{"as_of":"2026-08-19T09:11:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:e12aeb5314f50b3d48a377a70900ca88500dde62e5ac37a5f091ae8a2cbf9fa0","coverage":[{"denominator":27,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":27,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T15:37:16.716546Z","state":"measured"},{"denominator":27,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":27,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-19T06:32:44.657259+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/2608.00438/citation-record","integrity":"/paper/2608.00438/integrity","json":"/paper/2608.00438/citation-record.json","paper":"/paper/2608.00438"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:37:17.341129Z","title":"Homogenization of ﬁrst-o rder equations with u/ǫ-periodic Hamiltonian: Rate of convergence as ǫ → 0 and numerical methods","venue":null,"work_id":"15e5a0d8-e5e5-41f0-9f37-9f845132de1d","year":2011},"citing_paper":{"arxiv_id":"2608.00438","last_updated":"2026-08-01T04:33:07Z","snapshot_observed_at":"2026-08-15T15:17:37.868990Z","submitted_at":"2026-08-01T04:33:07Z","title":"Homogenization of Viscous Sublinear Hamilton--Jacobi Equations with $u/\\epsilon$-Dependence","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-15T15:37:16.554086Z"},"links":{"citing_paper":"/paper/2608.00438"},"observation_digest":"sha256:bb56c2437da6a29eab280effb3aeced684d2118d672c5b96ca4db3bc7c56fab4","observation_id":"2f8f54cc-97a7-4530-9a0c-7da63e815df2","resolution":{"observed_at":"2026-08-15T15:37:17.347998Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:37:17.321677Z","title":"Some homogenization results for non-c oercive Hamilton–Jacobi equations","venue":null,"work_id":"0e9c8368-3847-4146-8a1c-8f4fe9910d47","year":2007},"citing_paper":{"arxiv_id":"2608.00438","last_updated":"2026-08-01T04:33:07Z","snapshot_observed_at":"2026-08-15T15:17:37.868990Z","submitted_at":"2026-08-01T04:33:07Z","title":"Homogenization of Viscous Sublinear Hamilton--Jacobi Equations with $u/\\epsilon$-Dependence","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-15T15:37:16.561065Z"},"links":{"citing_paper":"/paper/2608.00438"},"observation_digest":"sha256:3c059197aa34720533ea1fc69125a28410391c388bd1a8f4e33f4e70078f3c12","observation_id":"2c42e175-02c8-444c-91b8-e66208390134","resolution":{"observed_at":"2026-08-15T15:37:17.326977Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:37:17.303141Z","title":"Space-time periodi c solutions and long-time behavior of solutions to quasi-linear parabolic equations","venue":null,"work_id":"97e76f90-21f1-403a-8a36-7f36ea167247","year":2001},"citing_paper":{"arxiv_id":"2608.00438","last_updated":"2026-08-01T04:33:07Z","snapshot_observed_at":"2026-08-15T15:17:37.868990Z","submitted_at":"2026-08-01T04:33:07Z","title":"Homogenization of Viscous Sublinear Hamilton--Jacobi Equations with $u/\\epsilon$-Dependence","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-15T15:37:16.566805Z"},"links":{"citing_paper":"/paper/2608.00438"},"observation_digest":"sha256:c9b3787910cbe72112ea7cce10829d7e5c86cf92a35c35b773ade73ca15e69c9","observation_id":"18ad3bdc-e577-46a1-a939-191014112368","resolution":{"observed_at":"2026-08-15T15:37:17.309475Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:37:17.275192Z","title":"Generalized travellin g waves for reaction-diffusion equations","venue":null,"work_id":"58b95fc2-be77-48b8-b77f-d4f269b6d993","year":2007},"citing_paper":{"arxiv_id":"2608.00438","last_updated":"2026-08-01T04:33:07Z","snapshot_observed_at":"2026-08-15T15:17:37.868990Z","submitted_at":"2026-08-01T04:33:07Z","title":"Homogenization