{"as_of":"2026-08-19T14:05:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:097cf64c3e595895708d58fc2393c8c55098ff648581465e2055e47afb1254a9","coverage":[{"denominator":21,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":21,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T12:46:08.208874Z","state":"measured"},{"denominator":22,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":22,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-19T06:32:44.657259+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":"2026-05-19T14:25:48.416301Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-19T14:27:24.154005Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2507.21604","last_updated":"2025-07-29T09:02:00Z","snapshot_observed_at":"2026-08-18T14:04:49.865755Z","submitted_at":"2025-07-29T09:02:00Z","title":"The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis","version":1},"cited_work":{"arxiv_id":"2507.21604","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.21604","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"66d0e2d9-c649-4fae-9295-f9b03116c324","year":2025},"citing_paper":{"arxiv_id":"2605.15479","last_updated":"2026-05-14T23:42:14Z","snapshot_observed_at":"2026-08-17T01:34:39.738539Z","submitted_at":"2026-05-14T23:42:14Z","title":"A tree-like fractal Dirichlet space lying between strong and weak elliptic Harnack inequalities","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-05-19T14:25:48.416301Z"},"links":{"cited_paper":"/paper/2507.21604","citing_paper":"/paper/2605.15479"},"observation_digest":"sha256:0c3cf388c4c26c5fedb5174de311d33947c712c305f0c29653da03b4f026ea6c","observation_id":"03753309-807d-46a5-b935-bf036f23e059","resolution":{"observed_at":"2026-05-19T14:27:24.155412Z","resolver_source":"arxiv_id","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"}}],"links":{"evidence":"/evidence","html":"/paper/2507.21604/citation-record","integrity":"/paper/2507.21604/integrity","json":"/paper/2507.21604/citation-record.json","paper":"/paper/2507.21604"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T12:46:08.430865Z","title":"Andres and M","venue":null,"work_id":"95e402bb-982a-4ab0-9da1-847d178372b1","year":2015},"citing_paper":{"arxiv_id":"2507.21604","last_updated":"2025-07-29T09:02:00Z","snapshot_observed_at":"2026-08-18T14:04:49.865755Z","submitted_at":"2025-07-29T09:02:00Z","title":"The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T12:46:08.151205Z"},"links":{"citing_paper":"/paper/2507.21604"},"observation_digest":"sha256:f5d8c3d0ec3423ba5516e7e31985cbb4991f0d16171f583c31c40d77caed6a8b","observation_id":"7336d912-5deb-4eb9-8e0d-fabccdb5a599","resolution":{"observed_at":"2026-08-06T12:46:08.433849Z","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":"2026-08-06T12:46:08.422298Z","title":null,"venue":null,"work_id":"496edc96-3d54-4f20-9b72-893efce6278f","year":2006},"citing_paper":{"arxiv_id":"2507.21604","last_updated":"2025-07-29T09:02:00Z","snapshot_observed_at":"2026-08-18T14:04:49.865755Z","submitted_at":"2025-07-29T09:02:00Z","title":"The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T12:46:08.154518Z"},"links":{"citing_paper":"/paper/2507.21604"},"observation_digest":"sha256:30f6ebce4add690eea7fadef45b566e7b1b03cd427ffe4d857e76bae1c92a32b","observation_id":"ce9ab93f-46da-4a97-8c6f-d0174b50b23a","resolution":{"observed_at":"2026-08-06T12:46:08.425211Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"2026-08-06T12:46:08.413710Z","title":null,"venue":null,"work_id":"84895130-eb18-46c8-862b-31cfd84c37d1","year":2009},"citing_paper":{"arxiv_id":"2507.21604","last_updated":"2025-07-29T09:02:00Z","