{"as_of":"2026-08-22T19:48:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:a1dce5104e4ccabc8d753f9e32e776425f54eff8b0f0cb79a0af36bb8bc516f0","coverage":[{"denominator":27,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":27,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-09T01:06:20.567828Z","state":"measured"},{"denominator":27,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":27,"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/2502.03768/citation-record","integrity":"/paper/2502.03768/integrity","json":"/paper/2502.03768/citation-record.json","paper":"/paper/2502.03768"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"1408.4718","last_updated":"2017-05-23T09:27:15Z","snapshot_observed_at":"2026-08-14T23:22:30.177587Z","submitted_at":"2014-08-20T16:45:11Z","title":"Quantum Integrability and Generalised Quantum Schubert Calculus","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1408.4718","snapshot_observed_at":"2026-08-09T01:06:20.435254Z","title":"Quantum integrability and generalised quantum Schubert calculus,","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2502.03768","last_updated":"2025-04-15T04:08:18Z","snapshot_observed_at":"2026-08-18T08:25:36.482499Z","submitted_at":"2025-02-06T04:06:35Z","title":"Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double $\\beta$-Grothendieck polynomials","version":3},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-09T01:06:20.435254Z"},"links":{"cited_paper":"/paper/1408.4718","citing_paper":"/paper/2502.03768"},"observation_digest":"sha256:c06b5ba2a67ff37ff0496f3e858ae0efeba3468f90b58922282653510b9c56da","observation_id":"1dfb96c3-ad75-4419-860c-733782cfaca9","resolution":{"observed_at":"2026-08-09T01:06:20.435254Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1912.03792","last_updated":"2020-08-31T05:15:47Z","snapshot_observed_at":"2026-08-18T01:51:02.574804Z","submitted_at":"2019-12-09T00:19:30Z","title":"3d N=2 Chern-Simons-matter theory, Bethe ansatz, and quantum K-theory of Grassmannians","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1912.03792","snapshot_observed_at":"2026-08-09T01:06:20.441545Z","title":"3d N = 2 Chern-Simons-matter theory, Bethe ansatz, and quantum K- theory of Grassmannians,","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2502.03768","last_updated":"2025-04-15T04:08:18Z","snapshot_observed_at":"2026-08-18T08:25:36.482499Z","submitted_at":"2025-02-06T04:06:35Z","title":"Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double $\\beta$-Grothendieck polynomials","version":3},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-09T01:06:20.441545Z"},"links":{"cited_paper":"/paper/1912.03792","citing_paper":"/paper/2502.03768"},"observation_digest":"sha256:65dca4251c84f8039117f871313ee8c0644c5b6be48569ffa93978e87c429f08","observation_id":"e1cf696e-b73b-4de0-9c86-4456861f2f4e","resolution":{"observed_at":"2026-08-09T01:06:20.441545Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/9312096","last_updated":"1993-12-13T07:58:59Z","snapshot_observed_at":"2026-08-13T18:07:19.638679Z","submitted_at":"1993-12-13T07:58:59Z","title":"Quantum cohomology of flag manifolds and Toda lattices","version":1},"cited_work":{"arxiv_id":"hep-th/9312096","doi":null,"metadata_source":"pith","pith_arxiv_id":"hep-th/9312096","snapshot_observed_at":"2026-08-09T01:06:21.014299Z","title":"Quantum cohomology of flag manifolds and Toda lattices","venue":"hep-th","work_id":"1261073a-ba6d-488f-8123-3edd13ab82ed","year":1993},"citing_paper":{"arxiv_id":"2502.03768","last_updated":"2025-04-15T04:08:18Z","snapshot_observed_at":"2026-08-18T08:25:36.482499Z","submitted_at":"2025-02-06T04:06:35Z","title":"Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double $\\beta$-Grothendieck polynomials","version":3},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-09T01:06:20.447391Z"},"links":{"cited_paper":"/paper/hep-th/9312096","citing_paper":"/paper/2502.03768"},"observation_digest":"sha256:791e8d29b3ae8381b578a71edd0c5ea163dab0b7f2226b6604843aa9c33e0b9f","observation_id":"168ecb57-2c63-44a8-a3fe-395b297a8e9b","resolution":{"observed_at":"2026-08-09T01:06:21.019385Z","resolver_source":"local_arxiv","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":{"arxiv_id":"math/0108105","last_updated":"2001-08-15T18:35:46Z","snapshot_observed_at":"2026-08-22T11:06:06.567610Z","submitted_at":"2001-08-15T18:35:46Z","title":"Quantum