{"as_of":"2026-08-11T13:47:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:5e4aeaf4c561d967a05f0d3fefb895c0c0c42b6898203d17e5207e52b50ccb1a","coverage":[{"denominator":23,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":23,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-08T05:05:50.605660Z","state":"measured"},{"denominator":25,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":25,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+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":"2026-07-13T02:48:08.655303Z","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":"2026-05-11T13:16:04.100264Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2502.08476","last_updated":"2025-02-12T15:10:18Z","snapshot_observed_at":"2026-08-08T04:54:10.365472Z","submitted_at":"2025-02-12T15:10:18Z","title":"Low rank MSO","version":1},"cited_work":{"arxiv_id":"2502.08476","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2502.08476","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Low rank MSO.CoRR, abs/2502.08476","venue":null,"work_id":"0f64e4fd-2d38-49d6-91a3-97214fc16f68","year":2025},"citing_paper":{"arxiv_id":"2604.19138","last_updated":"2026-04-21T06:40:44Z","snapshot_observed_at":"2026-07-06T23:05:48.885141Z","submitted_at":"2026-04-21T06:40:44Z","title":"Moderately beyond clique-width: reduced component max-leaf and related parameters","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-05-10T02:09:57.456434Z"},"links":{"cited_paper":"/paper/2502.08476","citing_paper":"/paper/2604.19138"},"observation_digest":"sha256:5b211e5a8741a648d3724ff1cb6a388e441d537327e8fa713948548e648b183b","observation_id":"0c9823cc-7bc1-4f23-a93b-429d32e46c6d","resolution":{"observed_at":"2026-05-11T13:16:04.106952Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2502.08476","last_updated":"2025-02-12T15:10:18Z","snapshot_observed_at":"2026-08-08T04:54:10.365472Z","submitted_at":"2025-02-12T15:10:18Z","title":"Low rank MSO","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.08476","snapshot_observed_at":"2026-07-13T02:48:08.655303Z","title":"Low rank","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09469","last_updated":"2026-07-10T14:42:55Z","snapshot_observed_at":"2026-08-11T07:42:47.707590Z","submitted_at":"2026-07-10T14:42:55Z","title":"A combinatorial framework for clustering graph states: Algorithms and hardness for rank-integrity","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-07-13T02:48:08.655303Z"},"links":{"cited_paper":"/paper/2502.08476","citing_paper":"/paper/2607.09469"},"observation_digest":"sha256:3775c3b0b0eec3036b4c1ff28725c2e44149243c13b038871c966c218f2992c9","observation_id":"70849e77-998d-4fdc-900b-2f9a4f795365","resolution":{"observed_at":"2026-07-13T02:48:08.655303Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2502.08476/citation-record","integrity":"/paper/2502.08476/integrity","json":"/paper/2502.08476/citation-record.json","paper":"/paper/2502.08476"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2107.13953","last_updated":"2021-09-02T11:53:26Z","snapshot_observed_at":"2026-07-06T11:33:39.654146Z","submitted_at":"2021-07-29T13:28:46Z","title":"Separator logic and star-free expressions for graphs","version":2},"cited_work":{"arxiv_id":"2107.13953","doi":null,"metadata_source":"pith","pith_arxiv_id":"2107.13953","snapshot_observed_at":"2026-08-08T05:05:50.681614Z","title":"Separator logic and star-free expressions for