{"as_of":"2026-08-11T00:04:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:f1e87ee0314cbf4381eaca553b2a65907ee7890adb503f9d56c84076b8ff70bd","coverage":[{"denominator":0,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":5,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":5,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-10T06:31:04.303077+00:00","state":"measured"},{"denominator":5,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":5,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T20:09:21.147694Z","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":"2026-06-29T10:53:19.115973Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2002.06164","last_updated":"2021-11-11T17:25:39Z","snapshot_observed_at":"2026-08-07T08:42:25.482159Z","submitted_at":"2020-02-14T18:30:49Z","title":"The positive tropical Grassmannian, the hypersimplex, and the m=2 amplituhedron","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2002.06164","snapshot_observed_at":"2026-08-10T20:09:21.147694Z","title":"Lukowski, M","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2501.09454","last_updated":"2025-02-04T13:27:59Z","snapshot_observed_at":"2026-08-10T19:58:55.152575Z","submitted_at":"2025-01-16T10:29:24Z","title":"Two-loop four-point amplitudes on the Coulomb branch of ${\\mathcal{N}}=4$ super Yang-Mills","version":2},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-10T20:09:21.147694Z"},"links":{"cited_paper":"/paper/2002.06164","citing_paper":"/paper/2501.09454"},"observation_digest":"sha256:7357b5381ec839b8faf70876655c2dbe24571f43b7f3b4d5b5aa3f4766304f5c","observation_id":"1e133ac5-de62-46b4-a011-f8a71e170ff2","resolution":{"observed_at":"2026-08-10T20:09:21.147694Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2002.06164","last_updated":"2021-11-11T17:25:39Z","snapshot_observed_at":"2026-08-07T08:42:25.482159Z","submitted_at":"2020-02-14T18:30:49Z","title":"The positive tropical Grassmannian, the hypersimplex, and the m=2 amplituhedron","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2002.06164","snapshot_observed_at":"2026-08-08T11:15:50.245920Z","title":"Lukowski, M","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2502.08016","last_updated":"2025-02-20T19:00:07Z","snapshot_observed_at":"2026-08-10T10:18:21.646364Z","submitted_at":"2025-02-11T23:31:39Z","title":"The CEGM NLSM","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-08T11:15:50.245920Z"},"links":{"cited_paper":"/paper/2002.06164","citing_paper":"/paper/2502.08016"},"observation_digest":"sha256:1ce711853c11d1d20076bebf50d3c3bc944987a4e43870b95412ee9b24aeea89","observation_id":"307cd268-9ca3-4180-b5a9-9e9d8a4bd679","resolution":{"observed_at":"2026-08-08T11:15:50.245920Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2002.06164","last_updated":"2021-11-11T17:25:39Z","snapshot_observed_at":"2026-08-07T08:42:25.482159Z","submitted_at":"2020-02-14T18:30:49Z","title":"The positive tropical Grassmannian, the hypersimplex, and the m=2 amplituhedron","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2002.06164","snapshot_observed_at":"2026-08-05T23:22:47.826134Z","title":"Lukowski, M","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2508.05443","last_updated":"2025-08-07T14:32:16Z","snapshot_observed_at":"2026-08-10T01:36:13.425750Z","submitted_at":"2025-08-07T14:32:16Z","title":"Geometric Landau Analysis and Symbol Bootstrap","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-05T23:22:47.826134Z"},"links":{"cited_paper":"/paper/2002.06164","citing_paper":"/paper/2508.05443"},"observation_digest":"sha256:0fdba3806756608488c022a231bf735cb8fe51995a1fb565e75d3a123abf0976","observation_id":"b0a83256-6915-47c5-98df-b17a3c8d9660","resolution":{"observed_at":"2026-08-05T23:22:47.826134Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2002.06164","last_updated":"2021-11-11T17:25:39Z","snapshot_observed_at":"2026-08-07T08:42:25.482159Z","submitted_at":"2020-02-14T18:30:49Z","title":"The positive tropical Grassmannian, the hypersimplex, and the m=2 amplituhedron","version":4},"cited_work":{"arxiv_id":"2002.06164","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2002.06164","snapshot_observed_at":"2026-06-29T10:53:19.115973Z","title":"Lukowski, M","venue":null,"work_id":"1b3ad47f-081f-412c-bb9f-e34b5405c312","year":2023},"citing_paper":{"arxiv_id":"2604.25212","last_updated":"2026-06-25T01:51:11Z","snapshot_observed_at":"2026-08-04T03:34:24.488076Z","submitted_at":"2026-04-28T04:30:55Z","title":"Noncrossing Duality and the Geometry of Positive Tropical Linear Spaces","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-05-07T16:16:21.355570Z"},"links":{"cited_paper":"/paper/2002.06164","citing_paper":"/paper/2604.25212"},"observation_digest":"sha256:96321b5761c9bcad2d9875291d6f7bc5f687535d4a8932dec6cfa119f3c7c121","observation_id":"36049f03-5b14-4584-ae08-5f8065f15e87","resolution":{"observed_at":"2026-05-11T23:46:57.023970Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2002.06164","last_updated":"2021-11-11T17:25:39Z","snapshot_observed_at":"2026-08-07T08:42:25.482159Z","submitted_at":"2020-02-14T18:30:49Z","title":"The positive tropical Grassmannian, the hypersimplex, and the m=2 amplituhedron","version":4},"cited_work":{"arxiv_id":"2002.06164","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2002.06164","snapshot_observed_at":"2026-06-29T10:53:19.115973Z","title":"Lukowski, M","venue":null,"work_id":"1b3ad47f-081f-412c-bb9f-e34b5405c312","year":2023},"citing_paper":{"arxiv_id":"2605.28926","last_updated":"2026-05-27T18:00:00Z","snapshot_observed_at":"2026-08-02T19:53:24.093781Z","submitted_at":"2026-05-27T18:00:00Z","title":"Multi-Loop Negative Geometries","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-06-29T10:53:13.001127Z"},"links":{"cited_paper":"/paper/2002.06164","citing_paper":"/paper/2605.28926"},"observation_digest":"sha256:b918ca327ef8c5265336b29d6a71d3d1ca25d1973592d77765c10c070974ecd2","observation_id":"27805f78-8345-42e2-9349-bc1f105f764b","resolution":{"observed_at":"2026-06-29T10:53:19.117265Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2002.06164/citation-record","integrity":"/paper/2002.06164/integrity","json":"/paper/2002.06164/citation-record.json","paper":"/paper/2002.06164"},"outbound":[],"paper":{"arxiv_id":"2002.06164","last_updated":"2021-11-11T17:25:39Z","latest_version":4,"primary_category":"math.CO","snapshot_observed_at":"2026-08-07T08:42:25.482159Z","submitted_at":"2020-02-14T18:30:49Z","title":"The positive tropical Grassmannian, the hypersimplex, and the m=2 amplituhedron"},"reference_resolution":{"displayed":0,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":0},"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":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 5 inbound Pith citation observations for arXiv:2002.06164."}