{"as_of":"2026-08-12T04:38:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:af1438202adfcc15fafdd87ea8d2bafe896b7c14eda36ebca0c0985600ec4509","coverage":[{"denominator":47,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":47,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T21:30:36.260263Z","state":"measured"},{"denominator":47,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":47,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+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/2607.16384/citation-record","integrity":"/paper/2607.16384/integrity","json":"/paper/2607.16384/citation-record.json","paper":"/paper/2607.16384"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.52202/079017-4379","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Allmeier and N","venue":null,"work_id":"4c3dca58-103e-43fd-aac9-4e90f423d029","year":2024},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:32.504405Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:d9189b82cfa71e7ba15b7c352a880a79d163d5de826568bdc2128dd0b6daf1a7","observation_id":"eaea4d38-8bdf-4a08-938c-a40fe1998756","resolution":{"observed_at":"2026-08-01T21:33:32.696310Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-01T21:30:32.583845Z","title":"Bach and ´E","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:32.583845Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:c59dc5542508c973ce992296651c8d3c78dd9fc8b75ec844cae7f84d3ded1fa7","observation_id":"cccc34f5-8a15-40dc-a219-c8831287422e","resolution":{"observed_at":"2026-08-01T21:30:32.583845Z","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":"2026-08-01T21:30:32.735980Z","title":null,"venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:32.735980Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:79d8cd34296d39bea742231d95f52fd31ab9dc7d0bac71e127a42b88b7ebb3e4","observation_id":"113b3c5d-2f3e-49cd-b37f-b55f9d7ff80f","resolution":{"observed_at":"2026-08-01T21:30:32.735980Z","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":"2026-08-01T21:30:32.928130Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:32.928130Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:5f5a9e2646d931f481ff93603718bdb5ccb2f450515bcc54d249a2ed4908fc7c","observation_id":"6f56d53b-8fec-405b-be8f-b9b64afdf686","resolution":{"observed_at":"2026-08-01T21:30:32.928130Z","resolver_source":null,"status":"malformed_identifier"},"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":"2026-08-01T21:30:33.070234Z","title":null,"venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:33.070234Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:ab299c56a99b959c3d72a47511dc84a34cd0fc1e8b0208145abcb05e60ea5699","observation_id":"fc00cfb9-415f-43a2-b336-a3a1a0e966f8","resolution":{"observed_at":"2026-08-01T21:30:33.070234Z","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":"2026-08-01T21:30:33.165016Z","title":null,"venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:33.165016Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:384a2312f2e94170bd2dbb2c7420693f09923621e2b290bb942d2cb64ff78572","observation_id":"83fa53ab-3b78-4250-859e-80a0fae21810","resolution":{"observed_at":"2026-08-01T21:30:33.165016Z","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":"2026-08-01T21:30:33.286462Z","title":"Benveniste, M","venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:33.286462Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:41aea8ff287453ff1a7dcf380675ca39db041cc2915c966230de322cbea98d2c","observation_id":"69034208-2bf2-4655-9706-e128ac64a1c8","resolution":{"observed_at":"2026-08-01T21:30:33.286462Z","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":"2026-08-01T21:30:33.405996Z","title":null,"venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:33.405996Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:76ab68219bb6e94c2159c49fbfd2f409481926f51bc6f7c61a26d955fb0c5a5f","observation_id":"b6a6ac5d-93eb-4769-a5f0-e5f00daabf1a","resolution":{"observed_at":"2026-08-01T21:30:33.405996Z","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":"2026-08-01T21:30:33.495057Z","title":null,"venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:33.495057Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:68894bcb12b44b599ff856efe3d600eb564bd32c23692dd476f12428a8dbb68f","observation_id":"d57ed374-c2a2-4303-80cb-ff8e9179bff9","resolution":{"observed_at":"2026-08-01T21:30:33.495057Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1214/15-ssy212","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Braverman, J","venue":"Stochastic