{"as_of":"2026-08-13T10:34:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:395fd149864d35018ab30623f32834d9fadbff590dcc4a91fe214f8eaee48ae7","coverage":[{"denominator":40,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":40,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T17:01:29.755069Z","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":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T00:56:32.536315Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-10T00:56:32.776108Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"cited_work":{"arxiv_id":"2411.13126","doi":null,"metadata_source":"pith","pith_arxiv_id":"2411.13126","snapshot_observed_at":"2026-08-10T00:56:32.776108Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","venue":"math.AP","work_id":"75e9a2f1-6804-4384-a0a9-040ec248f4e7","year":2024},"citing_paper":{"arxiv_id":"2501.18057","last_updated":"2025-01-29T23:53:12Z","snapshot_observed_at":"2026-08-13T01:05:50.530986Z","submitted_at":"2025-01-29T23:53:12Z","title":"Stochastic scattering control of spider diffusion governed by an optimal diffraction probability measure selected from its own local-time","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-10T00:56:32.536315Z"},"links":{"cited_paper":"/paper/2411.13126","citing_paper":"/paper/2501.18057"},"observation_digest":"sha256:0c6c293e7f04209f9af6c340be79f781210ae27b1bab9cccfacf481cdc61041e","observation_id":"c8e6de0f-c6be-4f51-9024-34e1031cf610","resolution":{"observed_at":"2026-08-10T00:56:32.780732Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2411.13126/citation-record","integrity":"/paper/2411.13126/integrity","json":"/paper/2411.13126/citation-record.json","paper":"/paper/2411.13126"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:30.412292Z","title":"Hamilton-Jacobi equations constrained on networks","venue":null,"work_id":"2ef768c3-1276-48e7-b255-e72a32490fcd","year":2013},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.570791Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:0623b4730897bdb32b01c319e7677006765199554df1a5569059fbbe86a21bda","observation_id":"a9dfa3ce-cb66-4c70-b28b-32c4addd90b2","resolution":{"observed_at":"2026-08-12T17:01:30.417166Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:30.397159Z","title":"A class of inﬁnite horizon mean ﬁeld games on networks","venue":null,"work_id":"0c49e58b-f07e-4c8c-ae85-3472611a9faa","year":2019},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.576229Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:5b42b8a0c8f41229de6453eaebe73847fd7d2e60f2aec439820f20ac11297652","observation_id":"214d3405-67a8-4cc6-9ef3-f7409b45f7ca","resolution":{"observed_at":"2026-08-12T17:01:30.402241Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:30.380596Z","title":"Finite horizon mean ﬁeld games on networks","venue":null,"work_id":"66327b52-0227-4930-8fa5-af8195999fbe","year":2020},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.581265Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:56532c827e27bc7abdbcc956abb7ed5af9495cf4fbfdd5d9a384bc313a4ae9ff","observation_id":"4e72b9c7-a1dc-4e61-a321-df4dd1fbc7fb","resolution":{"observed_at":"2026-08-12T17:01:30.386768Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:30.363278Z","title":"Hamilt on-Jacobi equations for optimal control on junctions and networks","venue":null,"work_id":"37a4f7da-25aa-48f4-9adc-4b916ed9f45b","year":2015},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.586147Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:ddf9fde48b7745c825d4ea1d3e36c03565a3acb6a48bfef5676f5c62a502019b","observation_id":"95a697be-a595-413d-950b-81c16e4ae068","resolution":{"observed_at":"2026-08-12T17:01:30.368468Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:30.347889Z","title":"Barles, A","venue":null,"work_id":"2487b9b2-363a-4333-86f2-51b8a84bce1f","year":2013},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.591199Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:891edf0761f71cb3fd50d12b7f8eff83aaa165e45a625d572b076cd2da69ac62","observation_id":"2857bb93-5d4d-4573-9ebb-438bc8e1c5fc","resolution":{"observed_at":"2026-08-12T17:01:30.352839Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:30.332993Z","title":"Barles, A","venue":null,"work_id":"b4bec1d8-ac0c-4b70-8782-85a418b5baf3","year":2014},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.596155Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:77f82aec197ae15daec11a0fdc027fe04aa8304d823c27ef496c4ee7aaf9686f","observation_id":"b386d3f6-44e4-4cb0-af43-0136749e7e5b","resolution":{"observed_at":"2026-08-12T17:01:30.337869Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:30.317701Z","title":"Barles, A","venue":null,"work_id":"70b35bfc-1cf7-4654-93db-a7c2052e1356","year":1906},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.601613Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:1183b3f76664115b8aff6af68f6fa72d2e085b4558de3c66bd561f12a575f57e","observation_id":"6a2b3dbc-88f8-40b1-be2b-deec599c677c","resolution":{"observed_at":"2026-08-12T17:01:30.322484Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:30.302184Z","title":"An