snapshot_observed_at":"2026-08-18T14:04:49.865755Z","submitted_at":"2025-07-29T09:02:00Z","title":"The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T12:46:08.157429Z"},"links":{"citing_paper":"/paper/2507.21604"},"observation_digest":"sha256:ca9c613c59ea12d7b7158bb7844a89cf40a4ac8db0e980d97a969b40737a82b4","observation_id":"a0afd580-5b13-489f-8549-b91478b25dee","resolution":{"observed_at":"2026-08-06T12:46:08.416512Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"2026-08-06T12:46:08.405108Z","title":null,"venue":null,"work_id":"26704043-aa5d-4d72-bb66-7afd0e2d3668","year":2019},"citing_paper":{"arxiv_id":"2507.21604","last_updated":"2025-07-29T09:02:00Z","snapshot_observed_at":"2026-08-18T14:04:49.865755Z","submitted_at":"2025-07-29T09:02:00Z","title":"The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T12:46:08.160253Z"},"links":{"citing_paper":"/paper/2507.21604"},"observation_digest":"sha256:9c07aefd7ad78fedff45e191a0975254ce2088dd0ab09836f2590109180a77ee","observation_id":"e9a14eb7-e8f7-4920-99ee-c15227e07bd5","resolution":{"observed_at":"2026-08-06T12:46:08.407935Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"2026-08-06T12:46:08.396491Z","title":null,"venue":null,"work_id":"758506c3-2a8d-4f99-8135-fa18b1be1327","year":2020},"citing_paper":{"arxiv_id":"2507.21604","last_updated":"2025-07-29T09:02:00Z","snapshot_observed_at":"2026-08-18T14:04:49.865755Z","submitted_at":"2025-07-29T09:02:00Z","title":"The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T12:46:08.163297Z"},"links":{"citing_paper":"/paper/2507.21604"},"observation_digest":"sha256:a62eff63a112583ffb7fbf3c86899f79c25f360a5387ab23b9ae4d29cb47f9af","observation_id":"e3232cf2-0499-4acc-99d6-702ff70c63e9","resolution":{"observed_at":"2026-08-06T12:46:08.399296Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"2026-08-06T12:46:08.387822Z","title":"Fabes and D","venue":null,"work_id":"84464abf-4e28-4678-9758-645f13661195","year":1986},"citing_paper":{"arxiv_id":"2507.21604","last_updated":"2025-07-29T09:02:00Z","snapshot_observed_at":"2026-08-18T14:04:49.865755Z","submitted_at":"2025-07-29T09:02:00Z","title":"The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T12:46:08.166212Z"},"links":{"citing_paper":"/paper/2507.21604"},"observation_digest":"sha256:d3ee1143a0f88065c4168841162b436e02427be4202240f15767a3a0ddca3128","observation_id":"a5e8101f-de04-42e6-967a-2177c89cbb8f","resolution":{"observed_at":"2026-08-06T12:46:08.390651Z","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":"2026-08-06T12:46:08.378722Z","title":"Fukushima, Y","venue":null,"work_id":"bffa7a05-5af4-437b-b803-532245e982f2","year":2011},"citing_paper":{"arxiv_id":"2507.21604","last_updated":"2025-07-29T09:02:00Z","snapshot_observed_at":"2026-08-18T14:04:49.865755Z","submitted_at":"2025-07-29T09:02:00Z","title":"The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T12:46:08.169723Z"},"links":{"citing_paper":"/paper/2507.21604"},"observation_digest":"sha256:6262e498745897751a2956651912552422f2e433c103c423aee0617a0df6c7f2","observation_id":"dacb0682-fd0d-472c-a745-e8a49b4b9679","resolution":{"observed_at":"2026-08-06T12:46:08.381648Z","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":"2026-08-06T12:46:08.370584Z","title":"Grigor’yan, E","venue":null,"work_id":"70af3d96-2296-4e27-90e4-ea10a93692d7","year":2017},"citing_paper":{"arxiv_id":"2507.21604","last_updated":"2025-07-29T09:02:00Z","snapshot_observed_at":"2026-08-18T14:04:49.865755Z","submitted_at":"2025-07-29T09:02:00Z","title":"The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T12:46:08.172543Z"},"links":{"citing_paper":"/paper/2507.21604"},