{"as_of":"2026-08-23T16:10:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:8490c25eb0070ff25dd316e4a95730a53da8e74d178c4e7f426bcdf759cfd3f7","coverage":[{"denominator":24,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":24,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-08T13:31:33.302028Z","state":"measured"},{"denominator":24,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":24,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-23T06:30:58.430688+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/2607.06228/citation-record","integrity":"/paper/2607.06228/integrity","json":"/paper/2607.06228/citation-record.json","paper":"/paper/2607.06228"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-08T13:34:53.985129Z","title":"thesis, Queen Mary University of London, 2024","venue":null,"work_id":"ab94bcb5-5916-4769-b1d5-3de0a871c728","year":2024},"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":1,"source":"pdf_text","source_observed_at":"2026-07-08T13:31:33.302028Z"},"links":{"citing_paper":"/paper/2607.06228"},"observation_digest":"sha256:0d4a1f9a947026a805ad36ae709d955b22bc944672d351ac34081d223f742f41","observation_id":"aaff6b7a-f324-42b8-89c3-3a2c2d1ba352","resolution":{"observed_at":"2026-07-08T13:34:53.986272Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-08T13:34:53.983240Z","title":null,"venue":null,"work_id":"5ff4fcf3-fabb-4adc-96de-48d520d33ec7","year":2024},"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":2,"source":"pdf_text","source_observed_at":"2026-07-08T13:31:33.302028Z"},"links":{"citing_paper":"/paper/2607.06228"},"observation_digest":"sha256:e04aa2c7c340f6b4ac8c79462ef6706771058d093aa0c98745d2174d910cf718","observation_id":"0322cd3f-e9ca-4098-8225-5b64c090092f","resolution":{"observed_at":"2026-07-08T13:34:53.984541Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-08T13:34:53.954325Z","title":"2074–2085","venue":null,"work_id":"e2c5e031-f1a3-4f68-a0bf-ac11e9c8ff0b","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":3,"source":"pdf_text","source_observed_at":"2026-07-08T13:31:33.302028Z"},"links":{"citing_paper":"/paper/2607.06228"},"observation_digest":"sha256:cae8441f5ada03341df7ea471fbe32a36f983d9304a48ed0f9a29903763fa87b","observation_id":"e19d3def-ac9b-4ff6-b3b2-b887e19e1cd7","resolution":{"observed_at":"2026-07-08T13:34:53.955614Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-08T13:34:53.972078Z","title":null,"venue":null,"work_id":"c9df7ad5-3c70-4592-a824-97cae48d8bc2","year":2026},"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":4,"source":"pdf_text","source_observed_at":"2026-07-08T13:31:33.302028Z"},"links":{"citing_paper":"/paper/2607.06228"},"observation_digest":"sha256:d8a4807e3b33bd7e39d2f9d34b74e797f6f718532a4d503ebb5d4c90ec4c1e3c","observation_id":"3850f138-3af7-4212-a191-1392461c99dc","resolution":{"observed_at":"2026-07-08T13:34:53.973162Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-08T13:34:53.956235Z","title":null,"venue":null,"work_id":"252ee87a-d6cd-4935-90cc-f36d0ecd4249","year":2026},"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":5,"source":"pdf_text","source_observed_at":"2026-07-08T13:31:33.302028Z"},"links":{"citing_paper":"/paper/2607.06228"},"observation_digest":"sha256:286f7bf5bf93862e03e7caabf3ab3c9869d8dc256a3bd8df8019c9dc3629f53a","observation_id":"0e40e38a-0671-421d-b983-a4d82dbd9505","resolution":{"observed_at":"2026-07-08T13:34:53.957545Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"sha256:84183f13d1711c983ea2347ab8dab908bc81e8f8b1a6635acf668d84cad76b6d","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 