{"as_of":"2026-08-16T12:57:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:5811c43a864e82e3a884dff3df42e4e3b3070d4f2c1909569a08023f23ed1f23","coverage":[{"denominator":20,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":20,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T14:22:34.350080Z","state":"measured"},{"denominator":21,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":21,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-24T02:11:08.847255Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-24T02:13:45.060558Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"1908.03420","last_updated":"2023-03-14T16:30:54Z","snapshot_observed_at":"2026-08-16T05:43:23.991468Z","submitted_at":"2019-08-09T11:43:12Z","title":"Perfect matroids over hyperfields","version":3},"cited_work":{"arxiv_id":"1908.03420","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1908.03420","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Pendavingh","venue":null,"work_id":"5e32eb60-3b3b-4f50-a467-87ae8fb6d430","year":1908},"citing_paper":{"arxiv_id":"2404.09255","last_updated":"2026-04-13T11:41:19Z","snapshot_observed_at":"2026-07-06T17:59:55.100798Z","submitted_at":"2024-04-14T13:42:57Z","title":"Quiver matroids -- Matroid morphisms, quiver Grassmannians, their Euler characteristics and $\\mathbb{F}_1$-points","version":2},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-05-24T02:11:08.847255Z"},"links":{"cited_paper":"/paper/1908.03420","citing_paper":"/paper/2404.09255"},"observation_digest":"sha256:04fa767c1bd3f3337e69752e2c1f71548edb3157dc640417dcf3ce777f63ed1f","observation_id":"317d9436-4aa7-41b5-878c-f7f01f7fa193","resolution":{"observed_at":"2026-05-24T02:13:45.062527Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/1908.03420/citation-record","integrity":"/paper/1908.03420/integrity","json":"/paper/1908.03420/citation-record.json","paper":"/paper/1908.03420"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T14:22:34.248597Z","title":"Vectors of matroids over tracts","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"1908.03420","last_updated":"2023-03-14T16:30:54Z","snapshot_observed_at":"2026-08-16T05:43:23.991468Z","submitted_at":"2019-08-09T11:43:12Z","title":"Perfect matroids over hyperfields","version":3},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-14T14:22:34.248597Z"},"links":{"citing_paper":"/paper/1908.03420"},"observation_digest":"sha256:d50172e2ac6d0462c307df0ae2dd1297617562ff8612b2f6f619c60b7adbe2e7","observation_id":"d5a83cd0-8776-4328-b1d2-2cfbce362864","resolution":{"observed_at":"2026-08-14T14:22:34.248597Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1709.09707","last_updated":"2018-12-12T12:33:30Z","snapshot_observed_at":"2026-08-14T20:31:25.435526Z","submitted_at":"2017-09-20T13:39:47Z","title":"Matroids over partial hyperstructures","version":2},"cited_work":{"arxiv_id":"1709.09707","doi":null,"metadata_source":"pith","pith_arxiv_id":"1709.09707","snapshot_observed_at":"2026-08-14T14:22:34.498921Z","title":"Matroids over partial hyperstructures","venue":"math.CO","work_id":"017fc89a-1770-4156-9280-34c04ecee8c9","year":2017},"citing_paper":{"arxiv_id":"1908.03420","last_updated":"2023-03-14T16:30:54Z","snapshot_observed_at":"2026-08-16T05:43:23.991468Z","submitted_at":"2019-08-09T11:43:12Z","title":"Perfect matroids over hyperfields","version":3},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-14T14:22:34.254031Z"},"links":{"cited_paper":"/paper/1709.09707","citing_paper":"/paper/1908.03420"},"observation_digest":"sha256:4576aee039ef25bccd14fb35cdde73f38a18f1b7e5923bb15534e00388603b6d","observation_id":"2ba4040f-3f32-40e3-b018-13b67b717b87","resolution":{"observed_at":"2026-08-14T14:22:34.504480Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:22:34.722456Z","title":"Bollen, Jan Draisma, and Rudi