"observation_digest":"sha256:bc36a7cb2d52de2706894cc0749a67c7052388deccb2e84f8dc46adec9b01d0c","observation_id":"58017e90-8f02-4272-ace8-082940e40a26","resolution":{"observed_at":"2026-08-06T12:46:08.373405Z","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":"2026-08-06T12:46:08.362497Z","title":"Grigor’yan, E","venue":null,"work_id":"3c28a4d4-845e-4ca9-bff7-3cebd8e568ee","year":2018},"citing_paper":{"arxiv_id":"2507.21604","last_updated":"2025-07-29T09:02:00Z","snapshot_observed_at":"2026-08-18T14:04:49.865755Z","submitted_at":"2025-07-29T09:02:00Z","title":"The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T12:46:08.175267Z"},"links":{"citing_paper":"/paper/2507.21604"},"observation_digest":"sha256:07e38d4bec658adeceffd1b73b1a19e59915eb76e45fea1742546a34eb33534f","observation_id":"4e9f82f4-7ded-4752-ac2a-d64969dd7b7d","resolution":{"observed_at":"2026-08-06T12:46:08.365203Z","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":"2026-08-06T12:46:08.353646Z","title":"Grigor’yan, E","venue":null,"work_id":"46cc1453-dab6-44ba-9eed-d4cf3eed7104","year":2023},"citing_paper":{"arxiv_id":"2507.21604","last_updated":"2025-07-29T09:02:00Z","snapshot_observed_at":"2026-08-18T14:04:49.865755Z","submitted_at":"2025-07-29T09:02:00Z","title":"The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T12:46:08.177996Z"},"links":{"citing_paper":"/paper/2507.21604"},"observation_digest":"sha256:92f4edc1f2b4ba1de19eac15d01d05a566cf4bd484e4fcae4e841c68ac3aa255","observation_id":"63280db4-e518-4e42-ac9d-15082ce437b9","resolution":{"observed_at":"2026-08-06T12:46:08.356421Z","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":"2026-08-06T12:46:08.345311Z","title":"Grigor’yan, E","venue":null,"work_id":"e4459913-8bda-47ee-ab6f-337186b425cc","year":2023},"citing_paper":{"arxiv_id":"2507.21604","last_updated":"2025-07-29T09:02:00Z","snapshot_observed_at":"2026-08-18T14:04:49.865755Z","submitted_at":"2025-07-29T09:02:00Z","title":"The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T12:46:08.180690Z"},"links":{"citing_paper":"/paper/2507.21604"},"observation_digest":"sha256:3d3f85457be930d46b9fcc835694081efe2af1285938910989b1e5eea3196ae7","observation_id":"e3db40f5-457b-4395-9b0a-7df59cec87cf","resolution":{"observed_at":"2026-08-06T12:46:08.348080Z","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":"2026-08-06T12:46:08.336469Z","title":"Grigor’yan, E","venue":null,"work_id":"8fcb5a86-3483-42f7-a39f-5d07ec1238dc","year":2024},"citing_paper":{"arxiv_id":"2507.21604","last_updated":"2025-07-29T09:02:00Z","snapshot_observed_at":"2026-08-18T14:04:49.865755Z","submitted_at":"2025-07-29T09:02:00Z","title":"The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T12:46:08.183251Z"},"links":{"citing_paper":"/paper/2507.21604"},"observation_digest":"sha256:09a0517a4c6246534aa4327aa3d968ee6f56b77b6937163ba70fd445cf32ee55","observation_id":"3012744a-40c5-4803-b106-ed5fab5893a2","resolution":{"observed_at":"2026-08-06T12:46:08.339388Z","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":"2026-08-06T12:46:08.327715Z","title":"Grigor’yan, E","venue":null,"work_id":"45c22d98-2a99-4306-9a14-0192a8cb3250","year":2024},"citing_paper":{"arxiv_id":"2507.21604","last_updated":"2025-07-29T09:02:00Z","snapshot_observed_at":"2026-08-18T14:04:49.865755Z","submitted_at":"2025-07-29T09:02:00Z","title":"The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T12:46:08.185875Z"},"links":{"citing_paper":"/paper/2507.21604"},"observation_digest":"sha256:0426f168a4d56005e02d9ffd54aa161cfaf3a8c5428c94fcd3639f0ac12f80b3","observation_id":"f61e12f5-2f2a-469f-a038-bba5a339568b","resolution":{"observed_at