Systems","work_id":"601e9c0e-3bfd-4bec-afeb-443b690a5c26","year":2016},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:33.605143Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:e3b5c4140b7161af0b1bcaa0a47ce1f4b8b02fea4e42dffbd4e6307a433d1809","observation_id":"f39c25b1-d740-4f12-929d-0212b717d625","resolution":{"observed_at":"2026-08-01T21:33:32.557236Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-01T21:30:33.668029Z","title":"Charbonnier, L","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:33.668029Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:4595173701015f27222a9ee7818f558a35a3e4149e6f89bf563dfd58fbed98fb","observation_id":"6dfdc1bc-7a96-4e5c-ac4f-c37d8bf83e01","resolution":{"observed_at":"2026-08-01T21:30:33.668029Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1145/3508039","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Proceedings of the ACM on Measurement and Analysis of Computing Systems","work_id":"abbf8c76-5c05-420e-a5e5-58fb8313c56e","year":2022},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:33.752071Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:31e5ee5f54f6822d0ee81a559d11f395154b3ff63b46b2d99fb6136fa9162b87","observation_id":"4fbfe0ef-4542-4159-9492-eedf942c7238","resolution":{"observed_at":"2026-08-01T21:33:32.393731Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-01T21:30:33.828005Z","title":"Dieuleveut, A","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:33.828005Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:58fc1e695780c3a9b6798ebbd72f87acb6d0885bb3f887d9d49fbc42f4eb6a93","observation_id":"080ffb3f-1e2d-4062-8c6e-96df30245fc9","resolution":{"observed_at":"2026-08-01T21:30:33.828005Z","resolver_source":null,"status":"malformed_identifier"},"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":"2026-08-01T21:30:33.906946Z","title":"Eberle, A","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:33.906946Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:b7945cf0ea699c9b840b88608c9b5813d80901a35a3d5cce5d2d064410d234d3","observation_id":"e707a280-779c-47ea-8891-9651ad6970ef","resolution":{"observed_at":"2026-08-01T21:30:33.906946Z","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":"2026-08-01T21:30:33.957940Z","title":null,"venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:33.957940Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:73d01df994b4ebd7c14e7fe9b67e23a27b7831eccf7c05f2cbb778e6f384e839","observation_id":"4efd9592-ec20-4ad8-906c-328cb4e65f1d","resolution":{"observed_at":"2026-08-01T21:30:33.957940Z","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":"2026-08-01T21:30:34.038394Z","title":null,"venue":null,"work_id":null,"year":1968},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:34.038394Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:08e8d86ecde38d7ccfb07ce1919210da04a7109f6a47eb22ce6b18476f537dd7","observation_id":"b174cb14-d46c-4f15-b7b7-1116d2c02e4a","resolution":{"observed_at":"2026-08-01T21:30:34.038394Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1145/3084454","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Proceedings of the ACM on Measurement and Analysis of Computing Systems","work_id":"35c08648-ea1f-475d-ae91-8f1acbc49f1d","year":2017},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:34.142052Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:cb6922cc4024ded5ecd2093d8b32b6ef5550cb2315226bae2fd5a59d718a41b6","observation_id":"f326c8eb-45ea-44ac-8150-611990db2302","resolution":{"observed_at":"2026-08-01T21:33:32.240547Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2604.13378","last_updated":"2026-04-15T01:02:42Z","snapshot_observed_at":"2026-07-06T23:01:23.771347Z","submitted_at":"2026-04-15T01:02:42Z","title":"Revisiting the Constant Stepsize Stochastic Approximation with Decision-Dependent Markovian