K-theory on flag manifolds, finite-difference Toda lattices and quantum groups","version":1},"cited_work":{"arxiv_id":"math/0108105","doi":null,"metadata_source":"pith","pith_arxiv_id":"math/0108105","snapshot_observed_at":"2026-08-09T01:06:20.992235Z","title":"Quantum K-theory on flag manifolds, finite-difference Toda lattices and quantum groups","venue":"math.AG","work_id":"fff46794-96b9-4917-bb0e-b3c486e321a9","year":2001},"citing_paper":{"arxiv_id":"2502.03768","last_updated":"2025-04-15T04:08:18Z","snapshot_observed_at":"2026-08-18T08:25:36.482499Z","submitted_at":"2025-02-06T04:06:35Z","title":"Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double $\\beta$-Grothendieck polynomials","version":3},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-09T01:06:20.452795Z"},"links":{"cited_paper":"/paper/math/0108105","citing_paper":"/paper/2502.03768"},"observation_digest":"sha256:0d46a67a59f4db8bd90de20e583401fc96e4df9b20bde63970741572926507e2","observation_id":"8e7002e7-240c-4a55-b826-7ac35ad44137","resolution":{"observed_at":"2026-08-09T01:06:20.997403Z","resolver_source":"local_arxiv","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":{"arxiv_id":"1705.10419","last_updated":"2021-09-24T22:22:34Z","snapshot_observed_at":"2026-08-20T21:14:12.914577Z","submitted_at":"2017-05-30T00:35:08Z","title":"Quantum K-theory of Quiver Varieties and Many-Body Systems","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1705.10419","snapshot_observed_at":"2026-08-09T01:06:20.458160Z","title":"Quantum K-theory of quiver varieties and many-body systems,","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2502.03768","last_updated":"2025-04-15T04:08:18Z","snapshot_observed_at":"2026-08-18T08:25:36.482499Z","submitted_at":"2025-02-06T04:06:35Z","title":"Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double $\\beta$-Grothendieck polynomials","version":3},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-09T01:06:20.458160Z"},"links":{"cited_paper":"/paper/1705.10419","citing_paper":"/paper/2502.03768"},"observation_digest":"sha256:c6b12f630e38437bfdb635d7bdeb9db7841b2d9db97cd8549f634110e9fbd693","observation_id":"9bb64391-97b9-441c-b43a-843a9ab4eb1a","resolution":{"observed_at":"2026-08-09T01:06:20.458160Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/9401103","last_updated":"1994-01-21T22:44:42Z","snapshot_observed_at":"2026-08-19T13:51:39.876468Z","submitted_at":"1994-01-20T23:18:52Z","title":"Quantum cohomology of partial flag manifolds","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"hep-th/9401103","snapshot_observed_at":"2026-08-09T01:06:20.463491Z","title":"Quantum cohomology of partial flag manifolds Fn1···nk ,","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2502.03768","last_updated":"2025-04-15T04:08:18Z","snapshot_observed_at":"2026-08-18T08:25:36.482499Z","submitted_at":"2025-02-06T04:06:35Z","title":"Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double $\\beta$-Grothendieck polynomials","version":3},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-09T01:06:20.463491Z"},"links":{"cited_paper":"/paper/hep-th/9401103","citing_paper":"/paper/2502.03768"},"observation_digest":"sha256:df5cf80750adfe39d607be36b5d721ff36511f23c8f52e7db94f3f0cddc7b0d1","observation_id":"ef7ad399-f4a0-41cf-8155-7749c418f00b","resolution":{"observed_at":"2026-08-09T01:06:20.463491Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/9405056","last_updated":"1994-10-18T23:23:22Z","snapshot_observed_at":"2026-08-13T09:56:16.420352Z","submitted_at":"1994-05-10T03:44:28Z","title":"Quantum Cohomology of Partial Flag Manifolds and a Residue Formula for Their Intersection Parings","version":2},"cited_work":{"arxiv_id":"hep-th/9405056","doi":null,"metadata_source":"pith","pith_arxiv_id":"hep-th/9405056","snapshot_observed_at":"2026-08-09T01:06:20.940681Z","title":"Quantum