":"2026-08-06T12:46:08.330606Z","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":"2026-08-06T12:46:08.318927Z","title":"Grigor’yan, J","venue":null,"work_id":"fe060370-90d7-4e33-8a66-5d5271e960f8","year":2015},"citing_paper":{"arxiv_id":"2507.21604","last_updated":"2025-07-29T09:02:00Z","snapshot_observed_at":"2026-08-18T14:04:49.865755Z","submitted_at":"2025-07-29T09:02:00Z","title":"The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T12:46:08.188586Z"},"links":{"citing_paper":"/paper/2507.21604"},"observation_digest":"sha256:ffe34d7a6a5c19adeff5f07410f5ee11975d7305e21c17609fdada5c7e558b27","observation_id":"d94b7206-6b29-4f66-9b18-55a7d27345b9","resolution":{"observed_at":"2026-08-06T12:46:08.321981Z","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":"2026-08-06T12:46:08.309776Z","title":"Hu and G","venue":null,"work_id":"9fae61a5-9ec9-4ede-bb1d-0865270c0569","year":2022},"citing_paper":{"arxiv_id":"2507.21604","last_updated":"2025-07-29T09:02:00Z","snapshot_observed_at":"2026-08-18T14:04:49.865755Z","submitted_at":"2025-07-29T09:02:00Z","title":"The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T12:46:08.191241Z"},"links":{"citing_paper":"/paper/2507.21604"},"observation_digest":"sha256:d7f5800a3a51d8d7adfb0ac9533bb2dfa8fe80dd71baa5b07f52c2e531382b40","observation_id":"f828386d-8c33-47e2-b18d-d343fe483a64","resolution":{"observed_at":"2026-08-06T12:46:08.312867Z","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":"2026-08-06T12:46:08.299018Z","title":"Hu and Z","venue":null,"work_id":"ec7a71fe-1d55-4132-bfaf-0d5a894c1582","year":2023},"citing_paper":{"arxiv_id":"2507.21604","last_updated":"2025-07-29T09:02:00Z","snapshot_observed_at":"2026-08-18T14:04:49.865755Z","submitted_at":"2025-07-29T09:02:00Z","title":"The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T12:46:08.194052Z"},"links":{"citing_paper":"/paper/2507.21604"},"observation_digest":"sha256:2c7b65a860ed602a63d23eaa89362c1867cd62cc18dfe2a4330bf34797bcfe24","observation_id":"0b1568b9-cee3-43bf-ba82-8d1913aad3ad","resolution":{"observed_at":"2026-08-06T12:46:08.302419Z","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":"2026-08-06T12:46:08.288292Z","title":"Kassmann, Harnack inequalities: An introduction, Bound","venue":null,"work_id":"4e2ec8a3-e8ab-481e-9be5-7cc3587346f0","year":2007},"citing_paper":{"arxiv_id":"2507.21604","last_updated":"2025-07-29T09:02:00Z","snapshot_observed_at":"2026-08-18T14:04:49.865755Z","submitted_at":"2025-07-29T09:02:00Z","title":"The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T12:46:08.197013Z"},"links":{"citing_paper":"/paper/2507.21604"},"observation_digest":"sha256:7f2c59a36f80dd11311820ed7038332410017428cd815cd70c8afec231f75762","observation_id":"aa2233a6-e6ae-4fea-b757-28b622305b8c","resolution":{"observed_at":"2026-08-06T12:46:08.291460Z","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":"2303.05975","last_updated":"2024-01-24T21:26:09Z","snapshot_observed_at":"2026-08-19T11:08:15.270722Z","submitted_at":"2023-03-10T15:13:54Z","title":"The parabolic Harnack inequality for nonlocal equations","version":2},"cited_work":{"arxiv_id":"2303.05975","doi":null,"metadata_source":"pith","pith_arxiv_id":"2303.05975","snapshot_observed_at":"2026-08-06T12:46:08.256070Z","title":"The parabolic Harnack inequality for nonlocal