{"as_of":"2026-08-22T10:31:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:2eb2555cd2b55dfc971364a7d3c7e7ab6d85efad63187c317258d4a3d8de50ca","coverage":[{"denominator":49,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":49,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T20:00:30.100287Z","state":"measured"},{"denominator":49,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":49,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-22T06:32:14.747728+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/2607.16797/citation-record","integrity":"/paper/2607.16797/integrity","json":"/paper/2607.16797/citation-record.json","paper":"/paper/2607.16797"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T20:00:24.827925Z","title":"Anderson and W","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:24.827925Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:3da93d7f591e6a3cd5cc99fee7fdcd0f58867ed5c30a6232301f8c606f78ead4","observation_id":"ce602323-dd1e-46fa-8ddc-9b5fb656545e","resolution":{"observed_at":"2026-08-01T20:00:24.827925Z","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":"2026-08-01T20:00:24.882787Z","title":"Barcucci, A.D","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:24.882787Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:7477b172dec6a2a8c688d121d57f1dcd75362fe8d9f502834628d2371faabd4f","observation_id":"bd11a65a-e492-4666-bb45-03fd9fbf5cd3","resolution":{"observed_at":"2026-08-01T20:00:24.882787Z","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":"2026-08-01T20:00:24.975685Z","title":"Bergeron and S","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:24.975685Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:ef84b5240e38a8b907dfe99b3fe808c471cedf23694997ac29efd32106e81e4d","observation_id":"754dc18c-91ef-45be-9000-36813bb044de","resolution":{"observed_at":"2026-08-01T20:00:24.975685Z","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":"2026-08-01T20:00:25.077359Z","title":"Billey, W","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:25.077359Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:155b4515eb1f118283a34fbe5b65d84e6c9d810796ddf903947b182bf975b92b","observation_id":"e19e5f4a-ec8c-4509-9817-a2b899d7e11c","resolution":{"observed_at":"2026-08-01T20:00:25.077359Z","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":"2026-08-01T20:00:25.202412Z","title":"Bobi ´nski, and G","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:25.202412Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:3dce3285600e9feb9008ae4128a18b9325cc0c611f6a2aac4a045b959ffa7496","observation_id":"99fa40b5-df50-4641-beb5-0dbeceacf4a2","resolution":{"observed_at":"2026-08-01T20:00:25.202412Z","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":"2026-08-01T20:00:25.397015Z","title":null,"venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:25.397015Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:89320836788bb713eebcafb47a43c77e28bd9af3c71be2e40b07c6b1bc8707f0","observation_id":"995e6156-a756-4d75-87b4-e2a8fb5e91ee","resolution":{"observed_at":"2026-08-01T20:00:25.397015Z","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":"2026-08-01T20:00:25.574331Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:25.574331Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:84c00ff6e3cbb20bc886d1297199e6e1f7fd3323ea4109ea9cbd374d08944073","observation_id":"cfdd86ef-df54-4d24-a171-0b84582f2a43","resolution":{"observed_at":"2026-08-01T20:00:25.574331Z","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":"2026-08-01T20:00:25.704441Z","title":"Chen, N.J.Y.Fan, R","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:25.704441Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:34f04697681a8a6e1f097ba28374b70158a124ea73c36007dcf6b2706fe73e01","observation_id":"4fca1499-ffb6-4845-9d75-3ae969a22c92","resolution":{"observed_at":"2026-08-01T20:00:25.704441Z","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":"2026-08-01T20:00:25.833377Z","title":"Chen, S.H.F","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:25.833377Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:1e4af8b2ebf962cf07df2cdedc385c4bf73a89a1d0e1825a7560610cfd0f53ac","observation_id":"d16a1826-1d35-470b-a0c7-74ba44daffcc","resolution":{"observed_at":"2026-08-01T20:00:25.833377Z","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":"2026-08-01T20:00:25.989222Z","title":"Edelman and