of Viscous Sublinear Hamilton--Jacobi Equations with $u/\\epsilon$-Dependence","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-15T15:37:16.572476Z"},"links":{"citing_paper":"/paper/2608.00438"},"observation_digest":"sha256:716391b47284c7ca4a4fb41b8368c0bbc70defc29585c134585e773453d77c10","observation_id":"057804e9-db5f-42d8-8f9d-64702ba20993","resolution":{"observed_at":"2026-08-15T15:37:17.282630Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:37:17.245576Z","title":"The s peed of propagation for kpp type problems","venue":null,"work_id":"9f5376c6-6740-44da-afa9-c5307d92cf67","year":2005},"citing_paper":{"arxiv_id":"2608.00438","last_updated":"2026-08-01T04:33:07Z","snapshot_observed_at":"2026-08-15T15:17:37.868990Z","submitted_at":"2026-08-01T04:33:07Z","title":"Homogenization of Viscous Sublinear Hamilton--Jacobi Equations with $u/\\epsilon$-Dependence","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-15T15:37:16.578267Z"},"links":{"citing_paper":"/paper/2608.00438"},"observation_digest":"sha256:33d18f9cfddd938fab4912b19921753fb2f0b8bc35b7552f61ba887afca6ab2b","observation_id":"4f59b8e6-a535-42e0-ba43-3af2fb6e065f","resolution":{"observed_at":"2026-08-15T15:37:17.256531Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:37:17.221893Z","title":"Homogenizatio n of a semilinear heat equation","venue":null,"work_id":"495cd566-b180-4726-99cf-2cd3d1cf94e6","year":2017},"citing_paper":{"arxiv_id":"2608.00438","last_updated":"2026-08-01T04:33:07Z","snapshot_observed_at":"2026-08-15T15:17:37.868990Z","submitted_at":"2026-08-01T04:33:07Z","title":"Homogenization of Viscous Sublinear Hamilton--Jacobi Equations with $u/\\epsilon$-Dependence","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-15T15:37:16.583309Z"},"links":{"citing_paper":"/paper/2608.00438"},"observation_digest":"sha256:2770634ea0818b78d18df17016dd40708c368121396cc55d245efa7ec2b34a79","observation_id":"0c1d9576-993f-4f45-b4a9-2589dc3e9cda","resolution":{"observed_at":"2026-08-15T15:37:17.228227Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/s0022-247x(02","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:37:16.796389Z","title":"Periodic travelling wave solu tions of a parabolic equation: a monotonicity re- sult","venue":null,"work_id":"5da97d9b-e44a-41b7-820d-2ae9a80e36a2","year":2002},"citing_paper":{"arxiv_id":"2608.00438","last_updated":"2026-08-01T04:33:07Z","snapshot_observed_at":"2026-08-15T15:17:37.868990Z","submitted_at":"2026-08-01T04:33:07Z","title":"Homogenization of Viscous Sublinear Hamilton--Jacobi Equations with $u/\\epsilon$-Dependence","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-15T15:37:16.588991Z"},"links":{"citing_paper":"/paper/2608.00438"},"observation_digest":"sha256:5659848169a5dfe95080c428b27d2c26f48cca8a29f85cc0b174e017030e4b08","observation_id":"7e062ce1-c10e-4f1f-b104-b59cc959a4ce","resolution":{"observed_at":"2026-08-15T15:37:16.802098Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:37:17.202405Z","title":"User’s gui de to viscosity solutions of second order partial differ- ential equations","venue":null,"work_id":"f0b6cff3-105a-4fc9-9d75-f4b885f917d1","year":1992},"citing_paper":{"arxiv_id":"2608.00438","last_updated":"2026-08-01T04:33:07Z","snapshot_observed_at":"2026-08-15T15:17:37.868990Z","submitted_at":"2026-08-01T04:33:07Z","title":"Homogenization of Viscous Sublinear Hamilton--Jacobi Equations with $u/\\epsilon$-Dependence","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-15T15:37:16.594955Z"},"links":{"citing_paper":"/paper/2608.00438"},"observation_digest":"sha256:590c6f2e44deb3058af746a9992687cc07ce605bfc121e1303aba3fb6bad7ca0","observation_id":"816edd00-db8e-462e-a147-56243fedd166","resolution":{"observed_at":"2026-08-15T15:37:17.209770Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:37:17.167527Z","title":"The perturbed test function method fo r viscosity solutions of nonlinear pde","venue":null,"work_id":"f683b45c-343b-413a-ba38-028bd34d379b","year":1989},"citing_paper":{"arxiv_id":"2608.00438","last_updated":"2026-08-01T04:33:07Z","snapshot_observed_at":"2026-08-15T15:17:37.868990Z","submitted_at":"2026-08-01T04:33:07Z","title":"Homogenization of Viscous Sublinear Hamilton--Jacobi Equations with $u/\\epsilon$-Dependence","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-15T15:37:16.600992Z"},"links":{"citing_paper":"/paper/2608.00438"},"observation_digest":"sha256:d6b1df567f9434172af09a8b0cf336e5b16f8fbdfe9063f113c9a4f8de8e8ed0","observation_id":"50925291-cf8c-4757-a858-8c6ae5cb77bb","resolution":{"observed_at":"2026-08-15T15:37:17.174362Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:37:17.143254Z","title":"Periodic homogenisation of certain fully nonlinear partial differential equations","venue":null,"work_id":"56e45197-08cb-4ed5-9402-5ae04299a5af","year":1992},"citing_paper":{"arxiv_id":"2608.00438","last_updated":"2026-08-01T04:33:07Z","snapshot_observed_at":"2026-08-15T15:17:37.868990Z","submitted_at":"2026-08-01T04:33:07Z","title":"Homogenization of Viscous Sublinear Hamilton--Jacobi Equations with $u/\\epsilon$-Dependence","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-15T15:37:16.606693Z"},"links":{"citing_paper":"/paper/2608.00438"},"observation_digest":"sha256:250a5df96c1ca7352702f22fdd42e05f1fe52c8b73690be96450588b8d2e2141","observation_id":"9871c53e-9cfc-40a0-9082-634345e51390","resolution":{"observed_at":"2026-08-15T15:37:17.149618Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1051/cocv:2006011","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:37:16.777347Z","title":"Exact controllability to the trajec- tories of the heat equation with fourier boundary condition s: The semilinear case","venue":null,"work_id":"29a4d08f-64e5-4971-971e-04536cf067b5","year":2006},"citing_paper":{"arxiv_id":"2608.00438","last_updated":"2026-08-01T04:33:07Z","snapshot_observed_at":"2026-08-15T15:17:37.868990Z","submitted_at":"2026-08-01T04:33:07Z","title":"Homogenization of Viscous Sublinear Hamilton--Jacobi Equations with $u/\\epsilon$-Dependence","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-15T15:37:16.612114Z"},"links":{"citing_paper":"/paper/2608.00438"},"observation_digest":"sha256:7b66abeb7107b9eade50666151f0f5eaf4baa65a5297f1355536a735e3a1f889","observation_id":"5ff774a7-9488-4de3-8f26-3dcd7531b859","resolution":{"observed_at":"2026-08-15T15:37:16.783498Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:37:17.123782Z","title":"Periodic-Parabolic Boundary V alue Problems and Positivity","venue":null,"work_id":"53802890-1b3c-48f0-b0b3-86118d6323ed","year":1991},"citing_paper":{"arxiv_id":"2608.00438","last_updated":"2026-08-01T04:33:07Z","snapshot_observed_at":"2026-08-15T15:17:37.868990Z","submitted_at":"2026-08-01T04:33:07Z","title":"Homogenization of Viscous Sublinear Hamilton--Jacobi Equations with $u/\\epsilon$-Dependence","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-15T15:37:16.619312Z"},"links":{"citing_paper":"/paper/2608.00438"},"observation_digest":"sha256:4bfb6f67334996eb82dae6da799e8136a81b5432ac1dbebfe3f428a8b883ffa1","observation_id":"c691fe55-f0bc-4e5b-b358-94b0c1f2d462","resolution":{"observed_at":"2026-08-15T15:37:17.129446Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:37:17.104530Z","title":"Homogenization