Cohomology of Partial Flag Manifolds and a Residue Formula for Their Intersection Parings","venue":"hep-th","work_id":"fea526cd-367f-46cd-b9af-98b6dff7267d","year":1994},"citing_paper":{"arxiv_id":"2502.03768","last_updated":"2025-04-15T04:08:18Z","snapshot_observed_at":"2026-08-18T08:25:36.482499Z","submitted_at":"2025-02-06T04:06:35Z","title":"Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double $\\beta$-Grothendieck polynomials","version":3},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-09T01:06:20.469478Z"},"links":{"cited_paper":"/paper/hep-th/9405056","citing_paper":"/paper/2502.03768"},"observation_digest":"sha256:008cd67a9a925a7a37b6893a093a0175faadbbb745ea3749a9f90b11dafd8ce3","observation_id":"7a83cf92-ce6d-4f0b-9a54-9647d3e12a4f","resolution":{"observed_at":"2026-08-09T01:06:20.945007Z","resolver_source":"local_arxiv","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":{"arxiv_id":"2306.11094","last_updated":"2023-10-16T01:20:10Z","snapshot_observed_at":"2026-08-16T15:22:46.643143Z","submitted_at":"2023-06-19T18:00:04Z","title":"Quantum K theory rings of partial flag manifolds","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2306.11094","snapshot_observed_at":"2026-08-09T01:06:20.475022Z","title":"Quantum K theory rings of partial flag manifolds,","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2502.03768","last_updated":"2025-04-15T04:08:18Z","snapshot_observed_at":"2026-08-18T08:25:36.482499Z","submitted_at":"2025-02-06T04:06:35Z","title":"Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double $\\beta$-Grothendieck polynomials","version":3},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-09T01:06:20.475022Z"},"links":{"cited_paper":"/paper/2306.11094","citing_paper":"/paper/2502.03768"},"observation_digest":"sha256:fc09879e76fc91e26cf412532fadfd7faf7bb598920f5f773ef3d56e7f44ba14","observation_id":"02b06989-659e-4985-840e-76c424475f88","resolution":{"observed_at":"2026-08-09T01:06:20.475022Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2208.01091","last_updated":"2024-09-23T10:30:46Z","snapshot_observed_at":"2026-08-18T02:04:36.504038Z","submitted_at":"2022-08-01T18:44:53Z","title":"Quantum K theory of Grassmannians, Wilson line operators, and Schur bundles","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2208.01091","snapshot_observed_at":"2026-08-09T01:06:20.480423Z","title":"Quantum K theory of Grassmannians, Wilson line operators, and Schur bundles,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2502.03768","last_updated":"2025-04-15T04:08:18Z","snapshot_observed_at":"2026-08-18T08:25:36.482499Z","submitted_at":"2025-02-06T04:06:35Z","title":"Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double $\\beta$-Grothendieck polynomials","version":3},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-09T01:06:20.480423Z"},"links":{"cited_paper":"/paper/2208.01091","citing_paper":"/paper/2502.03768"},"observation_digest":"sha256:dacde16b25244f3e8f89befa2d2be0a4923a817a16ee38ee1b77a7702bf3055e","observation_id":"c9e21e82-4221-443f-a8ca-30b73536847a","resolution":{"observed_at":"2026-08-09T01:06:20.480423Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2310.03826","last_updated":"2024-11-15T17:10:50Z","snapshot_observed_at":"2026-08-16T14:54:41.573852Z","submitted_at":"2023-10-05T18:19:50Z","title":"Quantum K Whitney relations for partial flag varieties","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2310.03826","snapshot_observed_at":"2026-08-09T01:06:20.485799Z","title":"Quantum K Whitney relations for partial flag varieties,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2502.03768","last_updated":"2025-04-15T04:08:18Z","snapshot_observed_at":"2026-08-18T08:25:36.482499Z","submitted_at":"2025-02-06T04:06:35Z","title":"Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double $\\beta$-Grothendieck