{"as_of":"2026-08-13T13:30:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:4a81449395f8ed0f8bcb5bbf667c572330f15d21dd00fbbd4207da1451177e49","coverage":[{"denominator":41,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":41,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T03:14:20.526356Z","state":"measured"},{"denominator":41,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":41,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+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/2607.25206/citation-record","integrity":"/paper/2607.25206/integrity","json":"/paper/2607.25206/citation-record.json","paper":"/paper/2607.25206"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T03:14:15.004995Z","title":"Allaire and R","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:15.004995Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:e83c2f1eb00de5fbfffc10614c3e8692460255c427a612d20ee3863f25d7f778","observation_id":"00028893-f2b2-4d02-9a1b-f4afedfd6a43","resolution":{"observed_at":"2026-08-01T03:14:15.004995Z","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":"2026-08-01T03:14:15.086198Z","title":"Alouges, Introduction to periodic homogenization, Interdiscip","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:15.086198Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:64dcd9dde9560466989d6bedbd9c3ff9bccfd77614d0844cb14390b5f4335cd0","observation_id":"3928ba22-9914-48cf-8848-db2efb8ca342","resolution":{"observed_at":"2026-08-01T03:14:15.086198Z","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":"2026-08-01T03:14:15.221068Z","title":"Ambrosio, N","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:15.221068Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:caddfffe57d6e8fdc635bf2370385e442a833f358fbd311af2aacf5e517867b1","observation_id":"4f99da41-1fae-4f86-8284-a734e79494e8","resolution":{"observed_at":"2026-08-01T03:14:15.221068Z","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":"2026-08-01T03:14:15.356153Z","title":"Bedrossian and I","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:15.356153Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:b57d98dcc81ed3cafc12ca5c8344ea56bedf8f0bb5a86fdf19082acfa9d392c7","observation_id":"cd1d7e2d-9faf-403c-af83-891cee324cdb","resolution":{"observed_at":"2026-08-01T03:14:15.356153Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1108.5167","last_updated":"2011-08-30T22:46:10Z","snapshot_observed_at":"2026-07-06T02:32:57.774902Z","submitted_at":"2011-08-25T19:42:33Z","title":"Inhomogeneous Patlak-Keller-Segel models and Aggregation Equations with Nonlinear Diffusion in $\\Real^d$","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1108.5167","snapshot_observed_at":"2026-08-01T03:14:15.480388Z","title":"Bedrossian and N","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:15.480388Z"},"links":{"cited_paper":"/paper/1108.5167","citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:dd6f3edfba699530a8f61c1b78c948a40107fa6dfa1573bca47b14c3f750a14d","observation_id":"7088df2f-16cf-4452-9b3c-12af50defaea","resolution":{"observed_at":"2026-08-01T03:14:15.480388Z","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":"2026-08-01T03:14:15.620526Z","title":"Bensoussan, Asymptotic analysis for periodic structures, vol","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:15.620526Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:7e64914c5cf93d158bfcaa56bcca16d6c76182ea643424dc65e67c63177e732c","observation_id":"673c8591-1a9e-4dd0-8f6f-29710525d35e","resolution":{"observed_at":"2026-08-01T03:14:15.620526Z","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":"2026-08-01T03:14:15.687088Z","title":"Braides, Gamma-convergence for Beginners, vol","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:15.687088Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:419c835d1a23cad1f534c21a10cf81b2068b0b5291c613d60f31caeaee4d5da0","observation_id":"9bf3ab8e-c651-4410-a9c3-54e2a3eed0c2","resolution":{"observed_at":"2026-08-01T03:14:15.687088Z","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":"2026-08-01T03:14:15.782628Z","title":"Braides, Local minimization, variational evolution and Γ-convergence, vol","venue":null,"work_id":null,"year":2094},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:15.782628Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:e578e8bf4638e614cb7c938c7e2a23bc9a9ea2ea48723c74632ae9eebac67c2e","observation_id":"045f767e-cc9f-45b0-b16e-e5b2606ff3e4","resolution":{"observed_at":"2026-08-01T03:14:15.782628Z","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":"2026-08-01T03:14:15.892435Z","title":"Braides, G","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:15.892435Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:cde83366c95215eb73701d075f18a01f4e2ff1e2a24cfce0e81e7dd1604722ac","observation_id":"90024298-13a2-4700-a309-76280690cf06","resolution":{"observed_at":"2026-08-01T03:14:15.892435Z","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":"2026-08-01T03:14:16.033168Z","title":null,"venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:16.033168Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:356dcfddf946064ce7b4f86994e3ea2666b5495b0b6e9377009760615426f15a","observation_id":"ba8783dc-f3b9-463c-9f95-1ac4ad1a74d8","resolution":{"observed_at":"2026-08-01T03:14:16.033168Z","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":"2026-08-01T03:14:16.281212Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:16.281212Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:2b84559721f2ee2e191d7eac5144e949f63bfc3c6eb76b0d191a46a3ea032c79","observation_id":"4e927702-4788-414e-ae4d-c02742050baf","resolution":{"observed_at":"2026-08-01T03:14:16.281212Z","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":"2026-08-01T03:14:16.605465Z","title":null,"venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:16.605465Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:7ac4792b9ee527c1b794401e9ae4911c635c5b38f279506e88ce282eb287f634","observation_id":"c7dcd5c8-b9cb-49d4-ac51-00565da2f0c4","resolution":{"observed_at":"2026-08-01T03:14:16.605465Z","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":"2026-08-01T03:14:17.007638Z","title":null,"venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:17.007638Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:27bd77ef788fb2c737956dd0090bf870a01a03ead55914ffdb763d60dfde9eef","observation_id":"c3a296ba-16b3-422f-9454-ccb70de061b1","resolution":{"observed_at":"2026-08-01T03:14:17.007638Z","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":"2026-08-01T03:14:17.180691Z","title":"Coudreuse, Li-Yau-Hamilton inequality on the JKO scheme for the granular-medium equa- tion, arXiv preprint arXiv:2510.09231, (2025)","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:17.180691Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:d7ea8055f1763751b6430bf1c7951cc5c4a0803b77478fde6edc9611797b0b2e","observation_id":"aaec2305-a5e4-40c4-a192-d1dbe57d8c02","resolution":{"observed_at":"2026-08-01T03:14:17.180691Z","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":"2026-08-01T03:14:17.290298Z","title":"Dacorogna, Direct methods in the calculus of variations , Springer, 2008","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:17.290298Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:50499652f2c4725f8ad94cf6c19b954374384df201a680be2f2f1ac00a136c40","observation_id":"ca4f3130-0a9f-43fd-a4bd-1de43b39770c","resolution":{"observed_at":"2026-08-01T03:14:17.290298Z","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":"2026-08-01T03:14:17.406220Z","title":"Dal Maso , An introduction to Γ-convergence, vol","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:17.406220Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:a532fe7c66d1982f2558a9548d4674bdc71ff65121ebff252b27b99aefdb2adf","observation_id":"431c2e50-464d-4cb0-a937-c753bec48bd3","resolution":{"observed_at":"2026-08-01T03:14:17.406220Z","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":"2026-08-01T03:14:17.508293Z","title":"Erbar, The heat equation on manifolds as a gradient flow in the Wasserstein space, Annales de l’IHP Probabilit´ es et statistiques, 46 (2010), pp","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:17.508293Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:f5aa5ee8f808c73ff03fc0bb09545d1ef24b8f955488aa2c4fb37025cd918a40","observation_id":"394ea64f-184c-443a-a87b-c58f3e43a044","resolution":{"observed_at":"2026-08-01T03:14:17.508293Z","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":"2026-08-01T03:14:17.619046Z","title":"Forkert, J","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:17.619046Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:5c5dee49f4083bfe09ca22920e5b4869d97a5f9b285d00c04e411fbae102edff","observation_id":"b4c0a451-b328-4f5f-be0e-dc3d61167f2d","resolution":{"observed_at":"2026-08-01T03:14:17.619046Z","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":"2026-08-01T03:14:17.685344Z","title":"Gangbo and A","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:17.685344Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:a6c31e9794070e12c8e74ffc1450653f21ced27f97e0f8d03495d68dd51b6cc7","observation_id":"055eeea8-61f0-45a0-b335-e33531097540","resolution":{"observed_at":"2026-08-01T03:14:17.685344Z","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":"2026-08-01T03:14:17.807353Z","title":"Gao and N","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:17.807353Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:281d301c248d1ae4fbb2ef1b906f0f01cd0167dae589943c42e22c5b73de79a1","observation_id":"a24d9ea3-8166-4aa6-b389-aa72ba533ed7","resolution":{"observed_at":"2026-08-01T03:14:17.807353Z","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":"2026-08-01T03:14:18.012334Z","title":"Gladbach, E","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:18.012334Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:33fd2a1ba707ab7a9759221a0665f6c33a9987401fefbc5665309ca9ca4c6abb","observation_id":"d7b25e18-63ed-48d7-8b2f-55d09e2e3f3a","resolution":{"observed_at":"2026-08-01T03:14:18.012334Z","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":"2026-08-01T03:14:18.108532Z","title":"Jacobs, W","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:18.108532Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:ee44539a3342ca1c2ec88f943c9c0d0baf554bb1961a266d6114e52bd07834cc","observation_id":"5cf7cb8c-c76a-4eac-90ce-1d3ceb78032b","resolution":{"observed_at":"2026-08-01T03:14:18.108532Z","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":"2026-08-01T03:14:18.224388Z","title":"Jacobs