{"as_of":"2026-08-13T00:04:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:0d75e947aaa4e7da534e6a378d33d7291d3f24db54579b6e2182b4d2c028ac38","coverage":[{"denominator":29,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":29,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-05T14:27:44.164776Z","state":"measured"},{"denominator":29,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":29,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+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/2508.21506/citation-record","integrity":"/paper/2508.21506/integrity","json":"/paper/2508.21506/citation-record.json","paper":"/paper/2508.21506"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T14:27:48.880206Z","title":"Ahmad, M","venue":null,"work_id":"faffa450-b5d7-4340-8269-eb44ae3b01f7","year":2020},"citing_paper":{"arxiv_id":"2508.21506","last_updated":"2025-08-29T10:38:39Z","snapshot_observed_at":"2026-08-07T15:35:11.803545Z","submitted_at":"2025-08-29T10:38:39Z","title":"The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-05T14:27:41.726902Z"},"links":{"citing_paper":"/paper/2508.21506"},"observation_digest":"sha256:d7edeea6d4bc51f021b9c1493921766c8e0e9d7d77f30e1b54a0f8ce3c0b495d","observation_id":"305a90de-ac0b-4a55-89bf-716467dc0189","resolution":{"observed_at":"2026-08-05T14:27:48.976034Z","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":{"arxiv_id":"2211.01495","last_updated":"2023-07-13T23:27:17Z","snapshot_observed_at":"2026-08-12T07:44:05.619784Z","submitted_at":"2022-11-02T21:48:12Z","title":"On the Edge Derivative of the Normalized Laplacian with Applications to Kemeny's Constant","version":2},"cited_work":{"arxiv_id":"2211.01495","doi":null,"metadata_source":"pith","pith_arxiv_id":"2211.01495","snapshot_observed_at":"2026-08-05T14:27:44.704119Z","title":"On the Edge Derivative of the Normalized Laplacian with Applications to Kemeny's Constant","venue":"math.CO","work_id":"7341f53f-66e8-46f6-8c93-b9c5267ad596","year":2022},"citing_paper":{"arxiv_id":"2508.21506","last_updated":"2025-08-29T10:38:39Z","snapshot_observed_at":"2026-08-07T15:35:11.803545Z","submitted_at":"2025-08-29T10:38:39Z","title":"The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-05T14:27:41.797534Z"},"links":{"cited_paper":"/paper/2211.01495","citing_paper":"/paper/2508.21506"},"observation_digest":"sha256:1b0c11646c5d9905f4d13f17a1f688530f45e758d0a4309e045529fb952e7299","observation_id":"694be528-178f-4cc5-a154-9318034add70","resolution":{"observed_at":"2026-08-05T14:27:44.766366Z","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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T14:27:48.732886Z","title":"Altafini, D","venue":null,"work_id":"2cb2a11e-b6a6-4904-ba5e-6003abfff6c8","year":2023},"citing_paper":{"arxiv_id":"2508.21506","last_updated":"2025-08-29T10:38:39Z","snapshot_observed_at":"2026-08-07T15:35:11.803545Z","submitted_at":"2025-08-29T10:38:39Z","title":"The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-05T14:27:41.904139Z"},"links":{"citing_paper":"/paper/2508.21506"},"observation_digest":"sha256:5fc923d11bde95a539fae1420070235d846e8813920175500487da5833416743","observation_id":"fd252772-2ac8-4e0e-8281-6431064c93ec","resolution":{"observed_at":"2026-08-05T14:27:48.821344Z","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":"2026-08-05T14:27:48.590668Z","title":"Benzi and P","venue":null,"work_id":"4bb73df1-6b75-40ef-8466-e6c59b37104d","year":2020},"citing_paper":{"arxiv_id":"2508.21506","last_updated":"2025-08-29T10:38:39Z","snapshot_observed_at":"2026-08-07T15:35:11.803545Z","submitted_at":"2025-08-29T10:38:39Z","title":"The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-05T14:27:41.985578Z"},"links":{"citing_paper":"/paper/2508.21506"},"observation_digest":"sha256:d7d4698983143f697d6ca24a90f2196b95331639dd7d30d11937d2945efee3ef","observation_id":"bec5e92e-bd11-48e9-b045-694ec5f1cbce","resolution":{"observed_at":"2026-08-05T14:27:48.673666Z","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":{"arxiv_id":"2501.10745","last_updated":"2025-08-13T09:25:07Z","snapshot_observed_at":"2026-08-10T18:59:00.656407Z","submitted_at":"2025-01-18T12:11:01Z","title":"Changing