graphs","venue":"cs.LO","work_id":"4bf88045-e466-4111-9c15-ad478c823614","year":2021},"citing_paper":{"arxiv_id":"2502.08476","last_updated":"2025-02-12T15:10:18Z","snapshot_observed_at":"2026-08-08T04:54:10.365472Z","submitted_at":"2025-02-12T15:10:18Z","title":"Low rank MSO","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-08T05:05:50.497397Z"},"links":{"cited_paper":"/paper/2107.13953","citing_paper":"/paper/2502.08476"},"observation_digest":"sha256:a576870511d21c54075ab408d7bc7f89edb4514b058a915122e1519cbc76c6b9","observation_id":"9a562eed-13b8-45e0-bfdd-487567f8e019","resolution":{"observed_at":"2026-08-08T05:05:50.686443Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-08T05:05:50.980868Z","title":"Model checking on interpretations of classes of bounded local cliquewidth","venue":null,"work_id":"e5c324e7-1a27-4093-97e3-91076438cd1f","year":2022},"citing_paper":{"arxiv_id":"2502.08476","last_updated":"2025-02-12T15:10:18Z","snapshot_observed_at":"2026-08-08T04:54:10.365472Z","submitted_at":"2025-02-12T15:10:18Z","title":"Low rank MSO","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-08T05:05:50.502689Z"},"links":{"citing_paper":"/paper/2502.08476"},"observation_digest":"sha256:a8d1fce1ad20f234a2cebd37e22e6327cd0a07ea7f549047ed9d43b4cf754493","observation_id":"eccd0cb9-ed44-4480-ad79-04b1f93dc156","resolution":{"observed_at":"2026-08-08T05:05:50.985372Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-08T05:05:50.966236Z","title":"The monadic second-order logic of graphs","venue":null,"work_id":"e1b08011-b47e-47bf-9bcd-25e98147913a","year":1990},"citing_paper":{"arxiv_id":"2502.08476","last_updated":"2025-02-12T15:10:18Z","snapshot_observed_at":"2026-08-08T04:54:10.365472Z","submitted_at":"2025-02-12T15:10:18Z","title":"Low rank MSO","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-08T05:05:50.508017Z"},"links":{"citing_paper":"/paper/2502.08476"},"observation_digest":"sha256:ade6ca364f60c7beaf382e94d4227aca517d76d16c295d24bb26904b574e4c01","observation_id":"d16cd3c4-aa11-49dd-b744-cd0ac4ad28b6","resolution":{"observed_at":"2026-08-08T05:05:50.970667Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-08T05:05:50.950973Z","title":"Makowsky, and Udi Rotics","venue":null,"work_id":"8c6fd256-2f91-4c02-8586-7e195982d96e","year":2000},"citing_paper":{"arxiv_id":"2502.08476","last_updated":"2025-02-12T15:10:18Z","snapshot_observed_at":"2026-08-08T04:54:10.365472Z","submitted_at":"2025-02-12T15:10:18Z","title":"Low rank MSO","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-08T05:05:50.512981Z"},"links":{"citing_paper":"/paper/2502.08476"},"observation_digest":"sha256:0440347ad719e6c141b0e9e78c34eab58c517d2d582ed1aef9f4f6d80574bb09","observation_id":"545ef41c-89fa-42de-a040-afbe1541eb2e","resolution":{"observed_at":"2026-08-08T05:05:50.955717Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-08T05:05:50.935421Z","title":"First-Order model checking on monadically stable graph classes","venue":null,"work_id":"801cd98d-41ac-4c42-80f9-9f5edc06e16a","year":2024},"citing_paper":{"arxiv_id":"2502.08476","last_updated":"2025-02-12T15:10:18Z","snapshot_observed_at":"2026-08-08T04:54:10.365472Z","submitted_at":"2025-02-12T15:10:18Z","title":"Low rank MSO","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-08T05:05:50.518271Z"},"links":{"citing_paper":"/paper/2502.08476"},"observation_digest":"sha256:0245f38c29341cd3b5a49d50c662efe1dc601c0b0ba4b9dc4b39e862a5996e58","observation_id":"4d72f524-0792-4ab0-ba72-1aa40c9ffb62","resolution":{"observed_at":"2026-08-08T05:05:50.939891Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-08T05:05:50.920542Z","title":"Indiscernibles and flatness in monadically