and F","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:18.224388Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:fbd6fe5bb2d4a4f5420cf9a4d8adc185e0697dd5495a840bf576406f239d40b5","observation_id":"473a9e86-3066-46d9-b207-52f9575ff772","resolution":{"observed_at":"2026-08-01T03:14:18.224388Z","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":"2026-08-01T03:14:18.332564Z","title":"Jordan, D","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:18.332564Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:92833af289ed38d47d38833e83ceb695e7c79912394028b006acd6ed7555537e","observation_id":"1470e43e-bb94-43e9-a4dd-7fc4b5f1b9b5","resolution":{"observed_at":"2026-08-01T03:14:18.332564Z","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":"2026-08-01T03:14:18.451262Z","title":"Jost, Riemannian geometry and geometric analysis , Springer, 2005","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:18.451262Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:9194214c8b58e0de1a283fe7b210d773ef7833c152a9f58c626a2e900464fbc4","observation_id":"865a4d2b-1a2d-4436-a6ad-b8797062e03f","resolution":{"observed_at":"2026-08-01T03:14:18.451262Z","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":"2026-08-01T03:14:18.570304Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:18.570304Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:3f507bcec1945146fd296e0ec6153351646b88686ad076da0bd98fd2bd6d568d","observation_id":"2b94a1bb-f15a-475d-87f5-5dabba96555d","resolution":{"observed_at":"2026-08-01T03:14:18.570304Z","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":"2026-08-01T03:14:18.679805Z","title":"Lisini, Nonlinear diffusion equations with variable coefficients as gradient flows in Wasser- stein spaces, ESAIM Control Optim","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:18.679805Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:9a9bfd9ef53dae95bfe517b6cb0f60e124ffc28bf877b4ffb87b49e584923671","observation_id":"4487eeef-b42b-4182-b1c3-a8ae07d83b69","resolution":{"observed_at":"2026-08-01T03:14:18.679805Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.10676","last_updated":"2025-05-15T19:41:49Z","snapshot_observed_at":"2026-08-07T15:44:56.234749Z","submitted_at":"2025-05-15T19:41:49Z","title":"Variational structure of Fokker-Planck equations with variable mobility","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.10676","snapshot_observed_at":"2026-08-01T03:14:18.817604Z","title":"Liu and A","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:18.817604Z"},"links":{"cited_paper":"/paper/2505.10676","citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:ea7a6810ba65906229d9ccf424ac9fb72b1ced68d7ad071a790dffa6b3dd741e","observation_id":"031fa480-1192-4316-963e-5232d5d9fd82","resolution":{"observed_at":"2026-08-01T03:14:18.817604Z","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":"2026-08-01T03:14:18.973592Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:18.973592Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:c8c92fa897a0cbefd2d31f45c0f7f88e49245d44d20a7614aedd98a65ffcaeda","observation_id":"a53df4f8-732f-4b68-8ee5-1cd828fabd05","resolution":{"observed_at":"2026-08-01T03:14:18.973592Z","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":"2026-08-01T03:14:19.140447Z","title":"Marcellini, Periodic solutions and homogenization of nonlinear variational problems, Ann","venue":null,"work_id":null,"year":1978},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:19.140447Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:72fa56f4584cdee091d95c1e85719c83bf8a3a864a761f8707b4d6d2ace68b5b","observation_id":"dc4363c7-7cff-4732-80b8-03e6b641c6bb","resolution":{"observed_at":"2026-08-01T03:14:19.140447Z","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":"2026-08-01T03:14:19.244185Z","title":"Otto, The geometry of dissipative evolution equations: the porous medium equation, (2001)","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:19.244185Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:86affd81eada0ef40716d95b2a7a4ac2fe25eccb7aea52dad82b9fbd97daca38","observation_id":"776478d6-aab2-406e-b032-ed1d61d85c81","resolution":{"observed_at":"2026-08-01T03:14:19.244185Z","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":"2026-08-01T03:14:19.390825Z","title":null,"venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:19.390825Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:2c102e9e61d1873d75949321b08b6bbebb291ffa1d3caf7b80bc4f9dc2ca1d30","observation_id":"6ffcec49-32ee-4ac2-8e26-6900a183f1f8","resolution":{"observed_at":"2026-08-01T03:14:19.390825Z","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":"2026-08-01T03:14:19.494985Z","title":"Pechstein