introduction to the theory of viscosity so lutions for ﬁrst-order Hamilton-Jacobi equations and applications","venue":null,"work_id":"64800c62-f9ff-43a5-a059-c179734d021e","year":2013},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.606282Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:98cc51e07181084777f733cce7c6fba6157b949939ee5c51cbcb284154aa2b5a","observation_id":"70e818a5-6b19-49ae-b45a-2b2f5abd2753","resolution":{"observed_at":"2026-08-12T17:01:30.307143Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:30.284754Z","title":"Backw ard stochastic diﬀeren- tial equations and integral-partial diﬀerential equation s","venue":null,"work_id":"4575dd37-6fd7-42ee-b1cf-2da7b2fd5254","year":1997},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.610995Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:9744d0f9956d823316f3374ccc228cadb2f74d26bac5ff9e9e4ca4b41ef76930","observation_id":"119491ad-ceee-471c-be00-02f7987e5301","resolution":{"observed_at":"2026-08-12T17:01:30.291005Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:30.269251Z","title":"(Almost) everythi ng you always wanted to know about deterministic control problems in stratiﬁed dom ains","venue":null,"work_id":"33981d2a-e610-4f8c-97dc-d861dad36a93","year":2015},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.615792Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:912f2305d83d7fe3bbb2a2e9a9267a4b6dddb759e31ef296b0859847569d9578","observation_id":"51e55b54-97ba-4785-961c-7fe3fd6db6ac","resolution":{"observed_at":"2026-08-12T17:01:30.274805Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:30.253501Z","title":"On Modern Approaches of Hamilton-Jacobi Equations and Control Problems with Discontinuities , volume 104 of Progress in Nonlinear Diﬀerential Equations and their Applications","venue":null,"work_id":"d360d368-0ad5-4144-a0b4-c0a01ebf720b","year":null},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.620354Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:a6721c248129251e28849e9d7aad9a300746d49a5fceeeb477e5a4cdb64a9c52","observation_id":"78680d92-73a3-41e1-9055-3d4213991a6d","resolution":{"observed_at":"2026-08-12T17:01:30.258945Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:30.220218Z","title":"H¨ o lder continuity of solutions of second-order non-linear elliptic integro-diﬀerential equations","venue":null,"work_id":"af975200-ef06-48c9-af74-dcd4cd4a239a","year":2011},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.629852Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:edda851429cddaadfa9f8a0274af6b100b7bac60df2da23900ec18b41bc21eb3","observation_id":"d45347f7-0397-43c7-9e86-b9e92f481d47","resolution":{"observed_at":"2026-08-12T17:01:30.225472Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:30.203916Z","title":"On the generalized Diri chlet problem for viscous Hamilton-Jacobi equations","venue":null,"work_id":"96c65c6e-d8f0-4dee-8a40-96b677d3fd6d","year":2004},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.634600Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:e90652e1fd3bd705bf54d16e9d0e3f64e754f84c176443baa5be70cd09c15d27","observation_id":"e7f613d6-862d-400b-8f79-91c6ca483b31","resolution":{"observed_at":"2026-08-12T17:01:30.209331Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:30.188314Z","title":"Second-order elliptic int egro-diﬀerential equations: viscosity solutions’ theory revisited","venue":null,"work_id":"7b80a291-8f1d-4ade-9cfc-c45144de901c","year":2008},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.639265Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:762fad836eb268dadf23d266657c09ab0a1edfe50de5cdc0e12ea3dc6d465486","observation_id":"c6e2dd48-6049-44e9-bd83-f15318d6f37f","resolution":{"observed_at":"2026-08-12T17:01:30.193419Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:30.170046Z","title":"Regularity results and large time behavior for integro-diﬀerential equations with coer cive