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-08T13:34:53.966324Z","title":null,"venue":null,"work_id":"ca50af22-784c-41ef-b000-26fd1c93d2db","year":2021},"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":7,"source":"pdf_text","source_observed_at":"2026-07-08T13:31:33.302028Z"},"links":{"citing_paper":"/paper/2607.06228"},"observation_digest":"sha256:52316d4f6624a110c735704e34760f2a758c447f3105cbe665967d6147fa8a5f","observation_id":"bd5461c3-f88f-4afc-b332-30b689639785","resolution":{"observed_at":"2026-07-08T13:34:53.967494Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-08T13:34:53.937050Z","title":"4, 241– 245","venue":null,"work_id":"81d2ce3c-3168-4b58-9a8d-3a80742f91cf","year":1967},"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":8,"source":"pdf_text","source_observed_at":"2026-07-08T13:31:33.302028Z"},"links":{"citing_paper":"/paper/2607.06228"},"observation_digest":"sha256:e6f30152676dffa002b872d808bdceb0b770cfe1cbc2a434f4e51c1e2cd2c282","observation_id":"2f96ccc7-edb2-422a-ba31-bdaf7e10c451","resolution":{"observed_at":"2026-07-08T13:34:53.940841Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-08T13:34:53.968087Z","title":"Graver,Rigidity matroids, SIAM Journal on Discrete Mathematics4(1991), 355–368","venue":null,"work_id":"33d67afc-6c01-4650-8abb-4926c92b2885","year":1991},"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":9,"source":"pdf_text","source_observed_at":"2026-07-08T13:31:33.302028Z"},"links":{"citing_paper":"/paper/2607.06228"},"observation_digest":"sha256:f6901a662811d8567edf985ed6c0a4802aa5bb41aa21dd77e2a23f3c0b357681","observation_id":"c9be1317-ff74-4f4f-86b5-f45691cb3376","resolution":{"observed_at":"2026-07-08T13:34:53.969384Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-08T13:34:53.958097Z","title":"Graver, Brigitte Servatius, and Herman Servatius,Combinatorial rigidity, American Mathematical Society, 1993","venue":null,"work_id":"63c691e1-62fb-494c-8364-3eafc29fd087","year":1993},"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":10,"source":"pdf_text","source_observed_at":"2026-07-08T13:31:33.302028Z"},"links":{"citing_paper":"/paper/2607.06228"},"observation_digest":"sha256:f7517c905df21ea1aa430580ec970c7e3fdf979dbb50cb2d966bba148442e4de","observation_id":"8e45040a-bc68-4417-bf18-d004cb0ca5fe","resolution":{"observed_at":"2026-07-08T13:34:53.959309Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-08T13:34:53.969932Z","title":"4, 1797–1819","venue":null,"work_id":"420a9685-de20-448a-b9c9-f19d052483fe","year":2014},"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":11,"source":"pdf_text","source_observed_at":"2026-07-08T13:31:33.302028Z"},"links":{"citing_paper":"/paper/2607.06228"},"observation_digest":"sha256:2cc9cb1da54af6dbdda8d27a5493563bc5449b86b5aa92717def291cddbc238d","observation_id":"dedfe452-ad45-4145-8585-14de5ae8da88","resolution":{"observed_at":"2026-07-08T13:34:53.971416Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-08T13:34:53.959874Z","title":null,"venue":null,"work_id":"122df85b-4c89-45ac-9308-c419be1e5ade","year":2024},"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":12,"source":"pdf_text","source_observed_at":"2026-07-08T13:31:33.302028Z"},"links":{"citing_paper":"/paper/2607.06228"},"observation_digest":"sha256:ef1b011a60ed65ddf6bdf57403087a1e76d57fca41b7a7403fcaaf3cd284527d","observation_id":"5a3c8419-192a-40b9-a821-fbc2fffb2ab7","resolution":{"observed_at":"2026-07-08T13:34:53.960939Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2503.14780","last_updated":"2025-03-18T23:10:44Z","snapshot_observed_at":"2026-08-16T12:48:47.933687Z","submitted_at":"2025-03-18T23:10:44Z","title":"Symmetric Tensor Matroids, Dual Rigidity Matroids, and the Maximality Conjecture","version":1},"cited_work":{"arxiv_id":"2503.14780","doi":null,"metadata_source":"pith","pith_arxiv_id":"2503.14780","snapshot_observed_at":"2026-07-08T13:34:53.842888Z","title":"Symmetric