{"as_of":"2026-08-18T03:48:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:1d8c48ec59703539ccf1c61277e03ec4ce589c995eb1deff014a0ca937d6a998","coverage":[{"denominator":31,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":31,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T14:11:35.900165Z","state":"measured"},{"denominator":31,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":31,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-17T06:30:58.91139+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/2505.20150/citation-record","integrity":"/paper/2505.20150/integrity","json":"/paper/2505.20150/citation-record.json","paper":"/paper/2505.20150"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:11:40.239405Z","title":"Fourier sliced-wasserstein embedding for multisets and measures","venue":null,"work_id":"8700e69e-7427-41b9-98fd-7be4a91f7cfa","year":2025},"citing_paper":{"arxiv_id":"2505.20150","last_updated":"2025-05-26T15:53:09Z","snapshot_observed_at":"2026-08-17T15:40:57.963007Z","submitted_at":"2025-05-26T15:53:09Z","title":"On the (Non) Injectivity of Piecewise Linear Janossy Pooling","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-07T14:11:34.076708Z"},"links":{"citing_paper":"/paper/2505.20150"},"observation_digest":"sha256:522d4081df1da3c541ed115a7abf4849e5802a7264035ceb038837bfd17ea2e9","observation_id":"ba4e0927-6de5-4164-b7e4-257b752ce074","resolution":{"observed_at":"2026-08-07T14:11:40.295124Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-07T14:11:40.044653Z","title":"Neural injective functions for multisets, measures and graphs via a finite witness theorem","venue":null,"work_id":"ce4aa63b-24c1-41e2-a0d8-0be912a551ba","year":2023},"citing_paper":{"arxiv_id":"2505.20150","last_updated":"2025-05-26T15:53:09Z","snapshot_observed_at":"2026-08-17T15:40:57.963007Z","submitted_at":"2025-05-26T15:53:09Z","title":"On the (Non) Injectivity of Piecewise Linear Janossy Pooling","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-07T14:11:34.109415Z"},"links":{"citing_paper":"/paper/2505.20150"},"observation_digest":"sha256:7f124af09e0688ca8d0db0c568d0ea607b3a9e942622efe40ca2117d3218224c","observation_id":"7e5c5e26-3770-4fa8-8f91-d546c5482d7e","resolution":{"observed_at":"2026-08-07T14:11:40.141968Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-07T14:11:39.780742Z","title":"G-invariant representations using coorbits: Bi- L ipschitz properties, 2023","venue":null,"work_id":"e38fa18f-8c2c-424f-ab21-7f45618a0d44","year":2023},"citing_paper":{"arxiv_id":"2505.20150","last_updated":"2025-05-26T15:53:09Z","snapshot_observed_at":"2026-08-17T15:40:57.963007Z","submitted_at":"2025-05-26T15:53:09Z","title":"On the (Non) Injectivity of Piecewise Linear Janossy Pooling","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-07T14:11:34.160326Z"},"links":{"citing_paper":"/paper/2505.20150"},"observation_digest":"sha256:dae95be2f76218c1483579897386a905d5d07153d73e240fec3080f3750fc2d4","observation_id":"d074c09b-d331-49a4-a7a9-d2475f2757d6","resolution":{"observed_at":"2026-08-07T14:11:39.916724Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2203.07546","last_updated":"2022-03-14T23:13:59Z","snapshot_observed_at":"2026-08-17T15:40:26.777122Z","submitted_at":"2022-03-14T23:13:59Z","title":"Permutation Invariant Representations with Applications to Graph Deep Learning","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2203.07546","snapshot_observed_at":"2026-08-07T14:11:34.233374Z","title":"Permutation invariant representations with applications to graph deep learning","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2505.20150","last_updated":"2025-05-26T15:53:09Z","snapshot_observed_at":"2026-08-17T15:40:57.963007Z","submitted_at":"2025-05-26T15:53:09Z","title":"On