{"as_of":"2026-08-15T13:47:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:cf69d4c8f251235148851fd9853c40cd5cd722774e16570fabd57949c4346edf","coverage":[{"denominator":55,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":55,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T01:10:37.750537Z","state":"measured"},{"denominator":55,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":55,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-15T06:32:42.880941+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/2506.12424/citation-record","integrity":"/paper/2506.12424/integrity","json":"/paper/2506.12424/citation-record.json","paper":"/paper/2506.12424"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:10:47.658551Z","title":"Halldórsson","venue":null,"work_id":"b86bf5e9-2022-4404-8b0e-b1d8ea921394","year":2003},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:32.248507Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:a5dc875797108b536fb2ffa32576cdc762a829376897fa84cb3fec7f3d695721","observation_id":"ff4dbb72-2f21-4a68-96b5-78c57869fe15","resolution":{"observed_at":"2026-08-07T01:10:47.820049Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:47.304446Z","title":"Opportunity cost algorithms for combinatorial auctions","venue":null,"work_id":"f59a9c99-aeae-4ac4-86cc-a1897ba1dee4","year":2002},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:32.298084Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:5bcd0d5669f34d8fadf2cf3965ef6e0aeace6c6230d3e3386a637977b6bdd46d","observation_id":"d9af7599-fd78-4f01-862a-1a498d21d4d1","resolution":{"observed_at":"2026-08-07T01:10:47.521546Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2311.03665","last_updated":"2023-11-07T02:21:35Z","snapshot_observed_at":"2026-08-13T05:30:59.237581Z","submitted_at":"2023-11-07T02:21:35Z","title":"Faster Algorithms for Cycle Hitting Problems on Disk Graphs","version":1},"cited_work":{"arxiv_id":"2311.03665","doi":null,"metadata_source":"pith","pith_arxiv_id":"2311.03665","snapshot_observed_at":"2026-08-07T01:10:38.470879Z","title":"Faster Algorithms for Cycle Hitting Problems on Disk Graphs","venue":"cs.CG","work_id":"15565502-3744-4132-944a-5aad42e007d7","year":2023},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:32.458934Z"},"links":{"cited_paper":"/paper/2311.03665","citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:ae7c3f81ebd31be75352ac093b184fe90da9ffa6b7e432767e7c3bf638a0af58","observation_id":"cb867947-ea86-4db6-aa7e-f1c1829b32ca","resolution":{"observed_at":"2026-08-07T01:10:38.538553Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:47.123126Z","title":"On forbidden induced subgraphs for unit disk graphs","venue":null,"work_id":"7659424a-d039-499d-be9c-5f944d25109c","year":2018},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:32.569402Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:091f2ec5bb3efd59e6748680f1ba985d1b2ddf1ec0363caa12e89f329f4ee6a1","observation_id":"94fe335c-5d97-460a-9dd0-5deb37f1a19f","resolution":{"observed_at":"2026-08-07T01:10:47.179919Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:47.023871Z","title":"On approximation properties of the independent set problem for low degree graphs.Theory of Computing Systems, 32(2):115–132, 1999","venue":null,"work_id":"6cec4670-e403-42d7-8776-15bd99ffe24a","year":1999},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:32.658194Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:9aa251645f9d60887c4af5108abc6f0872cb4d98936a1ee1684dc1140a50400b","observation_id":"6acf080f-b93e-4eb2-8bde-a2457685c556","resolution":{"observed_at":"2026-08-07T01:10:47.073897Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2410.23878","last_updated":"2024-10-31T12:39:13Z","snapshot_observed_at":"2026-08-12T22:10:53.511170Z","submitted_at":"2024-10-31T12:39:13Z","title":"Feedback Vertex Set for pseudo-disk graphs in subexponential FPT time","version":1},"cited_work":{"arxiv_id":"2410.23878","doi":null,"metadata_source":"pith","pith_arxiv_id":"2410.23878","snapshot_observed_at":"2026-08-07T01:10:38.271154Z","title":"Feedback Vertex Set for pseudo-disk graphs in subexponential FPT time","venue":"cs.DS","work_id":"53347540-d71a-4042-acd9-30ddb3729437","year":2024},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:32.764121Z"},"links":{"cited_paper":"/paper/2410.23878","citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:e2ea06db4eac3f05a563e588a93fe74d8cd47481d721c8267419fd6f70781c9b","observation_id":"79cdc0d9-4f17-42a9-aacb-d4ba1018dbc5","resolution":{"observed_at":"2026-08-07T01:10:38.348040Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2301.05550","last_updated":"2023-01-13T13:55:03Z","snapshot_observed_at":"2026-08-13T16:29:49.155031Z","submitted_at":"2023-01-13T13:55:03Z","title":"Recognizing