stable and monadically NIP classes","venue":null,"work_id":"c90d124a-c3f7-4458-b7fc-e9587919e942","year":2023},"citing_paper":{"arxiv_id":"2502.08476","last_updated":"2025-02-12T15:10:18Z","snapshot_observed_at":"2026-08-08T04:54:10.365472Z","submitted_at":"2025-02-12T15:10:18Z","title":"Low rank MSO","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-08T05:05:50.523511Z"},"links":{"citing_paper":"/paper/2502.08476"},"observation_digest":"sha256:8304719433db5dd6e288c16ac2cc78c4b8633d52a78d6877f27c1ad83036c925","observation_id":"2329b22b-c82a-400a-8489-aa80b9f250f8","resolution":{"observed_at":"2026-08-08T05:05:50.925584Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-08T05:05:50.905980Z","title":"Flip-breakability: A combinatorial dichotomy for monadically dependent graph classes","venue":null,"work_id":"1f9dcd8c-2d03-4c55-a057-6a5880835683","year":2024},"citing_paper":{"arxiv_id":"2502.08476","last_updated":"2025-02-12T15:10:18Z","snapshot_observed_at":"2026-08-08T04:54:10.365472Z","submitted_at":"2025-02-12T15:10:18Z","title":"Low rank MSO","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-08T05:05:50.529216Z"},"links":{"citing_paper":"/paper/2502.08476"},"observation_digest":"sha256:4979f402fd8eb52e616b46658a3b41a2b4957be0a30ce5295015dfa91f761950","observation_id":"3a5b5772-af84-401f-994a-1861c00dc657","resolution":{"observed_at":"2026-08-08T05:05:50.910409Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-08T05:05:50.891204Z","title":"Flipper games for monad- ically stable graph classes","venue":null,"work_id":"a5d7827e-ab8b-4e54-92f2-a71a42a36d6d","year":2023},"citing_paper":{"arxiv_id":"2502.08476","last_updated":"2025-02-12T15:10:18Z","snapshot_observed_at":"2026-08-08T04:54:10.365472Z","submitted_at":"2025-02-12T15:10:18Z","title":"Low rank MSO","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-08T05:05:50.534032Z"},"links":{"citing_paper":"/paper/2502.08476"},"observation_digest":"sha256:1ffbe64011bc89e454007e5196c90bcb4a3211649a9f0d5ba9138a9a982bdf06","observation_id":"53f13384-0c9c-44cb-b3ba-46ce7e6b829f","resolution":{"observed_at":"2026-08-08T05:05:50.896029Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2204.13742","last_updated":"2022-06-28T18:47:31Z","snapshot_observed_at":"2026-07-06T13:04:53.433479Z","submitted_at":"2022-04-28T19:00:12Z","title":"Twin-width and Limits of Tractability of FO Model Checking on Geometric Graphs","version":2},"cited_work":{"arxiv_id":"2204.13742","doi":null,"metadata_source":"pith","pith_arxiv_id":"2204.13742","snapshot_observed_at":"2026-08-08T05:05:50.658595Z","title":"Twin-width and Limits of Tractability of FO Model Checking on Geometric Graphs","venue":"cs.DM","work_id":"08558ec5-3046-4cce-9b86-e5b12f497731","year":2022},"citing_paper":{"arxiv_id":"2502.08476","last_updated":"2025-02-12T15:10:18Z","snapshot_observed_at":"2026-08-08T04:54:10.365472Z","submitted_at":"2025-02-12T15:10:18Z","title":"Low rank MSO","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-08T05:05:50.538922Z"},"links":{"cited_paper":"/paper/2204.13742","citing_paper":"/paper/2502.08476"},"observation_digest":"sha256:0c8b3b76471b120f71c1e95f4f20c7b0d458112f39b4471b6fada2ae29a0064f","observation_id":"f715cabe-1197-4397-aff8-4f92ed065018","resolution":{"observed_at":"2026-08-08T05:05:50.664979Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-08T05:05:50.875562Z","title":"Nondeterministic space is closed under