the (Non) Injectivity of Piecewise Linear Janossy Pooling","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-07T14:11:34.233374Z"},"links":{"cited_paper":"/paper/2203.07546","citing_paper":"/paper/2505.20150"},"observation_digest":"sha256:ad46ced40c83164fbd4d8ccb2df8296e5ca21dec06abf47fe0cb1a06688810a8","observation_id":"f3c956c2-2183-4055-a4f5-88457629258e","resolution":{"observed_at":"2026-08-07T14:11:34.233374Z","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":"2026-08-07T14:11:39.563977Z","title":"Convex Optimization","venue":null,"work_id":"b9f390e4-2eb3-4442-b454-5cf184ee6c7b","year":2004},"citing_paper":{"arxiv_id":"2505.20150","last_updated":"2025-05-26T15:53:09Z","snapshot_observed_at":"2026-08-17T15:40:57.963007Z","submitted_at":"2025-05-26T15:53:09Z","title":"On the (Non) Injectivity of Piecewise Linear Janossy Pooling","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-07T14:11:34.287442Z"},"links":{"citing_paper":"/paper/2505.20150"},"observation_digest":"sha256:342b832d508a6c640cbbaa52cfd0743296b9cd5769937e26ed3bdc4a93b6fbfb","observation_id":"56af3817-75b8-416f-af30-04cafc212e83","resolution":{"observed_at":"2026-08-07T14:11:39.681773Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-07T14:11:39.288160Z","title":"On dimensionality of feature vectors in MPNN s","venue":null,"work_id":"1137cc04-0149-4669-b16e-bf9a4f245217","year":2024},"citing_paper":{"arxiv_id":"2505.20150","last_updated":"2025-05-26T15:53:09Z","snapshot_observed_at":"2026-08-17T15:40:57.963007Z","submitted_at":"2025-05-26T15:53:09Z","title":"On the (Non) Injectivity of Piecewise Linear Janossy Pooling","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-07T14:11:34.352445Z"},"links":{"citing_paper":"/paper/2505.20150"},"observation_digest":"sha256:1ad03baf259724c18162b1af6ddfd90b167e5669b91220877d063b62a6b52def","observation_id":"ed45297b-cc2d-41e1-9281-214fb217fed2","resolution":{"observed_at":"2026-08-07T14:11:39.443249Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-07T14:11:34.398272Z","title":"Brenner and L","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2505.20150","last_updated":"2025-05-26T15:53:09Z","snapshot_observed_at":"2026-08-17T15:40:57.963007Z","submitted_at":"2025-05-26T15:53:09Z","title":"On the (Non) Injectivity of Piecewise Linear Janossy Pooling","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-07T14:11:34.398272Z"},"links":{"citing_paper":"/paper/2505.20150"},"observation_digest":"sha256:220138b656d1984dcbe37f5efb9cd700e67b491495b51cf8067ee840c9796828","observation_id":"1bd7a016-e22a-444c-8ae5-7c85787dd4ef","resolution":{"observed_at":"2026-08-07T14:11:34.398272Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2205.14039","last_updated":"2022-05-27T15:18:08Z","snapshot_observed_at":"2026-08-17T15:41:18.730854Z","submitted_at":"2022-05-27T15:18:08Z","title":"Group-invariant max filtering","version":1},"cited_work":{"arxiv_id":"2205.14039","doi":null,"metadata_source":"pith","pith_arxiv_id":"2205.14039","snapshot_observed_at":"2026-08-07T14:11:36.318474Z","title":"Group-invariant max filtering","venue":"cs.IT","work_id":"9fbd7907-50c7-4a57-a285-c8ee44efd38a","year":2022},"citing_paper":{"arxiv_id":"2505.20150","last_updated":"2025-05-26T15:53:09Z","snapshot_observed_at":"2026-08-17T15:40:57.963007Z","submitted_at":"2025-05-26T15:53:09Z","title":"On the (Non) Injectivity of Piecewise Linear Janossy Pooling","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-07T14:11:34.467850Z"},"links":{"cited_paper":"/paper/2205.14039","citing_paper":"/paper/2505.20150"},"observation_digest":"sha256:b5926803f89d4cfb0b08ea96496c27d1c27f883c419c3d69427b1eaca8bd16dd","observation_id":"d7591178-67bc-4da2-b0ae-f694769ef9a5","resolution":{"observed_at":"2026-08-07T14:11:36.356458Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-07T14:11:38.982346Z","title":"Iverson, and