{"as_of":"2026-08-12T10:32:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:3094113d0dcf4c3e2bcfa26ce73483221c51050a521a5e76ec61748988f22a3a","coverage":[{"denominator":8,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":8,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T20:39:43.660961Z","state":"measured"},{"denominator":10,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":10,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T18:04:31.244510Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-06T18:03:11.710103Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2507.03264","last_updated":"2025-07-04T02:48:45Z","snapshot_observed_at":"2026-08-06T20:12:07.208682Z","submitted_at":"2025-07-04T02:48:45Z","title":"Minimum degree and sparse connected spanning subgraphs","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.03264","snapshot_observed_at":"2026-08-06T18:04:31.244510Z","title":"Huang, Y","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.09827","last_updated":"2025-07-13T23:36:48Z","snapshot_observed_at":"2026-08-07T22:57:38.181844Z","submitted_at":"2025-07-13T23:36:48Z","title":"Ramsey numbers of sparse graphs versus disjoint books","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T18:04:31.244510Z"},"links":{"cited_paper":"/paper/2507.03264","citing_paper":"/paper/2507.09827"},"observation_digest":"sha256:2fee0e4303aae3b2fc9eace71220bd7727d5c07240c7fa36967b1fc2d7753237","observation_id":"ba262d83-13a5-474b-913e-9ea76ab2efc7","resolution":{"observed_at":"2026-08-06T18:04:31.244510Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2507.03264","last_updated":"2025-07-04T02:48:45Z","snapshot_observed_at":"2026-08-06T20:12:07.208682Z","submitted_at":"2025-07-04T02:48:45Z","title":"Minimum degree and sparse connected spanning subgraphs","version":1},"cited_work":{"arxiv_id":"2507.03264","doi":null,"metadata_source":"pith","pith_arxiv_id":"2507.03264","snapshot_observed_at":"2026-08-06T18:03:11.710103Z","title":"Minimum degree and sparse connected spanning subgraphs","venue":"math.CO","work_id":"030912fd-8963-4c3d-b68d-344be376b8ea","year":2025},"citing_paper":{"arxiv_id":"2507.09832","last_updated":"2025-07-13T23:59:39Z","snapshot_observed_at":"2026-08-09T10:34:06.822334Z","submitted_at":"2025-07-13T23:59:39Z","title":"Fan-goodness of sparse graphs","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T18:03:11.565162Z"},"links":{"cited_paper":"/paper/2507.03264","citing_paper":"/paper/2507.09832"},"observation_digest":"sha256:e14bf28fbf86e4815e3c8a56cbd3f559a635887efd719cbf1d497a004af51cce","observation_id":"4f7ee7af-eb8e-4532-9eae-f9a033899fe7","resolution":{"observed_at":"2026-08-06T18:03:11.714732Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2507.03264/citation-record","integrity":"/paper/2507.03264/integrity","json":"/paper/2507.03264/citation-record.json","paper":"/paper/2507.03264"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:39:44.469782Z","title":"Alon and J","venue":null,"work_id":"d4209f81-c4f4-4c7a-83da-def62b2b128c","year":2016},"citing_paper":{"arxiv_id":"2507.03264","last_updated":"2025-07-04T02:48:45Z","snapshot_observed_at":"2026-08-06T20:12:07.208682Z","submitted_at":"2025-07-04T02:48:45Z","title":"Minimum degree and sparse connected spanning subgraphs","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T20:39:42.584718Z"},"links":{"citing_paper":"/paper/2507.03264"},"observation_digest":"sha256:e76e68f637714b8dbfcd43b24d5ed4b41b5fa25d7234f37dd17c0338ca88dcf5","observation_id":"c991057d-1864-4281-8a6a-cfe3862f6c92","resolution":{"observed_at":"2026-08-06T20:39:44.568918Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T20:39:44.281336Z","title":null,"venue":null,"work_id":"7069824b-6bb7-4581-8570-f4d43835aee0","year":1974},"citing_paper":{"arxiv_id":"2507.03264","last_updated":"2025-07-04T02:48:45Z","snapshot_observed_at":"2026-08-06T20:12:07.208682Z","submitted_at":"2025-07-04T02:48:45Z","title":"Minimum degree and sparse connected spanning subgraphs","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T20:39:42.743422Z"},"links":{"citing_paper":"/paper/2507.03264"},"observation_digest":"sha256:b82b0640a717b4977c64d563f129417e2eff04df4c0e0d3f2f6dd70af489ab72","observation_id":"da3c623b-c4c8-40aa-95bb-673971acd8de","resolution":{"observed_at":"2026-08-06T20:39:44.375227Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T20:39:42.934052Z","title":null,"venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"2507.03264","last_updated":"2025-07-04T02:48:45Z","snapshot_observed_at":"2026-08-06T20:12:07.208682Z","submitted_at":"2025-07-04T02:48:45Z","title":"Minimum