Unit Disk Graphs in Hyperbolic Geometry is $\\exists\\mathbb{R}$-Complete","version":1},"cited_work":{"arxiv_id":"2301.05550","doi":null,"metadata_source":"pith","pith_arxiv_id":"2301.05550","snapshot_observed_at":"2026-08-07T01:10:38.107509Z","title":"Recognizing Unit Disk Graphs in Hyperbolic Geometry is $\\exists\\mathbb{R}$-Complete","venue":"cs.CG","work_id":"deb6cc68-d8ed-451b-bec2-c6b517302bf9","year":2023},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:32.882019Z"},"links":{"cited_paper":"/paper/2301.05550","citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:1256c3e44dd412cf8c4a0d6d1d38771f427b8c63343e73a86079a2e0724e9fb8","observation_id":"143c5e16-962c-415c-9220-79e0123bb709","resolution":{"observed_at":"2026-08-07T01:10:38.176714Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2407.09362","last_updated":"2025-03-27T12:35:40Z","snapshot_observed_at":"2026-08-15T12:08:36.362057Z","submitted_at":"2024-07-12T15:43:03Z","title":"Structure and Independence in Hyperbolic Uniform Disk Graphs","version":2},"cited_work":{"arxiv_id":"2407.09362","doi":null,"metadata_source":"pith","pith_arxiv_id":"2407.09362","snapshot_observed_at":"2026-08-07T01:10:37.959079Z","title":"Structure and Independence in Hyperbolic Uniform Disk Graphs","venue":"cs.CG","work_id":"18e68155-f5c4-4506-811c-ae2760674946","year":2024},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:32.965075Z"},"links":{"cited_paper":"/paper/2407.09362","citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:647071653fa3b990d0b10119408047ada61f6912936d19adfbdc516dcb27c881","observation_id":"84758c80-822b-4378-8aad-4a87a033ea75","resolution":{"observed_at":"2026-08-07T01:10:38.027734Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:46.911494Z","title":"https://formal.kastel.kit.edu/teaching/ projektgruppe/themen/WiSe2324/hyperbolicUnitDiskGraphs.pdf, 2023","venue":null,"work_id":"64c42772-8a79-4ce8-9082-51d8e87ae548","year":2023},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:33.085259Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:d109b3f47662cb1eb5c0640d88b501549a6594995a043e049fbb1dd9175ad2cd","observation_id":"fcc4cf6c-de58-4b0b-928f-0aa9e8b16a05","resolution":{"observed_at":"2026-08-07T01:10:46.968999Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:46.829120Z","title":"Bodlaender","venue":null,"work_id":"c18befc4-e572-43dc-be0b-39e93c5ea53b","year":1998},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:33.207876Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:542f3a7746b1181f8ab92d44d6e7657c119daee43ab4f62305833d6b39606628","observation_id":"7ab774b3-97f7-43e0-9866-7f5338e9a618","resolution":{"observed_at":"2026-08-07T01:10:46.867950Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:46.743064Z","title":"Bodlaender, Thomas Wolle, and Arie M","venue":null,"work_id":"46d62729-c34f-4d3d-b775-e077c5f419f9","year":2006},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:33.326755Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:09374e6427c57b2d83abcc53a543cb4c4467b5581201481293cf1aa75c10229c","observation_id":"acff8014-14eb-471c-a967-b941e0b34209","resolution":{"observed_at":"2026-08-07T01:10:46.779862Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:46.612233Z","title":"Comparing width parame- ters on graph classes.European Journal of Combinatorics, 127:104163, 2025","venue":null,"work_id":"257e611d-14ab-4500-9797-c4a0f374558b","year":2025},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:33.425576Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:07fdff0711dfe9f526e1df24a4df81970b7077d191f5fb4dc771be15d1e9da86","observation_id":"c155ee21-30f9-4663-a5c2-ba5b253b00c9","resolution":{"observed_at":"2026-08-07T01:10:46.658454Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:46.475418Z","title":"Separating polynomialχ-boundedness from χ-boundedness","venue":null,"work_id":"f40c5061-93e2-4e1b-a302-eefab1b35031","year":2024},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:33.587544Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:e87f045060b6dfe4ff0cc4390b2e0d3407892f06a37e81ff3a81cd1bc4db95d3","observation_id":"3ecff4df-cb79-4f29-8894-93957559b168","resolution":{"observed_at":"2026-08-07T01:10:46.546823Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:46.331271Z","title":"Sunil