complementation","venue":null,"work_id":"74b5fd30-d793-4f20-bf12-0edc36fe2acb","year":1988},"citing_paper":{"arxiv_id":"2502.08476","last_updated":"2025-02-12T15:10:18Z","snapshot_observed_at":"2026-08-08T04:54:10.365472Z","submitted_at":"2025-02-12T15:10:18Z","title":"Low rank MSO","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-08T05:05:50.544244Z"},"links":{"citing_paper":"/paper/2502.08476"},"observation_digest":"sha256:0e146ea7da9bf17751afce97600016cecf5ac519a477d84d7063dfaa3682cec7","observation_id":"549161cf-7b78-4255-9db7-311c1c0adc5d","resolution":{"observed_at":"2026-08-08T05:05:50.880460Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-08T05:05:50.549027Z","title":"Vertex-minors of graphs: A survey","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2502.08476","last_updated":"2025-02-12T15:10:18Z","snapshot_observed_at":"2026-08-08T04:54:10.365472Z","submitted_at":"2025-02-12T15:10:18Z","title":"Low rank MSO","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-08T05:05:50.549027Z"},"links":{"citing_paper":"/paper/2502.08476"},"observation_digest":"sha256:a23e580874019cacfccecacae5406b5a256c06a986cf6a217a44a049173150d4","observation_id":"abc2042d-ba02-4f8c-8613-b81d5cf816be","resolution":{"observed_at":"2026-08-08T05:05:50.549027Z","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":"2026-08-08T05:05:50.847866Z","title":"Local structure for vertex-minors","venue":null,"work_id":"e40dfc61-c94d-446f-a399-8323de5cb5c8","year":2021},"citing_paper":{"arxiv_id":"2502.08476","last_updated":"2025-02-12T15:10:18Z","snapshot_observed_at":"2026-08-08T04:54:10.365472Z","submitted_at":"2025-02-12T15:10:18Z","title":"Low rank MSO","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-08T05:05:50.553631Z"},"links":{"citing_paper":"/paper/2502.08476"},"observation_digest":"sha256:256ed73f41c285bead9efd3324c1b0bb3397dad24c0d761d605738b2ce9e654e","observation_id":"5969e951-33f2-490a-82e6-bc9eb9f4865b","resolution":{"observed_at":"2026-08-08T05:05:50.853178Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-08T05:05:50.832596Z","title":"Counter-free automata","venue":null,"work_id":"9284349a-24f0-48a6-b93d-3690680534fb","year":1971},"citing_paper":{"arxiv_id":"2502.08476","last_updated":"2025-02-12T15:10:18Z","snapshot_observed_at":"2026-08-08T04:54:10.365472Z","submitted_at":"2025-02-12T15:10:18Z","title":"Low rank MSO","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-08T05:05:50.558485Z"},"links":{"citing_paper":"/paper/2502.08476"},"observation_digest":"sha256:3a5cead9767dc3a7386971e37e6faefc3e20194dbb9c446334cc631cfcfffe51","observation_id":"1632dd9b-14eb-406e-aade-fc7be45ebf27","resolution":{"observed_at":"2026-08-08T05:05:50.837188Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-08T05:05:50.818182Z","title":"Rank-width and vertex-minors","venue":null,"work_id":"7fd758e3-4e0a-48b6-89e2-1a4a83e623f2","year":2005},"citing_paper":{"arxiv_id":"2502.08476","last_updated":"2025-02-12T15:10:18Z","snapshot_observed_at":"2026-08-08T04:54:10.365472Z","submitted_at":"2025-02-12T15:10:18Z","title":"Low rank MSO","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-08T05:05:50.563307Z"},"links":{"citing_paper":"/paper/2502.08476"},"observation_digest":"sha256:c59e259dabdda8b29600d13108686e2a5ac91c290508ce8a9c435828f9fecbac","observation_id":"711e6066-ed22-4473-9cd5-34c68ca77e9a","resolution":{"observed_at":"2026-08-08T05:05:50.822659Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-08T05:05:50.803447Z","title":null,"venue":null,"work_id":"d1d34567-ba9b-464c-b9ef-4b4a062eb306","year":2006},"citing_paper":{"arxiv_id":"2502.08476","last_updated":"2025-02-12T15:10:18Z","snapshot_observed_at":"2026-08-08T04:54:10.365472Z","submitted_at":"2025-02-12T15:10:18Z","title":"Low