degree and sparse connected spanning subgraphs","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T20:39:42.934052Z"},"links":{"citing_paper":"/paper/2507.03264"},"observation_digest":"sha256:b79afa3ceb24a67895e107f711de277dbef5b785933eb7798d26d47f539e087e","observation_id":"a1ef6cfe-7986-4153-b589-36c1e3038bf9","resolution":{"observed_at":"2026-08-06T20:39:42.934052Z","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":"2026-08-06T20:39:43.078214Z","title":"Chv´ atal, Tree-complete graph Ramsey numbers, J","venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2507.03264","last_updated":"2025-07-04T02:48:45Z","snapshot_observed_at":"2026-08-06T20:12:07.208682Z","submitted_at":"2025-07-04T02:48:45Z","title":"Minimum degree and sparse connected spanning subgraphs","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T20:39:43.078214Z"},"links":{"citing_paper":"/paper/2507.03264"},"observation_digest":"sha256:8e551ee1151a1e23384ad1d2a548f4cef12610cf83f50f68a4cdca611095161b","observation_id":"a576c3cf-9e38-4887-b926-d6dbf243e8d3","resolution":{"observed_at":"2026-08-06T20:39:43.078214Z","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":"2026-08-06T20:39:43.263216Z","title":"Erd˝ os, R.J","venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"2507.03264","last_updated":"2025-07-04T02:48:45Z","snapshot_observed_at":"2026-08-06T20:12:07.208682Z","submitted_at":"2025-07-04T02:48:45Z","title":"Minimum degree and sparse connected spanning subgraphs","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T20:39:43.263216Z"},"links":{"citing_paper":"/paper/2507.03264"},"observation_digest":"sha256:6801029644ecc72202eceab66a1365f47a0e83868c4258a9edb13e134a8fd5a2","observation_id":"6a16788f-d662-4da9-a8cf-b3ea4f71ba4c","resolution":{"observed_at":"2026-08-06T20:39:43.263216Z","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":"2026-08-06T20:39:44.043918Z","title":"Faudree, C.C","venue":null,"work_id":"a2658484-3461-4eb4-a526-517d8d2c686c","year":1980},"citing_paper":{"arxiv_id":"2507.03264","last_updated":"2025-07-04T02:48:45Z","snapshot_observed_at":"2026-08-06T20:12:07.208682Z","submitted_at":"2025-07-04T02:48:45Z","title":"Minimum degree and sparse connected spanning subgraphs","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T20:39:43.391273Z"},"links":{"citing_paper":"/paper/2507.03264"},"observation_digest":"sha256:ab0bdf7c1c1e09506dc8c390a125372f2b0c0b6d3852f6c094c450c5b0821d25","observation_id":"3481d371-33fb-4b0a-801d-40e8102fecea","resolution":{"observed_at":"2026-08-06T20:39:44.136365Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T20:39:43.887023Z","title":"Hall, On representatives of subsets, J","venue":null,"work_id":"8eaad77b-8ad0-4b7e-ba02-ce80dc0c1c02","year":1935},"citing_paper":{"arxiv_id":"2507.03264","last_updated":"2025-07-04T02:48:45Z","snapshot_observed_at":"2026-08-06T20:12:07.208682Z","submitted_at":"2025-07-04T02:48:45Z","title":"Minimum degree and sparse connected spanning subgraphs","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T20:39:43.578542Z"},"links":{"citing_paper":"/paper/2507.03264"},"observation_digest":"sha256:a38db9dfc73f8df3b977d05351d0a8569c15f4fcf7afe636c2d757d74b0b46b1","observation_id":"4b3b63a8-bc7f-4324-99df-86574adb26ab","resolution":{"observed_at":"2026-08-06T20:39:43.960654Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T20:39:43.660961Z","title":"Zhang and Y","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.03264","last_updated":"2025-07-04T02:48:45Z","snapshot_observed_at":"2026-08-06T20:12:07.208682Z","submitted_at":"2025-07-04T02:48:45Z","title":"Minimum degree and sparse connected spanning subgraphs","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T20:39:43.660961Z"},"links":{"citing_paper":"/paper/2507.03264"},"observation_digest":"sha256:1332dd20e462afe1c2de31f45365d6e4deb9aeb759fa715af0a78d808e6b57e0","observation_id":"85b5f714-beb8-4add-9ae9-711fe9c3a14b","resolution":{"observed_at":"2026-08-06T20:39:43.660961Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2507.03264","last_updated":"2025-07-04T02:48:45Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-08-06T20:12:07.208682Z","submitted_at":"2025-07-04T02:48:45Z","title":"Minimum degree and sparse connected spanning subgraphs"},"reference_resolution":{"displayed":8,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":5,"verified_exact":0,"verified_fuzzy":3},"total_outbound_references":8},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 8 of 8 outbound references and 2 inbound Pith citation observations for arXiv:2507.03264."}