Noise","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2604.13378","snapshot_observed_at":"2026-08-01T21:30:34.194127Z","title":"Hadavi, W","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:34.194127Z"},"links":{"cited_paper":"/paper/2604.13378","citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:b61fb4131beb36d68dadbbc75157ab76e0c68ccd3971f1ca57f966bc18067b0a","observation_id":"73dd5484-71b1-4fcb-840d-d746d4a1a7c8","resolution":{"observed_at":"2026-08-01T21:30:34.194127Z","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":"2026-08-01T21:30:34.253184Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:34.253184Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:d7357180b5f0eab0776552c5634e5bbdb1b99f9c01dae505c4f3703b1ed3e6a6","observation_id":"531ff92b-b06d-4767-98d7-704743a17242","resolution":{"observed_at":"2026-08-01T21:30:34.253184Z","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":"2026-08-01T21:30:34.380006Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:34.380006Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:df521e25c38334a41cf85cee72d3744b800fb49fa3713e2d24aaaa3773c7417e","observation_id":"4560abb9-ec10-4af4-a102-2715c5029754","resolution":{"observed_at":"2026-08-01T21:30:34.380006Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.52202/079017-0684","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":null,"work_id":"dfd93889-1201-4c95-828d-002be3b8ba94","year":2024},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:34.454629Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:68357556f948c8dec448a3f1df7272eaa098c658c264cc1318485f08da0de272","observation_id":"c0a6443d-12cf-48b9-af81-54bf6b76595b","resolution":{"observed_at":"2026-08-01T21:33:32.069165Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1214/12-aap841","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kang and T","venue":"The Annals of Applied Probability","work_id":"9f510939-c28a-44a6-aeda-cd3394e3dae5","year":2013},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:34.520967Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:38b24f0c3e63c5bb64caae410e3e18afbd0e4e464a97e90e6410795b7e9e0e31","observation_id":"1ee61c4f-9805-4faf-af35-7e14859fd244","resolution":{"observed_at":"2026-08-01T21:33:31.905437Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-01T21:30:34.556076Z","title":null,"venue":null,"work_id":null,"year":1968},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:34.556076Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:e346cc52f012c8e2965020371cba7abf6ecc94d94d499e11761a8c5a2f9e8ddd","observation_id":"9593073d-e3bf-4d1b-ab22-e166fba7288b","resolution":{"observed_at":"2026-08-01T21:30:34.556076Z","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":"2026-08-01T21:30:34.656704Z","title":null,"venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:34.656704Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:9e75b2d7e7627dcb822bdf45f5565657e32b345f4bf9d2dd7b2ff23afcd8eefa","observation_id":"c7ee06ff-0981-4f5f-b343-150dd0130b8c","resolution":{"observed_at":"2026-08-01T21:30:34.656704Z","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":"2026-08-01T21:30:34.723602Z","title":"Koenker and G","venue":null,"work_id":null,"year":1978},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:34.723602Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:04bdcca9bbd7457b7f19b2b7bdf6de7cfbd64b67c8a885ed3d8bc88c4b1dea48","observation_id":"97f1e421-97b6-44e5-925e-285b1e378641","resolution":{"observed_at":"2026-08-01T21:30:34.723602Z","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":"2026-08-01T21:30:34.752702Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:34.752702Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:ab0a64eb5e7d1a84ebaa50412cd7cc4704c75fba513df64e6f2d956b366a204f","observation_id":"7a56f092-fe68-4fbe-8a3a-290e4d90703f","resolution":{"observed_at":"2026-08-01T21:30:34.752702Z","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":"2026-08-01T21:30:34.809055Z","title":null,"venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:34.809055Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:278fd0653e78242c19229af193679239f860f2de7925d2e70a870a35957fa2fd","observation_id":"bc70137f-63dc-410c-a178-8f2b5b10e359","resolution":{"observed_at":"2026-08-01T21:30:34.809055Z","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":"2026-08-01T21:30:34.891566Z","title":"Mandt, M","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:34.891566Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:4607d2b54b3094b1daea3c3f7e9196b63bc9ef7852732509de975afd550c9482","observation_id":"2b1d91e7-1c7e-43c1-bf36-b7f62999e8aa","resolution":{"observed_at":"2026-08-01T21:30:34.891566Z","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":"2026-08-01T21:30:35.012721Z","title":"Merad