C","venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:25.989222Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:0cf74dac729e01165ae0e450a316ffbaa9de60fd382e0e28cfd1a921298f1b15","observation_id":"b2c3d999-4a49-45d6-8ba4-8a67f5e0088d","resolution":{"observed_at":"2026-08-01T20:00:25.989222Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1810.11916","last_updated":"2018-10-29T01:04:23Z","snapshot_observed_at":"2026-08-14T18:08:04.620470Z","submitted_at":"2018-10-29T01:04:23Z","title":"Bumpless Pipedreams, Reduced Word Tableaux and Stanley Symmetric Functions","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1810.11916","snapshot_observed_at":"2026-08-01T20:00:26.159951Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:26.159951Z"},"links":{"cited_paper":"/paper/1810.11916","citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:ec9a4a480c96a0c8aa5b08d2bb3a3a1541550227c298f0171216055530effa14","observation_id":"14c68f9b-bfda-4983-af7d-f615e91717b9","resolution":{"observed_at":"2026-08-01T20:00:26.159951Z","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":"2026-08-01T20:00:26.271296Z","title":"Fan, P .L","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:26.271296Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:db311ea50ae875d7534c5fdf98bdde26f506898a4c2780789d826249c6446ef2","observation_id":"190aa287-ec6a-4318-ad41-807ec11044b6","resolution":{"observed_at":"2026-08-01T20:00:26.271296Z","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":"2026-08-01T20:00:26.412711Z","title":"Gabriel, Unzerlegbare Darstellungen I, Manuscripta Math.6(1972), pp.71–103","venue":null,"work_id":null,"year":1972},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:26.412711Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:9fc3e282e6b0d45c0306366128da285ba6cdeb55daca7ba2b40ab68cff6b0701","observation_id":"9e08d2d5-7adf-4e12-8879-bb613c42d806","resolution":{"observed_at":"2026-08-01T20:00:26.412711Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2506.09421","last_updated":"2025-06-11T06:09:52Z","snapshot_observed_at":"2026-08-15T18:04:55.463715Z","submitted_at":"2025-06-11T06:09:52Z","title":"Graham positivity of triple Schubert calculus","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.09421","snapshot_observed_at":"2026-08-01T20:00:26.501210Z","title":"Gao and R","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:26.501210Z"},"links":{"cited_paper":"/paper/2506.09421","citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:33645da47b42c62c6a9b666b4c58a67ffb02cbe2dd77647cd73f1dda8eb8f28c","observation_id":"9e564fd7-2267-41b8-967c-1de8c8a4731b","resolution":{"observed_at":"2026-08-01T20:00:26.501210Z","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":"2026-08-01T20:00:26.587606Z","title":null,"venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:26.587606Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:338260d82eb51c8030abfa46e42b7bdec3b27af1f76f92268cde5a432b6f52e4","observation_id":"ca0bd0d0-115c-4dc3-a869-15fd03be6312","resolution":{"observed_at":"2026-08-01T20:00:26.587606Z","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":"2026-08-01T20:00:26.685686Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:26.685686Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:a58cafc0cbd040996ae474c6fd4d556b611fd91b1241f7df9dfd2563319c5598","observation_id":"8af287f6-3962-4cd9-b576-8843e423dfa1","resolution":{"observed_at":"2026-08-01T20:00:26.685686Z","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":"2026-08-01T20:00:26.788346Z","title":null,"venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:26.788346Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:aa77c67a6816edc0ba41f51b356645d15ace8aa367915f7b056fe90510edd9c1","observation_id":"96e8f964-75a0-4f25-b529-1a4813ca8652","resolution":{"observed_at":"2026-08-01T20:00:26.788346Z","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":"2026-08-01T20:00:26.901669Z","title":"Kinser and J","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:26.901669Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:8d783834c0f3a3cb4abd37db29ce0e9bf293f795a5cec8eaee35dbc1cfdf8e4e","observation_id":"5a847c1b-0733-48df-8c8c-5e4c02728d81","resolution":{"observed_at":"2026-08-01T20:00:26.901669Z","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":"2026-08-01T20:00:26.978680Z","title":null,"venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:26.978680Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:ebb4e7a8edd1908ca97c7e7befdbe59672df41c31a74d55859cb557ec90f01c7","observation_id":"5f0f1fd1-4b9a-4047-8d80-2da2b2a090e2","resolution":{"observed_at":"2026-08-01T20:00:26.978680Z","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":"2026-08-01T20:00:27.059097Z","title":"Knutson, T","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:27.059097Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:8272d27c3081e0ca47adeb12a8346c3cd71d949e9a51950f6e4e2a69bfd751c1","observation_id":"01f7181b-c320-4578-b67e-7a12d7db1c0e","resolution":{"observed_at":"2026-08-01T20:00:27.059097Z","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":"2026-08-01T20:00:27.159159Z","title":"Knutson