{"as_of":"2026-08-12T15:41:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c3882bd6a9fecab274271354a2c1e695f1609731a4690220116e8508ba4b5f95","coverage":[{"denominator":91,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":91,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T00:14:23.176737Z","state":"measured"},{"denominator":92,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":92,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T23:29:20.785752Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.19677","snapshot_observed_at":"2026-08-06T23:29:20.785752Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.18279","last_updated":"2025-06-23T04:20:24Z","snapshot_observed_at":"2026-08-11T15:46:37.089618Z","submitted_at":"2025-06-23T04:20:24Z","title":"Optimal spectral initializers impact on phase retrieval phase transitions -- an RDT view","version":1},"reference_index":102,"source":"pdf_text","source_observed_at":"2026-08-06T23:29:20.785752Z"},"links":{"cited_paper":"/paper/2412.19677","citing_paper":"/paper/2506.18279"},"observation_digest":"sha256:43ca6c23817fbb14b681ce24c5f64d11dde71f2cc04f6e2f414758be90fe01ba","observation_id":"8c03c6bd-8b6c-4482-b46c-088ac55146d8","resolution":{"observed_at":"2026-08-06T23:29:20.785752Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2412.19677/citation-record","integrity":"/paper/2412.19677/integrity","json":"/paper/2412.19677/citation-record.json","paper":"/paper/2412.19677"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:14:22.819480Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.819480Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:04d01a5d1e0362746d9bf3ef55b41bb36231ac64ccea67c9c63cea78703bd6a9","observation_id":"a770206d-6ce1-4a52-877e-2c3b6e3f4936","resolution":{"observed_at":"2026-08-11T00:14:22.819480Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:14:22.824222Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.824222Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:225ef86fa13fffeb6dde87cbb817ba12413736b07d30a9d8bde7cf840409ffe3","observation_id":"43404026-2514-44b6-bf42-336abdc5492d","resolution":{"observed_at":"2026-08-11T00:14:22.824222Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:14:22.829017Z","title":"Alweiss, Y","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.829017Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:a83275cb0228e92f9ba53381c7d324b9ce7ff04529ce9f1b9b06925a0f7cf727","observation_id":"88c20d59-bd5c-4974-a03e-6a5a1d257e60","resolution":{"observed_at":"2026-08-11T00:14:22.829017Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:14:22.833146Z","title":"Amelunxen, M","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.833146Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:e26e6e34e3762798b8e8e32b9b6bc7bf749808f18c12905acef360279ce9ee64","observation_id":"a23fad05-dbb3-4fe3-b6e9-dcfaa81481e5","resolution":{"observed_at":"2026-08-11T00:14:22.833146Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2410.06717","last_updated":"2025-04-01T11:50:00Z","snapshot_observed_at":"2026-08-10T19:41:15.337184Z","submitted_at":"2024-10-09T09:41:28Z","title":"Exact full-RSB SAT/UNSAT transition in infinitely wide two-layer neural networks","version":4},"cited_work":{"arxiv_id":"2410.06717","doi":null,"metadata_source":"pith","pith_arxiv_id":"2410.06717","snapshot_observed_at":"2026-08-11T00:14:23.598950Z","title":"Exact full-RSB SAT/UNSAT transition in infinitely wide two-layer neural networks","venue":"cond-mat.dis-nn","work_id":"fe8f959d-762c-4bd9-b388-ff3fc9c33f95","year":2024},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.837366Z"},"links":{"cited_paper":"/paper/2410.06717","citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:ee05fd040a6835a5c7eeb6a0a1f5f3620831bf9fa2afbd64a2c4de6d00115ce1","observation_id":"e0e020ab-4fb9-4787-85d1-a160424d2731","resolution":{"observed_at":"2026-08-11T00:14:23.603442Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:22.841856Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.841856Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:7fe241436f70a7cd02307ae37933eb22c3ffed02737232c55445c942123f46ec","observation_id":"3d26e3a6-dd64-40f7-8af7-6be1ca0bb190","resolution":{"observed_at":"2026-08-11T00:14:22.841856Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:14:22.846363Z","title":"Aubin, W","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.846363Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:5754d4e4c238c3a512d165defa6b6a42cdcd84dfad68dabec9d7e128e6f8e78b","observation_id":"4832a55c-bc56-4623-bb3e-9b3d17af8757","resolution":{"observed_at":"2026-08-11T00:14:22.846363Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:14:22.850651Z","title":"Baldassi, E","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.850651Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:fd403de9e27b93dc1c40be779b08f4a07b17e04312d1909bf43a5355a1e42244","observation_id":"706f032a-14d3-4fd5-b799-619faa76e62c","resolution":{"observed_at":"2026-08-11T00:14:22.850651Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:14:22.854784Z","title":"Baldi and S","venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.854784Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:374db438733a4d5d6ddd2c4e93399cba4ca89bd7ae6fc0e56c33c5418617baa3","observation_id":"1cb13657-da94-4529-8b78-904525b1a6b2","resolution":{"observed_at":"2026-08-11T00:14:22.854784Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:14:22.859006Z","title":"Barkai, D","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.859006Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:0309a8388a1fe8193898b7c45d5905d347d9edaad175ec283e1aff059c597f0c","observation_id":"34806907-aea5-4857-81f9-7f891ce6d738","resolution":{"observed_at":"2026-08-11T00:14:22.859006Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:14:22.862989Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.862989Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:fb0f4e444e88222ae40a5e712c145649e68a6e25f1f9eec9436a9551b941b22f","observation_id":"90aff830-0aa6-4f79-b35d-4a9dd51a8994","resolution":{"observed_at":"2026-08-11T00:14:22.862989Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:14:22.866664Z","title":null,"venue":null,"work_id":null,"year":1960},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.866664Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:a0660cb24769d1dba82f58c0efdb4eb7174b16bc27eb20019c5a61266e7d23b8","observation