Tensor Matroids, Dual Rigidity Matroids, and the Maximality Conjecture","venue":"math.CO","work_id":"e1787ff6-9480-4624-aecf-f5c129b157ff","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":13,"source":"pdf_text","source_observed_at":"2026-07-08T13:31:33.302028Z"},"links":{"cited_paper":"/paper/2503.14780","citing_paper":"/paper/2607.06228"},"observation_digest":"sha256:e6a1d9f167fdd7c850a034b3505ade667c173ba398374a76f9ffdb2d02838bf3","observation_id":"faa51555-1af2-4a9f-a965-888295ccaa6e","resolution":{"observed_at":"2026-07-08T13:34:53.844830Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-08T13:34:53.961450Z","title":null,"venue":null,"work_id":"f2087518-3a3d-47fe-96f2-d45444f243e7","year":1985},"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":14,"source":"pdf_text","source_observed_at":"2026-07-08T13:31:33.302028Z"},"links":{"citing_paper":"/paper/2607.06228"},"observation_digest":"sha256:b09fdc97f2b77d0e3d71321112cdadc3ee53fad0f7742996833d4edcc1a1d629","observation_id":"f70e35ca-1e29-47c2-9d0b-e75aca7fb8dd","resolution":{"observed_at":"2026-07-08T13:34:53.962513Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-08T13:34:53.945069Z","title":null,"venue":null,"work_id":"f4ec5f33-cca7-4243-97bf-c52b73cd6074","year":1986},"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":15,"source":"pdf_text","source_observed_at":"2026-07-08T13:31:33.302028Z"},"links":{"citing_paper":"/paper/2607.06228"},"observation_digest":"sha256:5c42586645152e4381b6eab66944e8bdb14bf1dc0af81f2666b744ef7e869c2e","observation_id":"f48eb3d0-aa60-479b-9256-75b19086c230","resolution":{"observed_at":"2026-07-08T13:34:53.946556Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-08T13:34:53.948928Z","title":null,"venue":null,"work_id":"c0550f20-f64c-428c-b66e-241916fdf333","year":1986},"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":16,"source":"pdf_text","source_observed_at":"2026-07-08T13:31:33.302028Z"},"links":{"citing_paper":"/paper/2607.06228"},"observation_digest":"sha256:52e9acf541b19c9c369d72d2367c5a154568b8d4a57cbf4ecd7e5c64b9076f17","observation_id":"ebcdd0db-78c7-40b3-9902-8f95cec6f987","resolution":{"observed_at":"2026-07-08T13:34:53.950036Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-08T13:34:53.963063Z","title":"1, 49–55","venue":null,"work_id":"1ded4798-e5c5-40d4-bd46-01577c87b9fc","year":1981},"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":17,"source":"pdf_text","source_observed_at":"2026-07-08T13:31:33.302028Z"},"links":{"citing_paper":"/paper/2607.06228"},"observation_digest":"sha256:cd33409d6e2b439547da1560008563a322fc830f3fca160a7fc29cf0ad5c5648","observation_id":"790fbcc4-0625-49b1-a09b-99d048e22b19","resolution":{"observed_at":"2026-07-08T13:34:53.964093Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-08T13:34:53.973848Z","title":"Cameron, ed.), Academic Press, 1977, Proceedings of the Sixth British Com- binatorial Conference, Royal Holloway College, Egham, pp","venue":null,"work_id":"14592f9d-09ea-489c-afcd-439167a86edb","year":1977},"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":18,"source":"pdf_text","source_observed_at":"2026-07-08T13:31:33.302028Z"},"links":{"citing_paper":"/paper/2607.06228"},"observation_digest":"sha256:db02ff82c5d159e31502b35b582db7127d7ab2caeb197d444b76d43567be8cc6","observation_id":"6ea6c877-9b63-4fba-a4fe-e0364982a439","resolution":{"observed_at":"2026-07-08T13:34:53.982409Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-08T13:34:53.943394Z","title":"3, 