{"as_of":"2026-08-13T18:57:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:1f76a502f9c0619f70d9c6eaf8a7f3b5d7ee5ccd8050557c02326326f7919b20","coverage":[{"denominator":14,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":14,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-02T03:59:04.633659Z","state":"measured"},{"denominator":14,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":14,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+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/2607.13783/citation-record","integrity":"/paper/2607.13783/integrity","json":"/paper/2607.13783/citation-record.json","paper":"/paper/2607.13783"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:59:03.976636Z","title":"Lorentzian polynomials","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.13783","last_updated":"2026-07-15T12:38:20Z","snapshot_observed_at":"2026-08-06T19:34:34.022882Z","submitted_at":"2026-07-15T12:38:20Z","title":"Matroid correspondence","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-02T03:59:03.976636Z"},"links":{"citing_paper":"/paper/2607.13783"},"observation_digest":"sha256:c813c1c0d61c0b96e57a1f7145ca1820a453f9de96ff3d83cc99656de8e67102","observation_id":"79c43351-f114-41a4-ab2d-e59145beabe9","resolution":{"observed_at":"2026-08-02T03:59:03.976636Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:59:04.036236Z","title":"Representation theory for polymatroids","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13783","last_updated":"2026-07-15T12:38:20Z","snapshot_observed_at":"2026-08-06T19:34:34.022882Z","submitted_at":"2026-07-15T12:38:20Z","title":"Matroid correspondence","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-02T03:59:04.036236Z"},"links":{"citing_paper":"/paper/2607.13783"},"observation_digest":"sha256:a2219e4d0b4839bc48682c869b2220585089fae932cf971fac474946d159593e","observation_id":"264aba0d-88f4-4c59-9707-46a4cd9345fc","resolution":{"observed_at":"2026-08-02T03:59:04.036236Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:59:04.099740Z","title":"Matchings and -matroids","venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2607.13783","last_updated":"2026-07-15T12:38:20Z","snapshot_observed_at":"2026-08-06T19:34:34.022882Z","submitted_at":"2026-07-15T12:38:20Z","title":"Matroid correspondence","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-02T03:59:04.099740Z"},"links":{"citing_paper":"/paper/2607.13783"},"observation_digest":"sha256:956d627786fbf48a0e21f7742b78740e2ba7ab15a0c85236a1443e504b73d367","observation_id":"ec1e584c-8d6d-4a2a-bbe9-994ede12ad79","resolution":{"observed_at":"2026-08-02T03:59:04.099740Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:59:04.154429Z","title":"When are multidegrees positive? Adv","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.13783","last_updated":"2026-07-15T12:38:20Z","snapshot_observed_at":"2026-08-06T19:34:34.022882Z","submitted_at":"2026-07-15T12:38:20Z","title":"Matroid correspondence","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-02T03:59:04.154429Z"},"links":{"citing_paper":"/paper/2607.13783"},"observation_digest":"sha256:7323b687c66fa59f7c937250023cfd36b368e8b251b6922d1f95588c9a37207d","observation_id":"a762cc4d-2bcb-4162-87a3-8deca5a5bae3","resolution":{"observed_at":"2026-08-02T03:59:04.154429Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:59:04.212971Z","title":"The B ergman fan of a polymatroid","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.13783","last_updated":"2026-07-15T12:38:20Z","snapshot_observed_at":"2026-08-06T19:34:34.022882Z","submitted_at":"2026-07-15T12:38:20Z","title":"Matroid correspondence","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-02T03:59:04.212971Z"},"links":{"citing_paper":"/paper/2607.13783"},"observation_digest":"sha256:5611839fcb02f81844e3a6e576e89c9320517a7627365694ab89e1478912478b","observation_id":"d37bd9a8-130f-4d54-a2fd-a75cdfc07dac","resolution":{"observed_at":"2026-08-02T03:59:04.212971Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:59:04.290991Z","title":"Combinatorial flats and S chubert varieties of subspace arrangements","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13783","last_updated":"2026-07-15T12:38:20Z","snapshot_observed_at":"2026-08-06T19:34:34.022882Z","submitted_at":"2026-07-15T12:38:20Z","title":"Matroid correspondence","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-02T03:59:04.290991Z"},"links":{"citing_paper":"/paper/2607.13783"},"observation_digest":"sha256:c3bbe35681cb20f53fb3d4e52f12e7adabe0b541d6d1bf2dd543870e4f546743","observation_id":"6638ab73-8c1e-4df0-a56f-c538ee9dd0ca","resolution":{"observed_at":"2026-08-02T03:59:04.290991Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:59:04.345834Z","title":"Logarithmic concavity for morphisms of matroids","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.13783","last_updated":"2026-07-15T12:38:20Z","snapshot_observed_at":"2026-08-06T19:34:34.022882Z","submitted_at":"2026-07-15T12:38:20Z","title":"Matroid correspondence","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-02T03:59:04.345834Z"},"links":{"citing_paper":"/paper/2607.13783"},"observation_digest":"sha256:ac32276802979693b0aaec61ca73d718104cc8d5db75b0529e4fa09bffd389d3","observation_id":"a26ad679-e0d1-42c4-a2bf-4ea29294b7a3","resolution":{"observed_at":"2026-08-02T03:59:04.345834Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:59:04.384013Z","title":"Intersection theory of polymatroids","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.13783","last_updated":"2026-07-15T12:38:20Z","snapshot_observed_at":"2026-08-06T19:34:34.022882Z","submitted_at":"2026-07-15T12:38:20Z","title":"Matroid