Chandran and C","venue":null,"work_id":"ac6b6334-1b5b-4676-aa61-a158c685c3f5","year":2005},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:33.698372Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:4fd6bcfebe7ce322e40b07a96c092262a7f2f0b0610838be19030cfde3156013","observation_id":"abfb3e4c-35f3-4133-9194-7fa45ac01658","resolution":{"observed_at":"2026-08-07T01:10:46.416101Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:46.177704Z","title":"Independent sets in elimination graphs with a submodular objective","venue":null,"work_id":"c00d2fb0-cb66-4f5d-b369-8422cb81e04f","year":2023},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:33.797664Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:d3b13b6cf9e6fd7d2fb7d46a2f9433ca7d30a23a0aa9306ff63ef6cdfc197b6d","observation_id":"76ac1af4-a774-4755-9be3-37d801e0fcc8","resolution":{"observed_at":"2026-08-07T01:10:46.233133Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:46.051958Z","title":"Papadimitriou","venue":null,"work_id":"83d5dd7e-938f-4290-8789-4e96759c1469","year":2002},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:33.934428Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:ac010542bb50a70bb2ff8438148850c72227dcd813ee109acff4954bd6705e26","observation_id":"ee106afa-7705-4762-9530-11556dc6355f","resolution":{"observed_at":"2026-08-07T01:10:46.108733Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:34.102661Z","title":"On treewidth and maximum cliques","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:34.102661Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:8ca6389daee164745e1b85b1398ac3f56002be646dda7b8781f77f6aeb0b757d","observation_id":"f41fff1a-7866-4a9d-8b0e-0c6167714039","resolution":{"observed_at":"2026-08-07T01:10:34.102661Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:10:34.215575Z","title":"Fomin, Łukasz Kowalik, Daniel Lokshtanov, Dániel Marx, Marcin Pilipczuk, Michał Pilipczuk, and Saket Saurabh.Parameterized Algorithms","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:34.215575Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:35413a0addd9366217306b55302866054323ace82560081e07d598b95a773a49","observation_id":"e4192e19-4d17-4256-81e5-bf24e634bfe0","resolution":{"observed_at":"2026-08-07T01:10:34.215575Z","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":"2026-08-07T01:10:45.926537Z","title":"Treewidth versus clique number","venue":null,"work_id":"f7a7687d-f06e-4ece-bd74-b186eaf99fcc","year":2024},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:34.343001Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:bce4cd157c085cce3386dc2d376d1347f15d160de36641495cfe4e87d64f5b3b","observation_id":"a0305e0d-d2f9-4248-8d48-64549d5c632f","resolution":{"observed_at":"2026-08-07T01:10:45.992566Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:45.839745Z","title":"Lower bounds for dominating set in ball graphs and for weighted dominating set in unit-ball graphs","venue":null,"work_id":"83100b16-7f0f-405a-9cb3-aefc9a848790","year":2020},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:34.462665Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:89bab76b3b1800e2e1959c6d4c49946e4ff67f7fa77b5653e781c63656afeccd","observation_id":"ade5a604-73e4-425d-96b4-c850bbc47b43","resolution":{"observed_at":"2026-08-07T01:10:45.859085Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:45.707908Z","title":"Bodlaender, Sándor Kisfaludi-Bak, Dániel Marx, and Tom C","venue":null,"work_id":"7b41749f-62a9-4dd8-9d1a-05910550dfd0","year":2020},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:34.537772Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:7dd351af942358f5ac6ee4582ed951d4e50b2dec95224429c3a93a4f7125b108","observation_id":"9ecb1938-4955-4982-95b7-9d28a52ba809","resolution":{"observed_at":"2026-08-07T01:10:45.781652Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:45.437398Z","title":"Clique- based separators for geometric intersection graphs.Algorithmica, 85(6):1652–1678, 2023","venue":null,"work_id":"c29a23c2-94e4-4c06-a1a4-6d70038a4b59","year":2023},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:34.608197Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:9d6716f921d2064dda66021d8e7fee9019c53e3e10cf5cf35523db05ed030fbd","observation_id":"a767872f-8b1e-49a3-b75a-9b89a1bbdeb0","resolution":{"observed_at":"2026-08-07T01:10:45.575279Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:45.135521Z","title":"Representations