Dustin G","venue":null,"work_id":"7e32ee9e-d836-4f7a-97e0-800780e35d18","year":2024},"citing_paper":{"arxiv_id":"2505.20150","last_updated":"2025-05-26T15:53:09Z","snapshot_observed_at":"2026-08-17T15:40:57.963007Z","submitted_at":"2025-05-26T15:53:09Z","title":"On the (Non) Injectivity of Piecewise Linear Janossy Pooling","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-07T14:11:34.518978Z"},"links":{"citing_paper":"/paper/2505.20150"},"observation_digest":"sha256:203f9b819a1bc8cae48f2a21af326a4c6a5e7c5fca20356f6d23b5016cfac552","observation_id":"5af6348b-9444-4e6e-a320-4d5c1ad00306","resolution":{"observed_at":"2026-08-07T14:11:39.156747Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-07T14:11:38.791285Z","title":"On the h\\\"older stability of multiset and graph neural networks","venue":null,"work_id":"0db8659b-24ae-4949-b649-e678ac20295c","year":2025},"citing_paper":{"arxiv_id":"2505.20150","last_updated":"2025-05-26T15:53:09Z","snapshot_observed_at":"2026-08-17T15:40:57.963007Z","submitted_at":"2025-05-26T15:53:09Z","title":"On the (Non) Injectivity of Piecewise Linear Janossy Pooling","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-07T14:11:34.552986Z"},"links":{"citing_paper":"/paper/2505.20150"},"observation_digest":"sha256:e0de4a7811fe69a52c27aa891ae14b7b5d2db8ed12bde784adf9399573a1a03b","observation_id":"3390153c-c924-4d09-bba1-c605f37220fc","resolution":{"observed_at":"2026-08-07T14:11:38.893096Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-07T14:11:34.581091Z","title":"Low-dimensional invariant embeddings for universal geometric learning","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.20150","last_updated":"2025-05-26T15:53:09Z","snapshot_observed_at":"2026-08-17T15:40:57.963007Z","submitted_at":"2025-05-26T15:53:09Z","title":"On the (Non) Injectivity of Piecewise Linear Janossy Pooling","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-07T14:11:34.581091Z"},"links":{"citing_paper":"/paper/2505.20150"},"observation_digest":"sha256:da70f802ea1228dfadb579bd777962f17e726d0aa92f282cd23b248f3cad146b","observation_id":"05e941b5-134e-46b8-8cd9-b43c02364e73","resolution":{"observed_at":"2026-08-07T14:11:34.581091Z","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":"10.1007/bf02787218","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T00:03:45.533247Z","title":"Goodman and J \\'a nos Pach","venue":"Israel Journal of Mathematics","work_id":"74dc64e0-a337-4cd5-ae84-664ac5f6bbfd","year":1988},"citing_paper":{"arxiv_id":"2505.20150","last_updated":"2025-05-26T15:53:09Z","snapshot_observed_at":"2026-08-17T15:40:57.963007Z","submitted_at":"2025-05-26T15:53:09Z","title":"On the (Non) Injectivity of Piecewise Linear Janossy Pooling","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-07T14:11:34.642304Z"},"links":{"citing_paper":"/paper/2505.20150"},"observation_digest":"sha256:14b0c74c28b36f58971667920fa663875834cadb96712d71fce2355d9181414f","observation_id":"4ae73a40-b114-4be5-b2b8-1a2bed4ec374","resolution":{"observed_at":"2026-08-07T14:11:36.114307Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-07T14:11:38.547282Z","title":"Weisfeiler leman for euclidean equivariant machine learning","venue":null,"work_id":"42196612-6e75-4739-8284-68110de90a12","year":2024},"citing_paper":{"arxiv_id":"2505.20150","last_updated":"2025-05-26T15:53:09Z","snapshot_observed_at":"2026-08-17T15:40:57.963007Z","submitted_at":"2025-05-26T15:53:09Z","title":"On the (Non) Injectivity of Piecewise Linear Janossy