polynomials","version":3},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-09T01:06:20.485799Z"},"links":{"cited_paper":"/paper/2310.03826","citing_paper":"/paper/2502.03768"},"observation_digest":"sha256:63de30590824ca056615807540e12f4d854cd8f7833e08eed20ba8d5626db489","observation_id":"c0c979dd-365e-4187-abf5-f92065a66898","resolution":{"observed_at":"2026-08-09T01:06:20.485799Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/9306005","last_updated":"1993-06-02T16:46:27Z","snapshot_observed_at":"2026-08-21T01:55:14.071889Z","submitted_at":"1993-06-01T18:23:59Z","title":"Yang-Baxter equation, symmetric functions and Grothendieck polynomials","version":2},"cited_work":{"arxiv_id":"hep-th/9306005","doi":null,"metadata_source":"pith","pith_arxiv_id":"hep-th/9306005","snapshot_observed_at":"2026-08-09T01:06:20.871755Z","title":"Yang-Baxter equation, symmetric functions and Grothendieck polynomials","venue":"hep-th","work_id":"7e13f36f-4f10-4e7f-a92c-e42a36c0d34e","year":1993},"citing_paper":{"arxiv_id":"2502.03768","last_updated":"2025-04-15T04:08:18Z","snapshot_observed_at":"2026-08-18T08:25:36.482499Z","submitted_at":"2025-02-06T04:06:35Z","title":"Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double $\\beta$-Grothendieck polynomials","version":3},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-09T01:06:20.491353Z"},"links":{"cited_paper":"/paper/hep-th/9306005","citing_paper":"/paper/2502.03768"},"observation_digest":"sha256:f8ae6df0fc5a08c8e9af2928bcab69aa2a4997a4eaf28099ee087b030cec69a5","observation_id":"96cea71c-a715-4b6c-84de-bb3461cd3eb2","resolution":{"observed_at":"2026-08-09T01:06:20.876203Z","resolver_source":"local_arxiv","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":{"arxiv_id":"1908.07364","last_updated":"2020-03-31T23:09:45Z","snapshot_observed_at":"2026-08-21T00:31:56.280114Z","submitted_at":"2019-08-20T14:02:19Z","title":"Colored five-vertex models and Lascoux polynomials and atoms","version":2},"cited_work":{"arxiv_id":"1908.07364","doi":null,"metadata_source":"pith","pith_arxiv_id":"1908.07364","snapshot_observed_at":"2026-08-09T01:06:20.852085Z","title":"Colored five-vertex models and Lascoux polynomials and atoms","venue":"math.CO","work_id":"6df09483-0322-489d-85c9-f884e58714e4","year":2019},"citing_paper":{"arxiv_id":"2502.03768","last_updated":"2025-04-15T04:08:18Z","snapshot_observed_at":"2026-08-18T08:25:36.482499Z","submitted_at":"2025-02-06T04:06:35Z","title":"Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double $\\beta$-Grothendieck polynomials","version":3},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-09T01:06:20.496874Z"},"links":{"cited_paper":"/paper/1908.07364","citing_paper":"/paper/2502.03768"},"observation_digest":"sha256:d06250791d14300579676b9a9140b610692726897b463bae75116476c25a0157","observation_id":"2e6a1dca-47b6-4c17-be5b-075d9ce6c89a","resolution":{"observed_at":"2026-08-09T01:06:20.857131Z","resolver_source":"local_arxiv","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":{"arxiv_id":"2007.04533","last_updated":"2020-10-27T03:00:34Z","snapshot_observed_at":"2026-08-19T14:03:25.908721Z","submitted_at":"2020-07-09T03:28:06Z","title":"Double Grothendieck polynomials and colored lattice models","version":2},"cited_work":{"arxiv_id":"2007.04533","doi":null,"metadata_source":"pith","pith_arxiv_id":"2007.04533","snapshot_observed_at":"2026-08-09T01:06:20.829619Z","title":"Double Grothendieck polynomials and colored lattice models","venue":"math.CO","work_id":"1199adb2-a9a0-41ed-9782-553977dbe564","year":2020},"citing_paper":{"arxiv_id":"2502.03768","last_updated":"2025-04-15T04:08:18Z","snapshot_observed_at":"2026-08-18T08:25:36.482499Z","submitted_at":"2025-02-06T04:06:35Z","title":"Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double $\\beta$-Grothendieck polynomials","version":3},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-09T01:06:20.501850Z"},"links":{"cited_paper":"/paper/2007.04533","citing_paper":"/paper/2502.03768"},"observation_digest":"sha256:180c74381995653311ccc70f1416934240f9dd7a98918bbdde8544a53f8320bc","observation_id":"4e73556a-05e0-4b75-8407-5490c02f3012","resolution":{"observed_at":"2026-08-09T01:06:20.835074Z","resolver_source":"local_arxiv","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":{"arxiv_id":"2007.04310","last_updated":"2021-09-10T17:47:01Z","snapshot_observed_at":"2026-08-10T11:51:20.067973Z","submitted_at":"2020-07-08T17:58:04Z","title":"Frozen