{"as_of":"2026-08-23T06:19:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:648c3644b12ba75dedf40cc28f539826c838bab2eb5db5858383ab2adbfe06df","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":"2026-08-06T12:14:47.945528Z","state":"measured"},{"denominator":20,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":20,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-22T06:32:14.747728+00:00","state":"measured"},{"denominator":4,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":4,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-04T09:45:36.478625Z","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":"2026-07-08T13:34:53.846341Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2508.11636","last_updated":"2025-07-29T19:01:55Z","snapshot_observed_at":"2026-08-21T08:02:00.710541Z","submitted_at":"2025-07-29T19:01:55Z","title":"Rigidity of Graphs and Frameworks: A Matroid Theoretic Approach","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2508.11636","snapshot_observed_at":"2026-08-04T09:45:36.478625Z","title":"Cruickshank, B","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2510.23614","last_updated":"2026-07-20T14:33:43Z","snapshot_observed_at":"2026-08-16T00:39:25.967065Z","submitted_at":"2025-10-16T07:49:49Z","title":"How to see the forest despite the trees","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-04T09:45:36.478625Z"},"links":{"cited_paper":"/paper/2508.11636","citing_paper":"/paper/2510.23614"},"observation_digest":"sha256:8ddbbad516eb93bfa177f5d645e70dda20e5f9951291af0bb734b2ef99ee850c","observation_id":"3f297022-a336-4bf5-8069-322ad8f831ef","resolution":{"observed_at":"2026-08-04T09:45:36.478625Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2508.11636","last_updated":"2025-07-29T19:01:55Z","snapshot_observed_at":"2026-08-21T08:02:00.710541Z","submitted_at":"2025-07-29T19:01:55Z","title":"Rigidity of Graphs and Frameworks: A Matroid Theoretic Approach","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2508.11636","snapshot_observed_at":"2026-08-04T00:31:30.350141Z","title":"Cruickshank, B","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2511.01537","last_updated":"2026-07-09T14:55:39Z","snapshot_observed_at":"2026-08-13T02:02:15.800440Z","submitted_at":"2025-11-03T12:58:49Z","title":"Explosive connectivity and mechanical rigidity in cubic lattice structures","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-04T00:31:30.350141Z"},"links":{"cited_paper":"/paper/2508.11636","citing_paper":"/paper/2511.01537"},"observation_digest":"sha256:8ad730e12c455c3263cc8c9d01c3fa1c5caea3327fbf3b6592dee2fa494a55e6","observation_id":"2f0f684a-ebee-4873-9580-cd79fedc48e7","resolution":{"observed_at":"2026-08-04T00:31:30.350141Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2508.11636","last_updated":"2025-07-29T19:01:55Z","snapshot_observed_at":"2026-08-21T08:02:00.710541Z","submitted_at":"2025-07-29T19:01:55Z","title":"Rigidity of Graphs and Frameworks: A Matroid Theoretic Approach","version":1},"cited_work":{"arxiv_id":"2508.11636","doi":null,"metadata_source":"pith","pith_arxiv_id":"2508.11636","snapshot_observed_at":"2026-07-08T13:34:53.846341Z","title":"Rigidity of graphs and frameworks: A matroid theoretic approach","venue":"math.HO","work_id":"27cb4ff9-d2d8-44cf-b85f-6dae17e5b3c2","year":2025},"citing_paper":{"arxiv_id":"2604.05442","last_updated":"2026-04-20T06:25:36Z","snapshot_observed_at":"2026-08-13T02:02:21.075162Z","submitted_at":"2026-04-07T05:22:52Z","title":"Generic Rigidity of Graph Frameworks in Euclidean Space","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-05-10T20:06:05.682324Z"},"links":{"cited_paper":"/paper/2508.11636","citing_paper":"/paper/2604.05442"},"observation_digest":"sha256:0c4b62a6773be4f9d683973dcd65a30b86dac682eb67a839236a08918282565e","observation_id":"a717af86-b5cc-40ab-a051-3ab22777aa8f","resolution":{"observed_at":"2026-05-10T22:15:48.710577Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2508.11636","last_updated":"2025-07-29T19:01:55Z","snapshot_observed_at":"2026-08-21T08:02:00.710541Z","submitted_at":"2025-07-29T19:01:55Z","title":"Rigidity