and R","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:19.494985Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:ae4d3a64452b29901e6a15c4b3fd70cdb58e5bbec44fa50bc04d155d2bd8bd01","observation_id":"5d167c7f-ff2e-4d92-99c6-772248a8e4d1","resolution":{"observed_at":"2026-08-01T03:14:19.494985Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2402.17681","last_updated":"2024-02-27T16:54:56Z","snapshot_observed_at":"2026-08-13T04:08:56.695653Z","submitted_at":"2024-02-27T16:54:56Z","title":"JKO schemes with general transport costs","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.17681","snapshot_observed_at":"2026-08-01T03:14:19.636541Z","title":"Rankin and T.-K","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:19.636541Z"},"links":{"cited_paper":"/paper/2402.17681","citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:c890e3c29a0c2ba5394d083ec9a7c1a0a152d0d11a5bbbca244761089d5d8ae4","observation_id":"8958d53b-d891-4f6e-83f5-9367251cdedf","resolution":{"observed_at":"2026-08-01T03:14:19.636541Z","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":"2026-08-01T03:14:19.734860Z","title":"Sandier and S","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:19.734860Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:b3a795a6df5bf8346934cb116291db7ef2ad62fe2611293be1ac8a7f3e69238f","observation_id":"f58ecb8c-5c43-4a37-bc03-d95d61cfb863","resolution":{"observed_at":"2026-08-01T03:14:19.734860Z","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":"2026-08-01T03:14:19.861039Z","title":"Santambrogio and G","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:19.861039Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:c58e2414e0f5cf38a9b7b69a550c686eb159e2fbc22722f5d967376ac3e2ef09","observation_id":"93ad6090-36ff-4393-b1fa-8322e235d198","resolution":{"observed_at":"2026-08-01T03:14:19.861039Z","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":"2026-08-01T03:14:19.971174Z","title":"Serfaty, Gamma-convergence of gradient flows on Hilbert and metric spaces and applica- tions, Discrete Contin","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:19.971174Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:d9f744a7fe2467a25cce2e3c65da24e033286521e3799c1e2d6a7b236d89a49a","observation_id":"1d1a862d-40f3-44b3-8c5b-87450dc9439a","resolution":{"observed_at":"2026-08-01T03:14:19.971174Z","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":"2026-08-01T03:14:20.102293Z","title":null,"venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:20.102293Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:d6efe644677bd76b49fc6cd295ecadd8177b42279c06431e3233004184048b42","observation_id":"927e8c5a-f162-4fe1-b065-68d49df3e487","resolution":{"observed_at":"2026-08-01T03:14:20.102293Z","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":"2026-08-01T03:14:20.260786Z","title":"Struwe, Variational methods: applications to nonlinear partial differential equations and Hamiltonian systems , Springer, 2008","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:20.260786Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:c6dab358d1c47ebdd54a913e90388c5edf32fac3277ee655a39a978072ee896a","observation_id":"9ea582fa-ec9d-4a09-9ebd-65660364ccb7","resolution":{"observed_at":"2026-08-01T03:14:20.260786Z","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":"2026-08-01T03:14:20.417496Z","title":"Villani, Optimal transport: old and new , vol","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:20.417496Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:b0ab6d7f56a372f118749af04705ac08e841ed2bcedbc5b7998a77dcf5369550","observation_id":"b8751ae1-27f0-4a51-9008-09c9ce5528b0","resolution":{"observed_at":"2026-08-01T03:14:20.417496Z","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":"2026-08-01T03:14:20.526356Z","title":"Weinan, A class of homogenization problems in the calculus of variations , Commun","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-01T03:14:20.526356Z"},"links":{"citing_paper":"/paper/2607.25206"},"observation_digest":"sha256:5baad4df9e16c5f2a68e3b3ed3833e8f62d725e4486cdaabd9a803debfbaa578","observation_id":"d58d121f-677e-4797-a489-1041682f27a0","resolution":{"observed_at":"2026-08-01T03:14:20.526356Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.25206","last_updated":"2026-07-28T02:22:42Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-01T03:14:11.062196Z","submitted_at":"2026-07-28T02:22:42Z","title":"Homogenization of Time-Discrete Gradient Flows"},"reference_resolution":{"displayed":41,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":41,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":41},"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":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 0 inbound Pith citation observations for arXiv:2607.25206."}