Hamiltonians","venue":null,"work_id":"8c1bfbba-9254-4de1-9d56-39a46922a3b9","year":2015},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.643974Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:ac74fa1def0d0c420bfacaf07d4a9c7985db16e88d50472f611b2af971384b55","observation_id":"2864c4ad-b1bc-4453-bc69-02aaca18a0e8","resolution":{"observed_at":"2026-08-12T17:01:30.176077Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:30.151544Z","title":"Lipschitz regularity for cen sored subdiﬀusive integro- diﬀerential equations with superfractional gradient term s","venue":null,"work_id":"68568adb-7b32-4e62-9411-10d0578cecc0","year":2016},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.648502Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:db46b7d632ed91ae3eed3d995518e878bd98812cc3d4773f587be9ba3372258b","observation_id":"bb9d536c-b3b4-4a65-8cd1-1f8aab4c5326","resolution":{"observed_at":"2026-08-12T17:01:30.156916Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:30.135520Z","title":"Optimal control proble ms on stratiﬁed domains","venue":null,"work_id":"3dcdc24d-7cd1-4079-8cc4-8ba1e68ec0a1","year":2007},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.653022Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:7606c567e056ed8416bd2fd09553b9de5f4c86fabfab8fe6778b0305c29711f3","observation_id":"bada1a41-690e-41e8-a093-24f05a7845a9","resolution":{"observed_at":"2026-08-12T17:01:30.140672Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:30.118316Z","title":"Regularity theory f or fully nonlinear integro- diﬀerential equations","venue":null,"work_id":"c5d7c22a-3853-4ed5-90a5-8a6bc74cec89","year":2009},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.658664Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:617defd7d3c61d1457142f59f7f8721311103d365e7a2a23cc34c2c3dc531e9c","observation_id":"36e8f471-2003-48ae-a232-6f0da79c3d41","resolution":{"observed_at":"2026-08-12T17:01:30.123832Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:30.101736Z","title":"Stationary mean ﬁeld games systems deﬁned on networks","venue":null,"work_id":"eed1cb91-b6aa-4ee6-adf7-fa3c756b7229","year":2016},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.663218Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:c5be162084f30071179a022a42ab1b29c4690f98cb065c2269184bd10db9349c","observation_id":"627ac94a-d498-4b87-b484-c020b5ca2934","resolution":{"observed_at":"2026-08-12T17:01:30.107099Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:30.084034Z","title":"The vanishing viscosity limit for Hamilton-Jacobi equations on networks","venue":null,"work_id":"4dc72d70-e1a2-4e6d-a032-13ee5efe4391","year":2013},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.667884Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:79deb62bde4221b67863120432b075b0529bf3ab1cb754d02671f839f54f9ec0","observation_id":"07390d0b-ace1-4ef3-b8fc-cb0a3b95fa8e","resolution":{"observed_at":"2026-08-12T17:01:30.089734Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:29.672536Z","title":null,"venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.672536Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:645dc26a64d156f7bc5b6a89c4338402a21da743a5cd99a841bea994f75e0554","observation_id":"72a5dcc0-04df-4b24-8b1a-f81363980317","resolution":{"observed_at":"2026-08-12T17:01:29.672536Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:30.055524Z","title":null,"venue":null,"work_id":"5eec27c7-104e-4965-84c9-ca79e2b61e65","year":1998},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.676882Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:44f2d26df4a07aff6f5e5238d671713d3587cf3b59dca56467eea4da65e326b6","observation_id":"c5bcdee7-0735-4f51-bd7e-1bb74b0d49f4","resolution":{"observed_at":"2026-08-12T17:01:30.061128Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:30.038783Z","title":"Homogenizatio n of a discrete model for a bifurcation and application to traﬃc ﬂow","venue":null,"work_id":"8bb5d52e-6bba-40e8-a5dc-7c9e60060859","year":2020},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.681395Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:9f1d5944f1b41a7119906e9f29a331ca59a3c3752aafc0c55cbb437f6ae73aec","observation_id":"bc69ad22-47c5-4c70-adca-dffab44317aa","resolution":{"observed_at":"2026-08-12T17:01:30.044044Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:30.021062Z","title":"On Neumann problems for nonlocal Hamilto n-Jacobi equations with dominating gradient