_id":"7e9f4a10-e239-4006-a2f3-1b7d8923bfbb","resolution":{"observed_at":"2026-08-11T00:14:22.866664Z","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":"2026-08-11T00:14:24.314492Z","title":null,"venue":null,"work_id":"05d35bcc-aaa4-4095-9b1a-ab52320cef72","year":2022},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.870171Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:d28ceb76de7c299e60e34343982b7804520d25c5dc5dad6a6535337cd5cad8bd","observation_id":"fd267886-70b8-401b-a5ed-b4c3f9b3ee9c","resolution":{"observed_at":"2026-08-11T00:14:24.319544Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:24.297434Z","title":null,"venue":null,"work_id":"b07e4bfe-7d92-4b22-80c9-1ab1f7f1c603","year":1965},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.873513Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:8c573e7f56c840154e1974da33d8508cf2198eb0e31ae03fb21b897d88303035","observation_id":"9b89e8ee-3f7e-4eef-9dd3-f48a0ecb23e4","resolution":{"observed_at":"2026-08-11T00:14:24.303674Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:24.283195Z","title":"Daskalakis, D","venue":null,"work_id":"f13794ba-7930-47a5-93c1-03309096bf4b","year":2020},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.876842Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:33894bace1487b37572d98303e493499c3b091faca767d8daac40d73ae39a288","observation_id":"35088075-3acc-40b9-ae82-a4a45b8d73e8","resolution":{"observed_at":"2026-08-11T00:14:24.287646Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:24.268321Z","title":null,"venue":null,"work_id":"299bb6e8-e595-4906-bea5-59dd88b786b4","year":2018},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.880876Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:d3b3171b3468fab30d6c041e07ec1e8ac0dca6ae54000702e5ef529b736373ab","observation_id":"fbcea610-7aef-488c-92e2-1314470921a7","resolution":{"observed_at":"2026-08-11T00:14:24.273053Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:24.254096Z","title":null,"venue":null,"work_id":"7730954c-a0f0-4671-ad57-fecfc8155f70","year":2006},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.884538Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:3b98b7804208723350eed8cf570c466e2a95d068c7621c6d5c05de8dc38074fd","observation_id":"b0adecfe-3748-4e4e-b7c3-8db562b489a6","resolution":{"observed_at":"2026-08-11T00:14:24.257828Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:24.241760Z","title":"Engel, H","venue":null,"work_id":"dcfe2a16-1bca-4fb7-b71f-85b550937b7e","year":1992},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.888271Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:8af4d0fdc05b765a4b248c5f08a0c77a3679a091468a2751b51c0559dc1e0e8a","observation_id":"961d5789-2386-4c69-a879-f6271a8a5f04","resolution":{"observed_at":"2026-08-11T00:14:24.245744Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:24.228161Z","title":null,"venue":null,"work_id":"962c87a4-d8bc-44ba-8046-0f583f1e4e31","year":2014},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.892436Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:7bb6996aa843ee6c602024a9306d2eefab37570e0d30f2e1eb941f53a4401b55","observation_id":"8dce4c42-c0d2-4d71-a074-070cc1b76dad","resolution":{"observed_at":"2026-08-11T00:14:24.232462Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:24.213768Z","title":"Fazlyab, A","venue":null,"work_id":"6797813e-7c0e-45d3-be0d-181777587120","year":2019},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.896427Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:0d095e16278984fe1e3925e183bb739883b339c9cc96026848bf8dcf244837ae","observation_id":"af7b5a30-a18c-400c-a7ba-296d15a96aae","resolution":{"observed_at":"2026-08-11T00:14:24.218373Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:24.199190Z","title":"Fletcher, Sundeep Rangan, and Philip Schnite r","venue":null,"work_id":"2e13ed52-dbce-4668-b020-d416d9f86860","year":2018},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.900311Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:45f59ddfdb45a1def8cdfc29c85b9f9a238e9bb1348b345b69d81a0e7825197b","observation_id":"99ae3fac-9286-445f-a752-317ea8d2221f","resolution":{"observed_at":"2026-08-11T00:14:24.203378Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:24.185423Z","title":"Franz, G","venue":null,"work_id":"931fb197-12e8-46d5-a4ec-c838910a8763","year":2017},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.904187Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:9516364eb052418bd5e27fdbaffc10a24ecfbb39bd37683cec07ea10e506e047","observation_id":"6e09a92c-84e1-445d-8ffd-df141e671e1a","resolution":{"observed_at":"2026-08-11T00:14:24.189602Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:24.172094Z","title":"Furuya, M","venue":null,"work_id":"e8d62b2a-2fa9-45ad-b558-6b00272faad9","year":2023},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.908050Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:ee0109211a451d6ad292c7e615bbb9afb7da89bf3a203e3860acc9e3ffdbfda9","observation_id":"d57eef86-c6b4-471c-9b05-d1709abf46c7","resolution":{"observed_at":"2026-08-11T00:14:24.176209Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:24.158759Z","title":null,"venue":null,"work_id":"22d269c2-56be-42d7-b70b-79389c0222c8","year":1989},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.911786Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:f6d68f7ad4d15bdfffed00758eaf4278ab2833d613f166023380bc00cf2b9e64","observation_id":"08af7588-272e-49f8-aa2a-e4f6d11e206b","resolution":{"observed_at":"2026-08-11T00:14:24.162777Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:24.144442Z","title":"Kizildag, Will Perkins, and Cha ngji Xu","venue":null,"work_id":"36da2db0-ea99-4e2e-924a-538dfaada29f","year":2022},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.915496Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:aadef5a0b6074db5caf5372926190b554271e7b05415922d11a3810ffefa7645","observation_id":"3d00cd9b-d626-45c3-a3bd-8e7fb0ba26d8","resolution":{"observed_at":"2026-08-11T00:14:24.148739Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:22.919204Z","title":null,"venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.919204Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:077e970028960b68e35f0c83e0b0a8ecab800906832230b153545ddeb4a09a3b","observation_id":"c6f67bc3-53e6-4cfd-b807-abf75ebcbbe7","resolution":{"observed_at":"2026-08-11T00:14:22.919204Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:14:22.923515Z","title":"Gardner