Pipes: Lattice Models for Grothendieck Polynomials","version":3},"cited_work":{"arxiv_id":"2007.04310","doi":null,"metadata_source":"pith","pith_arxiv_id":"2007.04310","snapshot_observed_at":"2026-08-09T01:06:20.807429Z","title":"Frozen Pipes: Lattice Models for Grothendieck Polynomials","venue":"math.CO","work_id":"70d35948-d2ad-4c3f-83cc-4ed4888ad0fc","year":2020},"citing_paper":{"arxiv_id":"2502.03768","last_updated":"2025-04-15T04:08:18Z","snapshot_observed_at":"2026-08-18T08:25:36.482499Z","submitted_at":"2025-02-06T04:06:35Z","title":"Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double $\\beta$-Grothendieck polynomials","version":3},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-09T01:06:20.505937Z"},"links":{"cited_paper":"/paper/2007.04310","citing_paper":"/paper/2502.03768"},"observation_digest":"sha256:f6568e65b10585e61846da6140d1c33849ea94f2de4c9bbeef7b96949562a1bb","observation_id":"776f9521-a9c4-469c-8399-308f174c0798","resolution":{"observed_at":"2026-08-09T01:06:20.812883Z","resolver_source":"local_arxiv","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T01:06:21.087487Z","title":"Diagonalisation of GL(N ) invariant transfer matrices and quantum N -wave system (Lee model),","venue":null,"work_id":"86237db1-03a9-4341-8e5d-56ed2fb27283","year":1983},"citing_paper":{"arxiv_id":"2502.03768","last_updated":"2025-04-15T04:08:18Z","snapshot_observed_at":"2026-08-18T08:25:36.482499Z","submitted_at":"2025-02-06T04:06:35Z","title":"Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double $\\beta$-Grothendieck polynomials","version":3},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-09T01:06:20.509882Z"},"links":{"citing_paper":"/paper/2502.03768"},"observation_digest":"sha256:9c9c134859f5c387651dffd0eedb9487f87e9450eb429ad7508f69171147eb41","observation_id":"c99eba93-4bfe-44f5-bbbd-e798fcd125cb","resolution":{"observed_at":"2026-08-09T01:06:21.092541Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":{"arxiv_id":"1808.00716","last_updated":"2019-05-17T09:02:14Z","snapshot_observed_at":"2026-08-14T18:45:11.884605Z","submitted_at":"2018-08-02T09:06:21Z","title":"Quantum Sheaf Cohomology and Duality of Flag Manifolds","version":2},"cited_work":{"arxiv_id":"1808.00716","doi":null,"metadata_source":"pith","pith_arxiv_id":"1808.00716","snapshot_observed_at":"2026-08-09T01:06:20.784445Z","title":"Quantum Sheaf Cohomology and Duality of Flag Manifolds","venue":"hep-th","work_id":"75775828-8204-4c63-a187-c3356511d601","year":2018},"citing_paper":{"arxiv_id":"2502.03768","last_updated":"2025-04-15T04:08:18Z","snapshot_observed_at":"2026-08-18T08:25:36.482499Z","submitted_at":"2025-02-06T04:06:35Z","title":"Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double $\\beta$-Grothendieck polynomials","version":3},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-09T01:06:20.513678Z"},"links":{"cited_paper":"/paper/1808.00716","citing_paper":"/paper/2502.03768"},"observation_digest":"sha256:99874430b12679c22b8e240b022da2c76edcf9e2ab79f16abdcd2d28f7086176","observation_id":"601bf2c8-583f-4936-9531-62fd5e93a5f6","resolution":{"observed_at":"2026-08-09T01:06:20.790242Z","resolver_source":"local_arxiv","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":{"arxiv_id":"0704.1761","last_updated":"2007-08-30T23:56:18Z","snapshot_observed_at":"2026-08-15T10:42:45.897201Z","submitted_at":"2007-04-13T14:06:31Z","title":"GLSM's for partial flag manifolds","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0704.1761","snapshot_observed_at":"2026-08-09T01:06:20.517513Z","title":"GLSM’s for partial flag manifolds,","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2502.03768","last_updated":"2025-04-15T04:08:18Z","snapshot_observed_at":"2026-08-18T08:25:36.482499Z","submitted_at":"2025-02-06T04:06:35Z","title":"Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double $\\beta$-Grothendieck