by contact and intersection of segments.Algorithmica, 47(4):453–463, 2007","venue":null,"work_id":"babab509-0cf1-4ffb-92a4-9688f5a6bc3b","year":2007},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:34.698125Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:0dfc70bab5362761039f835ea47d4b30024ba32cb753e2e07123d8f436aada9f","observation_id":"727d9dd0-4526-4f63-9099-7fed3bfb3825","resolution":{"observed_at":"2026-08-07T01:10:45.301027Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:44.850372Z","title":"On contact graphs of paths on a grid","venue":null,"work_id":"59cccf6a-8a9d-4013-9ccd-ce24c8d022ac","year":2018},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:34.816528Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:b9ef47a650277d9c108f2b820506f871071b9b18260c343f9136a1ee3777d808","observation_id":"9d18d42d-5b77-4773-b004-9458c0432fbf","resolution":{"observed_at":"2026-08-07T01:10:44.999969Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:44.569325Z","title":"A survey of degree-boundedness.European Journal of Combina- torics, page 104092, 2024","venue":null,"work_id":"1154ce4a-f75d-4e93-8320-b0b5a203efae","year":2024},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:34.899178Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:a7fae1fed69ff03b487a2eb066ee2052445f4093f42ee2cc4a6fbb57c741cbbe","observation_id":"f2c32e98-5ca4-472a-8abf-94dae04f41f0","resolution":{"observed_at":"2026-08-07T01:10:44.703591Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:44.335020Z","title":null,"venue":null,"work_id":"9e9432b0-00c4-400f-bf7c-2ca7a699c79d","year":2017},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:34.983531Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:e43a475ab277e3d8f535b10058b22a799b6e80d39e397556a01dae4f4cddb07c","observation_id":"b1c5739d-04b2-4041-9620-c92dd9aee84b","resolution":{"observed_at":"2026-08-07T01:10:44.446270Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:35.074858Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:35.074858Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:83518b19f1794eecba0988a026bc822c0d0f5658d7f8177be0e026863bc0e12b","observation_id":"a3eb0d14-3d3d-463c-b97d-d28c1c5557b9","resolution":{"observed_at":"2026-08-07T01:10:35.074858Z","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":"2026-08-07T01:10:44.135537Z","title":null,"venue":null,"work_id":"50444c73-2e3d-40c2-9513-26344e71cfc2","year":2022},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:35.173215Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:7c949e656abc22c30434890ec1e163d99745295fc12510946324a4a9d3614a20","observation_id":"2b052d83-ff31-4417-902b-15a5d3d4693f","resolution":{"observed_at":"2026-08-07T01:10:44.233699Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:43.886210Z","title":null,"venue":null,"work_id":"8887681f-1fd2-4bbd-8d5e-4db4a6d96125","year":2023},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:35.304566Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:dbc240aa5b36557c00b28ae918909c84b8f90839d6a382182ce70b24c29dafca","observation_id":"a09801cd-c4ad-44ad-be23-7496f358bd9e","resolution":{"observed_at":"2026-08-07T01:10:43.993692Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:35.398741Z","title":"Sublinear separators, fragility and subexponential expansion.European Journal of Combinatorics, 52:103–119, 2016","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:35.398741Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:ea9be8ed92506e2e58fab1d4b0f143e33865586c72e38b00cc1eb89a0a9e6ade","observation_id":"22a55d8a-3f43-4f6f-b187-e645fa421c6c","resolution":{"observed_at":"2026-08-07T01:10:35.398741Z","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":"2026-08-07T01:10:43.631210Z","title":"Polynomial-time approximation schemes for independent packing problems on fractionally tree-independence-number-fragile graphs","venue":null,"work_id":"6f6d54b4-5d14-4c80-9da6-c85531d3874d","year":2023},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:35.515990Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:c3525bf6cb581275d05a203bfff1f4cce646168855affb4e20329ffc0000d22a","observation_id":"da9cdea1-0f72-4e1e-8db6-153ba546439e","resolution":{"observed_at":"2026-08-07T01:10:43.757488Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.18352","last_updated":"2024-02-28T14:20:29Z","snapshot_observed_at":"2026-08-15T09:59:03.288620Z","submitted_at":"2024-02-28T14:20:29Z","title":"Polynomial-time