{"as_of":"2026-08-08T11:20:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:cc285f44bb4c55ecdf7b8553054398af0d188bc71a6edcc2deae87ee027b0a3f","coverage":[{"denominator":21,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":21,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-05T12:16:24.399793Z","state":"measured"},{"denominator":21,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":21,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+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/2509.01857/citation-record","integrity":"/paper/2509.01857/integrity","json":"/paper/2509.01857/citation-record.json","paper":"/paper/2509.01857"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T12:16:25.152242Z","title":null,"venue":null,"work_id":"00003306-dc3a-48ee-88c0-e9a2d973bb55","year":2024},"citing_paper":{"arxiv_id":"2509.01857","last_updated":"2025-09-02T00:52:17Z","snapshot_observed_at":"2026-08-05T12:16:20.694864Z","submitted_at":"2025-09-02T00:52:17Z","title":"Hybrid pipe dreams for the lower-upper scheme","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-05T12:16:24.272833Z"},"links":{"citing_paper":"/paper/2509.01857"},"observation_digest":"sha256:8945b0e898400f443285acf59943f7e65bdfcc74da6274011a0ab8d3478d3dbe","observation_id":"4f8da360-a97b-4760-9742-6333b0b7176f","resolution":{"observed_at":"2026-08-05T12:16:25.159366Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-05T12:16:25.134466Z","title":"4, 257 -- 269","venue":null,"work_id":"4530cbfa-2cc7-410c-960b-893f9f5bc6e3","year":1993},"citing_paper":{"arxiv_id":"2509.01857","last_updated":"2025-09-02T00:52:17Z","snapshot_observed_at":"2026-08-05T12:16:20.694864Z","submitted_at":"2025-09-02T00:52:17Z","title":"Hybrid pipe dreams for the lower-upper scheme","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-05T12:16:24.279114Z"},"links":{"citing_paper":"/paper/2509.01857"},"observation_digest":"sha256:1b501cb153171aa3f5ec476138c97018d9e6a34a9170bae41d1df2a646cc5f05","observation_id":"e93cc836-6425-422e-b057-f002d4151cda","resolution":{"observed_at":"2026-08-05T12:16:25.139759Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-05T12:16:25.115300Z","title":"Borho, J.-L","venue":null,"work_id":"90bc5eff-e025-4cd0-aa06-256c23f56bea","year":1989},"citing_paper":{"arxiv_id":"2509.01857","last_updated":"2025-09-02T00:52:17Z","snapshot_observed_at":"2026-08-05T12:16:20.694864Z","submitted_at":"2025-09-02T00:52:17Z","title":"Hybrid pipe dreams for the lower-upper scheme","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-05T12:16:24.285337Z"},"links":{"citing_paper":"/paper/2509.01857"},"observation_digest":"sha256:a5e8eeae4534286d4bf2988a12c346415a8b25f160d16193cf07f12e52bd05a5","observation_id":"1cc4dcde-5e1e-43ca-9392-330ac59d56c2","resolution":{"observed_at":"2026-08-05T12:16:25.122074Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"math-ph/0412031","last_updated":"2005-04-25T14:41:27Z","snapshot_observed_at":"2026-08-06T08:07:56.875823Z","submitted_at":"2004-12-10T15:31:55Z","title":"Inhomogenous model of crossing loops and multidegrees of some algebraic varieties","version":4},"cited_work":{"arxiv_id":"math-ph/0412031","doi":null,"metadata_source":"pith","pith_arxiv_id":"math-ph/0412031","snapshot_observed_at":"2026-08-05T12:16:24.958398Z","title":"Inhomogenous model of crossing loops and multidegrees of some algebraic varieties","venue":"math-ph","work_id":"2b7eea01-8c94-40ce-b1f7-1ab47846f085","year":2004},"citing_paper":{"arxiv_id":"2509.01857","last_updated":"2025-09-02T00:52:17Z","snapshot_observed_at":"2026-08-05T12:16:20.694864Z","submitted_at":"2025-09-02T00:52:17Z","title":"Hybrid pipe dreams for the lower-upper