and B","venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.923515Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:be149e263368caecc4df1623936e48aa0e975d1b87c335cd9440fa69d1146c1e","observation_id":"ef2ab17d-1255-4f2c-a3ae-452128158892","resolution":{"observed_at":"2026-08-11T00:14:22.923515Z","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":"2026-08-11T00:14:24.114242Z","title":null,"venue":null,"work_id":"29fa0e39-f7bd-4de7-86dc-f9cf95a46281","year":1985},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.927044Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:3a0eceee724e3bd80f2c8b34ffca3b0be652ddd34d51c08f27e3f2443207ab7b","observation_id":"5d91abc1-8b40-455a-85f2-d8b4d333ca6d","resolution":{"observed_at":"2026-08-11T00:14:24.117753Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:24.102456Z","title":null,"venue":null,"work_id":"31fcb5a0-48bf-4739-ad86-dd6c657e8127","year":1986},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.930761Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:0c69592e7c8dbd20f2437c09a45bbc719a59d86c1675d46ce743d4b5cef6b119","observation_id":"003f7588-f8f6-4a7a-a7ef-21a3efcb4fb3","resolution":{"observed_at":"2026-08-11T00:14:24.106232Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:24.089656Z","title":null,"venue":null,"work_id":"203bb365-bb67-4f7b-b940-df491ac795cb","year":2021},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.934540Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:01b0a827a6b7fd5b97c98efffb2363b72783b9dedfcdabc0f92d6cd5a3cfec5b","observation_id":"84179fe1-7a01-416b-8984-5e42d05ad5e9","resolution":{"observed_at":"2026-08-11T00:14:24.093716Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:24.077716Z","title":"Gutfreund and Y","venue":null,"work_id":"7691e721-1af6-40e2-9f34-b96ebb2abecd","year":1990},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.938691Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:cd65ff520d1e6fbd9d737b02297fc857215c8c5d714ca4a81bf5d013809977f1","observation_id":"abc2c280-4c97-460d-af4b-96545e38a383","resolution":{"observed_at":"2026-08-11T00:14:24.081424Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:24.065131Z","title":null,"venue":null,"work_id":"2e8dc884-bb81-40c0-9f2b-5f6ec4eec6a3","year":2018},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.942401Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:c6e951db14a4112ef6d52793c2f409169bf734535e686558de5f99427eb72309","observation_id":"d6a0bf0f-1a0a-4540-8d30-276e5e21e201","resolution":{"observed_at":"2026-08-11T00:14:24.069371Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:24.051765Z","title":"He, C.-K","venue":null,"work_id":"937bb337-c834-4895-a734-80dc91f07091","year":2017},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.946094Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:041f439a1bc4b8e264b36ef5e0b08d66a1ba3b9621f05cbd80ee1e5c52f56ebe","observation_id":"7c48dd85-90e9-48f7-8f1f-0383ec328be9","resolution":{"observed_at":"2026-08-11T00:14:24.055698Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1805.08855","last_updated":"2019-04-06T15:48:53Z","snapshot_observed_at":"2026-07-06T06:40:39.657425Z","submitted_at":"2018-05-22T20:33:52Z","title":"Rate-Optimal Denoising with Deep Neural Networks","version":2},"cited_work":{"arxiv_id":"1805.08855","doi":null,"metadata_source":"pith","pith_arxiv_id":"1805.08855","snapshot_observed_at":"2026-08-11T00:14:23.576268Z","title":"Rate-Optimal Denoising with Deep Neural Networks","venue":"cs.IT","work_id":"2bcded80-b3dc-4745-8150-c289fd675490","year":2018},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.949670Z"},"links":{"cited_paper":"/paper/1805.08855","citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:710d6cc7a3c9e7a81ccb9408404d62ffd8c76f9ad5abb7f4f4367ed7dff1482b","observation_id":"03d94aa3-1a91-4d93-a3f0-bb1f3417e6de","resolution":{"observed_at":"2026-08-11T00:14:23.581699Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:24.039283Z","title":"Hegde, M","venue":null,"work_id":"ca472d47-1c51-4568-a502-cd1937e34775","year":2007},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.953868Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:40286c83dc2c0e5bf5b2b5c529770345e9685d08e42d32861d8be4a35c3f63dd","observation_id":"1a1b4355-9227-4eae-bcb8-8580a9c073a1","resolution":{"observed_at":"2026-08-11T00:14:24.043082Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1812.04176","last_updated":"2018-12-11T01:25:04Z","snapshot_observed_at":"2026-07-06T07:20:24.163342Z","submitted_at":"2018-12-11T01:25:04Z","title":"A Provably Convergent Scheme for Compressive Sensing under Random Generative Priors","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1812.04176","snapshot_observed_at":"2026-08-11T00:14:22.957677Z","title":"Huang, P","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.957677Z"},"links":{"cited_paper":"/paper/1812.04176","citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:7435a603fc3acfb0f0159bb9d9837cb6b836ff3596e7fd125b1143729e742cef","observation_id":"3f83e9ac-7dab-4dc7-969b-2072a75a13c3","resolution":{"observed_at":"2026-08-11T00:14:22.957677Z","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":"2026-08-11T00:14:24.026027Z","title":"Jordan and A","venue":null,"work_id":"99c96a55-7189-4bd3-8fd6-b3c2977f8b1a","year":2020},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.962229Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:955d29602134cf0900667d390e5bbf7e9160ad145610a01c8d6fc0cf4c50062f","observation_id":"fe84d51d-7546-4b19-8b9c-08af748fce02","resolution":{"observed_at":"2026-08-11T00:14:24.030171Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:24.011733Z","title":null,"venue":null,"work_id":"af118b3d-45f9-4882-b52e-e6a94cbf1240","year":1960},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.966402Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:d87f6a51be908a2b313fe989b4a398167f5dbc7577e74759df47276e310ff1f8","observation_id":"35f04020-e5f7-40f0-a45d-138766d4c0c3","resolution":{"observed_at":"2026-08-11T00:14:24.016195Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:23.996658Z","title":"Kothari, A","venue":null,"work_id":"648efe18-56ea-450f-9998-d000d4b37dee","year":2021},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.970297Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:6189369912f73c9b2ed77fc0e96ad36f27ab88e032f7b0125ff504052e8f0753","observation_id":"042f17f6-24e6-411f-9286-54df91b11bd1","resolution":{"observed_at":"2026-08-11T00:14:24.001013Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:23.980483Z","title":"Krauth