polynomials","version":3},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-09T01:06:20.517513Z"},"links":{"cited_paper":"/paper/0704.1761","citing_paper":"/paper/2502.03768"},"observation_digest":"sha256:b08bf90ba28214b6bb0d2c31d613ac55717774dae3215eb502a57ae8e59336fe","observation_id":"cf8d8438-ed9b-4efd-9a4d-4c3f7f5c1da2","resolution":{"observed_at":"2026-08-09T01:06:20.517513Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0901.4744","last_updated":"2009-02-04T17:39:19Z","snapshot_observed_at":"2026-08-15T05:56:20.300808Z","submitted_at":"2009-01-29T19:02:40Z","title":"Supersymmetric vacua and Bethe ansatz","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0901.4744","snapshot_observed_at":"2026-08-09T01:06:20.521643Z","title":"Supersymmetric Vacua and Bethe Ansatz,","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2502.03768","last_updated":"2025-04-15T04:08:18Z","snapshot_observed_at":"2026-08-18T08:25:36.482499Z","submitted_at":"2025-02-06T04:06:35Z","title":"Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double $\\beta$-Grothendieck polynomials","version":3},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-09T01:06:20.521643Z"},"links":{"cited_paper":"/paper/0901.4744","citing_paper":"/paper/2502.03768"},"observation_digest":"sha256:6b81baffcb08543d40043ccd2f2bd6c60a1571900205eeb32d2f72cf6d9d6446","observation_id":"09d2cd47-a758-4a43-a1eb-a9c9527e7907","resolution":{"observed_at":"2026-08-09T01:06:20.521643Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0901.4748","last_updated":"2009-02-04T17:44:20Z","snapshot_observed_at":"2026-08-15T05:56:20.676366Z","submitted_at":"2009-01-29T19:50:53Z","title":"Quantum integrability and supersymmetric vacua","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0901.4748","snapshot_observed_at":"2026-08-09T01:06:20.526578Z","title":"Quantum Integrability and Supersymmetric Vacua,","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2502.03768","last_updated":"2025-04-15T04:08:18Z","snapshot_observed_at":"2026-08-18T08:25:36.482499Z","submitted_at":"2025-02-06T04:06:35Z","title":"Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double $\\beta$-Grothendieck polynomials","version":3},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-09T01:06:20.526578Z"},"links":{"cited_paper":"/paper/0901.4748","citing_paper":"/paper/2502.03768"},"observation_digest":"sha256:46899785b54bd115f77435549bf0c930bf0f597d8fd1a4769f87c5663b7e08df","observation_id":"7500e35f-b4d6-4530-8724-02c63eb2a388","resolution":{"observed_at":"2026-08-09T01:06:20.526578Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"q-alg/9610022","last_updated":"1996-11-10T17:04:29Z","snapshot_observed_at":"2026-07-07T07:00:34.721054Z","submitted_at":"1996-10-17T06:37:42Z","title":"Quantum double Schubert polynomials, quantum Schubert polynomials and Vafa-Intriligator formula","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"q-alg/9610022","snapshot_observed_at":"2026-08-09T01:06:20.531427Z","title":"Quantum double Schubert polynomials, quantum Schubert polynomials and Vafa-Intriligator formula,","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2502.03768","last_updated":"2025-04-15T04:08:18Z","snapshot_observed_at":"2026-08-18T08:25:36.482499Z","submitted_at":"2025-02-06T04:06:35Z","title":"Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double $\\beta$-Grothendieck polynomials","version":3},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-09T01:06:20.531427Z"},"links":{"cited_paper":"/paper/q-alg/9610022","citing_paper":"/paper/2502.03768"},"observation_digest":"sha256:92e3fae3c0eb9b6706bc0b32615322841b0048540eaa49c1a39dfb3d08107c1c","observation_id":"0fde1f7a-fdb1-4bfc-9113-4306f6fcab5f","resolution":{"observed_at":"2026-08-09T01:06:20.531427Z","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":"2026-08-09T01:06:21.067851Z","title":"Symmetry and flag manifolds,","venue":null,"work_id":"0380d29f-8333-4fa4-967a-cc0c1e4cdf47","year":1982},"citing_paper":{"arxiv_id":"2502.03768","last_updated":"2025-04-15T04:08:18Z","snapshot_observed_at":"2026-08-18T08:25:36.482499Z","submitted_at":"2025-02-06T04:06:35Z","title":"Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double $\\beta$-Grothendieck polynomials","version":3},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-09T01:06:20.536505Z"},"links":{"citing_paper":"/paper/2502.03768"},"observation_digest":"sha256:ddc58dcc3c66b4f6e8923dbd82a343aea2bf9b90d4002c85186440827264fc2f","observation_id":"95c0add9-7d92-4eac-8a77-6a5b5e1bfcbf","resolution":{"observed_at":"2026-08-09T01:06:21.074132Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":{"arxiv_id":"math/0608232","last_updated":"2006-08-09T22:39:29Z","snapshot_observed_at":"2026-08-22T04:52:17.710169Z","submitted_at":"2006-08-09T22:39:29Z","title":"Quantum Grothendieck Polynomials","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"math/0608232","snapshot_observed_at":"2026-08-09T01:06:20.541079Z","title":"Quantum Grothendieck Polynomials,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2502.03768","last_updated":"2025-04-15T04:08:18Z","snapshot_observed_at":"2026-08-18T08:25:36.482499Z","submitted_at":"2025-02-06T04:06:35Z","title":"Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double $\\beta$-Grothendieck polynomials","version":3},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-09T01:06:20.541079Z"},"links":{"cited_paper":"/paper/math/0608232","citing_paper":"/paper/2502.03768"},"observation_digest":"sha256:f9cacd02b29d9b998f5f253523a178fb755e173b71652c31f36335f1dd57ac6d","observation_id":"dbde154b-e28d-46bb-8021-c85db6913f38","resolution":{"observed_at":"2026-08-09T01:06:20.541079Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1310.0895","last_updated":"2013-10-03T04:51:38Z","snapshot_observed_at":"2026-08-16T04:12:03.529734Z","submitted_at":"2013-10-03T04:51:38Z","title":"A Thom-Porteous formula for connective K-theory using algebraic cobordism","version":1},"cited_work":{"arxiv_id":"1310.0895","doi":null,"metadata_source":"pith","pith_arxiv_id":"1310.0895","snapshot_observed_at":"2026-08-09T01:06:20.677259Z","title":"A Thom-Porteous formula for connective K-theory using algebraic cobordism","venue":"math.AG","work_id":"783fb0a4-bee6-497e-a0b6-014a0c291303","year":2013},"citing_paper":{"arxiv_id":"2502.03768","last_updated":"2025-04-15T04:08:18Z","snapshot_observed_at":"2026-08-18T08:25:36.482499Z","submitted_at":"2025-02-06T04:06:35Z","title":"Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double $\\beta$-Grothendieck polynomials","version":3},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-09T01:06:20.546263Z"},"links":{"cited_paper":"/paper/1310.0895","citing_paper":"/paper/2502.03768"},"observation_digest":"sha256:91112b7db4a816f10eea12b029ba553c09d5f87a01c2137b8df015674e4ffe8b","observation_id":"2f029312-db95-4982-877f-9ba9337e4cc9","resolution":{"observed_at":"2026-08-09T01:06:20.684473Z","resolver_source":"local_arxiv","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":{"arxiv_id":"math/0303245","last_updated":"2003-03-19T22:34:07Z","snapshot_observed_at":"2026-08-13T07:33:04.866705Z","submitted_at":"2003-03-19T22:34:07Z","title":"Quantum cohomology of partial flag manifolds","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"math/0303245","snapshot_observed_at":"2026-08-09T01:06:20.551346Z","title":"Quantum Cohomology of Partial Flag Manifolds,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2502.03768","last_updated":"2025-04-15T04:08:18Z","snapshot_observed_at":"2026-08-18T08:25:36.482499Z","submitted_at":"2025-02-06T04:06:35Z","title":"Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double $\\beta$-Grothendieck polynomials","version":3},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-09T01:06:20.551346Z"},"links":{"cited_paper":"/paper/math/0303245","citing_paper":"/paper/2502.03768"},"observation_digest":"sha256:fa82c82237a83bbb3fd049f65feca4754aaf22c6f04c87fa3dd845c6cd876a32","observation_id":"ff138012-39eb-487a-be28-b31d00e13401","resolution":{"observed_at":"2026-08-09T01:06:20.551346Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"math/0105014","last_updated":"2022-01-11T04:27:32Z","snapshot_observed_at":"2026-08-18T18:33:26.713747Z","submitted_at":"2001-05-02T18:59:57Z","title":"Quantum