scheme","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-05T12:16:24.290948Z"},"links":{"cited_paper":"/paper/math-ph/0412031","citing_paper":"/paper/2509.01857"},"observation_digest":"sha256:44ffcd4864fdadbe111bdd8e3250b13028fce43c4709e8e3eeb774cd5764d1cd","observation_id":"7c8685a4-4004-4634-8836-3657fcc38f25","resolution":{"observed_at":"2026-08-05T12:16:24.964694Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-05T12:16:25.094699Z","title":null,"venue":null,"work_id":"f41795f1-6fd1-4afd-a1e9-76f5b61f2e16","year":1994},"citing_paper":{"arxiv_id":"2509.01857","last_updated":"2025-09-02T00:52:17Z","snapshot_observed_at":"2026-08-05T12:16:20.694864Z","submitted_at":"2025-09-02T00:52:17Z","title":"Hybrid pipe dreams for the lower-upper scheme","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-05T12:16:24.298178Z"},"links":{"citing_paper":"/paper/2509.01857"},"observation_digest":"sha256:1606b0c66efb9c131718d89dea38fb5a8aec8dc52bf87fb54acb8c61b8b567c0","observation_id":"8be13bd7-018b-4368-abab-b30511b3b8d2","resolution":{"observed_at":"2026-08-05T12:16:25.100635Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-05T12:16:24.303871Z","title":null,"venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2509.01857","last_updated":"2025-09-02T00:52:17Z","snapshot_observed_at":"2026-08-05T12:16:20.694864Z","submitted_at":"2025-09-02T00:52:17Z","title":"Hybrid pipe dreams for the lower-upper scheme","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-05T12:16:24.303871Z"},"links":{"citing_paper":"/paper/2509.01857"},"observation_digest":"sha256:b6ba6448ffb749f21336cc56182bad2cbc758f845ac496bb371e817bd79a9d8a","observation_id":"f82a121d-e761-42a1-846a-381667f4120f","resolution":{"observed_at":"2026-08-05T12:16:24.303871Z","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":"2026-08-05T12:16:25.062929Z","title":"21, 18629--18663","venue":null,"work_id":"e593266f-7dcf-4455-8705-595550c32a8c","year":2023},"citing_paper":{"arxiv_id":"2509.01857","last_updated":"2025-09-02T00:52:17Z","snapshot_observed_at":"2026-08-05T12:16:20.694864Z","submitted_at":"2025-09-02T00:52:17Z","title":"Hybrid pipe dreams for the lower-upper scheme","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-05T12:16:24.311069Z"},"links":{"citing_paper":"/paper/2509.01857"},"observation_digest":"sha256:9135fc1e7c30f6061c17eafe3a6e9fe6f982e91d5d85948ab505b930c904b672","observation_id":"a03d4e65-c2e6-4892-908a-7cfe4e213aca","resolution":{"observed_at":"2026-08-05T12:16:25.068618Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2010.15048","last_updated":"2020-10-28T15:48:10Z","snapshot_observed_at":"2026-07-06T10:09:27.733347Z","submitted_at":"2020-10-28T15:48:10Z","title":"Bijective Proofs of Monk's rule for Schubert and Double Schubert Polynomials with Bumpless Pipe Dreams","version":1},"cited_work":{"arxiv_id":"2010.15048","doi":null,"metadata_source":"pith","pith_arxiv_id":"2010.15048","snapshot_observed_at":"2026-08-05T12:16:24.919523Z","title":"Bijective Proofs of Monk's rule for Schubert and Double Schubert Polynomials with Bumpless Pipe Dreams","venue":"math.CO","work_id":"03c9f33f-2dac-4342-8eca-3e6d19f4c3a3","year":2020},"citing_paper":{"arxiv_id":"2509.01857","last_updated":"2025-09-02T00:52:17Z","snapshot_observed_at":"2026-08-05T12:16:20.694864Z","submitted_at":"2025-09-02T00:52:17Z","title":"Hybrid pipe dreams for the lower-upper scheme","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-05T12:16:24.316444Z"},"links":{"cited_paper":"/paper/2010.15048","citing_paper":"/paper/2509.01857"},"observation_digest":"sha256:367207e2efa00ba6a27e5433761c4226e00f094f508a3b7507e82a5f2633a1c7","observation_id":"a805e8e3-9449-4dc9-af7c-bb8e9f9b5123","resolution":{"observed_at":"2026-08-05T12:16:24.927939Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-05T12:16:25.042552Z","title":null,"venue":null,"work_id":"20ec2224-4f34-4967-a8f5-7c52102c3bba","year":2005},"citing_paper":{"arxiv_id":"2509.01857","last_updated":"2025-09-02T00:52:17Z","snapshot_observed_at":"2026-08-05T12:16:20.694864Z","submitted_at":"2025-09-02T00:52:17Z","title":"Hybrid pipe dreams for the lower-upper scheme","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-05T12:16:24.322029Z"},"links":{"citing_paper":"/paper/2509.01857"},"observation_digest":"sha256:cd16897f86fa2e981c1d22f99a1c5af7981f527828f38fd8af2d6038b5293ae7","observation_id":"1358bdae-553a-4f00-a6bb-93b272221275","resolution":{"observed_at":"2026-08-05T12:16:25.049050Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"math.ag/0306275","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T12:16:24.873641Z","title":"Algebraic