equations","venue":"math.AP","work_id":"8d014aff-0141-44ca-8375-bea05c625ff3","year":2023},"citing_paper":{"arxiv_id":"2507.21604","last_updated":"2025-07-29T09:02:00Z","snapshot_observed_at":"2026-08-18T14:04:49.865755Z","submitted_at":"2025-07-29T09:02:00Z","title":"The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T12:46:08.199650Z"},"links":{"cited_paper":"/paper/2303.05975","citing_paper":"/paper/2507.21604"},"observation_digest":"sha256:b56b4d4432b28d301315a84eed97ce7c65bb5e6e5ba0c3430f710a1b11045e38","observation_id":"ec8c2a84-46a0-42b4-9d2b-962893cf8400","resolution":{"observed_at":"2026-08-06T12:46:08.259833Z","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":{"arxiv_id":"2410.23732","last_updated":"2025-02-07T14:59:39Z","snapshot_observed_at":"2026-08-16T13:04:14.599630Z","submitted_at":"2024-10-31T08:39:46Z","title":"Weak parabolic Harnack inequality and H\\\"older regularity for non-local Dirichlet forms","version":3},"cited_work":{"arxiv_id":"2410.23732","doi":null,"metadata_source":"pith","pith_arxiv_id":"2410.23732","snapshot_observed_at":"2026-08-06T12:46:08.236622Z","title":"Weak parabolic Harnack inequality and H\\\"older regularity for non-local Dirichlet forms","venue":"math.AP","work_id":"718abaff-37ad-4408-8649-ea067db0fbcf","year":2024},"citing_paper":{"arxiv_id":"2507.21604","last_updated":"2025-07-29T09:02:00Z","snapshot_observed_at":"2026-08-18T14:04:49.865755Z","submitted_at":"2025-07-29T09:02:00Z","title":"The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T12:46:08.202748Z"},"links":{"cited_paper":"/paper/2410.23732","citing_paper":"/paper/2507.21604"},"observation_digest":"sha256:93011c7ccfe5592329570ddabf177458c6d53868603ad4953cc84a449e2d44af","observation_id":"d1c0735b-b04d-4b7c-8593-baeebc02113d","resolution":{"observed_at":"2026-08-06T12:46:08.244798Z","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":"2026-08-06T12:46:08.277524Z","title":"Moser, A Harnack inequality for parabolic di fferential equations, Comm","venue":null,"work_id":"996ef21c-1f26-40e0-8bed-a3ea9c964375","year":1964},"citing_paper":{"arxiv_id":"2507.21604","last_updated":"2025-07-29T09:02:00Z","snapshot_observed_at":"2026-08-18T14:04:49.865755Z","submitted_at":"2025-07-29T09:02:00Z","title":"The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T12:46:08.205707Z"},"links":{"citing_paper":"/paper/2507.21604"},"observation_digest":"sha256:2135c407152bb99a156b76ab9323f9533c199badcd6cb528a79964d7fd77e5c7","observation_id":"b3151f89-d6f6-420a-a1b4-f8f7904667cc","resolution":{"observed_at":"2026-08-06T12:46:08.280924Z","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":"2026-08-06T12:46:08.266633Z","title":"Nash, Continuity of solutions of parabolic and elliptic equations, Amer","venue":null,"work_id":"f1c16faa-b4a8-40dc-96b5-c613985c220f","year":1958},"citing_paper":{"arxiv_id":"2507.21604","last_updated":"2025-07-29T09:02:00Z","snapshot_observed_at":"2026-08-18T14:04:49.865755Z","submitted_at":"2025-07-29T09:02:00Z","title":"The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T12:46:08.208874Z"},"links":{"citing_paper":"/paper/2507.21604"},"observation_digest":"sha256:72813d99c30ab58365a7f2a70fc949d5cf204c848b9606d36da39c3008cc8a9a","observation_id":"07d771d7-16ae-45c0-9421-39df057589f9","resolution":{"observed_at":"2026-08-06T12:46:08.270075Z","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"}}],"paper":{"arxiv_id":"2507.21604","last_updated":"2025-07-29T09:02:00Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-18T14:04:49.865755Z","submitted_at":"2025-07-29T09:02:00Z","title":"The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis"},"reference_resolution":{"displayed":21,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":4,"verified_exact":2,"verified_fuzzy":15},"total_outbound_references":21},"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 21 of 21 outbound references and 1 inbound Pith citation observation for arXiv:2507.21604."}