and T","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:27.159159Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:f29ce1061af47e05195c0440ec9e5b24deac444b8a0a5985c4557a0e6e8f1946","observation_id":"551c80bf-7c6b-43c6-b5ca-2e2b89b99ec2","resolution":{"observed_at":"2026-08-01T20:00:27.159159Z","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":"2026-08-01T20:00:27.280196Z","title":"Knutson and P","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:27.280196Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:276c8b0a1f5bf263c1ab12c2239cfaf57cc2b90732422f633d53ad996313e080","observation_id":"07dcf1c3-ab40-4bf2-a19e-6b372c945fbc","resolution":{"observed_at":"2026-08-01T20:00:27.280196Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2306.13855","last_updated":"2023-06-24T04:06:55Z","snapshot_observed_at":"2026-08-17T17:44:53.194208Z","submitted_at":"2023-06-24T04:06:55Z","title":"Schubert puzzles and integrability III: separated descents","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2306.13855","snapshot_observed_at":"2026-08-01T20:00:27.413251Z","title":"Knutson and P","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:27.413251Z"},"links":{"cited_paper":"/paper/2306.13855","citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:9bdface3544f87ca0b949a852abf93df77b7f35fdd5009a9679524d23c77eea7","observation_id":"66784741-5488-454b-a624-aa5e3ebbcf68","resolution":{"observed_at":"2026-08-01T20:00:27.413251Z","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":"2026-08-01T20:00:27.486036Z","title":null,"venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:27.486036Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:7922524d5d56aa30a5e916c0e4859ef513ad05fd3e224fe6b2d4cb36f80a76fc","observation_id":"cac29102-2cf4-48a1-a308-ace9d1f51ec1","resolution":{"observed_at":"2026-08-01T20:00:27.486036Z","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":"2026-08-01T20:00:27.619486Z","title":"Lam and M","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:27.619486Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:4f0dee70692439766fefd85c9d659bbe7713b6fdf3b40e328601aa497b7a6650","observation_id":"23ee44cf-f51a-4aaf-ac01-08f3e6bc2897","resolution":{"observed_at":"2026-08-01T20:00:27.619486Z","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":"2026-08-01T20:00:27.749313Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:27.749313Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:b240394639d69c0ac668169282792d2b5b1c8b6b58f01b340c27faad92de8f67","observation_id":"ba1f3e82-379b-43c0-8784-00fee0ee2b4d","resolution":{"observed_at":"2026-08-01T20:00:27.749313Z","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":"2026-08-01T20:00:27.881314Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:27.881314Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:503d8d53586ff9a262fb595d1fccb4dbe3fb39321de902e393f31d1f4d1b1fa4","observation_id":"14f5eb36-ff78-42d3-9c90-fcad8a72c777","resolution":{"observed_at":"2026-08-01T20:00:27.881314Z","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":"2026-08-01T20:00:27.994304Z","title":"Littelmann, On spherical double cones","venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:27.994304Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:9934ef18454015233e0f6d7b6a2d3595f1204da6083f4a4965594c9130c294cf","observation_id":"7c54c827-1436-4611-9133-35a2edcbc155","resolution":{"observed_at":"2026-08-01T20:00:27.994304Z","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":"2026-08-01T20:00:28.123018Z","title":"Lusztig, Introduction to quantum groups, Progress in