the ranking in eigenvector centrality of a weighted graph by small perturbations","version":3},"cited_work":{"arxiv_id":"2501.10745","doi":null,"metadata_source":"pith","pith_arxiv_id":"2501.10745","snapshot_observed_at":"2026-08-05T14:27:44.565279Z","title":"Changing the ranking in eigenvector centrality of a weighted graph by small perturbations","venue":"math.NA","work_id":"eba81b89-68ee-4da3-896e-71caee1adc48","year":2025},"citing_paper":{"arxiv_id":"2508.21506","last_updated":"2025-08-29T10:38:39Z","snapshot_observed_at":"2026-08-07T15:35:11.803545Z","submitted_at":"2025-08-29T10:38:39Z","title":"The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-05T14:27:42.063255Z"},"links":{"cited_paper":"/paper/2501.10745","citing_paper":"/paper/2508.21506"},"observation_digest":"sha256:20ad7160b6344af45ceb92bb74b6f9795674f3251ae0f837930a34a155dcd621","observation_id":"469fae23-5836-4066-8764-85f328884c56","resolution":{"observed_at":"2026-08-05T14:27:44.625878Z","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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T14:27:48.419605Z","title":"Benzi and C","venue":null,"work_id":"29e824c3-7baa-437b-a217-55c190702796","year":2013},"citing_paper":{"arxiv_id":"2508.21506","last_updated":"2025-08-29T10:38:39Z","snapshot_observed_at":"2026-08-07T15:35:11.803545Z","submitted_at":"2025-08-29T10:38:39Z","title":"The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-05T14:27:42.147829Z"},"links":{"citing_paper":"/paper/2508.21506"},"observation_digest":"sha256:1ca78b55b8a744a443875a43d3d65086b5010478a9f1f34287b4b5870c56658f","observation_id":"97d3632a-6447-4c55-b46a-2b8130e71ac7","resolution":{"observed_at":"2026-08-05T14:27:48.509810Z","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":"2026-08-05T14:27:48.276084Z","title":"Berkhout and B","venue":null,"work_id":"b614dbe7-d8ae-4bb8-8c1f-d43885174636","year":2019},"citing_paper":{"arxiv_id":"2508.21506","last_updated":"2025-08-29T10:38:39Z","snapshot_observed_at":"2026-08-07T15:35:11.803545Z","submitted_at":"2025-08-29T10:38:39Z","title":"The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-05T14:27:42.252358Z"},"links":{"citing_paper":"/paper/2508.21506"},"observation_digest":"sha256:73a973a84686975edd9725111e12d6b77cd5086d7e94125c4bae60d5322fdaad","observation_id":"be94ffad-a236-43b1-80cd-5bdda7cab56b","resolution":{"observed_at":"2026-08-05T14:27:48.353493Z","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":"2026-08-05T14:27:48.096611Z","title":null,"venue":null,"work_id":"bc1c07e0-0f75-4e87-b7da-97aca7b3dca2","year":2018},"citing_paper":{"arxiv_id":"2508.21506","last_updated":"2025-08-29T10:38:39Z","snapshot_observed_at":"2026-08-07T15:35:11.803545Z","submitted_at":"2025-08-29T10:38:39Z","title":"The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-05T14:27:42.355492Z"},"links":{"citing_paper":"/paper/2508.21506"},"observation_digest":"sha256:1523130464a98b87b80d774bd902cef418c0aa11492eafd48919dd529464b5fd","observation_id":"ab3f7a66-ff1d-4f05-b759-268fd48ab2c4","resolution":{"observed_at":"2026-08-05T14:27:48.170439Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T14:27:47.918886Z","title":null,"venue":null,"work_id":"2aab7753-2d14-43b7-8e87-c560a80aee9e","year":2025},"citing_paper":{"arxiv_id":"2508.21506","last_updated":"2025-08-29T10:38:39Z","snapshot_observed_at":"2026-08-07T15:35:11.803545Z","submitted_at":"2025-08-29T10:38:39Z","title":"The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-05T14:27:42.451029Z"},"links":{"citing_paper":"/paper/2508.21506"},"observation