correspondence","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-02T03:59:04.384013Z"},"links":{"citing_paper":"/paper/2607.13783"},"observation_digest":"sha256:a0842a119c403142408824ba771b7c1436cb8b87e3224f9bd84cfd173d4b2539","observation_id":"7ec9f15e-b9cb-4dcb-af49-3df163e6537c","resolution":{"observed_at":"2026-08-02T03:59:04.384013Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:59:04.459662Z","title":"Intersection Theory , volume 2 of Ergebnisse der Mathematik und ihrer Grenzgebiete","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2607.13783","last_updated":"2026-07-15T12:38:20Z","snapshot_observed_at":"2026-08-06T19:34:34.022882Z","submitted_at":"2026-07-15T12:38:20Z","title":"Matroid correspondence","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-02T03:59:04.459662Z"},"links":{"citing_paper":"/paper/2607.13783"},"observation_digest":"sha256:4fc244d2ac41b29908539474e51eb180ba1150f8a247ff873e4f8308bd83e27d","observation_id":"a033b340-6371-4285-95ab-d87e02346a8e","resolution":{"observed_at":"2026-08-02T03:59:04.459662Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2506.22415","last_updated":"2025-06-27T17:42:27Z","snapshot_observed_at":"2026-08-08T15:16:23.218063Z","submitted_at":"2025-06-27T17:42:27Z","title":"Linear operators preserving volume polynomials","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.22415","snapshot_observed_at":"2026-08-02T03:59:04.540212Z","title":"Linear operators preserving volume polynomials","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13783","last_updated":"2026-07-15T12:38:20Z","snapshot_observed_at":"2026-08-06T19:34:34.022882Z","submitted_at":"2026-07-15T12:38:20Z","title":"Matroid correspondence","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-02T03:59:04.540212Z"},"links":{"cited_paper":"/paper/2506.22415","citing_paper":"/paper/2607.13783"},"observation_digest":"sha256:cc5d263230095285c01a7402765f4a12666499678df905b95644144ed16a626e","observation_id":"9bbdb3e3-5a62-4903-a880-aeab63343756","resolution":{"observed_at":"2026-08-02T03:59:04.540212Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.08881","last_updated":"2025-06-14T11:10:11Z","snapshot_observed_at":"2026-08-07T15:45:39.204748Z","submitted_at":"2025-05-13T18:11:59Z","title":"Realizations of homology classes and projection areas","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.08881","snapshot_observed_at":"2026-08-02T03:59:04.591834Z","title":"Realizations of homology classes and projection areas","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13783","last_updated":"2026-07-15T12:38:20Z","snapshot_observed_at":"2026-08-06T19:34:34.022882Z","submitted_at":"2026-07-15T12:38:20Z","title":"Matroid correspondence","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-02T03:59:04.591834Z"},"links":{"cited_paper":"/paper/2505.08881","citing_paper":"/paper/2607.13783"},"observation_digest":"sha256:6590df2ff1afa57de8168c7ee83f53a55cae413c4fd7cde996fa1eb9fec57c7f","observation_id":"cbdae856-135d-4978-b9e8-411e082eb213","resolution":{"observed_at":"2026-08-02T03:59:04.591834Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:59:04.620128Z","title":"Weak maps of combinatorial geometries","venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"2607.13783","last_updated":"2026-07-15T12:38:20Z","snapshot_observed_at":"2026-08-06T19:34:34.022882Z","submitted_at":"2026-07-15T12:38:20Z","title":"Matroid correspondence","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-02T03:59:04.620128Z"},"links":{"citing_paper":"/paper/2607.13783"},"observation_digest":"sha256:1797c17699f9b2f82f2c88b5d66e5d7c8d70fe6da3fd14e006bcd9cb00cdb364","observation_id":"a968fee0-5dbf-4a9e-8579-90f2561bd42b","resolution":{"observed_at":"2026-08-02T03:59:04.620128Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:59:04.626271Z","title":"Matroid Theory , volume 21 of Oxford Graduate Texts in Mathematics","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.13783","last_updated":"2026-07-15T12:38:20Z","snapshot_observed_at":"2026-08-06T19:34:34.022882Z","submitted_at":"2026-07-15T12:38:20Z","title":"Matroid correspondence","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-02T03:59:04.626271Z"},"links":{"citing_paper":"/paper/2607.13783"},"observation_digest":"sha256:ecf122b58564f7318569012bcc10a3f4727aa89c4ef80314bd4fd3b85c6f03b0","observation_id":"fb09f2e7-200a-4d69-9b88-96afc179e216","resolution":{"observed_at":"2026-08-02T03:59:04.626271Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:59:04.633659Z","title":"Theory of Matroids , volume 26 of Encyclopedia of Mathematics and its Applications","venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2607.13783","last_updated":"2026-07-15T12:38:20Z","snapshot_observed_at":"2026-08-06T19:34:34.022882Z","submitted_at":"2026-07-15T12:38:20Z","title":"Matroid correspondence","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-02T03:59:04.633659Z"},"links":{"citing_paper":"/paper/2607.13783"},"observation_digest":"sha256:64e7810662e3fdca6af40300ea475e88e0cf32c699d43b9c4277e16b626dd4d1","observation_id":"be4928c1-2bd3-4243-a20d-317783984345","resolution":{"observed_at":"2026-08-02T03:59:04.633659Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.13783","last_updated":"2026-07-15T12:38:20Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-08-06T19:34:34.022882Z","submitted_at":"2026-07-15T12:38:20Z","title":"Matroid correspondence"},"reference_resolution":{"displayed":14,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":14,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":14},"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":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 14 of 14 outbound references and 0 inbound Pith citation observations for arXiv:2607.13783."}