Math.110, Birkh¨auser, Boston,1993","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:28.123018Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:e7f335a5cfa4b7cd3638a10494ba3bf01a1877a7900d5638eb5d39cd1dc79988","observation_id":"3514036f-4ad1-4bea-bf74-42e8c8aeee72","resolution":{"observed_at":"2026-08-01T20:00:28.123018Z","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":"2026-08-01T20:00:28.226000Z","title":null,"venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:28.226000Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:3f30edc19cdbe7af22e0b6c9e720b7f3b978ec59eb9c55714aaba986acb4c9be","observation_id":"428f8939-1313-4010-850d-c2e4b3904ba5","resolution":{"observed_at":"2026-08-01T20:00:28.226000Z","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":"2026-08-01T20:00:28.328040Z","title":"Magyar, J","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:28.328040Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:12655e4e00658ef88d27a2b0e10ba021409e4736ae2ae5b48554b10ceeb4556c","observation_id":"60ee7d9a-daa7-45ca-addc-4c78274351c5","resolution":{"observed_at":"2026-08-01T20:00:28.328040Z","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":"2026-08-01T20:00:28.436964Z","title":null,"venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:28.436964Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:d3646e55686566f2ec2bbca1ea089845a4ba3e08f37def7d47651e7551b24bbc","observation_id":"17f5f92d-003d-4d67-b8d6-b6055abd0447","resolution":{"observed_at":"2026-08-01T20:00:28.436964Z","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":"2026-08-01T20:00:28.539166Z","title":null,"venue":null,"work_id":null,"year":1979},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:28.539166Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:74f7ba51b286f2c46c07f6c959ca5e2170551ce4d91a52b17a45a37fcab34487","observation_id":"3bc7b098-cf6d-4516-80e3-d7ba3d87e72b","resolution":{"observed_at":"2026-08-01T20:00:28.539166Z","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":"2026-08-01T20:00:28.628007Z","title":"Molev and B.E","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:28.628007Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:c910f2ac8a833a8ad6e85ce9b1f04f1b676b7bec3a1a38b6369a82fb9cc945b5","observation_id":"2be7f69a-9c04-49ca-818c-b847a5d02210","resolution":{"observed_at":"2026-08-01T20:00:28.628007Z","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":"2026-08-01T20:00:28.710196Z","title":"Pechenik, A","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:28.710196Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:cab459bbeb21698e55e50871862f815293f63436fdf24e27593613335cd62781","observation_id":"7dae73a9-e049-4146-b457-4246f225cbc4","resolution":{"observed_at":"2026-08-01T20:00:28.710196Z","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":"10.1017/fmp.2017.4","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Pechenik, A.Yong","venue":"Forum of Mathematics Pi","work_id":"3ebd3f79-5581-4fcf-a68c-d1b7314938b0","year":2017},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:28.801876Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:70fbc406d1573e1da59b576bbcec39bc3c874c48b3ef1f13964974e160e19260","observation_id":"b15c70d8-30d7-437a-b877-0ac431e9c72d","resolution":{"observed_at":"2026-08-01T20:03:31.048066Z","resolver_source":"doi","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T20:00:28.908135Z","title":"Pechenik, A.Yong","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:28.908135Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:1a77415d9d193e3f07f911af0590c215259065cf3c624ea43ff52822516484e2","observation_id":"9e3468a5-b7e1-4da8-8f48-9d2b21e49665","resolution":{"observed_at":"2026-08-01T20:00:28.908135Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"math/0609764","last_updated":"2006-09-27T16:18:24Z","snapshot_observed_at":"2026-08-19T19:20:01.208099Z","submitted_at":"2006-09-27T16:18:24Z","title":"Total positivity, Grassmannians, and networks","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"math/0609764","snapshot_observed_at":"2026-08-01T20:00:28.981792Z","title":"Postnikov","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:28.981792Z"},"links":{"cited_paper":"/paper/math/0609764","citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:9ed102ad926984854e26db27530bde1bad08ff9f18030b58b5454f4c00ecb976","observation_id":"a4a1e40f-a607-45dc-a3dd-3ab75d077b27","resolution":{"observed_at":"2026-08-01T20:00:28.981792Z","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":"2026-08-01T20:00:29.091221Z","title":"Rajchgot","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:29.091221Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:d66d2e68f9bc625d76b274545317588ee02b3791d8451f6c7a73f2d65150797d","observation_id":"db8f41c3-0264-4c40-80f9-f8f6bcba4430","resolution":{"observed_at":"2026-08-01T20:00:29.091221Z","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":"2026-08-01T20:00:29.202958Z","title":null,"venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:29.202958Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:f5a30167c2927c8377308aca9943664f019999f17fd4dce79401d98863e22c32","observation_id":"ac8cfee3-9fe5-454b-b03c-07cb880800fd","resolution":{"observed_at":"2026-08-01T20:00:29.202958Z","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":"2026-08-01T20:00:29.303268Z","title":"Richardson