{"as_of":"2026-08-08T14:39:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:818e86eda3ccff840bf20897c4b5621d98d867ba2b6f03ae1847af28a6f9f889","coverage":[{"denominator":16,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":16,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T15:22:48.661739Z","state":"measured"},{"denominator":17,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":17,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T05:24:42.655973Z","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":"2026-08-07T06:16:28.064256Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2505.15655","last_updated":"2025-05-21T15:31:33Z","snapshot_observed_at":"2026-08-07T15:10:57.715180Z","submitted_at":"2025-05-21T15:31:33Z","title":"First-order transducibility among classes of sparse graphs","version":1},"cited_work":{"arxiv_id":"2505.15655","doi":"10.48550/arxiv.2505.15655","metadata_source":"pith","pith_arxiv_id":"2505.15655","snapshot_observed_at":"2026-08-07T06:16:28.064256Z","title":"First-order transducibility among classes of sparse graphs","venue":"cs.LO","work_id":"9760e39b-854b-4736-b5d6-372f8d8a81a7","year":2025},"citing_paper":{"arxiv_id":"2506.08585","last_updated":"2026-06-29T16:44:21Z","snapshot_observed_at":"2026-08-07T05:04:30.792265Z","submitted_at":"2025-06-10T08:54:08Z","title":"k-Planar and Fan-Crossing Drawings and Transductions of Embeddable Graphs","version":4},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T05:24:42.655973Z"},"links":{"cited_paper":"/paper/2505.15655","citing_paper":"/paper/2506.08585"},"observation_digest":"sha256:c0ab7e303a2439faa664d54e1b3b29395050c43392267ca8bb27014e2142474b","observation_id":"551569f1-1878-42d2-bf3b-9c549d617d57","resolution":{"observed_at":"2026-08-07T05:24:42.855928Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2505.15655/citation-record","integrity":"/paper/2505.15655/integrity","json":"/paper/2505.15655/citation-record.json","paper":"/paper/2505.15655"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:22:50.889322Z","title":"Twin-width I: Tractable FO model checking","venue":null,"work_id":"383f2fb4-11dd-41d6-8dd4-33f2ae5fc6d4","year":2022},"citing_paper":{"arxiv_id":"2505.15655","last_updated":"2025-05-21T15:31:33Z","snapshot_observed_at":"2026-08-07T15:10:57.715180Z","submitted_at":"2025-05-21T15:31:33Z","title":"First-order transducibility among classes of sparse graphs","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T15:22:47.394757Z"},"links":{"citing_paper":"/paper/2505.15655"},"observation_digest":"sha256:68b408f405cbdd8e483eae792a3b98a1372b830339017c2acd28f5d91148377e","observation_id":"f0dc35fd-11c3-47e6-8b5a-048e53da58cf","resolution":{"observed_at":"2026-08-07T15:22:50.959279Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2208.14412","last_updated":"2025-06-19T16:21:22Z","snapshot_observed_at":"2026-08-07T23:16:01.914504Z","submitted_at":"2022-08-30T17:26:34Z","title":"On first-order transductions of classes of graphs","version":8},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2208.14412","snapshot_observed_at":"2026-08-07T15:22:47.444099Z","title":"On first-order transductions of classes of graphs","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2505.15655","last_updated":"2025-05-21T15:31:33Z","snapshot_observed_at":"2026-08-07T15:10:57.715180Z","submitted_at":"2025-05-21T15:31:33Z","title":"First-order transducibility among classes of sparse graphs","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T15:22:47.444099Z"},"links":{"cited_paper":"/paper/2208.14412","citing_paper":"/paper/2505.15655"},"observation_digest":"sha256:a0fdfb41df5a111ddd729a10e05af268ce4a79836cac9d01b7f3853b296ba887","observation_id":"a7c22829-3380-4e30-adea-02ffd8165b9e","resolution":{"observed_at":"2026-08-07T15:22:47.444099Z","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":"2026-08-07T15:22:50.718088Z","title":"Lacon-, shrub- and parity-decompositions: Characterizing transductions of bounded ex- pansion