2c5c3c05426000b8426e0678ff63d6d88583b","observation_id":"a3839ec1-a19b-4bff-b5cd-0b83753c4fd0","resolution":{"observed_at":"2026-08-07T12:33:46.041768Z","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":"2026-08-07T12:33:45.847905Z","title":null,"venue":null,"work_id":"7a3fba43-8220-4e25-943a-2464c1deff46","year":null},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:44.603879Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:9913d9b4ca72b6e1773f486fdbb082c244306453575d7022d8c74cba38c8abf4","observation_id":"23173c7d-0c2a-422a-80fd-e208576ae23d","resolution":{"observed_at":"2026-08-07T12:33:45.928473Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"2026-08-07T12:33:45.558310Z","title":null,"venue":null,"work_id":"58bf1875-9186-4fc7-be6b-dd2ea099bf4e","year":null},"citing_paper":{"arxiv_id":"2505.24353","last_updated":"2025-05-30T08:45:53Z","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-07T12:33:44.678373Z"},"links":{"citing_paper":"/paper/2505.24353"},"observation_digest":"sha256:e44884e10b4877194697503aebee4b0a469b920341b5880d64cf2a9eb62af27d","observation_id":"e9be5bb9-4289-4222-8db9-8611b30e396e","resolution":{"observed_at":"2026-08-07T12:33:45.710124Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"2505.24353","last_updated":"2025-05-30T08:45:53Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-07T12:22:24.534862Z","submitted_at":"2025-05-30T08:45:53Z","title":"Cartan Networks: Group theoretical Hyperbolic Deep Learning"},"reference_resolution":{"displayed":55,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":16,"verified_exact":2,"verified_fuzzy":37},"total_outbound_references":55},"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 8 August 2026, this Paper Citation Record lists 55 of 55 outbound references and 4 inbound Pith citation observations for arXiv:2505.24353."}