and T.A","venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:29.303268Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:a40446b9418916f372895943d39ce8bbc544a84a3823d3e5c7b8e675d713a245","observation_id":"2de29865-df0c-4ee0-8a51-ce302ba6a7f2","resolution":{"observed_at":"2026-08-01T20:00:29.303268Z","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":"2026-08-01T20:00:29.397139Z","title":"Robinson, A Pieri-type formula forH ∗ T(SL n(C)/B), J","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:29.397139Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:987f716e5439230b1749251dfcec4c32f0d0a4c9f0d3315ae03f55f7ce1855f2","observation_id":"51e647ac-1427-4a19-b52e-f5be0b4a715f","resolution":{"observed_at":"2026-08-01T20:00:29.397139Z","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":"2026-08-01T20:00:29.487866Z","title":"Samuel, Molev–Sagan type formula for double Schubert polynomials, J","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:29.487866Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:de6f200525686a8cb90059240f23a5ab00876cb097f9b3532564f020fda82660","observation_id":"814d0a1b-1bf2-4ee1-b7fb-c9e516f9eb5b","resolution":{"observed_at":"2026-08-01T20:00:29.487866Z","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":"2026-08-01T20:00:29.641505Z","title":"Smirnov, Resolutions of singularities for Schubert varieties in double Grassmannians","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:29.641505Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:d3d231ab10772d62573fefd7e766c84e2c053497b10fc5d3dd7386b962b43503","observation_id":"8a993353-3587-458d-9b8b-4420304b34eb","resolution":{"observed_at":"2026-08-01T20:00:29.641505Z","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":"2026-08-01T20:00:29.729407Z","title":"Shimozono and S","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:29.729407Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:ff1935eeb365330fdc75146e34db601c50ea791009ae994ec4b0e4c0b98f44e9","observation_id":"7dd9fa9b-e295-4322-b09b-cb7d52a7f0d9","resolution":{"observed_at":"2026-08-01T20:00:29.729407Z","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":"2026-08-01T20:00:29.826195Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:29.826195Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:5aec9dffd5e3a9ebbaeae51d83f6ff48db337d03c4bda44536b635c11c87398b","observation_id":"1b6967c7-930c-4468-8636-ffd074c5eda1","resolution":{"observed_at":"2026-08-01T20:00:29.826195Z","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":"2026-08-01T20:00:29.911881Z","title":"Wheeler and P","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:29.911881Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:93c72f76f086a60a6a621324ec7913c9dec3dd4af5e5f82c38bad6b0248c8e7b","observation_id":"7707297b-2277-46f2-931a-a728abf94e0c","resolution":{"observed_at":"2026-08-01T20:00:29.911881Z","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":"2026-08-01T20:00:30.016263Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:30.016263Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:6aa4bd1fae8e276ec4ebe4ffecaa462ad7ecef66135a30262ac7f6ab51b86651","observation_id":"25ad326e-f5ee-4b50-a002-a3641b3bc377","resolution":{"observed_at":"2026-08-01T20:00:30.016263Z","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":"2026-08-01T20:00:30.100287Z","title":"Wyser and A","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-01T20:00:30.100287Z"},"links":{"citing_paper":"/paper/2607.16797"},"observation_digest":"sha256:787c6678dd5e5d3d1e177659ec4aabcefe646c858a1e5dd6966849e51f823c32","observation_id":"8feb2854-f37a-41eb-af84-e3ff8a95e7fc","resolution":{"observed_at":"2026-08-01T20:00:30.100287Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.16797","last_updated":"2026-07-18T12:28:09Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-08-16T09:51:24.011016Z","submitted_at":"2026-07-18T12:28:09Z","title":"Equivariant Schubert Calculus for Inverse Grassmannian Permutations"},"reference_resolution":{"displayed":49,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":48,"verified_exact":1,"verified_fuzzy":0},"total_outbound_references":49},"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 22 August 2026, this Paper Citation Record lists 49 of 49 outbound references and 0 inbound Pith citation observations for arXiv:2607.16797."}