{"as_of":"2026-08-16T20:03:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:41b1ae34e3ba27baed12c26318df3f27e95c822d6a7eabb20b5728826288b65d","coverage":[{"denominator":18,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":18,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T20:26:51.822108Z","state":"measured"},{"denominator":18,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":18,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2505.13582/citation-record","integrity":"/paper/2505.13582/integrity","json":"/paper/2505.13582/citation-record.json","paper":"/paper/2505.13582"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T20:26:52.045814Z","title":"Sun , author D","venue":null,"work_id":"6edc5d00-e771-4882-8e75-043d4a99f0a6","year":2020},"citing_paper":{"arxiv_id":"2505.13582","last_updated":"2025-05-19T15:50:36Z","snapshot_observed_at":"2026-08-15T20:14:12.089141Z","submitted_at":"2025-05-19T15:50:36Z","title":"Uncovering Critical Sets of Deep Neural Networks via Sample-Independent Critical Lifting","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-15T20:26:51.758690Z"},"links":{"citing_paper":"/paper/2505.13582"},"observation_digest":"sha256:99f7236518b58fbde957d53f699c2c60a3a067424c25a8eca3f2222e6ba52f12","observation_id":"175803ba-bf4f-40fc-a393-e72d658391ce","resolution":{"observed_at":"2026-08-15T20:26:52.049738Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T20:26:52.034296Z","title":"Zhang , author Y","venue":null,"work_id":"2e2eb218-20c8-408b-bdce-339555824155","year":2022},"citing_paper":{"arxiv_id":"2505.13582","last_updated":"2025-05-19T15:50:36Z","snapshot_observed_at":"2026-08-15T20:14:12.089141Z","submitted_at":"2025-05-19T15:50:36Z","title":"Uncovering Critical Sets of Deep Neural Networks via Sample-Independent Critical Lifting","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-15T20:26:51.762974Z"},"links":{"citing_paper":"/paper/2505.13582"},"observation_digest":"sha256:81e87ec831541af773b6106cc45673472fd2b567eaf740949b00f97b3bf5cee8","observation_id":"df104783-73ff-4dae-91d8-c7d22b7660db","resolution":{"observed_at":"2026-08-15T20:26:52.038076Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T20:26:52.022606Z","title":"Zhang , author Z","venue":null,"work_id":"f3c26bdf-799c-42ff-8257-1a47984634b2","year":2021},"citing_paper":{"arxiv_id":"2505.13582","last_updated":"2025-05-19T15:50:36Z","snapshot_observed_at":"2026-08-15T20:14:12.089141Z","submitted_at":"2025-05-19T15:50:36Z","title":"Uncovering Critical Sets of Deep Neural Networks via Sample-Independent Critical Lifting","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-15T20:26:51.766621Z"},"links":{"citing_paper":"/paper/2505.13582"},"observation_digest":"sha256:464f027e88379e4f0335de28aa3bb3228831457d24203f763853ca6a8916d615","observation_id":"17cae233-ae5a-4198-93bc-8e6eea89dc6c","resolution":{"observed_at":"2026-08-15T20:26:52.026661Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T20:26:52.010061Z","title":"Bai , author T","venue":null,"work_id":"e1ff03f1-f88b-41ea-9043-76ca751f3ff5","year":2024},"citing_paper":{"arxiv_id":"2505.13582","last_updated":"2025-05-19T15:50:36Z","snapshot_observed_at":"2026-08-15T20:14:12.089141Z","submitted_at":"2025-05-19T15:50:36Z","title":"Uncovering Critical Sets of Deep Neural Networks via Sample-Independent Critical Lifting","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-15T20:26:51.770531Z"},"links":{"citing_paper":"/paper/2505.13582"},"observation_digest":"sha256:e03df903d96d8dfa81e85b06d55102875c61aacc80ca373efa5334c2ecc21c7f","observation_id":"c6afe56e-58cd-48c1-b59d-09f84336327d","resolution":{"observed_at":"2026-08-15T20:26:52.014372Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T20:26:51.998141Z","title":"Cooper , title Global minima of overparameterized neural networks , journal SIAM Journal on Mathematics of Data Science volume 3 ( year 2021 ) pages 676--691","venue":null,"work_id":"92e112f1-b2fc-4b31-9af5-ed33a23b8a4e","year":2021},"citing_paper":{"arxiv_id":"2505.13582","last_updated":"2025-05-19T15:50:36Z","snapshot_observed_at":"2026-08-15T20:14:12.089141Z","submitted_at":"2025-05-19T15:50:36Z","title":"Uncovering