classes","venue":null,"work_id":"bca5c3e0-8735-4106-892c-226b6e0c1ee5","year":2023},"citing_paper":{"arxiv_id":"2505.15655","last_updated":"2025-05-21T15:31:33Z","snapshot_observed_at":"2026-08-07T15:10:57.715180Z","submitted_at":"2025-05-21T15:31:33Z","title":"First-order transducibility among classes of sparse graphs","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T15:22:47.532221Z"},"links":{"citing_paper":"/paper/2505.15655"},"observation_digest":"sha256:edb7218858673cdaa597d25469eea513c8bfc01fe94e5df16f678dc9c40b3e72","observation_id":"4863c138-fc33-43e6-ae78-37c422438049","resolution":{"observed_at":"2026-08-07T15:22:50.797326Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:22:50.523068Z","title":null,"venue":null,"work_id":"71e4c821-6955-4f90-93e8-8a57ab2ff585","year":2020},"citing_paper":{"arxiv_id":"2505.15655","last_updated":"2025-05-21T15:31:33Z","snapshot_observed_at":"2026-08-07T15:10:57.715180Z","submitted_at":"2025-05-21T15:31:33Z","title":"First-order transducibility among classes of sparse graphs","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T15:22:47.582840Z"},"links":{"citing_paper":"/paper/2505.15655"},"observation_digest":"sha256:6a1effba0266005828e0297f99fe5a9c5d5d82bdf560313ba3437acc0d54b5d9","observation_id":"ff1406ea-7def-4d5e-8516-5fff5677a6d2","resolution":{"observed_at":"2026-08-07T15:22:50.596030Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:22:50.356533Z","title":"First-order interpretations of bounded expansion classes","venue":null,"work_id":"29e57b8e-2a10-4ad9-a862-5269a12a792c","year":2020},"citing_paper":{"arxiv_id":"2505.15655","last_updated":"2025-05-21T15:31:33Z","snapshot_observed_at":"2026-08-07T15:10:57.715180Z","submitted_at":"2025-05-21T15:31:33Z","title":"First-order transducibility among classes of sparse graphs","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T15:22:47.691399Z"},"links":{"citing_paper":"/paper/2505.15655"},"observation_digest":"sha256:9173e4d94aec028228d715f440ffcfa6873712f6ba6d3fa4b0d4589824ee3d40","observation_id":"29bc4032-4e1b-4ec2-895e-a4fe6067db0b","resolution":{"observed_at":"2026-08-07T15:22:50.460923Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2501.07558","last_updated":"2025-01-13T18:42:09Z","snapshot_observed_at":"2026-07-06T20:20:28.171470Z","submitted_at":"2025-01-13T18:42:09Z","title":"3D-grids are not transducible from planar graphs","version":1},"cited_work":{"arxiv_id":"2501.07558","doi":null,"metadata_source":"pith","pith_arxiv_id":"2501.07558","snapshot_observed_at":"2026-08-07T15:22:48.918222Z","title":"3D-grids are not transducible from planar graphs","venue":"cs.LO","work_id":"e9a9f4f0-a85d-48ac-a705-346bae73a07e","year":2025},"citing_paper":{"arxiv_id":"2505.15655","last_updated":"2025-05-21T15:31:33Z","snapshot_observed_at":"2026-08-07T15:10:57.715180Z","submitted_at":"2025-05-21T15:31:33Z","title":"First-order transducibility among classes of sparse graphs","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T15:22:47.696696Z"},"links":{"cited_paper":"/paper/2501.07558","citing_paper":"/paper/2505.15655"},"observation_digest":"sha256:fb5c8c29dceda69d24bc1d769a0e595eef659fdaeda2ed1a10d646f6b2d09e9b","observation_id":"d5af29f3-d32c-4d55-917d-1604550bcd74","resolution":{"observed_at":"2026-08-07T15:22:49.010156Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:22:50.152475Z","title":"Shrub- depth: Capturing height of dense graphs","venue":null,"work_id":"3dbb7986-75d1-423d-b102-5f6b673f00a3","year":2019},"citing_paper":{"arxiv_id":"2505.15655","last_updated":"2025-05-21T15:31:33Z","snapshot_observed_at":"2026-08-07T15:10:57.715180Z","submitted_at":"2025-05-21T15:31:33Z","title":"First-order transducibility among classes of sparse graphs","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T15:22:47.702996Z"},"links":{"citing_paper":"/paper/2505.15655"},"observation_digest":"sha256:16cd81b13c6eb890fcaffa0a28a57d8d0eca6d9dfb815625898fed9ea60418d5","observation_id":"dec2a590-eea5-44bc-82cf-a6e9e870fc0e","resolution":{"observed_at":"2026-08-07T15:22:50.281586Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:22:49.960548Z","title":"Stavropoulos","venue":null,"work_id":"98fe2f76-1e93-4374-8ac7-b963fe937b98","year":2018},"citing_paper":{"arxiv_id":"2505.15655","last_updated":"2025-05-21T15:31:33Z","snapshot_observed_at":"2026-08-07T15:10:57.715180Z","submitted_at":"2025-05-21T15:31:33Z","title":"First-order