Pendavingh","venue":null,"work_id":"d0b716ed-c332-4df1-bcd6-3a4cc9254aab","year":2018},"citing_paper":{"arxiv_id":"1908.03420","last_updated":"2023-03-14T16:30:54Z","snapshot_observed_at":"2026-08-16T05:43:23.991468Z","submitted_at":"2019-08-09T11:43:12Z","title":"Perfect matroids over hyperfields","version":3},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-14T14:22:34.260222Z"},"links":{"citing_paper":"/paper/1908.03420"},"observation_digest":"sha256:c2f444e76224785e7da0a0e9b949af209ba3d9210ed02a9c4ec68152a42494fc","observation_id":"1b951f51-a492-4a85-b7b4-9d1855deae92","resolution":{"observed_at":"2026-08-14T14:22:34.727995Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T14:22:34.265220Z","title":"o rner, Michel Las Vergnas, Bernd Sturmfels, Neil White, and G\\","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"1908.03420","last_updated":"2023-03-14T16:30:54Z","snapshot_observed_at":"2026-08-16T05:43:23.991468Z","submitted_at":"2019-08-09T11:43:12Z","title":"Perfect matroids over hyperfields","version":3},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-14T14:22:34.265220Z"},"links":{"citing_paper":"/paper/1908.03420"},"observation_digest":"sha256:6eb024f754ea9dc3f317976edbef09550dc4f33a052e59ced126f46995809ed9","observation_id":"e735a076-eef0-46a9-bfc7-b6f996cc60b5","resolution":{"observed_at":"2026-08-14T14:22:34.265220Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1902.05592","last_updated":"2020-08-03T19:54:17Z","snapshot_observed_at":"2026-08-14T17:16:09.890427Z","submitted_at":"2019-02-14T20:20:38Z","title":"Matroids and their Dressians","version":2},"cited_work":{"arxiv_id":"1902.05592","doi":null,"metadata_source":"pith","pith_arxiv_id":"1902.05592","snapshot_observed_at":"2026-08-14T14:22:34.471162Z","title":"Matroids and their Dressians","venue":"math.CO","work_id":"1dce5dfa-4082-423d-b57b-5598072212ac","year":2019},"citing_paper":{"arxiv_id":"1908.03420","last_updated":"2023-03-14T16:30:54Z","snapshot_observed_at":"2026-08-16T05:43:23.991468Z","submitted_at":"2019-08-09T11:43:12Z","title":"Perfect matroids over hyperfields","version":3},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-14T14:22:34.270923Z"},"links":{"cited_paper":"/paper/1902.05592","citing_paper":"/paper/1908.03420"},"observation_digest":"sha256:36de41dcebe878c445f9dfcc19e148d45de0910a0fd4c62c050d24050e99025a","observation_id":"bd9414dd-0484-4ab5-adf3-fb4aac362a0c","resolution":{"observed_at":"2026-08-14T14:22:34.476478Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2003.03751","last_updated":"2020-12-25T13:50:45Z","snapshot_observed_at":"2026-08-04T20:29:53.483113Z","submitted_at":"2020-03-08T09:26:26Z","title":"Classification of doubly distributive skew hyperfields and stringent hypergroups","version":2},"cited_work":{"arxiv_id":"2003.03751","doi":null,"metadata_source":"pith","pith_arxiv_id":"2003.03751","snapshot_observed_at":"2026-08-14T14:22:34.448774Z","title":"Classification of doubly distributive skew hyperfields and stringent hypergroups","venue":"math.RA","work_id":"60551133-dccd-4c88-8009-9246f73af5bd","year":2020},"citing_paper":{"arxiv_id":"1908.03420","last_updated":"2023-03-14T16:30:54Z","snapshot_observed_at":"2026-08-16T05:43:23.991468Z","submitted_at":"2019-08-09T11:43:12Z","title":"Perfect matroids over hyperfields","version":3},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-14T14:22:34.276550Z"},"links":{"cited_paper":"/paper/2003.03751","citing_paper":"/paper/1908.03420"},"observation_digest":"sha256:f5b64f2121d68a14c7c6c17a960f9fb81b1b8b65f4652015cd65b8aaade26f2d","observation_id":"47366ea2-0446-4961-ae1e-be95cab03b71","resolution":{"observed_at":"2026-08-14T14:22:34.453877Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:22:34.693504Z","title":null,"venue":null,"work_id":"aa3b7dea-8aca-4b28-81c3-91727b3da99b","year":1986},"citing_paper":{"arxiv_id":"1908.03420","last_updated":"2023-03-14T16:30:54Z","snapshot_observed_at":"2026-08-16T05:43:23.991468Z","submitted_at":"2019-08-09T11:43:12Z","title":"Perfect