approximation schemes for induced subgraph problems on fractionally tree-independence-number-fragile graphs","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.18352","snapshot_observed_at":"2026-08-07T01:10:35.607683Z","title":"Polynomial-time approximation schemes for induced subgraph problems on fractionally tree-independence-number-fragile graphs.CoRR, abs/2402.18352, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:35.607683Z"},"links":{"cited_paper":"/paper/2402.18352","citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:6847b36ff55bf646721b9e0b0ca65993ba469649904ad2d8c14bbaa588a20bf5","observation_id":"ffb21350-756c-49a5-a6b7-f3d51d37f9b0","resolution":{"observed_at":"2026-08-07T01:10:35.607683Z","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":"2026-08-07T01:10:43.302800Z","title":"Problems from the world surrounding perfect graphs.Zastosowania Matematyki, 19(3-4):413–441, 1987","venue":null,"work_id":"cb6138d9-b01a-4ee9-8f77-b1f7b9a1e177","year":1987},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:35.701425Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:2f4a01a4f639d63f45e230f810bb99c20b7b61fee68753eccaf823decf7428a7","observation_id":"35f7f25a-5d6d-4bfb-9ab4-fe2f253a4463","resolution":{"observed_at":"2026-08-07T01:10:43.437582Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:43.060754Z","title":"Contact graphs of curves","venue":null,"work_id":"4691c529-3da9-43ef-9377-8842ffa17b4b","year":1995},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:35.797838Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:615e67d98ce7caf99050862825a0720088155dff772ce3dc0c8bf5c1dae860d0","observation_id":"862189cc-602e-4605-b260-7f54f7e363c5","resolution":{"observed_at":"2026-08-07T01:10:43.173081Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:42.806037Z","title":"The maximal clique and colourability of curve contact graphs.Discrete Applied Mathematics, 81(1-3):59–68, 1998","venue":null,"work_id":"4d39e581-b64f-4ace-bb42-89b900f76c89","year":1998},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:35.904659Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:ed5e251cf4893d556a63acda8c8eab15847209577ed5f3581c20f7c9b9dadd4c","observation_id":"f141b773-1150-40df-8b07-fdb557c62d42","resolution":{"observed_at":"2026-08-07T01:10:42.932817Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:42.498843Z","title":"Classes and recognition of curve contact graphs.Journal of Combinatorial Theory, Series B, 74(1):87–103, 1998","venue":null,"work_id":"71a8f884-9016-44d3-b05c-11c37008ae43","year":1998},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:35.972171Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:1ed9c8097ef39a3ee84559f7c4b70a1ca775b43a5d19857fa2daf30769c39bd6","observation_id":"08e7085d-fd2e-45c5-9d3d-697ddd8b1df4","resolution":{"observed_at":"2026-08-07T01:10:42.646405Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:42.234476Z","title":"What graphs are 2-dot product graphs? International Journal of Computational Geometry & Applications, 31(1):1–16, 2021","venue":null,"work_id":"dc8cb0ed-eeb3-4fe9-ba15-59da62b00ab9","year":2021},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:36.066554Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:f0747364cb88b21ae1725344ba28cb5b61e52533f66b51e7993e353d150325fb","observation_id":"e29da127-60f1-48c4-a406-10bc51a403c2","resolution":{"observed_at":"2026-08-07T01:10:42.366374Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:42.016790Z","title":"Approximation algorithms for intersection graphs.Algo- rithmica, 68(2):312–336, 2014","venue":null,"work_id":"510f0d9d-9f4e-461d-8e14-bb0d7c12784f","year":2014},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:36.186424Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:9b4c000a3b9b1b7e0c16e8f105ff0b20fd60463aea12d54bdd5f94fbfbb2b2e4","observation_id":"28d33f89-dea5-405e-94f8-cb77c107caf9","resolution":{"observed_at":"2026-08-07T01:10:42.112497Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:41.774728Z","title":"Hyperbolic intersection graphs and (quasi)-polynomial time","venue":null,"work_id":"a3ef8e32-cf8e-4c0a-8ce8-eb76861358e1","year":2020},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:36.266145Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:cbe31077efadda136ba06666cfb8c14dcc294cca52496a04a1c6608eaa54abf5","observation_id":"6b4797d4-a6df-4bb3-8286-119ef8b600ea","resolution":{"observed_at":"2026-08-07T01:10:41.886180Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:41.623277Z","title":"Coloring