K-Theory I: Foundations","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"math/0105014","snapshot_observed_at":"2026-08-09T01:06:20.556657Z","title":"Quantum K-theory I: foundations,","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2502.03768","last_updated":"2025-04-15T04:08:18Z","snapshot_observed_at":"2026-08-18T08:25:36.482499Z","submitted_at":"2025-02-06T04:06:35Z","title":"Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double $\\beta$-Grothendieck polynomials","version":3},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-09T01:06:20.556657Z"},"links":{"cited_paper":"/paper/math/0105014","citing_paper":"/paper/2502.03768"},"observation_digest":"sha256:66ca4166ffa4067d16acb8e51d26d96237569420d27f437dd4bfaaf00cb0b855","observation_id":"24d17c23-1cc4-4315-9c87-92877f0d4441","resolution":{"observed_at":"2026-08-09T01:06:20.556657Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2302.09485","last_updated":"2023-11-13T11:12:37Z","snapshot_observed_at":"2026-08-16T15:54:21.344473Z","submitted_at":"2023-02-19T05:45:08Z","title":"A presentation of the torus-equivariant quantum $K$-theory ring of flag manifolds of type $A$, Part I: the defining ideal","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2302.09485","snapshot_observed_at":"2026-08-09T01:06:20.561913Z","title":"A presentation of the torus-equivariant quantum K-theory ring of flag manifolds of type A, Part I: the defining ideal,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2502.03768","last_updated":"2025-04-15T04:08:18Z","snapshot_observed_at":"2026-08-18T08:25:36.482499Z","submitted_at":"2025-02-06T04:06:35Z","title":"Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double $\\beta$-Grothendieck polynomials","version":3},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-09T01:06:20.561913Z"},"links":{"cited_paper":"/paper/2302.09485","citing_paper":"/paper/2502.03768"},"observation_digest":"sha256:6e1a7211eb05a9d2f7ac8678e64e441086d4760024ea3328fa8f5879de30de74","observation_id":"fa7b4c30-2d76-4c96-98b9-24a4f39ba299","resolution":{"observed_at":"2026-08-09T01:06:20.561913Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2305.17685","last_updated":"2023-05-28T10:41:33Z","snapshot_observed_at":"2026-08-16T15:28:55.898682Z","submitted_at":"2023-05-28T10:41:33Z","title":"A presentation of the torus-equivariant quantum $K$-theory ring of flag manifolds of type $A$, Part II: quantum double Grothendieck polynomials","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2305.17685","snapshot_observed_at":"2026-08-09T01:06:20.567828Z","title":"A presentation of the torus-equivariant quantum K-theory ring of flag manifolds of type A, Part II: quantum double Grothendieck polynomials,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2502.03768","last_updated":"2025-04-15T04:08:18Z","snapshot_observed_at":"2026-08-18T08:25:36.482499Z","submitted_at":"2025-02-06T04:06:35Z","title":"Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double $\\beta$-Grothendieck polynomials","version":3},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-09T01:06:20.567828Z"},"links":{"cited_paper":"/paper/2305.17685","citing_paper":"/paper/2502.03768"},"observation_digest":"sha256:0b24a40daad4440d52d8471a3204ad7924a6f1af2e17c274ad17427083e00b3c","observation_id":"942ef539-f848-442a-9414-cb60bf4f3223","resolution":{"observed_at":"2026-08-09T01:06:20.567828Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2502.03768","last_updated":"2025-04-15T04:08:18Z","latest_version":3,"primary_category":"math-ph","snapshot_observed_at":"2026-08-18T08:25:36.482499Z","submitted_at":"2025-02-06T04:06:35Z","title":"Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double $\\beta$-Grothendieck polynomials"},"reference_resolution":{"displayed":27,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":16,"verified_exact":9,"verified_fuzzy":2},"total_outbound_references":27},"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 27 of 27 outbound references and 0 inbound Pith citation observations for arXiv:2502.03768."}