Pooling","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-07T14:11:34.698956Z"},"links":{"citing_paper":"/paper/2505.20150"},"observation_digest":"sha256:897332ed4f92de6e969381447c55d8c0bc736a36f77cc2dd7096bd466c09e89f","observation_id":"beeaec83-0815-4f19-862b-34788d209c9e","resolution":{"observed_at":"2026-08-07T14:11:38.642404Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-07T14:11:38.249813Z","title":"Complete neural networks for complete euclidean graphs","venue":null,"work_id":"32e4df40-8010-4454-a3a9-7d3a7d4d9e5b","year":2024},"citing_paper":{"arxiv_id":"2505.20150","last_updated":"2025-05-26T15:53:09Z","snapshot_observed_at":"2026-08-17T15:40:57.963007Z","submitted_at":"2025-05-26T15:53:09Z","title":"On the (Non) Injectivity of Piecewise Linear Janossy Pooling","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-07T14:11:34.762890Z"},"links":{"citing_paper":"/paper/2505.20150"},"observation_digest":"sha256:a8c3dc97c09807d0723693628fe05d01fc134726f53a5af9d45fba4cc6f4b1e9","observation_id":"7daa7e18-d83c-4196-a314-369507d74d85","resolution":{"observed_at":"2026-08-07T14:11:38.425755Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-07T14:11:38.140514Z","title":"Set transformer: A framework for attention-based permutation-invariant neural networks","venue":null,"work_id":"e03b7f14-6d55-4487-bd49-334cd8768dee","year":2019},"citing_paper":{"arxiv_id":"2505.20150","last_updated":"2025-05-26T15:53:09Z","snapshot_observed_at":"2026-08-17T15:40:57.963007Z","submitted_at":"2025-05-26T15:53:09Z","title":"On the (Non) Injectivity of Piecewise Linear Janossy Pooling","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-07T14:11:34.818937Z"},"links":{"citing_paper":"/paper/2505.20150"},"observation_digest":"sha256:ee6bc11e08f372ae525f66444336932d11ce5dec677bf734edb995711aa6818a","observation_id":"3c3288e8-6e1c-4c02-9669-da56a33b4e8f","resolution":{"observed_at":"2026-08-07T14:11:38.196620Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-07T14:11:37.939114Z","title":"Provably powerful graph networks","venue":null,"work_id":"345f03ff-ef3b-4879-a8ef-16f19aa21096","year":2019},"citing_paper":{"arxiv_id":"2505.20150","last_updated":"2025-05-26T15:53:09Z","snapshot_observed_at":"2026-08-17T15:40:57.963007Z","submitted_at":"2025-05-26T15:53:09Z","title":"On the (Non) Injectivity of Piecewise Linear Janossy Pooling","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-07T14:11:34.872787Z"},"links":{"citing_paper":"/paper/2505.20150"},"observation_digest":"sha256:7d979551cdacc86569bd8e63ac626fa7e301bbb253d8c3d8d7409f6caceec2ed","observation_id":"7ae5b823-49c6-4407-849b-0c9920a8e917","resolution":{"observed_at":"2026-08-07T14:11:38.005797Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-07T14:11:37.742221Z","title":"Weisfeiler and leman go neural: Higher-order graph neural networks","venue":null,"work_id":"ce8f429d-7777-4ebb-acc3-df1ccfd2a7f6","year":2019},"citing_paper":{"arxiv_id":"2505.20150","last_updated":"2025-05-26T15:53:09Z","snapshot_observed_at":"2026-08-17T15:40:57.963007Z","submitted_at":"2025-05-26T15:53:09Z","title":"On the (Non) Injectivity of Piecewise Linear Janossy Pooling","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-07T14:11:34.920005Z"},"links":{"citing_paper":"/paper/2505.20150"},"observation_digest":"sha256:6e6582e4ff3a0c8c70336a58fbb7239ac0a5065b8acfcc9e609a975b9578bb0c","observation_id":"f057b3fb-8616-4cc2-af94-328a9a63a953","resolution":{"observed_at":"2026-08-07T14:11:37.878786Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-07T14:11:37.638797Z","title":"Murphy, Balasubramaniam Srinivasan, Vinayak Rao, and Bruno Ribeiro","venue":null,"work_id":"bed5554f-1f15-42ff-8184-f4dfabe16ec3","year":2019},"citing_paper":{"arxiv_id":"2505.20150","last_updated":"2025-05-26T15:53:09Z","snapshot_observed_at":"2026-08-17T15:40:57.963007Z","submitted_at":"2025-05-26T15:53:09Z","title":"On