640–670","venue":null,"work_id":"f0819bc2-bb54-4516-b320-29caa1400f21","year":2018},"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":19,"source":"pdf_text","source_observed_at":"2026-07-08T13:31:33.302028Z"},"links":{"citing_paper":"/paper/2607.06228"},"observation_digest":"sha256:d34274a50ada9b7991cc7754a8415e040958493c1bd62b63c32a35fa3f77f52d","observation_id":"af9cd042-5aa2-4ef8-9fa9-29f46a3742e5","resolution":{"observed_at":"2026-07-08T13:34:53.944469Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-08T13:34:53.952671Z","title":null,"venue":null,"work_id":"7ddc49a5-256c-4981-b453-8fdced27df4a","year":1981},"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":20,"source":"pdf_text","source_observed_at":"2026-07-08T13:31:33.302028Z"},"links":{"citing_paper":"/paper/2607.06228"},"observation_digest":"sha256:48a734a3faae23cbd76f47f64df897f6179f6cad50a2bf8effa00969b294bdce","observation_id":"2c7358f5-bba7-4f84-b04a-a0850e492f18","resolution":{"observed_at":"2026-07-08T13:34:53.953714Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-08T13:34:53.947280Z","title":null,"venue":null,"work_id":"ed58f8a7-a9e6-4943-a3f0-e7f59d270a05","year":2010},"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":21,"source":"pdf_text","source_observed_at":"2026-07-08T13:31:33.302028Z"},"links":{"citing_paper":"/paper/2607.06228"},"observation_digest":"sha256:e2cff2fc1444b1ef36aae8af80c385fb17929ad4b4fcd26e6bd5ebbc0ef597f9","observation_id":"f4b0b9d5-c5e0-42a9-a47b-f93bac16496d","resolution":{"observed_at":"2026-07-08T13:34:53.948383Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-08T13:34:53.950670Z","title":"Oxley,Matroid theory, 2 ed., Oxford University Press, Oxford, 2011","venue":null,"work_id":"3fafdad1-cdf9-4d86-b202-43e5f860057a","year":2011},"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":22,"source":"pdf_text","source_observed_at":"2026-07-08T13:31:33.302028Z"},"links":{"citing_paper":"/paper/2607.06228"},"observation_digest":"sha256:a975c3ef879ca6366b87a618a289875ebd30bc406e8cfcb32df6fe28fed38752","observation_id":"788d7c0d-cf16-4147-94fc-a775417fa97f","resolution":{"observed_at":"2026-07-08T13:34:53.952024Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-08T13:34:53.964641Z","title":"4, 1621–1641","venue":null,"work_id":"e7cacf51-0cb3-42af-a936-ef484c130b53","year":2010},"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":23,"source":"pdf_text","source_observed_at":"2026-07-08T13:31:33.302028Z"},"links":{"citing_paper":"/paper/2607.06228"},"observation_digest":"sha256:b94bfcd924caa1e3981b7958407255ec4afa8056a6f35226eaaf9e240c68d357","observation_id":"d9158eb7-ef4f-4a56-8589-07124e2c7145","resolution":{"observed_at":"2026-07-08T13:34:53.965741Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-08T13:34:53.941702Z","title":"Bonin, James G","venue":null,"work_id":"394cf922-49df-44c2-91d5-71013d564705","year":1996},"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":24,"source":"pdf_text","source_observed_at":"2026-07-08T13:31:33.302028Z"},"links":{"citing_paper":"/paper/2607.06228"},"observation_digest":"sha256:b71ea5ed366d3c1fab8032465b71245f1b2263bf08bfaf3a6f195a93ca742418","observation_id":"9c6f309d-cce8-4c71-a90d-162991b00e0f","resolution":{"observed_at":"2026-07-08T13:34:53.942819Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2607.06228","last_updated":"2026-07-07T12:52:19Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-08-21T12:34:50.514431Z","submitted_at":"2026-07-07T12:52:19Z","title":"Symmetric Powers of Matroids"},"reference_resolution":{"displayed":24,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":10,"verified_exact":2,"verified_fuzzy":12},"total_outbound_references":24},"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":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"thesis":"As of 23 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 0 inbound Pith citation observations for arXiv:2607.06228."}