transducibility among classes of sparse graphs","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T15:22:47.765588Z"},"links":{"citing_paper":"/paper/2505.15655"},"observation_digest":"sha256:09ed6be04a6352b8d563a41f4d92cc0401a7bf2339a68e05e659f5d29b7eb91f","observation_id":"bc9f4fcc-440f-4a20-9507-e95a542cf955","resolution":{"observed_at":"2026-08-07T15:22:50.030316Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2501.18326","last_updated":"2025-06-11T14:15:00Z","snapshot_observed_at":"2026-07-06T20:28:24.203633Z","submitted_at":"2025-01-30T13:13:28Z","title":"Transductions of Graph Classes Admitting Product Structure","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.18326","snapshot_observed_at":"2026-08-07T15:22:47.919103Z","title":"Transductions of graph classes admitting product structure","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.15655","last_updated":"2025-05-21T15:31:33Z","snapshot_observed_at":"2026-08-07T15:10:57.715180Z","submitted_at":"2025-05-21T15:31:33Z","title":"First-order transducibility among classes of sparse graphs","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T15:22:47.919103Z"},"links":{"cited_paper":"/paper/2501.18326","citing_paper":"/paper/2505.15655"},"observation_digest":"sha256:75517390d2c030e8f55538b5f1b1c836b264dd7efcc2fff57d46640d2bd343b6","observation_id":"3d768e71-7b3c-42cc-b4fc-727c1952a4c0","resolution":{"observed_at":"2026-08-07T15:22:47.919103Z","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":"2026-08-07T15:22:49.793016Z","title":"Sparsity — Graphs, Structures, and Algorithms , vol- ume 28 of Algorithms and combinatorics","venue":null,"work_id":"493d015d-ca4c-48fc-b6ae-46849c701a68","year":2012},"citing_paper":{"arxiv_id":"2505.15655","last_updated":"2025-05-21T15:31:33Z","snapshot_observed_at":"2026-08-07T15:10:57.715180Z","submitted_at":"2025-05-21T15:31:33Z","title":"First-order transducibility among classes of sparse graphs","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T15:22:48.066518Z"},"links":{"citing_paper":"/paper/2505.15655"},"observation_digest":"sha256:8508feb6c6c6107bc3e43a363ea4123d97ba1a72616ba2271d9f315a11d063d5","observation_id":"124ff1a0-9556-4cae-9f4f-c618b2c9f12c","resolution":{"observed_at":"2026-08-07T15:22:49.889105Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:22:49.532064Z","title":"Sparsity","venue":null,"work_id":"b36263a2-9bec-4ea7-b5cf-b148ea7e632a","year":2017},"citing_paper":{"arxiv_id":"2505.15655","last_updated":"2025-05-21T15:31:33Z","snapshot_observed_at":"2026-08-07T15:10:57.715180Z","submitted_at":"2025-05-21T15:31:33Z","title":"First-order transducibility among classes of sparse graphs","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T15:22:48.197026Z"},"links":{"citing_paper":"/paper/2505.15655"},"observation_digest":"sha256:d1d535d18aaffe1530db598a8a3f8ddb49a574ae5a2684410f0d2044bc1d8661","observation_id":"c6bf9153-b305-421b-ad4c-0364f9c1165f","resolution":{"observed_at":"2026-08-07T15:22:49.655770Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:22:49.301880Z","title":"On the number of types in sparse graphs","venue":null,"work_id":"565cbf3b-3cc8-43e3-8d79-1b204f788769","year":2018},"citing_paper":{"arxiv_id":"2505.15655","last_updated":"2025-05-21T15:31:33Z","snapshot_observed_at":"2026-08-07T15:10:57.715180Z","submitted_at":"2025-05-21T15:31:33Z","title":"First-order transducibility among classes of sparse graphs","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T15:22:48.273101Z"},"links":{"citing_paper":"/paper/2505.15655"},"observation_digest":"sha256:97a9eb97d4514ff71b32e23c275769b3e73065ff0a321076a621fcec9e5e9d42","observation_id":"5a846041-7052-4f33-9eb6-78ffb634455d","resolution":{"observed_at":"2026-08-07T15:22:49.431735Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2501.04166","last_updated":"2025-01-07T22:27:31Z","snapshot_observed_at":"2026-08-07T07:39:32.603815Z","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":"2026-08-07T15:22:48.350737Z","title":"Graph