the (Non) Injectivity of Piecewise Linear Janossy Pooling","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-07T14:11:34.997248Z"},"links":{"citing_paper":"/paper/2505.20150"},"observation_digest":"sha256:ea581690c5824b76d14965e4af1f950934d3db457705b7a41558532d6485877d","observation_id":"068b51e9-a1e7-4b38-a4f2-a919081c860d","resolution":{"observed_at":"2026-08-07T14:11:37.692374Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-07T14:11:37.546555Z","title":"Quantum chemistry structures and properties of 134 kilo molecules","venue":null,"work_id":"900c6456-2a30-44e3-803b-1e46d9f32858","year":2014},"citing_paper":{"arxiv_id":"2505.20150","last_updated":"2025-05-26T15:53:09Z","snapshot_observed_at":"2026-08-17T15:40:57.963007Z","submitted_at":"2025-05-26T15:53:09Z","title":"On the (Non) Injectivity of Piecewise Linear Janossy Pooling","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-07T14:11:35.075317Z"},"links":{"citing_paper":"/paper/2505.20150"},"observation_digest":"sha256:0e19f89cdd5e39a14ab23b7dcc1443633ec8c2d984b0d25561008c54d7c4c8a1","observation_id":"a3db14f2-992c-4ac3-941f-008915228eb3","resolution":{"observed_at":"2026-08-07T14:11:37.593541Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-07T14:11:37.366877Z","title":"Tyrrell Rockafellar","venue":null,"work_id":"86429877-a383-48d6-a9e8-11d71e206e05","year":1970},"citing_paper":{"arxiv_id":"2505.20150","last_updated":"2025-05-26T15:53:09Z","snapshot_observed_at":"2026-08-17T15:40:57.963007Z","submitted_at":"2025-05-26T15:53:09Z","title":"On the (Non) Injectivity of Piecewise Linear Janossy Pooling","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-07T14:11:35.155962Z"},"links":{"citing_paper":"/paper/2505.20150"},"observation_digest":"sha256:512b88bd27e80e4d0712b56dd81584c208293c87c2888a63cd71c894ab23525b","observation_id":"4a01e4db-8259-4f3d-8cc5-9129629956bb","resolution":{"observed_at":"2026-08-07T14:11:37.485174Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-07T14:11:35.208121Z","title":"Blum, and Jean-Louis Reymond","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2505.20150","last_updated":"2025-05-26T15:53:09Z","snapshot_observed_at":"2026-08-17T15:40:57.963007Z","submitted_at":"2025-05-26T15:53:09Z","title":"On the (Non) Injectivity of Piecewise Linear Janossy Pooling","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-07T14:11:35.208121Z"},"links":{"citing_paper":"/paper/2505.20150"},"observation_digest":"sha256:0acd8395e87bf67d32f41d2e5e127cdff256ccc632c9c6cdec822411d1bce1d1","observation_id":"39b7dcce-a61a-4da2-a522-3a621028e2e2","resolution":{"observed_at":"2026-08-07T14:11:35.208121Z","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":"2026-08-07T14:11:37.220783Z","title":"Barrett, Mateusz Malinowski, Razvan Pascanu, Peter Battaglia, and Timothy Lillicrap","venue":null,"work_id":"e13ecbef-ae18-4b45-9488-30a2cc71c38e","year":2017},"citing_paper":{"arxiv_id":"2505.20150","last_updated":"2025-05-26T15:53:09Z","snapshot_observed_at":"2026-08-17T15:40:57.963007Z","submitted_at":"2025-05-26T15:53:09Z","title":"On the (Non) Injectivity of Piecewise Linear Janossy Pooling","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-07T14:11:35.267536Z"},"links":{"citing_paper":"/paper/2505.20150"},"observation_digest":"sha256:c9977837a9f797d56b120fed6f9f7c68e9a9492f03e42d475666fd6b4c020a23","observation_id":"f448fbfa-7761-4eaa-8ab5-c7d3b1f8990a","resolution":{"observed_at":"2026-08-07T14:11:37.274338Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-07T14:11:37.146005Z","title":"On the expressive power of sparse geometric MPNN