of ﬁrst- order equations with (u/ǫ)-periodic Hamiltonians","venue":null,"work_id":"125d7473-55a3-4c36-8462-79b970cc7ca4","year":2008},"citing_paper":{"arxiv_id":"2608.00438","last_updated":"2026-08-01T04:33:07Z","snapshot_observed_at":"2026-08-15T15:17:37.868990Z","submitted_at":"2026-08-01T04:33:07Z","title":"Homogenization of Viscous Sublinear Hamilton--Jacobi Equations with $u/\\epsilon$-Dependence","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-15T15:37:16.627047Z"},"links":{"citing_paper":"/paper/2608.00438"},"observation_digest":"sha256:1bc12067014a3b5418fd4ea44636e4c622700898d550d00142d2dc11531546e3","observation_id":"d8cb59c0-3c48-4a9d-bf32-346d75b0d658","resolution":{"observed_at":"2026-08-15T15:37:17.111745Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:37:17.083185Z","title":"Linear and Quasilinear Equations of Parabolic Type","venue":null,"work_id":"214ad298-f740-4c71-a3b9-6a858bededdc","year":1968},"citing_paper":{"arxiv_id":"2608.00438","last_updated":"2026-08-01T04:33:07Z","snapshot_observed_at":"2026-08-15T15:17:37.868990Z","submitted_at":"2026-08-01T04:33:07Z","title":"Homogenization of Viscous Sublinear Hamilton--Jacobi Equations with $u/\\epsilon$-Dependence","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-15T15:37:16.633387Z"},"links":{"citing_paper":"/paper/2608.00438"},"observation_digest":"sha256:766a3664b4af035a77e51944a0cd45d0701a4e81e69351581d3a69e1822bc059","observation_id":"b49dd162-6cee-4560-a8fe-97ca9c5ea577","resolution":{"observed_at":"2026-08-15T15:37:17.090354Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:37:17.061702Z","title":"Second Order Parabolic Differe ntial Equations","venue":null,"work_id":"272147f7-97b6-46f7-975d-2f5776666738","year":1996},"citing_paper":{"arxiv_id":"2608.00438","last_updated":"2026-08-01T04:33:07Z","snapshot_observed_at":"2026-08-15T15:17:37.868990Z","submitted_at":"2026-08-01T04:33:07Z","title":"Homogenization of Viscous Sublinear Hamilton--Jacobi Equations with $u/\\epsilon$-Dependence","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-15T15:37:16.641930Z"},"links":{"citing_paper":"/paper/2608.00438"},"observation_digest":"sha256:e7ed5c5156a6f8d5f5f2f4abeb0902d7034062954ae3385698e7e3b3c7de302d","observation_id":"618255ec-0ba0-4d5d-b543-562d81452408","resolution":{"observed_at":"2026-08-15T15:37:17.069256Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:37:17.040252Z","title":"Homogenization of hamilton–jacobi equations","venue":null,"work_id":"4f5f7ef5-7c26-490a-91cc-c9132b2726f3","year":1987},"citing_paper":{"arxiv_id":"2608.00438","last_updated":"2026-08-01T04:33:07Z","snapshot_observed_at":"2026-08-15T15:17:37.868990Z","submitted_at":"2026-08-01T04:33:07Z","title":"Homogenization of Viscous Sublinear Hamilton--Jacobi Equations with $u/\\epsilon$-Dependence","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-15T15:37:16.647318Z"},"links":{"citing_paper":"/paper/2608.00438"},"observation_digest":"sha256:697c8a53185bea945f7d1b2da44ecd906725ecfa5ebc2f8fa4f8f7e67a111869","observation_id":"de9305f0-267b-43d0-8bc5-c5e9e6bde3f3","resolution":{"observed_at":"2026-08-15T15:37:17.045540Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.anihpc.2004.10.009","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:37:16.756680Z","title":"Homogenization of degenerate second-order pde in periodic and almost periodic environments and