and S","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:35.012721Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:dd2050a83716c68aa2718d0d8e977490ab65f143a057f40009097cdde5c0212c","observation_id":"6f012b58-d606-4a36-862d-311dfac47c67","resolution":{"observed_at":"2026-08-01T21:30:35.012721Z","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":"2026-08-01T21:30:35.053846Z","title":null,"venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:35.053846Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:8e71c82d8f421ad8f632aac9d1ceb0694ec6a213baf5414dc7cf75971cbbf595","observation_id":"7ef84ac9-7c18-4feb-9f99-0b7b24f91d92","resolution":{"observed_at":"2026-08-01T21:30:35.053846Z","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":"2026-08-01T21:30:35.148449Z","title":"Moulines and F","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:35.148449Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:b58c2e251181acb9d1b71cc5a66b377277afd8959c915b2ed6bbd657dab1bbfc","observation_id":"a87f759a-8f86-44ae-a33c-83f32bc8e6ae","resolution":{"observed_at":"2026-08-01T21:30:35.148449Z","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":"2026-08-01T21:30:35.273717Z","title":"Nemirovski, A","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:35.273717Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:561d11131f31e2710b2fc85a39b875eeaf77dce6bc654a90d2259f6eb3bb66d8","observation_id":"71a131fb-c3ee-4a63-9586-4acfc58a007e","resolution":{"observed_at":"2026-08-01T21:30:35.273717Z","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":"2026-08-01T21:30:35.385007Z","title":"Pardoux and A","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:35.385007Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:5dba72f2ca39f8539a8096270248c16605f1d7513a96d4fb6a7774f095ad4d06","observation_id":"c6e02dc9-8fe9-4a48-953b-9898ac402f93","resolution":{"observed_at":"2026-08-01T21:30:35.385007Z","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":"2026-08-01T21:30:35.452772Z","title":"Pardoux and A","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:35.452772Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:e2f14f8643c960c29d9a7f8a99d79f684d62f24f8b5420673dcfa960a5fefcb1","observation_id":"214302aa-3c7e-426f-830c-fc06c0190e92","resolution":{"observed_at":"2026-08-01T21:30:35.452772Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1214/009117905000000062","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Pardoux and A","venue":"The Annals of Probability","work_id":"da766deb-85e9-4a15-9389-e3074fbfb1eb","year":2005},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:35.501396Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:850142eac8c7f396456cd670ef84bb46412edeb1300a851278efee9052cf7f2c","observation_id":"ea724896-ad66-4bc9-af0b-1cb2e6ed102b","resolution":{"observed_at":"2026-08-01T21:33:31.792676Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-01T21:30:35.573225Z","title":null,"venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:35.573225Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:ad45374e616dbdf206874b16839b2cbb353996d22ab8bb6c43b873abb1036cff","observation_id":"3ce581d3-4c2b-4754-9fde-0e426e29e22b","resolution":{"observed_at":"2026-08-01T21:30:35.573225Z","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":"2026-08-01T21:30:35.656907Z","title":null,"venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:35.656907Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:4ce4a08bd3907d239aefe87c97a7e3a337ab57313c1d62fa09e1489664250b24","observation_id":"f1cd3b7f-1dbf-45f8-9a2b-9fc4c6f48f4b","resolution":{"observed_at":"2026-08-01T21:30:35.656907Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1214/25-aap2184","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"The Annals of Applied Probability","work_id":"54c72889-522e-4fbf-a179-408abccb4b59","year":2025},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:35.720227Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:e7f73fee6fec7539dbf5521ffda4b1dc1ba0d0aa7a56b4cc3331874e5a178af7","observation_id":"1e6507d0-f19f-43de-8373-d3830b3b2564","resolution":{"observed_at":"2026-08-01T21:33:31.640601Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-01T21:30:35.769849Z","title":"Robbins