s","venue":null,"work_id":"74f63891-3166-4c10-9aa5-50e52e857358","year":2025},"citing_paper":{"arxiv_id":"2505.20150","last_updated":"2025-05-26T15:53:09Z","snapshot_observed_at":"2026-08-17T15:40:57.963007Z","submitted_at":"2025-05-26T15:53:09Z","title":"On the (Non) Injectivity of Piecewise Linear Janossy Pooling","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-07T14:11:35.326680Z"},"links":{"citing_paper":"/paper/2505.20150"},"observation_digest":"sha256:9d34e5526115058b6f4810118f6b5705bcf3810cbae8e220bb6b520a75afbb7d","observation_id":"b538a63d-20de-4bfc-a9cd-abc72b313e48","resolution":{"observed_at":"2026-08-07T14:11:37.185957Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-07T14:11:35.384970Z","title":"FSW-GNN : A bi- L ipschitz WL -equivalent graph neural network, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.20150","last_updated":"2025-05-26T15:53:09Z","snapshot_observed_at":"2026-08-17T15:40:57.963007Z","submitted_at":"2025-05-26T15:53:09Z","title":"On the (Non) Injectivity of Piecewise Linear Janossy Pooling","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-07T14:11:35.384970Z"},"links":{"citing_paper":"/paper/2505.20150"},"observation_digest":"sha256:79539dd6f3d1779664d9733184f555c5430a009d8e5e9a94f4c731d33440044a","observation_id":"b1a408a6-97ad-4ccf-bbe3-1f36496164a8","resolution":{"observed_at":"2026-08-07T14:11:35.384970Z","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":"2026-08-07T14:11:37.042449Z","title":"Universal representation of permutation-invariant functions on vectors and tensors","venue":null,"work_id":"2c13d4be-3069-4f20-b31e-e3f8e85313a7","year":2024},"citing_paper":{"arxiv_id":"2505.20150","last_updated":"2025-05-26T15:53:09Z","snapshot_observed_at":"2026-08-17T15:40:57.963007Z","submitted_at":"2025-05-26T15:53:09Z","title":"On the (Non) Injectivity of Piecewise Linear Janossy Pooling","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-07T14:11:35.454631Z"},"links":{"citing_paper":"/paper/2505.20150"},"observation_digest":"sha256:437c5c9c02300e6f61c7b876c697cfb4adf559f87a5ffbc1a05868adf1aae7f2","observation_id":"0fb54e9c-87a5-47ec-bad1-edc7d9a3518c","resolution":{"observed_at":"2026-08-07T14:11:37.103950Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-07T14:11:36.918566Z","title":"Universal approximation of functions on sets","venue":null,"work_id":"532dfeda-9153-472c-88fd-ca9586d21b7d","year":2022},"citing_paper":{"arxiv_id":"2505.20150","last_updated":"2025-05-26T15:53:09Z","snapshot_observed_at":"2026-08-17T15:40:57.963007Z","submitted_at":"2025-05-26T15:53:09Z","title":"On the (Non) Injectivity of Piecewise Linear Janossy Pooling","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-07T14:11:35.513365Z"},"links":{"citing_paper":"/paper/2505.20150"},"observation_digest":"sha256:d9940a66e7b1af4ed1125d0eeaa0530e12746ef7c5a144e99f34b9afa4c7f04c","observation_id":"7da3d029-6022-4749-91e9-bd3234bccc3a","resolution":{"observed_at":"2026-08-07T14:11:36.957292Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-07T14:11:36.822516Z","title":"Polynomial width is sufficient for set representation with high-dimensional features","venue":null,"work_id":"dadef4ac-7740-412e-9538-ba502e6b4d8e","year":2024},"citing_paper":{"arxiv_id":"2505.20150","last_updated":"2025-05-26T15:53:09Z","snapshot_observed_at":"2026-08-17T15:40:57.963007Z","submitted_at":"2025-05-26T15:53:09Z","title":"On the (Non) Injectivity of Piecewise Linear Janossy Pooling","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-07T14:11:35.585143Z"},"links":{"citing_paper":"/paper/2505.20150"},"observation_digest":"sha256:5d8548885b1cb3ee0076243c7c9514b0a85256b7e747a04ba99f63da001d84b2","observation_id":"6c7ec0fa-ae86-4b89-9397-dfdedaf423d8","resolution":{"observed_at":"2026-08-07T14:11:36.865476Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-07T14:11:36.737651Z","title":"How