matroids over hyperfields","version":3},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-14T14:22:34.284387Z"},"links":{"citing_paper":"/paper/1908.03420"},"observation_digest":"sha256:b4f79dec8e5b264453cac77a36cde135659c6ac8784e99da3e4b9988da6bf042","observation_id":"68ab28c9-6a4c-4380-9e8e-a9093b7fcdcf","resolution":{"observed_at":"2026-08-14T14:22:34.700023Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:22:34.672941Z","title":null,"venue":null,"work_id":"5ba2eb1d-b041-4fa6-a832-fffb8e2759fc","year":1992},"citing_paper":{"arxiv_id":"1908.03420","last_updated":"2023-03-14T16:30:54Z","snapshot_observed_at":"2026-08-16T05:43:23.991468Z","submitted_at":"2019-08-09T11:43:12Z","title":"Perfect matroids over hyperfields","version":3},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-14T14:22:34.290407Z"},"links":{"citing_paper":"/paper/1908.03420"},"observation_digest":"sha256:956993764ae955a1308c729bb62d6d1f2f0bb599a0f0b35eecec1bd4e56381e6","observation_id":"90fb3b87-c2f8-4b2c-85be-10982f439f9b","resolution":{"observed_at":"2026-08-14T14:22:34.677895Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T14:22:34.295354Z","title":null,"venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"1908.03420","last_updated":"2023-03-14T16:30:54Z","snapshot_observed_at":"2026-08-16T05:43:23.991468Z","submitted_at":"2019-08-09T11:43:12Z","title":"Perfect matroids over hyperfields","version":3},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-14T14:22:34.295354Z"},"links":{"citing_paper":"/paper/1908.03420"},"observation_digest":"sha256:2fdc9e137c688850d885891582d1899241e405562d95f80323db059278e89f6a","observation_id":"b4cc5682-486b-464d-b6f0-c2a3e9137a12","resolution":{"observed_at":"2026-08-14T14:22:34.295354Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T14:22:34.647065Z","title":"The diagonal of tropical matroid varieties and cycle intersections","venue":null,"work_id":"6620e2b7-c23f-4574-b2c5-76dac12e7d89","year":2013},"citing_paper":{"arxiv_id":"1908.03420","last_updated":"2023-03-14T16:30:54Z","snapshot_observed_at":"2026-08-16T05:43:23.991468Z","submitted_at":"2019-08-09T11:43:12Z","title":"Perfect matroids over hyperfields","version":3},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-14T14:22:34.300288Z"},"links":{"citing_paper":"/paper/1908.03420"},"observation_digest":"sha256:09ee4c25f7ebedbf1ff38a2d31765e8ab93f2590175f6e0ed7aa0d1088969470","observation_id":"62740df4-724e-439d-90f5-6bd7a9440af2","resolution":{"observed_at":"2026-08-14T14:22:34.652752Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T14:22:34.305234Z","title":"On the relation between hyperrings and fuzzy rings","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"1908.03420","last_updated":"2023-03-14T16:30:54Z","snapshot_observed_at":"2026-08-16T05:43:23.991468Z","submitted_at":"2019-08-09T11:43:12Z","title":"Perfect matroids over hyperfields","version":3},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-14T14:22:34.305234Z"},"links":{"citing_paper":"/paper/1908.03420"},"observation_digest":"sha256:5f2f2ed0815178c154ec0dfd62bd1bcdcef9c2f870b9a4e18bd99728c5fd7557","observation_id":"58ecd2bd-c2aa-47d7-b5f8-73029ce6d826","resolution":{"observed_at":"2026-08-14T14:22:34.305234Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1802.01838","last_updated":"2018-02-06T08:14:36Z","snapshot_observed_at":"2026-08-14T19:48:30.513262Z","submitted_at":"2018-02-06T08:14:36Z","title":"Real Tropical Singularities and Bergman Fans","version":1},"cited_work":{"arxiv_id":"1802.01838","doi":null,"metadata_source":"pith","pith_arxiv_id":"1802.01838","snapshot_observed_at":"2026-08-14T14:22:34.426133Z","title":"Real Tropical Singularities