of Graphs and Frameworks: A Matroid Theoretic Approach","version":1},"cited_work":{"arxiv_id":"2508.11636","doi":null,"metadata_source":"pith","pith_arxiv_id":"2508.11636","snapshot_observed_at":"2026-07-08T13:34:53.846341Z","title":"Rigidity of graphs and frameworks: A matroid theoretic approach","venue":"math.HO","work_id":"27cb4ff9-d2d8-44cf-b85f-6dae17e5b3c2","year":2025},"citing_paper":{"arxiv_id":"2607.06228","last_updated":"2026-07-07T12:52:19Z","snapshot_observed_at":"2026-08-21T12:34:50.514431Z","submitted_at":"2026-07-07T12:52:19Z","title":"Symmetric Powers of Matroids","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-07-08T13:31:33.302028Z"},"links":{"cited_paper":"/paper/2508.11636","citing_paper":"/paper/2607.06228"},"observation_digest":"sha256:93d80c6c5973e3d282635becaeb98479d31484ab4b2a8000f2aeb4f3c8fdfe02","observation_id":"5b4e348e-a98d-441a-b483-cdabdfa670e5","resolution":{"observed_at":"2026-07-08T13:34:53.848283Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2508.11636/citation-record","integrity":"/paper/2508.11636/integrity","json":"/paper/2508.11636/citation-record.json","paper":"/paper/2508.11636"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T12:14:50.876922Z","title":"Generalizations of Kempe’s universality theorem","venue":null,"work_id":"b0f907ca-81fd-4adb-8753-6b3a6d902f5d","year":2008},"citing_paper":{"arxiv_id":"2508.11636","last_updated":"2025-07-29T19:01:55Z","snapshot_observed_at":"2026-08-21T08:02:00.710541Z","submitted_at":"2025-07-29T19:01:55Z","title":"Rigidity of Graphs and Frameworks: A Matroid Theoretic Approach","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T12:14:46.660447Z"},"links":{"citing_paper":"/paper/2508.11636"},"observation_digest":"sha256:523d797d5e19818624959aa6274e41b5df8188bf75b4bd6ec93549a0533ec510","observation_id":"4c0f13f6-d85d-4657-9bbf-adb8974a93bf","resolution":{"observed_at":"2026-08-06T12:14:51.092638Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-06T12:14:50.501971Z","title":"FAQ on the g-theorem and the hard Lefschetz theorem for face rings","venue":null,"work_id":"4248e374-7177-4aa8-a282-b8cce8dc8a49","year":2019},"citing_paper":{"arxiv_id":"2508.11636","last_updated":"2025-07-29T19:01:55Z","snapshot_observed_at":"2026-08-21T08:02:00.710541Z","submitted_at":"2025-07-29T19:01:55Z","title":"Rigidity of Graphs and Frameworks: A Matroid Theoretic Approach","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T12:14:46.730418Z"},"links":{"citing_paper":"/paper/2508.11636"},"observation_digest":"sha256:9bcad833ae87f60b3f3bf311de74b1f396c0a82e08b27fddeef6b6dcc6ed608a","observation_id":"09c3cfd1-4f9c-49e2-ba11-9d31d5b87576","resolution":{"observed_at":"2026-08-06T12:14:50.697583Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-06T12:14:50.153409Z","title":null,"venue":null,"work_id":"89bbbdf2-7273-42b6-912c-d387843091d5","year":2005},"citing_paper":{"arxiv_id":"2508.11636","last_updated":"2025-07-29T19:01:55Z","snapshot_observed_at":"2026-08-21T08:02:00.710541Z","submitted_at":"2025-07-29T19:01:55Z","title":"Rigidity of Graphs and Frameworks: A Matroid Theoretic Approach","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T12:14:46.807177Z"},"links":{"citing_paper":"/paper/2508.11636"},"observation_digest":"sha256:d5e2a461e7f278040e8bce089ce54aebd04504a81a085e3e242f4b6aa1e15d6c","observation_id":"776c295c-c488-42bd-ba1a-5da7bd69e405","resolution":{"observed_at":"2026-08-06T12:14:50.323460Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-06T12:14:49.899827Z","title":"The rigidity of