powerful are graph neural networks? In International Conference on Learning Representations, 2018","venue":null,"work_id":"30beba40-4fd3-407b-a411-ae5bcc7da1af","year":2018},"citing_paper":{"arxiv_id":"2505.20150","last_updated":"2025-05-26T15:53:09Z","snapshot_observed_at":"2026-08-17T15:40:57.963007Z","submitted_at":"2025-05-26T15:53:09Z","title":"On the (Non) Injectivity of Piecewise Linear Janossy Pooling","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-07T14:11:35.666076Z"},"links":{"citing_paper":"/paper/2505.20150"},"observation_digest":"sha256:97471e86d283ac9205c126d6bcd6a3332a872f188aac3a85241e7dce1c26858c","observation_id":"d5cd87a0-41d3-4621-9f33-7fba758cfa34","resolution":{"observed_at":"2026-08-07T14:11:36.784906Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-07T14:11:36.602295Z","title":"Deep sets","venue":null,"work_id":"8a2e597d-5f10-42d2-bbf8-06e20e6d28b8","year":2017},"citing_paper":{"arxiv_id":"2505.20150","last_updated":"2025-05-26T15:53:09Z","snapshot_observed_at":"2026-08-17T15:40:57.963007Z","submitted_at":"2025-05-26T15:53:09Z","title":"On the (Non) Injectivity of Piecewise Linear Janossy Pooling","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-07T14:11:35.729227Z"},"links":{"citing_paper":"/paper/2505.20150"},"observation_digest":"sha256:ea4a79dde93502bea688ccb9fa8b4002bbb98675356c74c8a026764d0e93b5ce","observation_id":"1bb07c85-4994-49c0-84f1-7cbd84d683f6","resolution":{"observed_at":"2026-08-07T14:11:36.635054Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-07T14:11:36.519555Z","title":"On the expressive power of spectral invariant graph neural networks","venue":null,"work_id":"734747e6-9021-4be6-b53c-f75c5522bece","year":2024},"citing_paper":{"arxiv_id":"2505.20150","last_updated":"2025-05-26T15:53:09Z","snapshot_observed_at":"2026-08-17T15:40:57.963007Z","submitted_at":"2025-05-26T15:53:09Z","title":"On the (Non) Injectivity of Piecewise Linear Janossy Pooling","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-07T14:11:35.819240Z"},"links":{"citing_paper":"/paper/2505.20150"},"observation_digest":"sha256:decd45028165da0621068da66136fcbbafa632c7666cb96370843cb7d9b6e0bc","observation_id":"7e18b2fe-ff51-441a-8de7-ef1aa1e27bdd","resolution":{"observed_at":"2026-08-07T14:11:36.551678Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-07T14:11:36.380007Z","title":"Exponential separations in symmetric neural networks","venue":null,"work_id":"34114c07-c808-43ee-81bd-e2bf1a04ef40","year":2022},"citing_paper":{"arxiv_id":"2505.20150","last_updated":"2025-05-26T15:53:09Z","snapshot_observed_at":"2026-08-17T15:40:57.963007Z","submitted_at":"2025-05-26T15:53:09Z","title":"On the (Non) Injectivity of Piecewise Linear Janossy Pooling","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-07T14:11:35.900165Z"},"links":{"citing_paper":"/paper/2505.20150"},"observation_digest":"sha256:def17c2cbf2124382a565019d9af09d636e9e031bf218263e1821f6120732cd2","observation_id":"91e80b1c-e7b5-4faf-8116-dea0c86ceb3f","resolution":{"observed_at":"2026-08-07T14:11:36.433640Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2505.20150","last_updated":"2025-05-26T15:53:09Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-17T15:40:57.963007Z","submitted_at":"2025-05-26T15:53:09Z","title":"On the (Non) Injectivity of Piecewise Linear Janossy Pooling"},"reference_resolution":{"displayed":31,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":5,"verified_exact":2,"verified_fuzzy":24},"total_outbound_references":31},"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":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"thesis":"As of 18 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 0 inbound Pith citation observations for arXiv:2505.20150."}