and Bergman Fans","venue":"math.AG","work_id":"8d1b221c-9863-4323-8bc3-352e072dd43f","year":2018},"citing_paper":{"arxiv_id":"1908.03420","last_updated":"2023-03-14T16:30:54Z","snapshot_observed_at":"2026-08-16T05:43:23.991468Z","submitted_at":"2019-08-09T11:43:12Z","title":"Perfect matroids over hyperfields","version":3},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-14T14:22:34.310806Z"},"links":{"cited_paper":"/paper/1802.01838","citing_paper":"/paper/1908.03420"},"observation_digest":"sha256:be4b25162d77d46aa25287bfb27a2568e956d0674f4df74975161adbc5ee4d67","observation_id":"0b534eb8-d219-4c81-8224-3c2285c529d4","resolution":{"observed_at":"2026-08-14T14:22:34.431287Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:22:34.619993Z","title":"Approximation des corps valu\\' e s complets de caract\\' e ristique p =0 par ceux de caract\\' e ristique 0","venue":null,"work_id":"2e6e4c47-fbe1-439b-a4bc-3f5f104a6700","year":1956},"citing_paper":{"arxiv_id":"1908.03420","last_updated":"2023-03-14T16:30:54Z","snapshot_observed_at":"2026-08-16T05:43:23.991468Z","submitted_at":"2019-08-09T11:43:12Z","title":"Perfect matroids over hyperfields","version":3},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-14T14:22:34.316300Z"},"links":{"citing_paper":"/paper/1908.03420"},"observation_digest":"sha256:5435e95e57a832a2a9ec33fb62fb1bcd3803b1ff1495db7fdf9ef1f8422e89e5","observation_id":"373428e6-68bf-4572-8090-40c3ae5b2e7a","resolution":{"observed_at":"2026-08-14T14:22:34.625835Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:22:34.598658Z","title":"A class of hyperrings and hyperfields","venue":null,"work_id":"b15933de-057d-44e3-8dec-54d0ae249de2","year":1983},"citing_paper":{"arxiv_id":"1908.03420","last_updated":"2023-03-14T16:30:54Z","snapshot_observed_at":"2026-08-16T05:43:23.991468Z","submitted_at":"2019-08-09T11:43:12Z","title":"Perfect matroids over hyperfields","version":3},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-14T14:22:34.321234Z"},"links":{"citing_paper":"/paper/1908.03420"},"observation_digest":"sha256:9b6d45e56574f09311eb2b323443c24c4a08db9286181eca0ac24d7b136c6cdc","observation_id":"264966b4-78a9-4bc3-9aca-b9e1b7f2213c","resolution":{"observed_at":"2026-08-14T14:22:34.605577Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:22:34.580330Z","title":null,"venue":null,"work_id":"f34d6984-ffee-4205-8af0-cacf91d389ff","year":1966},"citing_paper":{"arxiv_id":"1908.03420","last_updated":"2023-03-14T16:30:54Z","snapshot_observed_at":"2026-08-16T05:43:23.991468Z","submitted_at":"2019-08-09T11:43:12Z","title":"Perfect matroids over hyperfields","version":3},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-14T14:22:34.325902Z"},"links":{"citing_paper":"/paper/1908.03420"},"observation_digest":"sha256:33e79275e95539bd207e3fd25e63b60a19d9fd62e573012ec51e6c77538c4e77","observation_id":"22c7f4e2-a9fa-4440-8e7c-bfc28afda7c3","resolution":{"observed_at":"2026-08-14T14:22:34.586234Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:22:34.562978Z","title":"On circuit valuation of matroids","venue":null,"work_id":"2e35c3b9-fb15-4f9b-8706-bcfe0fb1a6ca","year":2001},"citing_paper":{"arxiv_id":"1908.03420","last_updated":"2023-03-14T16:30:54Z","snapshot_observed_at":"2026-08-16T05:43:23.991468Z","submitted_at":"2019-08-09T11:43:12Z","title":"Perfect matroids over hyperfields","version":3},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-14T14:22:34.330461Z"},"links":{"citing_paper":"/paper/1908.03420"},"observation_digest":"sha256:0ac60a051cbaa2e6122b8dd3209a8994cb817029dd8d097f199e5bfa446be0e2","observation_id":"229c56a7-98ac-44ec-a416-82c4faaccd02","resolution":{"observed_at":"2026-08-14T14:22:34.568077Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1802.02447","last_updated":"2018-04-20T11:25:03Z","snapshot_observed_at":"2026-08-14T19:47:57.078523Z","submitted_at":"2018-02-07T14:45:57Z","title":"Field