classes through the lens of logic","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.15655","last_updated":"2025-05-21T15:31:33Z","snapshot_observed_at":"2026-08-07T15:10:57.715180Z","submitted_at":"2025-05-21T15:31:33Z","title":"First-order transducibility among classes of sparse graphs","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T15:22:48.350737Z"},"links":{"cited_paper":"/paper/2501.04166","citing_paper":"/paper/2505.15655"},"observation_digest":"sha256:3d7405d52944459449331c4da7cb955ea717957a4856d80de9ae00e178fc35ab","observation_id":"0e2e4f6a-8260-4722-bec0-c6e80c144fe6","resolution":{"observed_at":"2026-08-07T15:22:48.350737Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2501.08698","last_updated":"2025-07-24T15:15:50Z","snapshot_observed_at":"2026-07-06T20:21:18.369732Z","submitted_at":"2025-01-15T10:17:52Z","title":"On the generalized coloring numbers","version":3},"cited_work":{"arxiv_id":"2501.08698","doi":null,"metadata_source":"pith","pith_arxiv_id":"2501.08698","snapshot_observed_at":"2026-08-07T15:22:48.763214Z","title":"On the generalized coloring numbers","venue":"cs.DM","work_id":"5b58fc30-a6d5-4099-a8ee-064a047c0481","year":2025},"citing_paper":{"arxiv_id":"2505.15655","last_updated":"2025-05-21T15:31:33Z","snapshot_observed_at":"2026-08-07T15:10:57.715180Z","submitted_at":"2025-05-21T15:31:33Z","title":"First-order transducibility among classes of sparse graphs","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T15:22:48.463131Z"},"links":{"cited_paper":"/paper/2501.08698","citing_paper":"/paper/2505.15655"},"observation_digest":"sha256:bd95bb43681fe35daf8ef09fc290658286a6efee7d61bfb9feff7e15f5cc9ef5","observation_id":"89a95101-6ac9-4a48-9d12-fd0d7b6ad640","resolution":{"observed_at":"2026-08-07T15:22:48.837482Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:22:49.199951Z","title":"On the generalised colouring numbers of graphs that exclude a fixed minor","venue":null,"work_id":"5da635b6-1cf7-4d67-9e97-3cdcffd2b229","year":2017},"citing_paper":{"arxiv_id":"2505.15655","last_updated":"2025-05-21T15:31:33Z","snapshot_observed_at":"2026-08-07T15:10:57.715180Z","submitted_at":"2025-05-21T15:31:33Z","title":"First-order transducibility among classes of sparse graphs","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T15:22:48.548519Z"},"links":{"citing_paper":"/paper/2505.15655"},"observation_digest":"sha256:6f279c08d2f75b39d7c2244c950a4b2615223669773cdaf3e8d857dd9170dbda","observation_id":"837131a0-c469-4e10-ace5-a6b746f40898","resolution":{"observed_at":"2026-08-07T15:22:49.233296Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:22:49.073110Z","title":"Colouring graphs with bounded generalized colouring number","venue":null,"work_id":"6429581e-e30f-46da-83fc-6221826ce69d","year":2009},"citing_paper":{"arxiv_id":"2505.15655","last_updated":"2025-05-21T15:31:33Z","snapshot_observed_at":"2026-08-07T15:10:57.715180Z","submitted_at":"2025-05-21T15:31:33Z","title":"First-order transducibility among classes of sparse graphs","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T15:22:48.661739Z"},"links":{"citing_paper":"/paper/2505.15655"},"observation_digest":"sha256:4ddc3db8cbe0da64ab75b02ac1c1ba4489c02d782786c0768f65ed8c5e7989b8","observation_id":"83de6608-3162-4e75-975f-26427713e371","resolution":{"observed_at":"2026-08-07T15:22:49.122105Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2505.15655","last_updated":"2025-05-21T15:31:33Z","latest_version":1,"primary_category":"cs.LO","snapshot_observed_at":"2026-08-07T15:10:57.715180Z","submitted_at":"2025-05-21T15:31:33Z","title":"First-order transducibility among classes of sparse graphs"},"reference_resolution":{"displayed":16,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":4,"verified_exact":2,"verified_fuzzy":10},"total_outbound_references":16},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 16 of 16 outbound references and 1 inbound Pith citation observation for arXiv:2505.15655."}