graphs","venue":null,"work_id":"420cbd47-5d0d-4af4-9817-85ef48f4fb1e","year":1978},"citing_paper":{"arxiv_id":"2508.11636","last_updated":"2025-07-29T19:01:55Z","snapshot_observed_at":"2026-08-21T08:02:00.710541Z","submitted_at":"2025-07-29T19:01:55Z","title":"Rigidity of Graphs and Frameworks: A Matroid Theoretic Approach","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T12:14:46.885875Z"},"links":{"citing_paper":"/paper/2508.11636"},"observation_digest":"sha256:ad4c469d72251f422d99af5b3c179c0a18e2f398faf0f772e90c8c01bc6ed753","observation_id":"69862562-4a4d-4803-85bc-04987cd7126f","resolution":{"observed_at":"2026-08-06T12:14:49.968032Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-06T12:14:49.673685Z","title":"A proof of the lower bound conjecture for convex polytopes","venue":null,"work_id":"ad3dc361-796c-448f-bfd3-958ba0c7688f","year":1973},"citing_paper":{"arxiv_id":"2508.11636","last_updated":"2025-07-29T19:01:55Z","snapshot_observed_at":"2026-08-21T08:02:00.710541Z","submitted_at":"2025-07-29T19:01:55Z","title":"Rigidity of Graphs and Frameworks: A Matroid Theoretic Approach","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T12:14:46.950880Z"},"links":{"citing_paper":"/paper/2508.11636"},"observation_digest":"sha256:f3f1de4450632036208cae9f1e7734bf0086b3b14a07c4f417d04922a093a4b8","observation_id":"2190cb0b-8af3-43cb-b58f-f3d8d0d5e7f7","resolution":{"observed_at":"2026-08-06T12:14:49.785329Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-06T12:14:49.481521Z","title":"The minimum number of vertices of a simple polytope","venue":null,"work_id":"90fe22db-ff92-41d0-93d1-e110af9cabf2","year":1971},"citing_paper":{"arxiv_id":"2508.11636","last_updated":"2025-07-29T19:01:55Z","snapshot_observed_at":"2026-08-21T08:02:00.710541Z","submitted_at":"2025-07-29T19:01:55Z","title":"Rigidity of Graphs and Frameworks: A Matroid Theoretic Approach","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T12:14:47.014041Z"},"links":{"citing_paper":"/paper/2508.11636"},"observation_digest":"sha256:ba17abf60ccb01e2ee31cb7d6cb5758b436bcaa3a9343cd52156db6da05b8542","observation_id":"78e201d3-9378-4dc9-9b0e-df987a4da56e","resolution":{"observed_at":"2026-08-06T12:14:49.557294Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.10709","last_updated":"2025-07-14T18:22:35Z","snapshot_observed_at":"2026-08-13T02:01:26.580954Z","submitted_at":"2025-07-14T18:22:35Z","title":"Interaction between skew-representability, tensor products, extension properties, and rank inequalities","version":1},"cited_work":{"arxiv_id":"2507.10709","doi":null,"metadata_source":"pith","pith_arxiv_id":"2507.10709","snapshot_observed_at":"2026-08-06T12:14:48.183892Z","title":"Interaction between skew-representability, tensor products, extension properties, and rank inequalities","venue":"math.CO","work_id":"d7e7453a-bbcf-4af7-bd32-be46aa7a377c","year":2025},"citing_paper":{"arxiv_id":"2508.11636","last_updated":"2025-07-29T19:01:55Z","snapshot_observed_at":"2026-08-21T08:02:00.710541Z","submitted_at":"2025-07-29T19:01:55Z","title":"Rigidity of Graphs and Frameworks: A Matroid Theoretic Approach","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T12:14:47.110657Z"},"links":{"cited_paper":"/paper/2507.10709","citing_paper":"/paper/2508.11636"},"observation_digest":"sha256:8c2a2a6af17f13098a0d7f06a31ff79efe3f2354bb68ede8a2ff3a861f53ce1e","observation_id":"c69e8b86-e505-414f-ba45-516974f7de94","resolution":{"observed_at":"2026-08-06T12:14:48.269125Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-06T12:14:49.264168Z","title":"A proof of Connelly’s conjecture on 3-connected circuits of the rigidity matroid","venue":null,"work_id":"96e11340-7e1c-4a1f-94ad-4cbf4e902895","year":2003},"citing_paper":{"arxiv_id":"2508.11636","last_updated":"2025-07-29T19:01:55Z","snapshot_observed_at":"2026-08-21T08:02:00.710541Z","submitted_at":"2025-07-29T19:01:55Z","title":"Rigidity of Graphs and Frameworks: A Matroid Theoretic