{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:KTLMIYMB3SFP52LDBFKOKCX53K","short_pith_number":"pith:KTLMIYMB","schema_version":"1.0","canonical_sha256":"54d6c46181dc8afee9630954e50afddaa8130945b7f0121b0af608e31cfb3288","source":{"kind":"arxiv","id":"1904.10187","version":2},"attestation_state":"computed","paper":{"title":"Toric Bruhat interval polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"Eunjeong Lee, Mikiya Masuda, Seonjeong Park","submitted_at":"2019-04-23T07:49:26Z","abstract_excerpt":"For two elements $v$ and $w$ of the symmetric group $\\mathfrak{S}_n$ with $v\\leq w$ in Bruhat order, the Bruhat interval polytope $Q_{v,w}$ is the convex hull of the points $(z(1),\\ldots,z(n))\\in \\mathbb{R}^n$ with $v\\leq z\\leq w$. It is known that the Bruhat interval polytope $Q_{v,w}$ is the moment map image of the Richardson variety $X^{v^{-1}}_{w^{-1}}$. We say that $Q_{v,w}$ is \\emph{toric} if the corresponding Richardson variety $X_{w^{-1}}^{v^{-1}}$ is a toric variety. We show that when $Q_{v,w}$ is toric, its combinatorial type is determined by the poset structure of the Bruhat interva"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1904.10187","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-04-23T07:49:26Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"5a86a138e4a5d6e9fe3f3a99618e208a70257000cb944b1b591cae9ab027a137","abstract_canon_sha256":"951c12ce135780c609a30bbef837bcbb79848a977b9ef8ade7eab380789d0829"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:38:26.969704Z","signature_b64":"rtJaN/uelUakmckoYmSUd23jmABbZ+olJvxyRaY9UsOir8gUcAuneZWTDA2xHeE8mzRo7JD7rv3yAGv8c+nNAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54d6c46181dc8afee9630954e50afddaa8130945b7f0121b0af608e31cfb3288","last_reissued_at":"2026-07-05T02:38:26.969210Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:38:26.969210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Toric Bruhat interval polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"Eunjeong Lee, Mikiya Masuda, Seonjeong Park","submitted_at":"2019-04-23T07:49:26Z","abstract_excerpt":"For two elements $v$ and $w$ of the symmetric group $\\mathfrak{S}_n$ with $v\\leq w$ in Bruhat order, the Bruhat interval polytope $Q_{v,w}$ is the convex hull of the points $(z(1),\\ldots,z(n))\\in \\mathbb{R}^n$ with $v\\leq z\\leq w$. It is known that the Bruhat interval polytope $Q_{v,w}$ is the moment map image of the Richardson variety $X^{v^{-1}}_{w^{-1}}$. We say that $Q_{v,w}$ is \\emph{toric} if the corresponding Richardson variety $X_{w^{-1}}^{v^{-1}}$ is a toric variety. We show that when $Q_{v,w}$ is toric, its combinatorial type is determined by the poset structure of the Bruhat interva"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.10187","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1904.10187/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1904.10187","created_at":"2026-07-05T02:38:26.969282+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.10187v2","created_at":"2026-07-05T02:38:26.969282+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.10187","created_at":"2026-07-05T02:38:26.969282+00:00"},{"alias_kind":"pith_short_12","alias_value":"KTLMIYMB3SFP","created_at":"2026-07-05T02:38:26.969282+00:00"},{"alias_kind":"pith_short_16","alias_value":"KTLMIYMB3SFP52LD","created_at":"2026-07-05T02:38:26.969282+00:00"},{"alias_kind":"pith_short_8","alias_value":"KTLMIYMB","created_at":"2026-07-05T02:38:26.969282+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.08310","citing_title":"Torus orbit closures in flag varieties and retractions on Weyl groups","ref_index":12,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KTLMIYMB3SFP52LDBFKOKCX53K","json":"https://pith.science/pith/KTLMIYMB3SFP52LDBFKOKCX53K.json","graph_json":"https://pith.science/api/pith-number/KTLMIYMB3SFP52LDBFKOKCX53K/graph.json","events_json":"https://pith.science/api/pith-number/KTLMIYMB3SFP52LDBFKOKCX53K/events.json","paper":"https://pith.science/paper/KTLMIYMB"},"agent_actions":{"view_html":"https://pith.science/pith/KTLMIYMB3SFP52LDBFKOKCX53K","download_json":"https://pith.science/pith/KTLMIYMB3SFP52LDBFKOKCX53K.json","view_paper":"https://pith.science/paper/KTLMIYMB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.10187&json=true","fetch_graph":"https://pith.science/api/pith-number/KTLMIYMB3SFP52LDBFKOKCX53K/graph.json","fetch_events":"https://pith.science/api/pith-number/KTLMIYMB3SFP52LDBFKOKCX53K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KTLMIYMB3SFP52LDBFKOKCX53K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KTLMIYMB3SFP52LDBFKOKCX53K/action/storage_attestation","attest_author":"https://pith.science/pith/KTLMIYMB3SFP52LDBFKOKCX53K/action/author_attestation","sign_citation":"https://pith.science/pith/KTLMIYMB3SFP52LDBFKOKCX53K/action/citation_signature","submit_replication":"https://pith.science/pith/KTLMIYMB3SFP52LDBFKOKCX53K/action/replication_record"}},"created_at":"2026-07-05T02:38:26.969282+00:00","updated_at":"2026-07-05T02:38:26.969282+00:00"}