Geom","venue":null,"work_id":"42c16d9f-0b5f-417c-945f-a4de57add0d6","year":2005},"citing_paper":{"arxiv_id":"2509.01857","last_updated":"2025-09-02T00:52:17Z","snapshot_observed_at":"2026-08-05T12:16:20.694864Z","submitted_at":"2025-09-02T00:52:17Z","title":"Hybrid pipe dreams for the lower-upper scheme","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-05T12:16:24.327469Z"},"links":{"citing_paper":"/paper/2509.01857"},"observation_digest":"sha256:c84aa9fed349b4065b1fe90ef4846c9ff15925859f79e88d69a1d348b121496e","observation_id":"d63add84-77ad-4aed-b5e3-82fb6836b98b","resolution":{"observed_at":"2026-08-05T12:16:24.888767Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1909.13777","last_updated":"2022-02-05T19:31:15Z","snapshot_observed_at":"2026-08-03T18:39:48.704904Z","submitted_at":"2019-09-30T15:17:01Z","title":"Schubert polynomials, pipe dreams, equivariant classes, and a co-transition formula","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1909.13777","snapshot_observed_at":"2026-08-05T12:16:24.332984Z","title":"63–83, Cambridge University Press, 2022, http://arxiv.org/abs/1909.13777 arXiv:1909.13777","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2509.01857","last_updated":"2025-09-02T00:52:17Z","snapshot_observed_at":"2026-08-05T12:16:20.694864Z","submitted_at":"2025-09-02T00:52:17Z","title":"Hybrid pipe dreams for the lower-upper scheme","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-05T12:16:24.332984Z"},"links":{"cited_paper":"/paper/1909.13777","citing_paper":"/paper/2509.01857"},"observation_digest":"sha256:cdc641189848c7c812c887a9e26972e77b0607e6a17408cf2030616ede0c0e20","observation_id":"394d4b43-08dd-4a7d-bccb-3d4db2babfe1","resolution":{"observed_at":"2026-08-05T12:16:24.332984Z","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":"2026-08-05T12:16:25.017300Z","title":null,"venue":null,"work_id":"b9d0b7d6-2923-444d-b18e-6468c44b7c7e","year":2023},"citing_paper":{"arxiv_id":"2509.01857","last_updated":"2025-09-02T00:52:17Z","snapshot_observed_at":"2026-08-05T12:16:20.694864Z","submitted_at":"2025-09-02T00:52:17Z","title":"Hybrid pipe dreams for the lower-upper scheme","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-05T12:16:24.340473Z"},"links":{"citing_paper":"/paper/2509.01857"},"observation_digest":"sha256:e9cb4d438b8cb31dacd6dbc00a9eadaa6e1ff5c624ecad53fb6be37f393074db","observation_id":"3d8d80bb-ac78-4616-b073-c7f89a742177","resolution":{"observed_at":"2026-08-05T12:16:25.023978Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08370","last_updated":"2025-09-02T00:29:46Z","snapshot_observed_at":"2026-07-06T11:39:26.575335Z","submitted_at":"2021-08-18T20:07:56Z","title":"Bumpless pipe dreams encode Gr\\\"obner geometry of Schubert polynomials","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08370","snapshot_observed_at":"2026-08-05T12:16:24.345937Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2509.01857","last_updated":"2025-09-02T00:52:17Z","snapshot_observed_at":"2026-08-05T12:16:20.694864Z","submitted_at":"2025-09-02T00:52:17Z","title":"Hybrid pipe dreams for the lower-upper scheme","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-05T12:16:24.345937Z"},"links":{"cited_paper":"/paper/2108.08370","citing_paper":"/paper/2509.01857"},"observation_digest":"sha256:d6fb6223a990e6ebda3491cb735eec9d1bfa75f8ea116f8c666ead2491713820","observation_id":"abe48d34-a421-4e10-91f8-a4feb51ffd73","resolution":{"observed_at":"2026-08-05T12:16:24.345937Z","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":"math.ag/0503224","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T12:16:24.724421Z","title":null,"venue":null,"work_id":"3da496e0-5923-44b4-b970-18ad7287f6ae","year":2007},"citing_paper":{"arxiv_id":"2509.01857","last_updated":"2025-09-02T00:52:17Z","snapshot_observed_at":"2026-08-05T12:16:20.694864Z","submitted_at":"2025-09-02T00:52:17Z","title":"Hybrid