powers of chordal graphs.SIAM Journal on Discrete Mathematics, 18(3): 451–461, 2004","venue":null,"work_id":"91671727-b71a-491c-b432-902a3e02e77b","year":2004},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:36.360573Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:7084140d9a376a4063eb9db5b95ff69c7b7089bbf1b1b09e60973b2ab5527d8c","observation_id":"c50b13b6-49d4-4d72-9670-35293f85678e","resolution":{"observed_at":"2026-08-07T01:10:41.709598Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:41.444263Z","title":"Leiserson","venue":null,"work_id":"17dd91a8-8860-41df-8504-a65d6d191ef3","year":2021},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:36.451124Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:7ea73eb3bce74a7ba07b7089a8b30ed54c1f197f638617af59f88fe9f623c8d1","observation_id":"a09c9b40-77be-4c50-a2e5-276ec1a3721d","resolution":{"observed_at":"2026-08-07T01:10:41.564765Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:41.281366Z","title":"Lee.Riemannian Manifolds: An Introduction to Curvature","venue":null,"work_id":"6fbf4ba8-eaf1-49e1-9b56-7a7adec81142","year":1997},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:36.555856Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:625a1f3b6589bae30e4f602049671ae2fb6ffdafecd24d43bd1993a055479da0","observation_id":"2c1231d6-f694-4f1c-bea7-874ffcae0c61","resolution":{"observed_at":"2026-08-07T01:10:41.383850Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:41.101842Z","title":"Lima, Martin Milanič, Peter Muršič, Karolina Okrasa, Paweł Rzążewski, and Kenny Štorgel","venue":null,"work_id":"c0652d4d-0d57-4927-a357-61d1c5905600","year":2024},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:36.660242Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:751f6e215c2bc819db9b3e6eda1fcfc9919eb7ccf965d9df31cd910545ec84a3","observation_id":"de691649-0b03-4641-b3ba-14ca7a1e7870","resolution":{"observed_at":"2026-08-07T01:10:41.166389Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:40.860945Z","title":"Bipartizing (pseudo-)disk graphs: Approximation with a ratio better than 3","venue":null,"work_id":"3e8a710d-5940-40d5-bc70-998b68f5a29b","year":2024},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:36.771944Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:46f37d6ba0c08bff53828ed16a73a781a2d3b6ced07b2550b3e3838b9c071af1","observation_id":"762aa6f5-c658-4765-96e5-bd3e7eb2e02f","resolution":{"observed_at":"2026-08-07T01:10:40.989189Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:40.616268Z","title":"On a condition for the union of spherical caps to be connected.Journal of Combinatorial Theory, Series A, 101(2):264–270, 2003","venue":null,"work_id":"eaf0ab32-bcf1-4a9c-ab78-6c976c414832","year":2003},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:36.874104Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:bc82120fa2656d7e7a23bf253da5aa3b28823cf7f981d47218e06bf06f45ceb5","observation_id":"be057abb-e866-4cc9-b298-0d5034bd4211","resolution":{"observed_at":"2026-08-07T01:10:40.746642Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:40.419441Z","title":"On the intersection graph of random caps on a sphere.European Journal of Combinatorics, 25(5):707–718, 2004","venue":null,"work_id":"f25361cb-0d2a-4e00-a452-b3be1fdad279","year":2004},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:36.959352Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:ac97b51b6c30b6a74dce9a72ced9af4e17f49f6e6d35b1d4a02ef1efe842ade0","observation_id":"d10ebabb-965f-4a20-9441-db0e1dfd31c6","resolution":{"observed_at":"2026-08-07T01:10:40.515806Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:40.182436Z","title":"Geometric probability on the sphere.Jahresbericht der Deutschen Mathematiker-Vereinigung, 119:93–132, 2017","venue":null,"work_id":"7de1fa67-27f8-42b3-8f12-36ac735ce143","year":2017},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:37.042799Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:5e9706433544a24a4eddc11fb166e32980b8efef3bfa2644bfa47fa192a2944a","observation_id":"221ef497-9887-4010-9f43-ce6439317487","resolution":{"observed_at":"2026-08-07T01:10:40.306344Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:39.998767Z","title":"Birkhäuser, 