applications","venue":null,"work_id":"ceef2821-1256-4033-9912-1173cdccd8e2","year":null},"citing_paper":{"arxiv_id":"2608.00438","last_updated":"2026-08-01T04:33:07Z","snapshot_observed_at":"2026-08-15T15:17:37.868990Z","submitted_at":"2026-08-01T04:33:07Z","title":"Homogenization of Viscous Sublinear Hamilton--Jacobi Equations with $u/\\epsilon$-Dependence","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-15T15:37:16.655451Z"},"links":{"citing_paper":"/paper/2608.00438"},"observation_digest":"sha256:40fe9ada1c24e741f2ca4666f9a3177b5c403bcae0326962aba5b1d08d6ae6a9","observation_id":"f045403c-8f13-46fb-a781-25db79d08e9d","resolution":{"observed_at":"2026-08-15T15:37:16.764296Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:37:17.019658Z","title":"Homogenization of “viscous” hamilton–jacobi equations in sta- tionary ergodic media","venue":null,"work_id":"5b1d7e2a-e3f0-4c90-8bd4-0c58b5ec0a6a","year":null},"citing_paper":{"arxiv_id":"2608.00438","last_updated":"2026-08-01T04:33:07Z","snapshot_observed_at":"2026-08-15T15:17:37.868990Z","submitted_at":"2026-08-01T04:33:07Z","title":"Homogenization of Viscous Sublinear Hamilton--Jacobi Equations with $u/\\epsilon$-Dependence","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-15T15:37:16.661080Z"},"links":{"citing_paper":"/paper/2608.00438"},"observation_digest":"sha256:3d1b2f9260212c800dae548da31f30b20cd086e719ba216cf93cd6f3ef626f38","observation_id":"2b3778a2-beaf-4e5f-83e2-a91d547424e3","resolution":{"observed_at":"2026-08-15T15:37:17.025630Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.00663","last_updated":"2025-07-01T11:02:39Z","snapshot_observed_at":"2026-08-15T18:24:06.858386Z","submitted_at":"2025-07-01T11:02:39Z","title":"Quantitative homogenization of convex Hamilton-Jacobi equations with $u/\\varepsilon$-periodic Hamiltonians","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.00663","snapshot_observed_at":"2026-08-15T15:37:16.667944Z","title":"Quantitative homogenization of convex Hamilton–Jacobi equations with u/ε-periodic hamiltonians","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.00438","last_updated":"2026-08-01T04:33:07Z","snapshot_observed_at":"2026-08-15T15:17:37.868990Z","submitted_at":"2026-08-01T04:33:07Z","title":"Homogenization of Viscous Sublinear Hamilton--Jacobi Equations with $u/\\epsilon$-Dependence","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-15T15:37:16.667944Z"},"links":{"cited_paper":"/paper/2507.00663","citing_paper":"/paper/2608.00438"},"observation_digest":"sha256:f8484fea7662dc0873de1e38e5d27d06658b9279fdbfd9aa85812a2b228857a1","observation_id":"a50bfe61-24b3-4953-9c49-e92efa7806ff","resolution":{"observed_at":"2026-08-15T15:37:16.667944Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2508.17628","last_updated":"2025-08-25T03:17:47Z","snapshot_observed_at":"2026-08-16T08:31:55.740664Z","submitted_at":"2025-08-25T03:17:47Z","title":"Quantitative homogenization of first-order ODEs","version":1},"cited_work":{"arxiv_id":"2508.17628","doi":null,"metadata_source":"pith","pith_arxiv_id":"2508.17628","snapshot_observed_at":"2026-08-15T15:37:16.846740Z","title":"Quantitative homogenization of first-order ODEs","venue":"math.CA","work_id":"17539f3a-175f-45ed-8e95-3dd8a0d61934","year":2025},"citing_paper":{"arxiv_id":"2608.00438","last_updated":"2026-08-01T04:33:07Z","snapshot_observed_at":"2026-08-15T15:17:37.868990Z","submitted_at":"2026-08-01T04:33:07Z","title":"Homogenization of Viscous Sublinear Hamilton--Jacobi Equations with $u/\\epsilon$-Dependence","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-15T15:37:16.674257Z"},"links":{"cited_paper":"/paper/2508.17628","citing_paper":"/paper/2608.00438"},"observation_digest":"sha256:53db93c7172b0f5d85eade637a1aafced040934d01f659cb36293698ea1c60ff","observation_id":"fff5ddd8-3cc8-4e6c-bbab-bf8c2f7ae533","resolution":{"observed_at":"2026-08-15T15:37:16.854698Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:37:16.991491Z","title":"Viscosity solutions of c ontact hamilton-jacobi equations with hamiltonians depending periodically on unknown functions","venue":null,"work_id":"5a092f16-42b3-4a1e-96a0-e9abebad5441","year":2023},"citing_paper":{"arxiv_id":"2608.00438","last_updated":"2026-08-01T04:33:07Z","snapshot_observed_at":"2026-08-15T15:17:37.868990Z","submitted_at":"2026-08-01T04:33:07Z","title":"Homogenization of Viscous Sublinear Hamilton--Jacobi Equations with $u/\\epsilon$-Dependence","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-15T15:37:16.680315Z"},"links":{"citing_paper":"/paper/2608.00438"},"observation_digest":"sha256:a0a062ba898d73cb6f813b4aad9321ad09f7168ebcfc9009a8ff331e43804f94","observation_id":"8d7a7062-d91e-47ca-85bc-fb1af4c3a702","resolution":{"observed_at":"2026-08-15T15:37:16.996987Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:37:16.967397Z","title":"Optimal rate of convergence in periodic homogenization of viscous Hamilton-Jacobi equations","venue":null,"work_id":"bd927f48-9ee6-43ae-a3a7-7697e7359a02","year":2024},"citing_paper":{"arxiv_id":"2608.00438","last_updated":"2026-08-01T04:33:07Z","snapshot_observed_at":"2026-08-15T15:17:37.868990Z","submitted_at":"2026-08-01T04:33:07Z","title":"Homogenization of Viscous Sublinear Hamilton--Jacobi Equations with $u/\\epsilon$-Dependence","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-15T15:37:16.686390Z"},"links":{"citing_paper":"/paper/2608.00438"},"observation_digest":"sha256:2ca10ee4fc76c10250d1984e47c174825ac939d27efaa798022e26b2aac07d97","observation_id":"78c571cb-6db0-4e26-b862-12ceb6ace025","resolution":{"observed_at":"2026-08-15T15:37:16.974769Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:37:16.950144Z","title":"Hamilton–Jacobi equations: theory a nd applications","venue":null,"work_id":"dc5ec260-8a8e-40ae-95a5-c4a326dc0823","year":2021},"citing_paper":{"arxiv_id":"2608.00438","last_updated":"2026-08-01T04:33:07Z","snapshot_observed_at":"2026-08-15T15:17:37.868990Z","submitted_at":"2026-08-01T04:33:07Z","title":"Homogenization of Viscous Sublinear Hamilton--Jacobi Equations with $u/\\epsilon$-Dependence","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-15T15:37:16.693587Z"},"links":{"citing_paper":"/paper/2608.00438"},"observation_digest":"sha256:c28e749c3fa2079d57cbd56f2b232fa7eecb7aa9848349bc886a783420433366","observation_id":"a36152af-6796-4f65-b65f-0b67bedbce42","resolution":{"observed_at":"2026-08-15T15:37:16.955349Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:37:16.932133Z","title":"Implicit variational principle for contact hamiltonian systems","venue":null,"work_id":"0cf91c87-de6f-4a36-a637-3b3d8d9083c3","year":2017},"citing_paper":{"arxiv_id":"2608.00438","last_updated":"2026-08-01T04:33:07Z","snapshot_observed_at":"2026-08-15T15:17:37.868990Z","submitted_at":"2026-08-01T04:33:07Z","title":"Homogenization of Viscous Sublinear Hamilton--Jacobi Equations with $u/\\epsilon$-Dependence","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-15T15:37:16.699675Z"},"links":{"citing_paper":"/paper/2608.00438"},"observation_digest":"sha256:7fba98c596b9265e411b62661dd89304f5dab163afa8dfeb4f53f52a827fa885","observation_id":"9e3dd72c-f9fa-444a-84bd-8ad016f8feaa","resolution":{"observed_at":"2026-08-15T15:37:16.937679Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:37:16.913052Z","title":"Aubry–mather