pipe dreams for the lower-upper scheme","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-05T12:16:24.352659Z"},"links":{"citing_paper":"/paper/2509.01857"},"observation_digest":"sha256:4c43ab345cb0eb72a9d1ce3548fb2269e12e8da44f4e55fbf88918d0929372e5","observation_id":"dd646b97-b037-4265-9013-1ed027250496","resolution":{"observed_at":"2026-08-05T12:16:24.733067Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1001.3335","last_updated":"2014-10-02T16:14:01Z","snapshot_observed_at":"2026-07-06T02:06:41.679342Z","submitted_at":"2010-01-19T18:59:35Z","title":"The Brauer loop scheme and orbital varieties","version":3},"cited_work":{"arxiv_id":"1001.3335","doi":null,"metadata_source":"pith","pith_arxiv_id":"1001.3335","snapshot_observed_at":"2026-08-05T12:16:24.575853Z","title":"The Brauer loop scheme and orbital varieties","venue":"math.AG","work_id":"865d8811-4e0f-4504-957c-4a3c166208fd","year":2010},"citing_paper":{"arxiv_id":"2509.01857","last_updated":"2025-09-02T00:52:17Z","snapshot_observed_at":"2026-08-05T12:16:20.694864Z","submitted_at":"2025-09-02T00:52:17Z","title":"Hybrid pipe dreams for the lower-upper scheme","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-05T12:16:24.359247Z"},"links":{"cited_paper":"/paper/1001.3335","citing_paper":"/paper/2509.01857"},"observation_digest":"sha256:8e7d78e36e95e9bcae77ea831c6901d5c75118aaeb3501fd74f521929097853a","observation_id":"82127585-b3d9-4885-998c-cdd64ae3b4dc","resolution":{"observed_at":"2026-08-05T12:16:24.583410Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2411.11208","last_updated":"2024-11-17T23:47:58Z","snapshot_observed_at":"2026-07-06T19:51:41.646058Z","submitted_at":"2024-11-17T23:47:58Z","title":"Generic pipe dreams, lower-upper varieties, and Schwartz-MacPherson classes","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.11208","snapshot_observed_at":"2026-08-05T12:16:24.365085Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.01857","last_updated":"2025-09-02T00:52:17Z","snapshot_observed_at":"2026-08-05T12:16:20.694864Z","submitted_at":"2025-09-02T00:52:17Z","title":"Hybrid pipe dreams for the lower-upper scheme","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-05T12:16:24.365085Z"},"links":{"cited_paper":"/paper/2411.11208","citing_paper":"/paper/2509.01857"},"observation_digest":"sha256:bb3b00605d5031eb296aeef4fcceab6ee37d1ce29ebb39f6ab9fffda9626124b","observation_id":"8f2515f9-6eee-421c-8cf5-2e9e81a78b5b","resolution":{"observed_at":"2026-08-05T12:16:24.365085Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1806.11233","last_updated":"2021-03-22T13:45:05Z","snapshot_observed_at":"2026-07-06T06:47:28.407673Z","submitted_at":"2018-06-29T00:14:31Z","title":"Back stable Schubert calculus","version":2},"cited_work":{"arxiv_id":"1806.11233","doi":null,"metadata_source":"pith","pith_arxiv_id":"1806.11233","snapshot_observed_at":"2026-08-05T12:16:24.521466Z","title":"Back stable Schubert calculus","venue":"math.CO","work_id":"96c40ac2-6678-4cff-89a5-79742913012b","year":2018},"citing_paper":{"arxiv_id":"2509.01857","last_updated":"2025-09-02T00:52:17Z","snapshot_observed_at":"2026-08-05T12:16:20.694864Z","submitted_at":"2025-09-02T00:52:17Z","title":"Hybrid pipe dreams for the lower-upper scheme","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-05T12:16:24.371247Z"},"links":{"cited_paper":"/paper/1806.11233","citing_paper":"/paper/2509.01857"},"observation_digest":"sha256:1e39c36661ee12a3b2b85a7d7d4f34b8d1e929b36628dccdea0ed437fb583699","observation_id":"9145b689-2154-4bcd-a9f6-9adeaab5960b","resolution":{"observed_at":"2026-08-05T12:16:24.528855Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-05T12:16:24.996255Z","title":"227, Springer-Verlag, New York, 2005","venue":null,"work_id":"23c096ab-c54e-44b2-b9c9-5229cbfaee3c","year":2005},"citing_paper":{"arxiv_id":"2509.01857","last_updated":"2025-09-02T00:52:17Z","snapshot_observed_at":"2026-08-05T12:16:20.694864Z","submitted_at":"2025-09-02T00:52:17Z","title":"Hybrid