_digest":"sha256:fc38ddfdf67b4f4762319b778667664fa31a5609e28954849be50cd666d74fae","observation_id":"2cb55229-96c1-4970-9cda-147275716482","resolution":{"observed_at":"2026-08-05T14:27:48.016156Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T14:27:47.705947Z","title":null,"venue":null,"work_id":"5801cd11-dab7-4e7d-8bc9-14eeaa071ab4","year":1952},"citing_paper":{"arxiv_id":"2508.21506","last_updated":"2025-08-29T10:38:39Z","snapshot_observed_at":"2026-08-07T15:35:11.803545Z","submitted_at":"2025-08-29T10:38:39Z","title":"The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-05T14:27:42.528534Z"},"links":{"citing_paper":"/paper/2508.21506"},"observation_digest":"sha256:3ecf93306914f9dae68a81a0f1cec6cd011fa49268d2c79eb157b77af2df23b5","observation_id":"a73c11ab-cd0b-46dc-967c-6c3651b9e62f","resolution":{"observed_at":"2026-08-05T14:27:47.809199Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T14:27:47.550839Z","title":"Breen and S","venue":null,"work_id":"5be8cdd1-7d5d-49e5-8da0-229320bf6602","year":2019},"citing_paper":{"arxiv_id":"2508.21506","last_updated":"2025-08-29T10:38:39Z","snapshot_observed_at":"2026-08-07T15:35:11.803545Z","submitted_at":"2025-08-29T10:38:39Z","title":"The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-05T14:27:42.616126Z"},"links":{"citing_paper":"/paper/2508.21506"},"observation_digest":"sha256:ea78d22a88a1a8cd425b176ff5898204444229bb4bb12fb117e7278f1ce4a71b","observation_id":"db3e6e91-09d9-4ae3-b11d-9d6ced30155a","resolution":{"observed_at":"2026-08-05T14:27:47.625399Z","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":"2026-08-05T14:27:47.403544Z","title":"Cipolla, F","venue":null,"work_id":"a4ef7bde-06db-4250-84bc-cf16fc4da6f0","year":2025},"citing_paper":{"arxiv_id":"2508.21506","last_updated":"2025-08-29T10:38:39Z","snapshot_observed_at":"2026-08-07T15:35:11.803545Z","submitted_at":"2025-08-29T10:38:39Z","title":"The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-05T14:27:42.715837Z"},"links":{"citing_paper":"/paper/2508.21506"},"observation_digest":"sha256:a599276d2af6ccbc8e3843c38569bcd0886fd36af9309eb71e989f7b9c66ea69","observation_id":"5cc83786-f6af-4e5f-9e1c-6a2d8953938a","resolution":{"observed_at":"2026-08-05T14:27:47.476452Z","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":"2026-08-05T14:27:47.252652Z","title":"Crisostomi, S","venue":null,"work_id":"2aed23e7-a10c-480a-beb8-0284e4e17d47","year":2011},"citing_paper":{"arxiv_id":"2508.21506","last_updated":"2025-08-29T10:38:39Z","snapshot_observed_at":"2026-08-07T15:35:11.803545Z","submitted_at":"2025-08-29T10:38:39Z","title":"The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-05T14:27:42.797852Z"},"links":{"citing_paper":"/paper/2508.21506"},"observation_digest":"sha256:410e39bc05d808546e5ce18800e94f206e7f807a51d52c3447aae55274562f70","observation_id":"a7418a59-1061-40ef-85e4-aa2077f11b61","resolution":{"observed_at":"2026-08-05T14:27:47.341780Z","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":"2026-08-05T14:27:47.087473Z","title":"Cuthill and J","venue":null,"work_id":"ed084522-a577-4c4e-9746-67eafee1cd42","year":1969},"citing_paper":{"arxiv_id":"2508.21506","last_updated":"2025-08-29T10:38:39Z","snapshot_observed_at":"2026-08-07T15:35:11.803545Z","submitted_at":"2025-08-29T10:38:39Z","title":"The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-05T14:27:42.897395Z"},"links":{"citing_paper":"/paper/2508.21506"},"observation_digest":"sha256:4df2c52407834bbe968005cb97126a5cf03e8d1e8d482e850189dbdc69b414df","observation_id":"d2bc4b66-c573-4633-b021-1d0b4172117b","resolution":{"observed_at":"2026-08-05T14:27:47.157247Z","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":"2026-08-05T14:27:46.932274Z","title":null,"venue":null,"work_id":"5635cb3e-b41d-4f4d-ac63-5601397c47a6","year":1985},"citing_paper":{"arxiv_id":"2508.21506","last_updated":"2025-08-29T10:38:39Z