terms","venue":null,"work_id":"3d295e80-6bde-425e-9d93-5f4b61bbed44","year":2017},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.686059Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:493b642a204ee860d3bf6628fa15a289b3d6a2b0b0d67d7f4c51adbca72f3ef1","observation_id":"95258bef-51d4-4363-8226-514a2adb5dd1","resolution":{"observed_at":"2026-08-12T17:01:30.026872Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:30.000843Z","title":"Reﬂected symmetric α -stable processes and re- gional fractional Laplacian","venue":null,"work_id":"9c7ec470-e37f-47c0-b7a1-5fb37f743a87","year":2006},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.691169Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:ef053f443ffd9e2765dec0a36919894c13347dacbac35d2624fd9625a864ac15","observation_id":"6634b744-d299-4b0d-8069-659a21992e6e","resolution":{"observed_at":"2026-08-12T17:01:30.006116Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:29.984881Z","title":"Elliptic partial diﬀerential equations , volume 1 of Courant Lecture Notes in Mathematics","venue":null,"work_id":"df1ba382-d068-4f0e-9842-3392d28e158b","year":1997},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.695739Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:3d48028e91f15f7105360bf65ce2b64267cec5fd1212e1d3c1a7b3fc3b78f720","observation_id":"4b1ed6b6-a4ac-4bb0-a8f7-eb71d9cd50d5","resolution":{"observed_at":"2026-08-12T17:01:29.990221Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:29.969531Z","title":"Flux-limited solutio ns for quasi-convex Hamilton- Jacobi equations on networks","venue":null,"work_id":"d6d8d29c-e1da-4bf8-bedc-de0c5ec7ba9b","year":2017},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.700234Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:8b8c6cd6ee04c7479e9356031d53dd83496d7228ca53892d8875a8a1074e8b8a","observation_id":"26846afe-334a-42ee-a1c5-48823a330365","resolution":{"observed_at":"2026-08-12T17:01:29.974356Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:29.954776Z","title":"A Hami lton-Jacobi approach to junction problems and application to traﬃc ﬂows","venue":null,"work_id":"67aa8f04-3b99-466a-b0b3-1a16aa846aa6","year":2013},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.704957Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:4483b47834b45beb85f0f314c892550158cef5fdebfbd8a256e1d18a6300e6b3","observation_id":"a7ad2aa4-0fac-4345-aaf7-d3eb520f64cb","resolution":{"observed_at":"2026-08-12T17:01:29.959922Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:29.940082Z","title":"Eﬀective junction con ditions for degenerate parabolic equations","venue":null,"work_id":"394b0c12-206b-4d33-a1d7-0ffa5a50f643","year":2017},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.709520Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:8c710b8b3817d22fa554f4facb9fdca04e8e4d9c208a4a482b9d5b7d3908a0c7","observation_id":"442e6af0-eb71-4996-9d70-0736b72cc241","resolution":{"observed_at":"2026-08-12T17:01:29.944804Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:29.926281Z","title":"The Poincar´ e-Miranda theorem","venue":null,"work_id":"d5c585a3-d396-4220-a773-53ac02dcb3f5","year":1997},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.714218Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:45b23f586a56df8efe260337a569c7b6b198745d0891dd328a68ac96102ba7a7","observation_id":"d92418bb-83af-45dc-a2a0-2fe32495a4fc","resolution":{"observed_at":"2026-08-12T17:01:29.930662Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:29.912027Z","title":"Viscos ity solutions for junctions: well posedness and stability","venue":null,"work_id":"af21be13-7d80-490f-a81e-154956c73a16","year":2016},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.718813Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:9b4483a643718f9056319fad1e804f03e07ede76d6f89cc1123a329af055af1c","observation_id":"9b75acba-d7be-44ba-9d08-ee1bf85fe970","resolution":{"observed_at":"2026-08-12T17:01:29.916652Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:29.897174Z","title":"Well-p osedness for multi-dimensional junction problems with Kirchoﬀ-type conditions","venue":null,"work_id":"ef8c1ac3-b20c-45f2-a81a-620e5fc80b3f","year":2017},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.723366Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:d188309e21014b2d2597cb75cac1541cd69042fd2d031c293b21579a53864050","observation_id":"49d134ff-dcee-47c9-b26a-923e4e5f9b76","resolution":{"observed_at":"2026-08-12T17:01:29.902067Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:29.882370Z","title":null,"venue":null,"work_id":"189307bc-afbe-4350-8709-9cb111afbfab","year":2020},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.727874Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:a11272ea631b3d5187a5e21d95ac290914b096291a79edb98364f5077346c162","observation_id":"7c96dc70-a2e2-410d-8d29-551e97512785","resolution":{"observed_at":"2026-08-12T17:01:29.887447Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:29.866040Z","title":"Quasi