Approach","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T12:14:47.334922Z"},"links":{"citing_paper":"/paper/2508.11636"},"observation_digest":"sha256:babbe693b57cac43a248afdf2f97323891bdb649ce123f731819032a1e3478ea","observation_id":"1866f6e5-0f1e-43cc-b69e-32f38772dc60","resolution":{"observed_at":"2026-08-06T12:14:49.321063Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1612.06797","last_updated":"2017-07-14T16:23:32Z","snapshot_observed_at":"2026-08-14T21:24:28.444171Z","submitted_at":"2016-12-20T18:36:07Z","title":"Completion of tree metrics and rank-2 matrices","version":2},"cited_work":{"arxiv_id":"1612.06797","doi":null,"metadata_source":"pith","pith_arxiv_id":"1612.06797","snapshot_observed_at":"2026-08-06T12:14:48.048874Z","title":"Completion of tree metrics and rank-2 matrices","venue":"math.CO","work_id":"e909fc75-99d0-4b8d-b92a-72d10f299afe","year":2016},"citing_paper":{"arxiv_id":"2508.11636","last_updated":"2025-07-29T19:01:55Z","snapshot_observed_at":"2026-08-21T08:02:00.710541Z","submitted_at":"2025-07-29T19:01:55Z","title":"Rigidity of Graphs and Frameworks: A Matroid Theoretic Approach","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T12:14:47.494717Z"},"links":{"cited_paper":"/paper/1612.06797","citing_paper":"/paper/2508.11636"},"observation_digest":"sha256:798db9a13cd75f8b4ed01e722291003fd50bd49dc796c0920d855c06243d529d","observation_id":"63fc11d2-ffc9-424e-b181-67459642a492","resolution":{"observed_at":"2026-08-06T12:14:48.106950Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-06T12:14:48.923319Z","title":"When is a bipartite graph a rigid framework?","venue":null,"work_id":"c2a15901-ac82-4c1b-9e7b-b991dc1e9372","year":1980},"citing_paper":{"arxiv_id":"2508.11636","last_updated":"2025-07-29T19:01:55Z","snapshot_observed_at":"2026-08-21T08:02:00.710541Z","submitted_at":"2025-07-29T19:01:55Z","title":"Rigidity of Graphs and Frameworks: A Matroid Theoretic Approach","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T12:14:47.593803Z"},"links":{"citing_paper":"/paper/2508.11636"},"observation_digest":"sha256:bcd12bf8aef1571d09d29aa1477f95d3280e340884c7f89c232635266e9d0731","observation_id":"22096eb4-3c46-4412-961a-161cc77060dd","resolution":{"observed_at":"2026-08-06T12:14:48.997514Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-06T12:14:48.805356Z","title":"Rigidity matroids and linear algebraic matroids with appli- cations to matrix completion and tensor codes","venue":null,"work_id":"b02167f1-5f4e-4763-a07f-d6ccd9b271e9","year":2024},"citing_paper":{"arxiv_id":"2508.11636","last_updated":"2025-07-29T19:01:55Z","snapshot_observed_at":"2026-08-21T08:02:00.710541Z","submitted_at":"2025-07-29T19:01:55Z","title":"Rigidity of Graphs and Frameworks: A Matroid Theoretic Approach","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T12:14:47.689810Z"},"links":{"citing_paper":"/paper/2508.11636"},"observation_digest":"sha256:ab8374d33b1e0583d24ef88f413c121474247eddbebbd75fc1b325404b6c5c5f","observation_id":"50a543a1-8f9c-469e-9715-438a9c0ef559","resolution":{"observed_at":"2026-08-06T12:14:48.872096Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-06T12:14:48.656254Z","title":"Cohen-Macaulay rings","venue":null,"work_id":"a5cb72cc-5aec-487d-9136-a03b6f7579c0","year":1993},"citing_paper":{"arxiv_id":"2508.11636","last_updated":"2025-07-29T19:01:55Z","snapshot_observed_at":"2026-08-21T08:02:00.710541Z","submitted_at":"2025-07-29T19:01:55Z","title":"Rigidity of Graphs and Frameworks: A Matroid Theoretic Approach","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T12:14:47.785742Z"},"links":{"citing_paper":"/paper/2508.11636"},"observation_digest":"sha256:7a262d187d6286d616b320fb2b43643d8a1d0205415acac1723cedde066488a2","observation_id":"51ecfcbf-3e34-4695-9266-1334655e329b","resolution":{"observed_at":"2026-08-06T12:14:48.723646Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-06T12:14:48.504512Z","title":"Volume