and M","venue":null,"work_id":"60bbce37-967f-4c05-b205-b850fe8e678c","year":1989},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.974034Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:3a6866603e4069d530c9f1796080ad27f1b9e52031484ec34ce5abecdf81d32f","observation_id":"8fa0e912-e8c0-4155-9bea-79aaf7fbc421","resolution":{"observed_at":"2026-08-11T00:14:23.985470Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:23.967040Z","title":null,"venue":null,"work_id":"1f82f005-c87f-464f-899d-bc27a8673c27","year":2019},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.977753Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:5d4660d1b035ea7cffd2f80d59411ebcb9befe657ba958b51a8ca4752150d8f2","observation_id":"2e9fdef5-db79-40e2-841a-9d2fd758c731","resolution":{"observed_at":"2026-08-11T00:14:23.971201Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1702.05419","last_updated":"2017-06-29T08:27:26Z","snapshot_observed_at":"2026-08-10T00:04:16.116462Z","submitted_at":"2017-02-17T16:16:01Z","title":"A Random Matrix Approach to Neural Networks","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1702.05419","snapshot_observed_at":"2026-08-11T00:14:22.981694Z","title":"Louart, Z","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.981694Z"},"links":{"cited_paper":"/paper/1702.05419","citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:d6a3c91ef66133200ae14d8568ad56184965dc1c0fa872ec52579b05bea1d11b","observation_id":"7a39be40-7c36-4fe6-8e14-4961e16d527f","resolution":{"observed_at":"2026-08-11T00:14:22.981694Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2302.14112","last_updated":"2024-12-12T13:15:42Z","snapshot_observed_at":"2026-08-12T13:03:44.838852Z","submitted_at":"2023-02-27T19:51:42Z","title":"Injectivity of ReLU networks: perspectives from statistical physics","version":2},"cited_work":{"arxiv_id":"2302.14112","doi":null,"metadata_source":"pith","pith_arxiv_id":"2302.14112","snapshot_observed_at":"2026-08-11T00:14:23.525802Z","title":"Injectivity of ReLU networks: perspectives from statistical physics","venue":"cond-mat.dis-nn","work_id":"986a801f-6669-474b-809e-25e3b9eac1f4","year":2023},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.985685Z"},"links":{"cited_paper":"/paper/2302.14112","citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:5c7373e036288418b22810b005ddc421c499436ea67875fe4c50bf35c449b731","observation_id":"739af28b-ce7c-4e09-b9d6-794e5867bd62","resolution":{"observed_at":"2026-08-11T00:14:23.532940Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:23.953100Z","title":"Mardani, Q","venue":null,"work_id":"58ce5329-42fd-4030-874b-d6888b112f60","year":2018},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.989404Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:013e71f1d854a557f7a98d7fcd790e1dc95fd398cd6142cdaa56e35f14cdcce8","observation_id":"606e3889-e7ce-427d-8029-c26a68a105f7","resolution":{"observed_at":"2026-08-11T00:14:23.957251Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:23.938750Z","title":null,"venue":null,"work_id":"59a47666-9a2b-49d1-ab7b-8e98c2e5c497","year":2021},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.993553Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:d30cf84fe1071367e78346097fbc373df890414f51a948b73213043258e39735","observation_id":"89578b60-d964-489e-b98f-ba935c637d36","resolution":{"observed_at":"2026-08-11T00:14:23.942999Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:23.925697Z","title":"Pennington and P","venue":null,"work_id":"bf956a37-582c-4939-8c1f-c38c02125fdd","year":2017},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:22.997248Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:b7909780911ed4019ce6cb137583191b0f4b806a14f230b38f2e772a843f348d","observation_id":"46deb051-3caa-4030-b7b6-b43682b39601","resolution":{"observed_at":"2026-08-11T00:14:23.929871Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:23.001293Z","title":"Perkins and C","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.001293Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:7ea7fcf3e9971db81336f129dd0f3b4d81092c3d9a4fd971d4bd4e9aa6061a46","observation_id":"2cc6cc82-fb2c-405f-8097-d101464f9485","resolution":{"observed_at":"2026-08-11T00:14:23.001293Z","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":"2026-08-11T00:14:23.902993Z","title":"Puthawala, K","venue":null,"work_id":"ed11616e-c1a8-4e8d-942f-c4168577194a","year":2022},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.004926Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:9d8b27e8844a53d7da65cabfc853b29a419d29dd4fa812b3b9cbc9b6245092ad","observation_id":"1da87fcd-50e3-4fcd-bf97-5d13f6658fdc","resolution":{"observed_at":"2026-08-11T00:14:23.906941Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:23.889715Z","title":"Puthawala, M","venue":null,"work_id":"a5c0083f-9ee8-47d4-89fa-f210d8935309","year":2022},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.008650Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:28bb6d5dbbb0b45bb2270bafbb410e07ca3178a8a9d708379a0c3649b0d0ad65","observation_id":"9ba0da82-0a44-43ca-9c5f-f64a3e13006e","resolution":{"observed_at":"2026-08-11T00:14:23.893652Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:23.876163Z","title":"Rangan, P","venue":null,"work_id":"acb2ceb3-db5c-44a2-a210-689a6d9befc0","year":2017},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.012326Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:254c7119f7a3e101dd2446d98e14655b1dfd46b8139ce2f3d933c4467c58b0c1","observation_id":"bdb1fb6f-9dd2-4516-9a12-f1ab70bbfd27","resolution":{"observed_at":"2026-08-11T00:14:23.880382Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:23.863388Z","title":"Romano, M","venue":null,"work_id":"12c9d9ff-de89-4173-8f1c-55272120f8c5","year":2017},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.016188Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:c33a19a7f2f48cef48a45d07041dff6910650e639de5a9f135394a894862ac89","observation_id":"47191eb8-7b28-49a0-ad5f-36e4f119da91","resolution":{"observed_at":"2026-08-11T00:14:23.867230Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:23.849114Z","title":"Leigh Ross and