rank MSO","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-08T05:05:50.567898Z"},"links":{"citing_paper":"/paper/2502.08476"},"observation_digest":"sha256:88fa2dee0cf46cf2dc781464058d605985e955b94d55f22da1c5b8b55ff10ffc","observation_id":"de4c2c3a-a479-4278-bea1-5bee64ccd2f6","resolution":{"observed_at":"2026-08-08T05:05:50.808268Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2501.04166","last_updated":"2025-01-07T22:27:31Z","snapshot_observed_at":"2026-08-10T21:37:39.742442Z","submitted_at":"2025-01-07T22:27:31Z","title":"Graph classes through the lens of logic","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.04166","snapshot_observed_at":"2026-08-08T05:05:50.572721Z","title":"Graph classes through the lens of logic","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2502.08476","last_updated":"2025-02-12T15:10:18Z","snapshot_observed_at":"2026-08-08T04:54:10.365472Z","submitted_at":"2025-02-12T15:10:18Z","title":"Low rank MSO","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-08T05:05:50.572721Z"},"links":{"cited_paper":"/paper/2501.04166","citing_paper":"/paper/2502.08476"},"observation_digest":"sha256:e82358f8e3bafdd61e9cf38d710570eb2924eb8a7fc644cf955342bfc37782ca","observation_id":"271c5950-e8b8-4b88-bcc3-99bf4ab5a1a3","resolution":{"observed_at":"2026-08-08T05:05:50.572721Z","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":"2026-08-08T05:05:50.788382Z","title":"Algorithms and data structures for first-order logic with connectivity under vertex failures","venue":null,"work_id":"61906d1c-457f-4c3e-b852-7b19c66639d7","year":2022},"citing_paper":{"arxiv_id":"2502.08476","last_updated":"2025-02-12T15:10:18Z","snapshot_observed_at":"2026-08-08T04:54:10.365472Z","submitted_at":"2025-02-12T15:10:18Z","title":"Low rank MSO","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-08T05:05:50.577990Z"},"links":{"citing_paper":"/paper/2502.08476"},"observation_digest":"sha256:56ad77ae693e71d34dc362b3505d645f23d6b18e88b5b60a6d6c1fc2246eb9bb","observation_id":"ba9867c7-8ff6-430c-bffe-cb03be1316d3","resolution":{"observed_at":"2026-08-08T05:05:50.793203Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-08T05:05:50.773426Z","title":"Undirected connectivity in log-space","venue":null,"work_id":"98d247b7-7cdd-4d73-9ced-c2d21dd44abc","year":2008},"citing_paper":{"arxiv_id":"2502.08476","last_updated":"2025-02-12T15:10:18Z","snapshot_observed_at":"2026-08-08T04:54:10.365472Z","submitted_at":"2025-02-12T15:10:18Z","title":"Low rank MSO","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-08T05:05:50.582622Z"},"links":{"citing_paper":"/paper/2502.08476"},"observation_digest":"sha256:117d5f49d666ea13becd8cccc660a3fa1c0c4e54e9df7175c097ebf943e45e0d","observation_id":"b076f7fa-ea41-4740-a79e-86d8fc648d33","resolution":{"observed_at":"2026-08-08T05:05:50.778034Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-08T05:05:50.757383Z","title":"Flip-width: Cops and Robber on dense graphs","venue":null,"work_id":"949e7cd2-b6c6-4fb2-b408-debbab917956","year":2023},"citing_paper":{"arxiv_id":"2502.08476","last_updated":"2025-02-12T15:10:18Z","snapshot_observed_at":"2026-08-08T04:54:10.365472Z","submitted_at":"2025-02-12T15:10:18Z","title":"Low rank MSO","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-08T05:05:50.587220Z"},"links":{"citing_paper":"/paper/2502.08476"},"observation_digest":"sha256:4dff32280b1e8e9bf9382d5cff321c52c2f1e15e2bd953a0c10a1c7eee3c5251","observation_id":"22d9851e-8f26-41af-9582-8d91ab2318aa","resolution":{"observed_at":"2026-08-08T05:05:50.762272Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-08T05:05:50.741422Z","title":"First-order