","snapshot_observed_at":"2026-08-07T15:35:11.803545Z","submitted_at":"2025-08-29T10:38:39Z","title":"The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-05T14:27:43.002537Z"},"links":{"citing_paper":"/paper/2508.21506"},"observation_digest":"sha256:65139a2b0f874c60e4761b163f9f4230fe2c9bac2374030ff8f6e8df08fad3d0","observation_id":"5e874cb9-4d05-4965-aa65-b4b315fbd249","resolution":{"observed_at":"2026-08-05T14:27:47.013628Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T14:27:46.716354Z","title":null,"venue":null,"work_id":"f67f790d-254a-41e3-8809-b07919dc1c4e","year":2008},"citing_paper":{"arxiv_id":"2508.21506","last_updated":"2025-08-29T10:38:39Z","snapshot_observed_at":"2026-08-07T15:35:11.803545Z","submitted_at":"2025-08-29T10:38:39Z","title":"The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-05T14:27:43.104283Z"},"links":{"citing_paper":"/paper/2508.21506"},"observation_digest":"sha256:b09906c238c7d444ff779ea4483d836487b3f5da0b97c065835c2bda50458e35","observation_id":"f3345bab-4184-46bb-9a2d-cead03141b18","resolution":{"observed_at":"2026-08-05T14:27:46.809485Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T14:27:46.479187Z","title":null,"venue":null,"work_id":"526b0f3c-dbcb-4aba-a12e-ddca6dcc2d5e","year":2011},"citing_paper":{"arxiv_id":"2508.21506","last_updated":"2025-08-29T10:38:39Z","snapshot_observed_at":"2026-08-07T15:35:11.803545Z","submitted_at":"2025-08-29T10:38:39Z","title":"The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-05T14:27:43.214748Z"},"links":{"citing_paper":"/paper/2508.21506"},"observation_digest":"sha256:b51d45064d86f88cf572faa9cc9db3b948aaccbf0bc749ce2be6e32e11d3cd60","observation_id":"b415f4a3-c6ab-4996-86cd-18f9a8eb704e","resolution":{"observed_at":"2026-08-05T14:27:46.545334Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T14:27:46.434909Z","title":null,"venue":null,"work_id":"52b335e8-665c-48cb-93f3-80b9c6467863","year":2002},"citing_paper":{"arxiv_id":"2508.21506","last_updated":"2025-08-29T10:38:39Z","snapshot_observed_at":"2026-08-07T15:35:11.803545Z","submitted_at":"2025-08-29T10:38:39Z","title":"The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-05T14:27:43.310887Z"},"links":{"citing_paper":"/paper/2508.21506"},"observation_digest":"sha256:3a54130d1a866bc951cb472e1699d49a9ed6c80accd295b7d8ec662e32684534","observation_id":"bff83e76-f1ab-49de-8941-93a7328e46fa","resolution":{"observed_at":"2026-08-05T14:27:46.475099Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T14:27:46.278450Z","title":null,"venue":null,"work_id":"9d5c0a0f-eb31-4276-9d44-94a1d1d82d9b","year":2008},"citing_paper":{"arxiv_id":"2508.21506","last_updated":"2025-08-29T10:38:39Z","snapshot_observed_at":"2026-08-07T15:35:11.803545Z","submitted_at":"2025-08-29T10:38:39Z","title":"The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-05T14:27:43.390217Z"},"links":{"citing_paper":"/paper/2508.21506"},"observation_digest":"sha256:2b8ee6a1275583526d066713fc7943770fb7e876ec8bd2ee2e990e451c5f8fda","observation_id":"57146f20-1fff-40d0-96d9-508211e13576","resolution":{"observed_at":"2026-08-05T14:27:46.344381Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T14:27:46.092166Z","title":null,"venue":null,"work_id":"876c9be0-e49d-4044-8032-d4687bf90654","year":2014},"citing_paper":{"arxiv_id":"2508.21506","last_updated":"2025-08-29T10:38:39Z","snapshot_observed_at":"2026-08-07T15:35:11.803545Z","submitted_at":"2025-08-29T10:38:39Z","title":"The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-05T14:27:43.446406Z"},"links":{"citing_paper":"/paper/2508.21506"},"observation_digest":"sha256:b30f8c72a2775b99b3489260d895fe09b4ab6fbba9db04d2b7a3b525377067c8","observation_id":"d1ff8996-10c5-4776-b4a0-e528e9fbff1b","resolution":{"observed_at":"2026-08-05T14:27:46.181790Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T14:27:45.893678Z","title":"Kemeny and