2024","venue":null,"work_id":"53064b57-0de5-4be7-ab7b-de82286047f8","year":2024},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:37.097352Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:aca4ea0b9e4d811950e9ed2b31dddca0ed8d96e306456b2e773b437ac6cc8b9c","observation_id":"a7f7c465-d81d-41a3-bbe8-f1754c29aa0a","resolution":{"observed_at":"2026-08-07T01:10:40.066422Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:39.791551Z","title":"Springer, 2012","venue":null,"work_id":"0b682e86-8e1a-4ffa-9436-b2427cc360f0","year":2012},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:37.186201Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:25db9e1cf48352668df20a0f7bad7599b8203419fb71ffd958396d42d353c314","observation_id":"595fde1c-b16b-4fab-b54d-cbc8863258b2","resolution":{"observed_at":"2026-08-07T01:10:39.866248Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:39.563605Z","title":"On coloringj-unit sphere graphs","venue":null,"work_id":"ec416adf-66ee-46ff-a75d-96a93882b7e6","year":1991},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:37.254585Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:b69f8db0ae3ae90ad2998e7483e3eecdd202133964a3c8c1854af6e3a8d181f8","observation_id":"4dc2a18f-cb01-4581-9993-d70834637d1c","resolution":{"observed_at":"2026-08-07T01:10:39.684208Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:39.347061Z","title":"A finite family of pseudodiscs must include a “small” pseudodisc.SIAM Journal on Discrete Mathematics, 28(4):1930–1934, 2014","venue":null,"work_id":"332111c1-393a-4650-a637-9cec36f7a36d","year":1930},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:37.337488Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:17162910fc0088e424809ec3b03f25199456ff3a61bb831cdc240fad7c397008","observation_id":"b7bc91b5-bb61-43e9-8192-50d1440f5836","resolution":{"observed_at":"2026-08-07T01:10:39.450606Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:39.201843Z","title":"Richtmyer.Introduction to Hyperbolic Geometry","venue":null,"work_id":"e6a824d4-e783-41f8-b765-afe516cbd7ee","year":1995},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:37.431846Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:3765ed75f21a6f7e55af9d38e23970df73aaee1d00a7aec1bd51b6f77711048e","observation_id":"6b2e43ac-6c26-4301-a653-febac0974d93","resolution":{"observed_at":"2026-08-07T01:10:39.280507Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:39.033113Z","title":null,"venue":null,"work_id":"1b3472c4-9f9b-4534-b5dc-d8747b50114e","year":2006},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:37.532427Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:6ed21e3b5ac4877ad526267e0a18459b5faeda27d4b6ae37c3e004a7ad67886a","observation_id":"f9a37ddd-cb4d-43c0-8031-10ec8ff2668f","resolution":{"observed_at":"2026-08-07T01:10:39.121938Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:38.824140Z","title":"A survey ofχ-boundedness","venue":null,"work_id":"a0458648-5dab-403a-a629-3e977414698f","year":2020},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:37.633782Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:babd14b12ba1aafec8b7c5e8916ed65618c406dec738597b7649a4268c4c4032","observation_id":"f67984db-0ae5-41b2-90b3-0ecfbbbb59cf","resolution":{"observed_at":"2026-08-07T01:10:38.927557Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-07T01:10:38.621683Z","title":"Elimination graphs","venue":null,"work_id":"7c4f2879-251b-47fa-aab1-578e827e4ebf","year":2012},"citing_paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-07T01:10:37.750537Z"},"links":{"citing_paper":"/paper/2506.12424"},"observation_digest":"sha256:4c3d60420d5657c5e2952b7a8c13b4c2ff6f90fadd89f6ecdb6d349f3e553c36","observation_id":"3881f11f-a5c5-44d2-9a22-3eb8dc460a28","resolution":{"observed_at":"2026-08-07T01:10:38.728349Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.12424","last_updated":"2025-06-14T09:50:44Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-08-13T20:44:43.801932Z","submitted_at":"2025-06-14T09:50:44Z","title":"Layered tree-independence number and clique-based separators"},"reference_resolution":{"displayed":55,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":9,"verified_exact":4,"verified_fuzzy":42},"total_outbound_references":55},"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":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"thesis":"As of 15 August 2026, this Paper Citation Record lists 55 of 55 outbound references and 0 inbound Pith citation observations for arXiv:2506.12424."}