logic with connectivity operators","venue":null,"work_id":"efc29d72-545b-49e8-b14b-99e6120ff8b5","year":2023},"citing_paper":{"arxiv_id":"2502.08476","last_updated":"2025-02-12T15:10:18Z","snapshot_observed_at":"2026-08-08T04:54:10.365472Z","submitted_at":"2025-02-12T15:10:18Z","title":"Low rank MSO","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-08T05:05:50.591910Z"},"links":{"citing_paper":"/paper/2502.08476"},"observation_digest":"sha256:5d874a1927872fe33e7b82cf06f261826cb8624dd6dcab32431211e7b11a63d2","observation_id":"3b4d723d-380d-4115-8e9e-dcf0ed9409a5","resolution":{"observed_at":"2026-08-08T05:05:50.746456Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-08T05:05:50.726555Z","title":"On finite monoids having only trivial subgroups","venue":null,"work_id":"98b46848-daad-4a81-8aa9-80a512515b57","year":1965},"citing_paper":{"arxiv_id":"2502.08476","last_updated":"2025-02-12T15:10:18Z","snapshot_observed_at":"2026-08-08T04:54:10.365472Z","submitted_at":"2025-02-12T15:10:18Z","title":"Low rank MSO","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-08T05:05:50.597099Z"},"links":{"citing_paper":"/paper/2502.08476"},"observation_digest":"sha256:7d9c4ffb4e3d1652a8e09d4d887e05ab5af6cccd5da541a60f19e220be425570","observation_id":"ff86faf5-df3d-450a-907b-31d8fb5cacb0","resolution":{"observed_at":"2026-08-08T05:05:50.731168Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-08T05:05:50.712060Z","title":"The method of forced enumeration for nondeterministic automata","venue":null,"work_id":"1bdacc12-9636-4b2e-91eb-cb2f385e38c7","year":1988},"citing_paper":{"arxiv_id":"2502.08476","last_updated":"2025-02-12T15:10:18Z","snapshot_observed_at":"2026-08-08T04:54:10.365472Z","submitted_at":"2025-02-12T15:10:18Z","title":"Low rank MSO","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-08T05:05:50.601622Z"},"links":{"citing_paper":"/paper/2502.08476"},"observation_digest":"sha256:b5ebb2d1b4ea7f8fc2339cc78eacd3801c39839ef540755d40b3b72100af0fe7","observation_id":"a59595c1-01a3-4ed3-a533-03445ef65ee7","resolution":{"observed_at":"2026-08-08T05:05:50.716523Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-08T05:05:50.697199Z","title":"k-NLC graphs and polynomial algorithms","venue":null,"work_id":"3d0ead95-39c2-4368-93b6-2e4115da2717","year":1994},"citing_paper":{"arxiv_id":"2502.08476","last_updated":"2025-02-12T15:10:18Z","snapshot_observed_at":"2026-08-08T04:54:10.365472Z","submitted_at":"2025-02-12T15:10:18Z","title":"Low rank MSO","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-08T05:05:50.605660Z"},"links":{"citing_paper":"/paper/2502.08476"},"observation_digest":"sha256:ffcc4bcca0db991bb3cdbbe5a553e0094b5cbe2883ef15642f7d32a4affbd89a","observation_id":"b99bad40-09ed-4a17-be30-3183ae0d2ed7","resolution":{"observed_at":"2026-08-08T05:05:50.701568Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2502.08476","last_updated":"2025-02-12T15:10:18Z","latest_version":1,"primary_category":"cs.LO","snapshot_observed_at":"2026-08-08T04:54:10.365472Z","submitted_at":"2025-02-12T15:10:18Z","title":"Low rank MSO"},"reference_resolution":{"displayed":23,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":3,"verified_exact":2,"verified_fuzzy":18},"total_outbound_references":23},"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":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 2 inbound Pith citation observations for arXiv:2502.08476."}