J","venue":null,"work_id":"e1e427a3-e603-452a-b681-8916d761f04a","year":2021},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.019903Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:e01d95dd6d93b1ea1a6b3f93e06a155922e03357b1f44c6f778d13e69fcb45e8","observation_id":"a12ca419-e329-45c4-8c10-06781e078871","resolution":{"observed_at":"2026-08-11T00:14:23.853640Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:23.834494Z","title":null,"venue":null,"work_id":"1bef6f4c-e31a-4f98-bad4-9abfba6a3a00","year":1950},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.023507Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:f6633299a5f1e2c9819807c81bbb33fa0820d782cca29f8cd91511d7f904c3af","observation_id":"765f2647-aaf5-47c0-8b00-6c2e322f40a6","resolution":{"observed_at":"2026-08-11T00:14:23.838718Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:23.821035Z","title":"Schneider and W","venue":null,"work_id":"05d8eb5a-983c-4a03-8fcc-d6e0fd71c1bf","year":2008},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.027087Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:0c0c4f4643405ca8b3966fe66e137c76e90ca30e5b60583b171d133e44a1922a","observation_id":"02eaf810-08c4-4a50-8ffc-e4ffe3f53080","resolution":{"observed_at":"2026-08-11T00:14:23.825243Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:23.807535Z","title":"Schniter, S","venue":null,"work_id":"ec63941d-c671-48f6-b3f8-48f45dd3a411","year":2016},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.030549Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:542ff41965a6bd219b9fc4cfdb80240126099050c00bdb43ebc065c8acc25198","observation_id":"8a0b24b0-8156-4061-88c5-824d33914c51","resolution":{"observed_at":"2026-08-11T00:14:23.811901Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:23.794221Z","title":"Shah and C","venue":null,"work_id":"1fc6f3b6-8510-4aaa-a678-4f123829dcac","year":2018},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.034545Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:c10f4a6bddeda6e45bbea47479495f528a6c4b4ddd0f829a283c467621535410","observation_id":"41ea093f-3b57-4452-87be-17e9615efa26","resolution":{"observed_at":"2026-08-11T00:14:23.798476Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:23.780842Z","title":"Shcherbina and B","venue":null,"work_id":"9453e80b-3c53-4386-9523-4d8edb6a99a6","year":2002},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.038045Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:1f6a2c87553ec5715ade570c69dc6c080b6907ac94a6faa469670d57fd1c3c83","observation_id":"d9b11198-e1bd-45e0-a3cc-78d365bb4606","resolution":{"observed_at":"2026-08-11T00:14:23.785252Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:23.041368Z","title":"Shcherbina and B","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.041368Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:27b8110100ae132e66740375de0d6c7d34ba16935785521542c89244ec1fbb0c","observation_id":"76ac3b10-fabf-46ca-bff1-059b5499265a","resolution":{"observed_at":"2026-08-11T00:14:23.041368Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0907.3679","last_updated":"2009-07-21T15:13:07Z","snapshot_observed_at":"2026-07-06T01:55:44.393173Z","submitted_at":"2009-07-21T15:13:07Z","title":"Block-length dependent thresholds in block-sparse compressed sensing","version":1},"cited_work":{"arxiv_id":"0907.3679","doi":null,"metadata_source":"pith","pith_arxiv_id":"0907.3679","snapshot_observed_at":"2026-08-11T00:14:23.505802Z","title":"Block-length dependent thresholds in block-sparse compressed sensing","venue":"cs.IT","work_id":"e5eb09d4-6ca2-48c6-9bb3-a46430f38847","year":2009},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.045054Z"},"links":{"cited_paper":"/paper/0907.3679","citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:3cf827b2a5220ce739a0bff2c2fb868ee7ea6e97705be06ca8677a7c294a1d03","observation_id":"502dd818-1f63-4f29-9269-48fd4f771fd7","resolution":{"observed_at":"2026-08-11T00:14:23.510271Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0907.3666","last_updated":"2009-07-21T14:40:27Z","snapshot_observed_at":"2026-07-06T01:56:39.254979Z","submitted_at":"2009-07-21T14:40:27Z","title":"Various thresholds for $\\ell_1$-optimization in compressed sensing","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0907.3666","snapshot_observed_at":"2026-08-11T00:14:23.049149Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.049149Z"},"links":{"cited_paper":"/paper/0907.3666","citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:4a737790cfc2742ddbbf6a37e5502d4a530faf4538df2132586b0e7d2250f4bd","observation_id":"9f5b1ad6-365c-4664-860b-c634d614883f","resolution":{"observed_at":"2026-08-11T00:14:23.049149Z","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":"2026-08-11T00:14:23.757266Z","title":null,"venue":null,"work_id":"46bb2b60-512d-4dd2-96a4-d3d61deb9847","year":2010},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.053315Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:10467930a58578957cd7e1e3c55ffae9d60600f8d69711a1f03bfbba0c6884c6","observation_id":"4977795d-31d2-4aa9-8d56-4b0ae90171d8","resolution":{"observed_at":"2026-08-11T00:14:23.761178Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:23.744113Z","title":null,"venue":null,"work_id":"87d68a02-0abc-402b-a2a3-b905f85756ae","year":2010},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.056818Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:d3f9953f455b87e595a50a2298d0d06653a661f1c4cdd4dbc66a079f716c296b","observation_id":"d6785f24-a2f6-449e-beac-ec8e2290c60d","resolution":{"observed_at":"2026-08-11T00:14:23.748340Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1306.3979","last_updated":"2013-06-17T10:45:16Z","snapshot_observed_at":"2026-08-04T08:24:06.532378Z","submitted_at":"2013-06-17T10:45:16Z","title":"Another look at the Gardner problem","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1306.3979","snapshot_observed_at":"2026-08-11T00:14:23.060501Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.060501Z"},"links":{"cited_paper":"/paper/1306.3979","citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:4bc70d3c9ac6b6b75706435ea81785584a55acf2697b60a9337195e78c823b0e","observation_id":"c8cd031b-28bc-4979-9a6a-91e73d98d1b1","resolution":{"observed_at":"2026-08-11T00:14:23.060501Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1303.4375","last_updated":"2013-03-18T19:42:10Z","snapshot_observed_at":"2026-07-06T03:09:01.623028Z","submitted_at":"2013-03-18T19:42:10Z","title":"On the Computing of the Minimum Distance of Linear Block Codes by Heuristic