extensions, Derivations, and Matroids over Skew Hyperfields","version":3},"cited_work":{"arxiv_id":"1802.02447","doi":null,"metadata_source":"pith","pith_arxiv_id":"1802.02447","snapshot_observed_at":"2026-08-14T14:22:34.398515Z","title":"Field extensions, Derivations, and Matroids over Skew Hyperfields","venue":"math.CO","work_id":"0ce70393-ba28-4333-8a90-ac4179d6aadf","year":2018},"citing_paper":{"arxiv_id":"1908.03420","last_updated":"2023-03-14T16:30:54Z","snapshot_observed_at":"2026-08-16T05:43:23.991468Z","submitted_at":"2019-08-09T11:43:12Z","title":"Perfect matroids over hyperfields","version":3},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-14T14:22:34.335376Z"},"links":{"cited_paper":"/paper/1802.02447","citing_paper":"/paper/1908.03420"},"observation_digest":"sha256:665e20df579e2be2e5ec4bd4e14ba8e4a27af1902a514f23064edcb3374bef30","observation_id":"e231799e-bd7f-4819-bacc-197c1016cd2d","resolution":{"observed_at":"2026-08-14T14:22:34.407391Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:22:34.544779Z","title":"Computing tropical linear spaces","venue":null,"work_id":"d71552b5-3920-4c76-bff0-e7bd806a4a6b","year":2013},"citing_paper":{"arxiv_id":"1908.03420","last_updated":"2023-03-14T16:30:54Z","snapshot_observed_at":"2026-08-16T05:43:23.991468Z","submitted_at":"2019-08-09T11:43:12Z","title":"Perfect matroids over hyperfields","version":3},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-14T14:22:34.340632Z"},"links":{"citing_paper":"/paper/1908.03420"},"observation_digest":"sha256:39561e82f42920a80a715146681361e9a1824c9d45eaf569b4d20da0a55d19f6","observation_id":"96343401-6b2a-4588-9938-f1d003a920c6","resolution":{"observed_at":"2026-08-14T14:22:34.549876Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:22:34.528259Z","title":"A tropical intersection product in matroidal fans","venue":null,"work_id":"91ea0029-0975-4b21-96be-32f9e44f9655","year":2013},"citing_paper":{"arxiv_id":"1908.03420","last_updated":"2023-03-14T16:30:54Z","snapshot_observed_at":"2026-08-16T05:43:23.991468Z","submitted_at":"2019-08-09T11:43:12Z","title":"Perfect matroids over hyperfields","version":3},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-14T14:22:34.345415Z"},"links":{"citing_paper":"/paper/1908.03420"},"observation_digest":"sha256:9591f9e7fd132f61e933e0ae7d91cceb1d8ac1ae357373997b315d8c6c1f0b41","observation_id":"1793b182-9e2f-448c-a5ff-e64f1bd4d403","resolution":{"observed_at":"2026-08-14T14:22:34.533728Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T14:22:34.350080Z","title":null,"venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"1908.03420","last_updated":"2023-03-14T16:30:54Z","snapshot_observed_at":"2026-08-16T05:43:23.991468Z","submitted_at":"2019-08-09T11:43:12Z","title":"Perfect matroids over hyperfields","version":3},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-14T14:22:34.350080Z"},"links":{"citing_paper":"/paper/1908.03420"},"observation_digest":"sha256:b1a2f656b68d8bfd11f648a21264a7189add37b936c387a32bfe909fda47a927","observation_id":"67105d75-1f52-4d69-9bae-017c25d0926f","resolution":{"observed_at":"2026-08-14T14:22:34.350080Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"1908.03420","last_updated":"2023-03-14T16:30:54Z","latest_version":3,"primary_category":"math.CO","snapshot_observed_at":"2026-08-16T05:43:23.991468Z","submitted_at":"2019-08-09T11:43:12Z","title":"Perfect matroids over hyperfields"},"reference_resolution":{"displayed":20,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":8,"verified_exact":5,"verified_fuzzy":7},"total_outbound_references":20},"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":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 20 of 20 outbound references and 1 inbound Pith citation observation for arXiv:1908.03420."}