pipe dreams for the lower-upper scheme","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-05T12:16:24.377168Z"},"links":{"citing_paper":"/paper/2509.01857"},"observation_digest":"sha256:5ef560c7f2971777e056906a3fc8d9c7c8c5611bfbc3c2897dd97cf4624c3faf","observation_id":"c0011671-2c03-4336-8412-3188c9219df9","resolution":{"observed_at":"2026-08-05T12:16:25.002731Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-05T12:16:24.977992Z","title":null,"venue":null,"work_id":"7c9fff1a-65a1-4a86-9fcc-2fa579548c6b","year":2010},"citing_paper":{"arxiv_id":"2509.01857","last_updated":"2025-09-02T00:52:17Z","snapshot_observed_at":"2026-08-05T12:16:20.694864Z","submitted_at":"2025-09-02T00:52:17Z","title":"Hybrid pipe dreams for the lower-upper scheme","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-05T12:16:24.383199Z"},"links":{"citing_paper":"/paper/2509.01857"},"observation_digest":"sha256:9feb00e492639fc2939cc90382fcb75ce09e6063b600e367a7fb16039adc411e","observation_id":"d30e2b45-f9db-4a94-9688-95f79c5f81dd","resolution":{"observed_at":"2026-08-05T12:16:24.983764Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2003.07342","last_updated":"2020-03-16T17:33:04Z","snapshot_observed_at":"2026-07-06T09:05:05.055186Z","submitted_at":"2020-03-16T17:33:04Z","title":"Bumpless pipe dreams and alternating sign matrices","version":1},"cited_work":{"arxiv_id":"2003.07342","doi":null,"metadata_source":"pith","pith_arxiv_id":"2003.07342","snapshot_observed_at":"2026-08-05T12:16:24.487061Z","title":"Bumpless pipe dreams and alternating sign matrices","venue":"math.CO","work_id":"67080fbd-2424-4560-b10d-509cdbd2c216","year":2020},"citing_paper":{"arxiv_id":"2509.01857","last_updated":"2025-09-02T00:52:17Z","snapshot_observed_at":"2026-08-05T12:16:20.694864Z","submitted_at":"2025-09-02T00:52:17Z","title":"Hybrid pipe dreams for the lower-upper scheme","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-05T12:16:24.390874Z"},"links":{"cited_paper":"/paper/2003.07342","citing_paper":"/paper/2509.01857"},"observation_digest":"sha256:ff11444367184495bdef0952ddac085e4e2a0f5304cba82be8f2d1efb744f997","observation_id":"dd06e46f-df1a-4781-8b35-654431082bdd","resolution":{"observed_at":"2026-08-05T12:16:24.495234Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2506.07306","last_updated":"2025-06-08T22:39:23Z","snapshot_observed_at":"2026-08-07T05:34:28.963186Z","submitted_at":"2025-06-08T22:39:23Z","title":"Changing Bases with Pipe Dream Combinatorics","version":1},"cited_work":{"arxiv_id":"2506.07306","doi":null,"metadata_source":"pith","pith_arxiv_id":"2506.07306","snapshot_observed_at":"2026-08-05T12:16:24.455346Z","title":"Changing Bases with Pipe Dream Combinatorics","venue":"math.CO","work_id":"390c6361-b8db-46c5-9de7-04eac97dbb34","year":2025},"citing_paper":{"arxiv_id":"2509.01857","last_updated":"2025-09-02T00:52:17Z","snapshot_observed_at":"2026-08-05T12:16:20.694864Z","submitted_at":"2025-09-02T00:52:17Z","title":"Hybrid pipe dreams for the lower-upper scheme","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-05T12:16:24.399793Z"},"links":{"cited_paper":"/paper/2506.07306","citing_paper":"/paper/2509.01857"},"observation_digest":"sha256:61fe9c092cdc3224920f82c5c62414516f06bfbc94ad24c620c214f0f96825f3","observation_id":"96bbbb3e-1b8d-4cb4-adc5-269a732684f7","resolution":{"observed_at":"2026-08-05T12:16:24.464238Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2509.01857","last_updated":"2025-09-02T00:52:17Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-08-05T12:16:20.694864Z","submitted_at":"2025-09-02T00:52:17Z","title":"Hybrid pipe dreams for the lower-upper scheme"},"reference_resolution":{"displayed":21,"state_counts":{"malformed_identifier":0,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":9,"verified_exact":7,"verified_fuzzy":4},"total_outbound_references":21},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 0 inbound Pith citation observations for arXiv:2509.01857."}