Critical Sets of Deep Neural Networks via Sample-Independent Critical Lifting","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-15T20:26:51.774684Z"},"links":{"citing_paper":"/paper/2505.13582"},"observation_digest":"sha256:02fd95a81632ea39621f7d1c38297d6aa4cfa00872c24e82538e50c34c3f3a94","observation_id":"181e17ca-1bcb-4107-b6c1-f70dabd43a29","resolution":{"observed_at":"2026-08-15T20:26:52.002230Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2309.00508","last_updated":"2025-04-10T13:56:57Z","snapshot_observed_at":"2026-08-16T19:41:11.184404Z","submitted_at":"2023-09-01T14:53:51Z","title":"Geometry and Local Recovery of Global Minima of Two-layer Neural Networks at Overparameterization","version":4},"cited_work":{"arxiv_id":"2309.00508","doi":null,"metadata_source":"pith","pith_arxiv_id":"2309.00508","snapshot_observed_at":"2026-08-15T20:26:51.871467Z","title":"Geometry and Local Recovery of Global Minima of Two-layer Neural Networks at Overparameterization","venue":"cs.LG","work_id":"206b1da0-4462-429b-841e-6ed414c918ae","year":2023},"citing_paper":{"arxiv_id":"2505.13582","last_updated":"2025-05-19T15:50:36Z","snapshot_observed_at":"2026-08-15T20:14:12.089141Z","submitted_at":"2025-05-19T15:50:36Z","title":"Uncovering Critical Sets of Deep Neural Networks via Sample-Independent Critical Lifting","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-15T20:26:51.778478Z"},"links":{"cited_paper":"/paper/2309.00508","citing_paper":"/paper/2505.13582"},"observation_digest":"sha256:0259a7d692accdbc7a41e2b65cc067b099dbdf4684f1e5007654fa1cf55544aa","observation_id":"be21ac24-4e66-4747-933e-b3b76c77dec7","resolution":{"observed_at":"2026-08-15T20:26:51.877708Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T20:26:51.986178Z","title":"Fukumizu , author S","venue":null,"work_id":"bf8508d2-a668-48bf-89eb-9f791ad443d6","year":2000},"citing_paper":{"arxiv_id":"2505.13582","last_updated":"2025-05-19T15:50:36Z","snapshot_observed_at":"2026-08-15T20:14:12.089141Z","submitted_at":"2025-05-19T15:50:36Z","title":"Uncovering Critical Sets of Deep Neural Networks via Sample-Independent Critical Lifting","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-15T20:26:51.782598Z"},"links":{"citing_paper":"/paper/2505.13582"},"observation_digest":"sha256:929638f01d0a6de7349cffd9169bc83e5331ebec827339e747c9216f920a88c2","observation_id":"edb85516-fe1a-4480-9d24-13e5664d0b2d","resolution":{"observed_at":"2026-08-15T20:26:51.989879Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T20:26:51.975418Z","title":"Fukumizu , author S","venue":null,"work_id":"8e850305-bb07-4129-a5e6-eb02ca2fc5fd","year":2019},"citing_paper":{"arxiv_id":"2505.13582","last_updated":"2025-05-19T15:50:36Z","snapshot_observed_at":"2026-08-15T20:14:12.089141Z","submitted_at":"2025-05-19T15:50:36Z","title":"Uncovering Critical Sets of Deep Neural Networks via Sample-Independent Critical Lifting","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-15T20:26:51.786234Z"},"links":{"citing_paper":"/paper/2505.13582"},"observation_digest":"sha256:44bc09281c28c4e025300d21a1d28be79f8e468af6f272830195f1708cc43c88","observation_id":"a38c8338-4335-4eac-bccb-62f5b9ee6ae7","resolution":{"observed_at":"2026-08-15T20:26:51.979082Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T20:26:51.965185Z","title":"Simsek , author F","venue":null,"work_id":"c33d724a-2bfd-4184-ae8e-5c460540e9ff","year":2021},"citing_paper":{"arxiv_id":"2505.13582","last_updated":"2025-05-19T15:50:36Z","snapshot_observed_at":"2026-08-15T20:14:12.089141Z","submitted_at":"2025-05-19T15:50:36Z","title":"Uncovering Critical Sets of Deep Neural Networks via Sample-Independent Critical Lifting","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-15T20:26:51.789777Z"},"links":{"citing_paper":"/paper/2505.13582"},"observation_digest":"sha256:b3a69ac8b0549f096fe1fd19fe5e1029af561aee15be1be5bc3e87322141ea3c","observation_id":"99355e3f-e009-4e81-bc24-0b2751916dd4","resolution":{"observed_at":"2026-08-15T20:26:51.968738Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T20:26:51.954555Z","title":"Simsek , author A","venue":null,"work_id":"599c8a46-d0d2-4eef-9d54-60b7647d828a","year":2023},"citing_paper":{"arxiv_id":"2505.13582","last_updated":"2025-05-19T15:50:36Z","snapshot_observed_at":"2026-08-15T20:14:12.089141Z","submitted_at":"2025-05-19T15:50:36Z","title":"Uncovering Critical Sets of Deep Neural Networks via Sample-Independent Critical Lifting","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-15T20:26:51.793291Z"},"links":{"citing_paper":"/paper/2505.13582"},"observation_digest":"sha256:0e61e98e2b2df5a0b1b8fbcc6043017958385d25cebc2447db56c673887a0640","observation_id":"83561a7f-f612-4a8e-9b0e-d7baa679b7f7","resolution":{"observed_at":"2026-08-15T20:26:51.958281Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1710.07406","last_updated":"2017-10-20T03:34:56Z","snapshot_observed_at":"2026-08-14T20:21:59.319940Z","submitted_at":"2017-10-20T03:34:56Z","title":"First-order Methods Almost Always Avoid Saddle Points","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1710.07406","snapshot_observed_at":"2026-08-15T20:26:51.797163Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2505.13582","last_updated":"2025-05-19T15:50:36Z","snapshot_observed_at":"2026-08-15T20:14:12.089141Z","submitted_at":"2025-05-19T15:50:36Z","title":"Uncovering Critical Sets of Deep Neural Networks via Sample-Independent Critical Lifting","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-15T20:26:51.797163Z"},"links":{"cited_paper":"/paper/1710.07406","citing_paper":"/paper/2505.13582"},"observation_digest":"sha256:d00c68f0ae9f9eb0a3f26c8ccb60324632587d13791fcc66ffc378d40c04ac90","observation_id":"aff3332f-ccb3-49cc-ad0a-c49c1bf8b27d","resolution":{"observed_at":"2026-08-15T20:26:51.797163Z","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":"2026-08-15T20:26:51.943916Z","title":"Venturi , author A","venue":null,"work_id":"9b0a5122-0ee3-4536-8040-fa4c6ff57284","year":2019},"citing_paper":{"arxiv_id":"2505.13582","last_updated":"2025-05-19T15:50:36Z","snapshot_observed_at":"2026-08-15T20:14:12.089141Z","submitted_at":"2025-05-19T15:50:36Z","title":"Uncovering Critical Sets of Deep Neural Networks via Sample-Independent Critical Lifting","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-15T20:26:51.800883Z"},"links":{"citing_paper":"/paper/2505.13582"},"observation_digest":"sha256:9a80dafe47e671c5d9f27ed5e1058a0f01ea707430eba55dab34d92e539dc560","observation_id":"853f164a-ff0e-4d3b-a89b-e5e3abe6daf2","resolution":{"observed_at":"2026-08-15T20:26:51.947575Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T20:26:51.931436Z","title":"Li , author T","venue":null,"work_id":"c9ec552e-e022-424d-b956-f26e673c163a","year":2022},"citing_paper":{"arxiv_id":"2505.13582","last_updated":"2025-05-19T15:50:36Z","snapshot_observed_at":"2026-08-15T20:14:12.089141Z","submitted_at":"2025-05-19T15:50:36Z","title":"Uncovering Critical Sets of Deep Neural Networks via Sample-Independent Critical Lifting","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-15T20:26:51.804723Z"},"links":{"citing_paper":"/paper/2505.13582"},"observation_digest":"sha256:b8f79a005b5256aa4d6aeb6756e17a7006da337ed3f4f88762a49a68b1c2cc3b","observation_id":"145aaefa-706e-4f63-bdfc-1efe96cf5110","resolution":{"observed_at":"2026-08-15T20:26:51.935748Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T20:26:51.919900Z","title":"Nguyen , author M","venue":null,"work_id":"edc8fda1-4145-4907-aaa5-9ce4a2189ac0","year":2017},"citing_paper":{"arxiv_id":"2505.13582","last_updated":"2025-05-19T15:50:36Z","snapshot_observed_at":"2026-08-15T20:14:12.089141Z","submitted_at":"2025-05-19T15:50:36Z","title":"Uncovering Critical Sets of Deep Neural Networks via Sample-Independent Critical Lifting","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-15T20:26:51.808279Z"},"links":{"citing_paper":"/paper/2505.13582"},"observation_digest":"sha256:45e5a7d3ab770ec8ddbf9b7a1b427ba617f191a247e3073620403f8c473dfe15","observation_id":"fe1539e0-2292-4bad-a7f4-1ce991de7998","resolution":{"observed_at":"2026-08-15T20:26:51.923613Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T20:26:51.908341Z","title":"Nguyen , title