theory for contact hamiltonian systems","venue":null,"work_id":"4b2822ff-dc64-4b18-bbb9-0bf16e331212","year":null},"citing_paper":{"arxiv_id":"2608.00438","last_updated":"2026-08-01T04:33:07Z","snapshot_observed_at":"2026-08-15T15:17:37.868990Z","submitted_at":"2026-08-01T04:33:07Z","title":"Homogenization of Viscous Sublinear Hamilton--Jacobi Equations with $u/\\epsilon$-Dependence","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-15T15:37:16.704892Z"},"links":{"citing_paper":"/paper/2608.00438"},"observation_digest":"sha256:a8845c581d86a1cbcd07fd6df51a4b5b4aa7ea2c858cf4e34e84cbad284f790d","observation_id":"29fc0446-a3dc-4f33-8e7c-3072fe9bff1e","resolution":{"observed_at":"2026-08-15T15:37:16.918290Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:37:16.894436Z","title":"V ariational principle for contact hamiltonian systems and its applications","venue":null,"work_id":"0549eab5-fdd9-4e56-9b1f-9e5b33295298","year":null},"citing_paper":{"arxiv_id":"2608.00438","last_updated":"2026-08-01T04:33:07Z","snapshot_observed_at":"2026-08-15T15:17:37.868990Z","submitted_at":"2026-08-01T04:33:07Z","title":"Homogenization of Viscous Sublinear Hamilton--Jacobi Equations with $u/\\epsilon$-Dependence","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-15T15:37:16.710249Z"},"links":{"citing_paper":"/paper/2608.00438"},"observation_digest":"sha256:2b2f8ec0221cf51384a13bb057e4469ae7628dd373eca9ff01847192b5b99798","observation_id":"97459de7-bcef-4462-b00a-d96121b5ea6e","resolution":{"observed_at":"2026-08-15T15:37:16.900896Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2202.08254","last_updated":"2022-03-02T02:16:52Z","snapshot_observed_at":"2026-08-19T08:58:05.036650Z","submitted_at":"2022-02-16T18:55:52Z","title":"Homogenization for Space-Time-Dependent KPP Reaction-Diffusion Equations and G-Equations","version":2},"cited_work":{"arxiv_id":"2202.08254","doi":null,"metadata_source":"pith","pith_arxiv_id":"2202.08254","snapshot_observed_at":"2026-08-15T15:37:16.821684Z","title":"Homogenization for Space-Time-Dependent KPP Reaction-Diffusion Equations and G-Equations","venue":"math.AP","work_id":"bfbee124-622d-46e9-88ab-7c026a56f8eb","year":2022},"citing_paper":{"arxiv_id":"2608.00438","last_updated":"2026-08-01T04:33:07Z","snapshot_observed_at":"2026-08-15T15:17:37.868990Z","submitted_at":"2026-08-01T04:33:07Z","title":"Homogenization of Viscous Sublinear Hamilton--Jacobi Equations with $u/\\epsilon$-Dependence","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-15T15:37:16.716546Z"},"links":{"cited_paper":"/paper/2202.08254","citing_paper":"/paper/2608.00438"},"observation_digest":"sha256:998051d0c3d7ab3aa33e7a27e8370fa338ac3ccfc0eae95e8115706ccbee9acb","observation_id":"4dbcba91-b50e-4f01-ba51-91b9e7082221","resolution":{"observed_at":"2026-08-15T15:37:16.827407Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2608.00438","last_updated":"2026-08-01T04:33:07Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-15T15:17:37.868990Z","submitted_at":"2026-08-01T04:33:07Z","title":"Homogenization of Viscous Sublinear Hamilton--Jacobi Equations with $u/\\epsilon$-Dependence"},"reference_resolution":{"displayed":27,"state_counts":{"malformed_identifier":1,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":1,"verified_exact":5,"verified_fuzzy":20},"total_outbound_references":27},"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":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"thesis":"As of 19 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 0 inbound Pith citation observations for arXiv:2608.00438."}