J","venue":null,"work_id":"998a4fd3-b7bc-4fcb-99a6-6a3a54923349","year":1960},"citing_paper":{"arxiv_id":"2508.21506","last_updated":"2025-08-29T10:38:39Z","snapshot_observed_at":"2026-08-07T15:35:11.803545Z","submitted_at":"2025-08-29T10:38:39Z","title":"The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-05T14:27:43.547988Z"},"links":{"citing_paper":"/paper/2508.21506"},"observation_digest":"sha256:8dbac6a9599e53ec2283fc382a363b85937d2a1f9ecc018bfa7ea81feaac2e4e","observation_id":"93ba1434-4097-4a56-a6fc-82bb5ea4d972","resolution":{"observed_at":"2026-08-05T14:27:45.990234Z","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":"2026-08-05T14:27:45.702254Z","title":null,"venue":null,"work_id":"bd2bf5ba-a9fe-4904-9a65-cd02d805be41","year":1981},"citing_paper":{"arxiv_id":"2508.21506","last_updated":"2025-08-29T10:38:39Z","snapshot_observed_at":"2026-08-07T15:35:11.803545Z","submitted_at":"2025-08-29T10:38:39Z","title":"The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-05T14:27:43.639546Z"},"links":{"citing_paper":"/paper/2508.21506"},"observation_digest":"sha256:45a06edec43eacea78fe33340d3e87bd58b1f97db5f75b2f0f1879975ff54d0c","observation_id":"fb8991a7-0902-4cb0-9c73-3183412b9cf7","resolution":{"observed_at":"2026-08-05T14:27:45.793104Z","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":{"arxiv_id":"2306.04005","last_updated":"2025-01-29T20:49:04Z","snapshot_observed_at":"2026-08-12T13:03:03.279257Z","submitted_at":"2023-06-06T20:35:50Z","title":"Edge Addition and the Change in Kemeny's Constant","version":2},"cited_work":{"arxiv_id":"2306.04005","doi":null,"metadata_source":"pith","pith_arxiv_id":"2306.04005","snapshot_observed_at":"2026-08-05T14:27:44.396489Z","title":"Edge Addition and the Change in Kemeny's Constant","venue":"math.CO","work_id":"c043bcc4-f331-4a42-a8cd-940b921aecc3","year":2023},"citing_paper":{"arxiv_id":"2508.21506","last_updated":"2025-08-29T10:38:39Z","snapshot_observed_at":"2026-08-07T15:35:11.803545Z","submitted_at":"2025-08-29T10:38:39Z","title":"The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-05T14:27:43.713978Z"},"links":{"cited_paper":"/paper/2306.04005","citing_paper":"/paper/2508.21506"},"observation_digest":"sha256:181fcb8677507498b6a83c64425ee8de9c123d155567b97f5dbf2666fa5b868c","observation_id":"43a84b37-6d6f-48de-b282-e27ad0266897","resolution":{"observed_at":"2026-08-05T14:27:44.470537Z","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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T14:27:45.497274Z","title":"Liben-Nowell and J","venue":null,"work_id":"13c211c2-d425-4331-bc6f-296fcfb7f332","year":2007},"citing_paper":{"arxiv_id":"2508.21506","last_updated":"2025-08-29T10:38:39Z","snapshot_observed_at":"2026-08-07T15:35:11.803545Z","submitted_at":"2025-08-29T10:38:39Z","title":"The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-05T14:27:43.778170Z"},"links":{"citing_paper":"/paper/2508.21506"},"observation_digest":"sha256:23a1b68b9d5ea8b0a66c5179c82deffdb02eaec0ff83e6e2c3b2610fdc84b1da","observation_id":"14e6813a-fcd1-4a3b-815b-3a2832e85235","resolution":{"observed_at":"2026-08-05T14:27:45.591136Z","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":{"arxiv_id":"physics/0605087","last_updated":"2006-07-23T20:25:46Z","snapshot_observed_at":"2026-07-07T06:55:19.948101Z","submitted_at":"2006-05-10T18:36:26Z","title":"Finding community structure in networks using the eigenvectors of matrices","version":3},"cited_work":{"arxiv_id":"physics/0605087","doi":null,"metadata_source":"pith","pith_arxiv_id":"physics/0605087","snapshot_observed_at":"2026-08-05T14:27:44.279114Z","title":"Finding community structure in networks using the eigenvectors of