On connected sublevel sets in deep learning , journal ICML ( year 2019 ) pages 4790–4799","venue":null,"work_id":"6c397f5c-bf13-45db-884f-42179a6f65d9","year":2019},"citing_paper":{"arxiv_id":"2505.13582","last_updated":"2025-05-19T15:50:36Z","snapshot_observed_at":"2026-08-15T20:14:12.089141Z","submitted_at":"2025-05-19T15:50:36Z","title":"Uncovering Critical Sets of Deep Neural Networks via Sample-Independent Critical Lifting","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-15T20:26:51.811841Z"},"links":{"citing_paper":"/paper/2505.13582"},"observation_digest":"sha256:a023a782006c38f30c090fc89294f858c7ef42475bdd82e2069ea577849269f2","observation_id":"8d6241cd-2df7-4d48-b504-94e0ce28924e","resolution":{"observed_at":"2026-08-15T20:26:51.912509Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T20:26:51.896759Z","title":"Kawaguchi , title Deep learning without poor local minima , journal NeurIPS ( year 2016 )","venue":null,"work_id":"28d28bc3-cf4a-4f1e-bc9d-20a37ce3e19a","year":2016},"citing_paper":{"arxiv_id":"2505.13582","last_updated":"2025-05-19T15:50:36Z","snapshot_observed_at":"2026-08-15T20:14:12.089141Z","submitted_at":"2025-05-19T15:50:36Z","title":"Uncovering Critical Sets of Deep Neural Networks via Sample-Independent Critical Lifting","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-15T20:26:51.815285Z"},"links":{"citing_paper":"/paper/2505.13582"},"observation_digest":"sha256:d4bb78370243ad07262c6df6b0defb264be5ed528e26ed555945a1e19ad474a7","observation_id":"4ccb5560-f661-4d37-9b4a-b1146fb9ea4c","resolution":{"observed_at":"2026-08-15T20:26:51.900708Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T20:26:51.885559Z","title":null,"venue":null,"work_id":"e92bf4de-1e69-4174-95a9-3e184baa183c","year":2002},"citing_paper":{"arxiv_id":"2505.13582","last_updated":"2025-05-19T15:50:36Z","snapshot_observed_at":"2026-08-15T20:14:12.089141Z","submitted_at":"2025-05-19T15:50:36Z","title":"Uncovering Critical Sets of Deep Neural Networks via Sample-Independent Critical Lifting","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-15T20:26:51.818411Z"},"links":{"citing_paper":"/paper/2505.13582"},"observation_digest":"sha256:b9745f99cefd6bfd1c6bd70b4af476f675df58ca2024a75015538eaf625a1a7e","observation_id":"5f080e62-2875-4ffd-8ab3-c7366dee7134","resolution":{"observed_at":"2026-08-15T20:26:51.889377Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1512.07276","last_updated":"2015-12-22T22:01:22Z","snapshot_observed_at":"2026-08-14T22:17:19.284360Z","submitted_at":"2015-12-22T22:01:22Z","title":"The Zero Set of a Real Analytic Function","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1512.07276","snapshot_observed_at":"2026-08-15T20:26:51.822108Z","title":"Mityagin , title The zero set of a real analytic function , journal arxiv:1512.07276 ( year 2015 )","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2505.13582","last_updated":"2025-05-19T15:50:36Z","snapshot_observed_at":"2026-08-15T20:14:12.089141Z","submitted_at":"2025-05-19T15:50:36Z","title":"Uncovering Critical Sets of Deep Neural Networks via Sample-Independent Critical Lifting","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-15T20:26:51.822108Z"},"links":{"cited_paper":"/paper/1512.07276","citing_paper":"/paper/2505.13582"},"observation_digest":"sha256:5fa452c19c3750151b106de88a73e94e4e9010405667dfdd54036988187c66ce","observation_id":"e027b58e-6de1-4f44-a949-80e2e700085a","resolution":{"observed_at":"2026-08-15T20:26:51.822108Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2505.13582","last_updated":"2025-05-19T15:50:36Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-15T20:14:12.089141Z","submitted_at":"2025-05-19T15:50:36Z","title":"Uncovering Critical Sets of Deep Neural Networks via Sample-Independent Critical Lifting"},"reference_resolution":{"displayed":18,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":3,"verified_exact":1,"verified_fuzzy":14},"total_outbound_references":18},"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":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 0 inbound Pith citation observations for arXiv:2505.13582."}