Methods","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1303.4375","snapshot_observed_at":"2026-08-11T00:14:23.064423Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.064423Z"},"links":{"cited_paper":"/paper/1303.4375","citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:928e0f24f91bd51fcc8db175259a1dd5c1eeae01bc53149d185da9f5a4cad48f","observation_id":"04ca195f-ad4f-4099-a478-0c7ba24d793e","resolution":{"observed_at":"2026-08-11T00:14:23.064423Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1306.3770","last_updated":"2013-06-17T08:41:39Z","snapshot_observed_at":"2026-07-06T03:15:58.206519Z","submitted_at":"2013-06-17T08:41:39Z","title":"Lifting $\\ell_1$-optimization strong and sectional thresholds","version":1},"cited_work":{"arxiv_id":"1306.3770","doi":null,"metadata_source":"pith","pith_arxiv_id":"1306.3770","snapshot_observed_at":"2026-08-11T00:14:23.442506Z","title":"Lifting $\\ell_1$-optimization strong and sectional thresholds","venue":"cs.IT","work_id":"858b1624-2f47-4b63-88f3-b1e27d1f953c","year":2013},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.068898Z"},"links":{"cited_paper":"/paper/1306.3770","citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:cf4a65576617e83c234a861870c793edfe06f0b9a1ca70e084767b342dc42032","observation_id":"dd81d6d2-602a-4995-922c-8e07d1b13b59","resolution":{"observed_at":"2026-08-11T00:14:23.447042Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1306.3975","last_updated":"2013-06-17T08:30:56Z","snapshot_observed_at":"2026-07-06T03:16:01.396351Z","submitted_at":"2013-06-17T08:30:56Z","title":"Lifting/lowering Hopfield models ground state energies","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1306.3975","snapshot_observed_at":"2026-08-11T00:14:23.072639Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.072639Z"},"links":{"cited_paper":"/paper/1306.3975","citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:5e7af469599d29a5e6254a6bbe0fd0e0ed3fd33c828774229acdbe510a5aeb12","observation_id":"2eeaa5c3-7d97-461c-8dc1-e44a701c55a5","resolution":{"observed_at":"2026-08-11T00:14:23.072639Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1304.0003","last_updated":"2013-03-29T04:39:26Z","snapshot_observed_at":"2026-07-06T03:09:57.079782Z","submitted_at":"2013-03-29T04:39:26Z","title":"Meshes that trap random subspaces","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1304.0003","snapshot_observed_at":"2026-08-11T00:14:23.076730Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.076730Z"},"links":{"cited_paper":"/paper/1304.0003","citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:bfc32f31f0ad7a6cdf25fb7bceb91c0f10769f7cf82570dc49a79465f1602b67","observation_id":"5028a117-9780-4634-bfa0-e416b04f80f2","resolution":{"observed_at":"2026-08-11T00:14:23.076730Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:14:23.080573Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.080573Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:9b77eb4c78a5e80e76451963bbdec72d8226bf26dd91244ad94a92c84c815eda","observation_id":"cbfbb468-2aef-4287-83c5-b35204578b0b","resolution":{"observed_at":"2026-08-11T00:14:23.080573Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1303.7295","last_updated":"2013-03-29T04:41:51Z","snapshot_observed_at":"2026-08-10T19:37:05.237669Z","submitted_at":"2013-03-29T04:41:51Z","title":"Regularly random duality","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1303.7295","snapshot_observed_at":"2026-08-11T00:14:23.084277Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.084277Z"},"links":{"cited_paper":"/paper/1303.7295","citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:4d916b356a6a9058e98f9c92054afd952b91cb127702c3a78a3372dca202e0d4","observation_id":"bc93a770-2cb1-4ffa-b4e6-2f589b3572c7","resolution":{"observed_at":"2026-08-11T00:14:23.084277Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1306.3809","last_updated":"2013-06-17T10:59:50Z","snapshot_observed_at":"2026-07-06T03:15:58.206519Z","submitted_at":"2013-06-17T10:59:50Z","title":"Spherical perceptron as a storage memory with limited errors","version":1},"cited_work":{"arxiv_id":"1306.3809","doi":null,"metadata_source":"pith","pith_arxiv_id":"1306.3809","snapshot_observed_at":"2026-08-11T00:14:23.378658Z","title":"Spherical perceptron as a storage memory with limited errors","venue":"math.PR","work_id":"a8d0e9d3-1688-4756-b59e-5d6715b46265","year":2013},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.088401Z"},"links":{"cited_paper":"/paper/1306.3809","citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:84cfd0eb0bb621daf825c14340e7095a3be9c7eaefaf6b2156ff92e161505062","observation_id":"76b04fa7-f219-457d-8a95-8501cda66db9","resolution":{"observed_at":"2026-08-11T00:14:23.383232Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1612.08516","last_updated":"2016-12-27T07:03:29Z","snapshot_observed_at":"2026-07-06T05:24:11.258389Z","submitted_at":"2016-12-27T07:03:29Z","title":"Fully bilinear generic and lifted random processes comparisons","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1612.08516","snapshot_observed_at":"2026-08-11T00:14:23.092225Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.092225Z"},"links":{"cited_paper":"/paper/1612.08516","citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:7197b360b95d8170d915222ec02fa9de20a6b426fc8b358ea3a9e00b409b8e26","observation_id":"fcecc65b-acc5-4245-a1d9-177734881da0","resolution":{"observed_at":"2026-08-11T00:14:23.092225Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1612.08506","last_updated":"2016-12-27T06:21:07Z","snapshot_observed_at":"2026-07-06T05:24:11.258389Z","submitted_at":"2016-12-27T06:21:07Z","title":"Generic and lifted probabilistic comparisons -- max replaces minmax","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1612.08506","snapshot_observed_at":"2026-08-11T00:14:23.096050Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":72,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.096050Z"},"links":{"cited_paper":"/paper/1612.08506","citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:9a30f066bdb1381d2c40db4a3298ff65db0aee45fd9e22dcacf7f25252271a45","observation_id":"7c556cde-b880-41a5-a0fc-e87e01c7ae12","resolution":{"observed_at":"2026-08-11T00:14:23.096050Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2311.18097","last_updated":"2023-11-29T21:28:08Z","snapshot_observed_at":"2026-08-05T20:27:13.203163Z","submitted_at":"2023-11-29T21:28:08Z","title":"Bilinearly indexed random processes -- \\emph{stationarization} of