matrices","venue":"physics.data-an","work_id":"2cec7286-b376-4156-9ea0-5f7f4ea8071b","year":2006},"citing_paper":{"arxiv_id":"2508.21506","last_updated":"2025-08-29T10:38:39Z","snapshot_observed_at":"2026-08-07T15:35:11.803545Z","submitted_at":"2025-08-29T10:38:39Z","title":"The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-05T14:27:43.842923Z"},"links":{"cited_paper":"/paper/physics/0605087","citing_paper":"/paper/2508.21506"},"observation_digest":"sha256:280ea935e55f53df7a8519a06a9d8bf032fd53289753862fcff1467f57e37c80","observation_id":"c050b856-7bfb-441e-8ac8-985ff4c3fe87","resolution":{"observed_at":"2026-08-05T14:27:44.329354Z","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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T14:27:45.343398Z","title":"Patel, P","venue":null,"work_id":"c44424dd-5238-46be-a726-a24d8175d775","year":2015},"citing_paper":{"arxiv_id":"2508.21506","last_updated":"2025-08-29T10:38:39Z","snapshot_observed_at":"2026-08-07T15:35:11.803545Z","submitted_at":"2025-08-29T10:38:39Z","title":"The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-05T14:27:43.918604Z"},"links":{"citing_paper":"/paper/2508.21506"},"observation_digest":"sha256:b5c74b985a34df70e2011bbecd1c0bf81a0faa530a373ac4f70abdcfb17eac23","observation_id":"e97712e6-6210-4b05-9798-7f51f2d994e2","resolution":{"observed_at":"2026-08-05T14:27:45.412552Z","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":"2026-08-05T14:27:45.174330Z","title":null,"venue":null,"work_id":"9528fba6-ea05-46b3-b057-4403a8cf2414","year":2017},"citing_paper":{"arxiv_id":"2508.21506","last_updated":"2025-08-29T10:38:39Z","snapshot_observed_at":"2026-08-07T15:35:11.803545Z","submitted_at":"2025-08-29T10:38:39Z","title":"The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-05T14:27:43.985757Z"},"links":{"citing_paper":"/paper/2508.21506"},"observation_digest":"sha256:4db808a1494c8eaf505035ee8d9fd908eaa517c6d30a973b3707e4f535c7474d","observation_id":"9c31a04f-9414-403a-b39a-92c0013c9b76","resolution":{"observed_at":"2026-08-05T14:27:45.276581Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T14:27:45.030368Z","title":null,"venue":null,"work_id":"d5353d0d-9e13-4242-83bd-f25782515735","year":2021},"citing_paper":{"arxiv_id":"2508.21506","last_updated":"2025-08-29T10:38:39Z","snapshot_observed_at":"2026-08-07T15:35:11.803545Z","submitted_at":"2025-08-29T10:38:39Z","title":"The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-05T14:27:44.063540Z"},"links":{"citing_paper":"/paper/2508.21506"},"observation_digest":"sha256:759a8097600b41c512002dbe3bb67087ba5814a308cf1be51e54c8a106287b11","observation_id":"fc651aeb-9fb8-4ecc-8558-eee6782378cf","resolution":{"observed_at":"2026-08-05T14:27:45.091981Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T14:27:44.861910Z","title":null,"venue":null,"work_id":"a6e419ec-b5f2-4d2b-832e-817a20b8b2e8","year":2009},"citing_paper":{"arxiv_id":"2508.21506","last_updated":"2025-08-29T10:38:39Z","snapshot_observed_at":"2026-08-07T15:35:11.803545Z","submitted_at":"2025-08-29T10:38:39Z","title":"The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-05T14:27:44.164776Z"},"links":{"citing_paper":"/paper/2508.21506"},"observation_digest":"sha256:fbc2c6f10ad9ea4474ba95ed7b3d44ff0b12fdd487a56a79d8796566aae5563a","observation_id":"efcf2b1e-cb4f-4520-9ec3-096817a815d4","resolution":{"observed_at":"2026-08-05T14:27:44.925401Z","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"}}],"paper":{"arxiv_id":"2508.21506","last_updated":"2025-08-29T10:38:39Z","latest_version":1,"primary_category":"math.NA","snapshot_observed_at":"2026-08-07T15:35:11.803545Z","submitted_at":"2025-08-29T10:38:39Z","title":"The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs"},"reference_resolution":{"displayed":29,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":13,"verified_exact":4,"verified_fuzzy":12},"total_outbound_references":29},"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 13 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 0 inbound Pith citation observations for arXiv:2508.21506."}