{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:EZ3IEIYNV7LEBNWHNTXSLHTFZB","short_pith_number":"pith:EZ3IEIYN","schema_version":"1.0","canonical_sha256":"267682230dafd640b6c76cef259e65c86d1060b67bede149c6fd13e1b10434d5","source":{"kind":"arxiv","id":"2506.04002","version":1},"attestation_state":"computed","paper":{"title":"From Weingarten calculus for real Grassmannians to deformations of monotone Hurwitz numbers and Jucys-Murphy elements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.RT"],"primary_cat":"math.CO","authors_text":"Norman Do, Xavier Coulter","submitted_at":"2025-06-04T14:31:32Z","abstract_excerpt":"The present work is inspired by three interrelated themes: Weingarten calculus for integration over unitary groups, monotone Hurwitz numbers which enumerate certain factorisations of permutations into transpositions, and Jucys-Murphy elements in the symmetric group algebra. The authors and Moskovsky recently extended this picture to integration on complex Grassmannians, leading to a deformation of the monotone Hurwitz numbers to polynomials that are conjectured to satisfy remarkable interlacing phenomena.\n  In this paper, we consider integration on the real Grassmannian $\\mathrm{Gr}_\\mathbb{R}"},"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":"2506.04002","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-04T14:31:32Z","cross_cats_sorted":["math-ph","math.MP","math.RT"],"title_canon_sha256":"e6740284a1c28f11dc62e6498d619490c41c49c9781dc2137e0e52178cab671a","abstract_canon_sha256":"53573551ae6d030aa1df755d84b789b5449bc15d0b73c3fa5105d00a2894572a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:15:55.108013Z","signature_b64":"MRby/E7NooWEVESrIByP9JjZTOWf1JdLHR4jJT0amCKiCJm6ByXmnV7S2xa1UQOb7T5HY+6UEMGaFL3tWYzSBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"267682230dafd640b6c76cef259e65c86d1060b67bede149c6fd13e1b10434d5","last_reissued_at":"2026-07-05T11:15:55.107500Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:15:55.107500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"From Weingarten calculus for real Grassmannians to deformations of monotone Hurwitz numbers and Jucys-Murphy elements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.RT"],"primary_cat":"math.CO","authors_text":"Norman Do, Xavier Coulter","submitted_at":"2025-06-04T14:31:32Z","abstract_excerpt":"The present work is inspired by three interrelated themes: Weingarten calculus for integration over unitary groups, monotone Hurwitz numbers which enumerate certain factorisations of permutations into transpositions, and Jucys-Murphy elements in the symmetric group algebra. The authors and Moskovsky recently extended this picture to integration on complex Grassmannians, leading to a deformation of the monotone Hurwitz numbers to polynomials that are conjectured to satisfy remarkable interlacing phenomena.\n  In this paper, we consider integration on the real Grassmannian $\\mathrm{Gr}_\\mathbb{R}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.04002","kind":"arxiv","version":1},"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/2506.04002/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":"2506.04002","created_at":"2026-07-05T11:15:55.107554+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.04002v1","created_at":"2026-07-05T11:15:55.107554+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.04002","created_at":"2026-07-05T11:15:55.107554+00:00"},{"alias_kind":"pith_short_12","alias_value":"EZ3IEIYNV7LE","created_at":"2026-07-05T11:15:55.107554+00:00"},{"alias_kind":"pith_short_16","alias_value":"EZ3IEIYNV7LEBNWH","created_at":"2026-07-05T11:15:55.107554+00:00"},{"alias_kind":"pith_short_8","alias_value":"EZ3IEIYN","created_at":"2026-07-05T11:15:55.107554+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2508.06188","citing_title":"A refined twist on Hurwitz numbers","ref_index":22,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EZ3IEIYNV7LEBNWHNTXSLHTFZB","json":"https://pith.science/pith/EZ3IEIYNV7LEBNWHNTXSLHTFZB.json","graph_json":"https://pith.science/api/pith-number/EZ3IEIYNV7LEBNWHNTXSLHTFZB/graph.json","events_json":"https://pith.science/api/pith-number/EZ3IEIYNV7LEBNWHNTXSLHTFZB/events.json","paper":"https://pith.science/paper/EZ3IEIYN"},"agent_actions":{"view_html":"https://pith.science/pith/EZ3IEIYNV7LEBNWHNTXSLHTFZB","download_json":"https://pith.science/pith/EZ3IEIYNV7LEBNWHNTXSLHTFZB.json","view_paper":"https://pith.science/paper/EZ3IEIYN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.04002&json=true","fetch_graph":"https://pith.science/api/pith-number/EZ3IEIYNV7LEBNWHNTXSLHTFZB/graph.json","fetch_events":"https://pith.science/api/pith-number/EZ3IEIYNV7LEBNWHNTXSLHTFZB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EZ3IEIYNV7LEBNWHNTXSLHTFZB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EZ3IEIYNV7LEBNWHNTXSLHTFZB/action/storage_attestation","attest_author":"https://pith.science/pith/EZ3IEIYNV7LEBNWHNTXSLHTFZB/action/author_attestation","sign_citation":"https://pith.science/pith/EZ3IEIYNV7LEBNWHNTXSLHTFZB/action/citation_signature","submit_replication":"https://pith.science/pith/EZ3IEIYNV7LEBNWHNTXSLHTFZB/action/replication_record"}},"created_at":"2026-07-05T11:15:55.107554+00:00","updated_at":"2026-07-05T11:15:55.107554+00:00"}