fully lifted interpolation","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2311.18097","snapshot_observed_at":"2026-08-11T00:14:23.100381Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":73,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.100381Z"},"links":{"cited_paper":"/paper/2311.18097","citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:06ebecab93624e132e50baa5402fafc5c02b9b1c9d1de0379cae4bb5f00c543b","observation_id":"ba80d0fb-e0b4-4136-8228-999f1b2be320","resolution":{"observed_at":"2026-08-11T00:14:23.100381Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2312.00073","last_updated":"2023-11-29T22:22:32Z","snapshot_observed_at":"2026-08-11T09:59:39.155302Z","submitted_at":"2023-11-29T22:22:32Z","title":"Binary perceptrons capacity via fully lifted random duality theory","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2312.00073","snapshot_observed_at":"2026-08-11T00:14:23.104558Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":74,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.104558Z"},"links":{"cited_paper":"/paper/2312.00073","citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:2377c5766e10fd9fd0fb50f6d435674c7205d21f14b5138b98aa874de2eb16ba","observation_id":"6c2207c8-6af6-47ae-a1bc-1f75cb9b289a","resolution":{"observed_at":"2026-08-11T00:14:23.104558Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2312.08244","last_updated":"2023-12-13T16:06:18Z","snapshot_observed_at":"2026-08-12T12:01:01.749804Z","submitted_at":"2023-12-13T16:06:18Z","title":"Capacity of the treelike sign perceptrons neural networks with one hidden layer -- RDT based upper bounds","version":1},"cited_work":{"arxiv_id":"2312.08244","doi":null,"metadata_source":"pith","pith_arxiv_id":"2312.08244","snapshot_observed_at":"2026-08-11T00:14:23.300752Z","title":"Capacity of the treelike sign perceptrons neural networks with one hidden layer -- RDT based upper bounds","venue":"cond-mat.dis-nn","work_id":"603c8d88-050a-4326-8299-8d5bea3d13bd","year":2023},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":75,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.108993Z"},"links":{"cited_paper":"/paper/2312.08244","citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:9c707ba77bc53075aebe752a3ed9db7af3bf590e7df969746387bcef6ced9907","observation_id":"cb6fc16e-de48-4c41-baad-aedee293e2c1","resolution":{"observed_at":"2026-08-11T00:14:23.305071Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2312.16531","last_updated":"2023-12-27T11:23:40Z","snapshot_observed_at":"2026-07-06T17:08:37.841969Z","submitted_at":"2023-12-27T11:23:40Z","title":"Fl RDT based ultimate lowering of the negative spherical perceptron capacity","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2312.16531","snapshot_observed_at":"2026-08-11T00:14:23.113282Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":76,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.113282Z"},"links":{"cited_paper":"/paper/2312.16531","citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:bc3eb9f0f537d3e525a202609d5a8ba251ea5334507c1789782e567623554cbf","observation_id":"3eeb2456-cd2c-48a6-b52d-382a3de4075c","resolution":{"observed_at":"2026-08-11T00:14:23.113282Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2311.18092","last_updated":"2023-11-29T21:20:49Z","snapshot_observed_at":"2026-07-06T16:54:41.858193Z","submitted_at":"2023-11-29T21:20:49Z","title":"Fully lifted interpolating comparisons of bilinearly indexed random processes","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2311.18092","snapshot_observed_at":"2026-08-11T00:14:23.117187Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":77,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.117187Z"},"links":{"cited_paper":"/paper/2311.18092","citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:3de4eabf57406b90ee22f49fe073c0f04655e5aa9b78054294663fd52688f0b4","observation_id":"1ca4c658-effd-46bd-9e20-47a074515e07","resolution":{"observed_at":"2026-08-11T00:14:23.117187Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:14:23.121319Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":78,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.121319Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:3c7e7c7ed426ce2742591fdab99208212c54cb5e7dc28e70b7ca2cd90fbfcad5","observation_id":"97720d8e-45c7-4a1d-b722-f505694a870b","resolution":{"observed_at":"2026-08-11T00:14:23.121319Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2312.08257","last_updated":"2023-12-13T16:19:58Z","snapshot_observed_at":"2026-08-02T19:41:24.413866Z","submitted_at":"2023-12-13T16:19:58Z","title":"\\emph{Lifted} RDT based capacity analysis of the 1-hidden layer treelike \\emph{sign} perceptrons neural networks","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2312.08257","snapshot_observed_at":"2026-08-11T00:14:23.125402Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":79,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.125402Z"},"links":{"cited_paper":"/paper/2312.08257","citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:e882a464e2b5db896bea1d86c65474e63b1f246032cb28084d565ac36a25455b","observation_id":"1e263452-5765-402a-9850-0cfea534e43a","resolution":{"observed_at":"2026-08-11T00:14:23.125402Z","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":"2026-08-11T00:14:23.712717Z","title":null,"venue":null,"work_id":"5b012e94-a672-43c8-b3d3-2bde2f23b256","year":null},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":80,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.129326Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:ac1c9d2444f4e313c84d04bf9f7168111ae416e6d0033645acd0f26445a9f4a9","observation_id":"871fd412-fd84-458a-b62c-3150253eaa47","resolution":{"observed_at":"2026-08-11T00:14:23.716829Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.05696","last_updated":"2024-02-08T14:19:29Z","snapshot_observed_at":"2026-07-06T17:27:29.050237Z","submitted_at":"2024-02-08T14:19:29Z","title":"Fixed width treelike neural networks capacity analysis -- generic activations","version":1},"cited_work":{"arxiv_id":"2402.05696","doi":null,"metadata_source":"pith","pith_arxiv_id":"2402.05696","snapshot_observed_at":"2026-08-11T00:14:23.214369Z","title":"Fixed width treelike neural networks capacity analysis -- generic