linear parabolic pde posed on a netwo rk with non linear Neumann boundary condition at vertices","venue":null,"work_id":"92a4597e-1a9c-4b28-b6ed-c188640b4e0b","year":2021},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.732410Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:b1a36610fbcada9c6ad64cbc6191d1da3bbd37f08a10e0d03db6f11d85345390","observation_id":"16ccfedd-bf50-41c7-ac17-c258cc8034ab","resolution":{"observed_at":"2026-08-12T17:01:29.871679Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:29.849956Z","title":"Viscosity solutions of Eikonal equations on topo- logical networks","venue":null,"work_id":"20cbdce1-c170-4909-8f96-98649b7108aa","year":2013},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.736848Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:041a2ec0080ed59651bbc83cf89848d919dced7e79ff7891f38c070c8fe8c68f","observation_id":"45f48e13-c41c-414f-bed0-87192ebe1227","resolution":{"observed_at":"2026-08-12T17:01:29.854941Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:29.835033Z","title":"Time-dependent Hamilton-Jacobi eq uations on networks","venue":null,"work_id":"89e04765-fd57-432a-a3c3-889c97617495","year":2022},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.741585Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:f4573cb86ef2097273f6429058d08d589ef02ea1cca22cc5ae121c3417872e35","observation_id":"60bc26f3-cfaa-48df-bc6c-940aaa3d9d0a","resolution":{"observed_at":"2026-08-12T17:01:29.839684Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:29.819406Z","title":"Optimal control with state-space con straint","venue":null,"work_id":"69f70ccb-637d-44ec-a36e-bafca43e2030","year":1986},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.746128Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:b2f3591779c38979b79542234d326f54e5a97a1c69a8047ec61be777685d1aff","observation_id":"008867b4-530b-4c63-a431-4d8c25d2cbf4","resolution":{"observed_at":"2026-08-12T17:01:29.824373Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:29.803783Z","title":"Existence and uniqueness for integro-diﬀe rential equations with domi- nating drift terms","venue":null,"work_id":"4b7d2ab3-47b5-4c34-8c6c-f0e6e6002ffd","year":2014},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.750613Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:0782a733d603af0236ada4f03093e2b6d838251e3717a3710c422da198e4b18c","observation_id":"8e68c360-c0e3-40e3-821f-6c75a0493d0a","resolution":{"observed_at":"2026-08-12T17:01:29.808789Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:29.786250Z","title":"Classical solvability of linear par abolic equations on networks","venue":null,"work_id":"4a4683bf-a354-4ede-b2fd-723aeb9074a4","year":1988},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.755069Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:e2212c5d03c817c7598e1eb648f14889eb2a09ce1bf5eff825ed326f7fbde275","observation_id":"abc97a91-710a-4336-82e3-315fd446e6ee","resolution":{"observed_at":"2026-08-12T17:01:29.792979Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:01:30.236719Z","title":null,"venue":null,"work_id":"62133bcf-9c94-467f-a059-a522d9c32f01","year":null},"citing_paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","version":1},"reference_index":2024,"source":"pdf_text","source_observed_at":"2026-08-12T17:01:29.624983Z"},"links":{"citing_paper":"/paper/2411.13126"},"observation_digest":"sha256:9a7adeb12c59746b8408cbeabc52e00514da0d4abe5393ea37fd672367661167","observation_id":"d0179203-03aa-490a-a9aa-6fa6ca6d3708","resolution":{"observed_at":"2026-08-12T17:01:30.241915Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}}],"paper":{"arxiv_id":"2411.13126","last_updated":"2024-11-20T08:37:16Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-12T16:46:02.325906Z","submitted_at":"2024-11-20T08:37:16Z","title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions"},"reference_resolution":{"displayed":40,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":4,"verified_exact":0,"verified_fuzzy":36},"total_outbound_references":40},"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 40 of 40 outbound references and 1 inbound Pith citation observation for arXiv:2411.13126."}