rigidity and algebraic shift- ing","venue":null,"work_id":"a2e4bebb-ef9f-4d9d-a1db-2c46b9f51a54","year":2025},"citing_paper":{"arxiv_id":"2508.11636","last_updated":"2025-07-29T19:01:55Z","snapshot_observed_at":"2026-08-21T08:02:00.710541Z","submitted_at":"2025-07-29T19:01:55Z","title":"Rigidity of Graphs and Frameworks: A Matroid Theoretic Approach","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T12:14:47.867269Z"},"links":{"citing_paper":"/paper/2508.11636"},"observation_digest":"sha256:984c096f95167cc00d0be0c9d501c1bdde9dc77a4e7c38e071d349f47e424e56","observation_id":"f5179339-da64-4b08-ae38-f19448224230","resolution":{"observed_at":"2026-08-06T12:14:48.576546Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-06T12:14:49.088261Z","title":"doi: �� � ���� � ����� � ������� � ����� � �","venue":null,"work_id":"bfa4ab4d-4adb-4887-9cce-4ed40ee6a953","year":null},"citing_paper":{"arxiv_id":"2508.11636","last_updated":"2025-07-29T19:01:55Z","snapshot_observed_at":"2026-08-21T08:02:00.710541Z","submitted_at":"2025-07-29T19:01:55Z","title":"Rigidity of Graphs and Frameworks: A Matroid Theoretic Approach","version":1},"reference_index":97,"source":"pdf_text","source_observed_at":"2026-08-06T12:14:47.406791Z"},"links":{"citing_paper":"/paper/2508.11636"},"observation_digest":"sha256:815b6123d13b4b8da758db8eb7850a21f6afb261071577ce8d735814c9b47475","observation_id":"85382a94-5416-4b09-8006-a4591e8101eb","resolution":{"observed_at":"2026-08-06T12:14:49.184399Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-06T12:14:48.353598Z","title":"url: �������������������������� ����������������","venue":null,"work_id":"b7592b51-3404-4c4b-9428-92e5fbf430dd","year":null},"citing_paper":{"arxiv_id":"2508.11636","last_updated":"2025-07-29T19:01:55Z","snapshot_observed_at":"2026-08-21T08:02:00.710541Z","submitted_at":"2025-07-29T19:01:55Z","title":"Rigidity of Graphs and Frameworks: A Matroid Theoretic Approach","version":1},"reference_index":902,"source":"pdf_text","source_observed_at":"2026-08-06T12:14:47.945528Z"},"links":{"citing_paper":"/paper/2508.11636"},"observation_digest":"sha256:03fec5bc732124f102be27604ad48e9ed557ed9cdbf0e10344e8c10a2dd296b3","observation_id":"01d976d1-0138-4f1a-bffd-39e91792f93e","resolution":{"observed_at":"2026-08-06T12:14:48.431520Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-06T12:14:49.395331Z","title":null,"venue":null,"work_id":"55d0335c-c1f4-4ae6-8c32-7697c1e604de","year":null},"citing_paper":{"arxiv_id":"2508.11636","last_updated":"2025-07-29T19:01:55Z","snapshot_observed_at":"2026-08-21T08:02:00.710541Z","submitted_at":"2025-07-29T19:01:55Z","title":"Rigidity of Graphs and Frameworks: A Matroid Theoretic Approach","version":1},"reference_index":2025,"source":"pdf_text","source_observed_at":"2026-08-06T12:14:47.208209Z"},"links":{"citing_paper":"/paper/2508.11636"},"observation_digest":"sha256:1998e8a1d306b108b6beb1d614af32b1500b6bdd463aa1f3d0ba6c62ec11c63c","observation_id":"29c358bc-d6e0-4a72-bd79-8378a163fea4","resolution":{"observed_at":"2026-08-06T12:14:49.453236Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2508.11636","last_updated":"2025-07-29T19:01:55Z","latest_version":1,"primary_category":"math.HO","snapshot_observed_at":"2026-08-21T08:02:00.710541Z","submitted_at":"2025-07-29T19:01:55Z","title":"Rigidity of Graphs and Frameworks: A Matroid Theoretic Approach"},"reference_resolution":{"displayed":16,"state_counts":{"malformed_identifier":0,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":2,"verified_exact":1,"verified_fuzzy":12},"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":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"thesis":"As of 23 August 2026, this Paper Citation Record lists 16 of 16 outbound references and 4 inbound Pith citation observations for arXiv:2508.11636."}