activations","venue":"stat.ML","work_id":"7bf4aafa-1e4e-4942-85eb-f2bf4e4f0e2d","year":2024},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":81,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.138004Z"},"links":{"cited_paper":"/paper/2402.05696","citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:a58683f53a49baa78ea2bc75e4823e1dcf30c530dcd9538533faa9bea3a08c27","observation_id":"13d75a76-1b92-407c-b4b5-21aa8eba4455","resolution":{"observed_at":"2026-08-11T00:14:23.221139Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:23.699205Z","title":null,"venue":null,"work_id":"f0c45428-7c4c-4717-b3a7-d3b0e2e8d3ac","year":2024},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":82,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.142576Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:8f6a5832e046cdf39c080a9734998b8e47ca68f57f7ad20d96b98bb641ca56f3","observation_id":"6aac608c-7fce-4455-81b0-16ec9288806a","resolution":{"observed_at":"2026-08-11T00:14:23.703164Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:23.146567Z","title":"Talagrand","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":83,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.146567Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:82931a66a2a6af8f70520f6f41b7cef8225b85290c65ad9253041bca57177100","observation_id":"15176c29-a009-4883-b4d6-10fb15bbd0f1","resolution":{"observed_at":"2026-08-11T00:14:23.146567Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:14:23.150445Z","title":"Talagrand","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":84,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.150445Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:b725c8bfdf54150f1a755f224d0decaa90ff3a9ab7224aeab731403d0234b0b3","observation_id":"020eb0a4-72a8-4556-8083-a78d99b04f56","resolution":{"observed_at":"2026-08-11T00:14:23.150445Z","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":"2026-08-11T00:14:23.668433Z","title":"Venkatesh","venue":null,"work_id":"782c1fc3-36d1-4a6f-acd0-399cdb497cbf","year":1986},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":85,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.154588Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:004cab81a247f254ecb80c3a3dfdf40766db8b2d38e59bfb8b2ba42f9959095a","observation_id":"58a7d077-487e-4bef-bea8-6525752ccd34","resolution":{"observed_at":"2026-08-11T00:14:23.672392Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:23.159219Z","title":null,"venue":null,"work_id":null,"year":1962},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":86,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.159219Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:bcf5eca3bc1aaabb67ad0667bdffa694e65cac0f245e00421aebeb3c6205ec58","observation_id":"4964d67a-dab7-4b60-8500-010ecd67be42","resolution":{"observed_at":"2026-08-11T00:14:23.159219Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:14:23.163736Z","title":null,"venue":null,"work_id":null,"year":1961},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":87,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.163736Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:c7496df436cb602468998d0910a014c14d5eb0d15e653e7541e520a78974ccb3","observation_id":"2b63a589-d62b-4d62-bdff-0af57758462f","resolution":{"observed_at":"2026-08-11T00:14:23.163736Z","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":"2026-08-11T00:14:23.637386Z","title":null,"venue":null,"work_id":"7bc7672b-65bf-411c-aa4f-dca03783eb55","year":1962},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":88,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.168473Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:bf7eeeacc63f461ff13cc7731a1cf66a944118397d6a78bbfe6ab7da8a3f4d74","observation_id":"b7cd6013-4acf-4c31-8607-9dcd5b307e3d","resolution":{"observed_at":"2026-08-11T00:14:23.641351Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:23.624941Z","title":null,"venue":null,"work_id":"9cee59c4-7ecb-4a16-b80c-103c87d2d0d8","year":2019},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":89,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.172523Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:594b259bdee79853303b955f42b7e07d2f260971fc2eeb56fc64a48ad38b63ec","observation_id":"7a7574da-dcd7-4e2f-bd0f-e571dbb43481","resolution":{"observed_at":"2026-08-11T00:14:23.628939Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T00:14:23.612673Z","title":null,"venue":null,"work_id":"96c4b375-f3b0-483d-9c73-022b7e53c20a","year":2021},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":90,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.176737Z"},"links":{"citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:42a6edcf350c7727c66b2d6930784e27997765ea914cd843f0c08d020395828e","observation_id":"e8aafc14-e96a-4650-b247-e226229df38b","resolution":{"observed_at":"2026-08-11T00:14:23.616439Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.05719","last_updated":"2024-02-08T14:50:07Z","snapshot_observed_at":"2026-08-07T07:34:13.082494Z","submitted_at":"2024-02-08T14:50:07Z","title":"Exact capacity of the \\emph{wide} hidden layer treelike neural networks with generic activations","version":1},"cited_work":{"arxiv_id":"2402.05719","doi":null,"metadata_source":"pith","pith_arxiv_id":"2402.05719","snapshot_observed_at":"2026-08-11T00:14:23.237001Z","title":"Exact capacity of the \\emph{wide} hidden layer treelike neural networks with generic activations","venue":"stat.ML","work_id":"845d9d2a-4a8d-41a3-af4f-f320f243aac4","year":2024},"citing_paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds","version":1},"reference_index":2024,"source":"pdf_text","source_observed_at":"2026-08-11T00:14:23.133190Z"},"links":{"cited_paper":"/paper/2402.05719","citing_paper":"/paper/2412.19677"},"observation_digest":"sha256:c898978f2d998081bf253e25adc3262d0c13e314afcc6d633b9910c5f4feb738","observation_id":"db152ac8-277d-4418-8bee-d50af53e9dc3","resolution":{"observed_at":"2026-08-11T00:14:23.241493Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2412.19677","last_updated":"2024-12-27T14:57:40Z","latest_version":1,"primary_category":"stat.ML","snapshot_observed_at":"2026-08-11T05:15:41.563935Z","submitted_at":"2024-12-27T14:57:40Z","title":"Deep ReLU networks -- injectivity capacity upper bounds"},"reference_resolution":{"displayed":91,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":57,"verified_exact":9,"verified_fuzzy":25},"total_outbound_references":91},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 91 of 91 outbound references and 1 inbound Pith citation observation for arXiv:2412.19677."}