and S","venue":null,"work_id":null,"year":1951},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:35.769849Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:aa6381ae7c449951942371ea375ae974304292fb9b31af7d67b63b8a170f91e5","observation_id":"e8b43c8d-cb39-4ba0-9576-ddf8246cedce","resolution":{"observed_at":"2026-08-01T21:30:35.769849Z","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":"2026-08-01T21:30:35.832246Z","title":null,"venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:35.832246Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:8ee7eb83db355dddc2e43f60fbdf5f55f66828d092fe7ddc88ab95210f10b80a","observation_id":"923b8eb1-b917-4098-8606-32783813c574","resolution":{"observed_at":"2026-08-01T21:30:35.832246Z","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":"2026-08-01T21:30:35.911524Z","title":null,"venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:35.911524Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:672dd2714bfd567dbd5de0b590408b2191c08896febf7bd3d8630c218a0201e6","observation_id":"96bf2c29-a494-4aa5-a460-b37f543bb462","resolution":{"observed_at":"2026-08-01T21:30:35.911524Z","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":"2026-08-01T21:30:35.975500Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:35.975500Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:76f47de8287e8e973ce9e0b8e1d381963ff8d11f3c1a935accb5b44b38c9c95b","observation_id":"d441bc73-79fc-477b-8928-bfecc1ac0bc0","resolution":{"observed_at":"2026-08-01T21:30:35.975500Z","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":"2026-08-01T21:30:36.065555Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:36.065555Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:0c3f191514bf2cba05585c764bf48a75176857a812ab0f22be574b123dece637","observation_id":"af16fbde-ef9d-4387-bb2a-80ed07cf2d26","resolution":{"observed_at":"2026-08-01T21:30:36.065555Z","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":"2026-08-01T21:30:36.129093Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:36.129093Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:3efb543f2805761d500c2e12ec32d76447736e98d7e02aa5f1b66343f042a1a4","observation_id":"a6f97174-e92b-4858-b39c-5b306b043a43","resolution":{"observed_at":"2026-08-01T21:30:36.129093Z","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":"2026-08-01T21:30:36.178250Z","title":"Zhang, D","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:36.178250Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:e9d5fea2acacb5b96a206c573c45e49c32b91a863da5d8d8f7f43c8144b0afae","observation_id":"0fb4df79-8fc0-42d0-b517-11a3a72ce98a","resolution":{"observed_at":"2026-08-01T21:30:36.178250Z","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":"2026-08-01T21:30:36.260263Z","title":"Zhang, D","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:36.260263Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:6119c8ae2f7dc6b5494e19f1ec9eb6621c0fe4ae18f67c76627fc920a171748b","observation_id":"da45a624-4e48-4e6d-9cbc-7b592dff60cc","resolution":{"observed_at":"2026-08-01T21:30:36.260263Z","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":"2026-08-01T21:30:34.324071Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima","version":1},"reference_index":1964,"source":"pdf_text","source_observed_at":"2026-08-01T21:30:34.324071Z"},"links":{"citing_paper":"/paper/2607.16384"},"observation_digest":"sha256:11d5d18ddaeaa02ff4fa897b5985f232ffaaf3048853cc3c9ea69a1a0423d23b","observation_id":"8c0cdd1e-7fdf-44f1-8623-36866711700c","resolution":{"observed_at":"2026-08-01T21:30:34.324071Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.16384","last_updated":"2026-07-17T17:22:46Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-09T23:10:18.320003Z","submitted_at":"2026-07-17T17:22:46Z","title":"Scaling Limits of Constant-Stepsize SGD at Flat Minima"},"reference_resolution":{"displayed":47,"state_counts":{"malformed_identifier":3,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":36,"verified_exact":8,"verified_fuzzy":0},"total_outbound_references":47},"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":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 47 of 47 outbound references and 0 inbound Pith citation observations for arXiv:2607.16384."}