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We then obtain that $\\mathcal N(s_{\\lambda/\\mu})$, $\\mathcal N(P_{\\lambda/\\mu})$, $\\mathcal N(Q_{\\lambda/\\mu})$ are realizable volume polynomials. This settles the skew-Schur and Schur-$P$ Lorentzian conjectures of Huh--Matherne--M\\'esz\\'aros--St.~Dizier and strengthens the latter to arbitrary skew $P/Q$-functions.\n  The construction extends to cycle transforms attached to arbitrary irreducible subvarieties"},"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":"2608.10516","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-08-11T05:40:40Z","cross_cats_sorted":[],"title_canon_sha256":"abd860321bf1f675710bc9b3005473240c753213998d01b1e5af4ebe34668fcb","abstract_canon_sha256":"a41e3af6c24f90ec900ea1b382ce340a87808b823bf6797d0555071a9a862a7a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-12T01:22:39.179878Z","signature_b64":"MMsaCCVqVNXCJElFT4P/D/8RjPYVEVq5tYi3W+YxwoOYegpltjALa/qmIsJVcmswb895RB3ViD6xsrrUXoyVDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9486777bff9f536d2380c56523381391918e0816eface508637f5a4b6d2e5ddd","last_reissued_at":"2026-08-12T01:22:39.178276Z","signature_status":"signed_v1","first_computed_at":"2026-08-12T01:22:39.178276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Richardson volume models for skew Schur and skew Schur $P/Q$-functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Khai-Hoan Nguyen-Dang","submitted_at":"2026-08-11T05:40:40Z","abstract_excerpt":"We identify ordinary skew Schur polynomials and skew Schur $P$-functions as top-degree total-Chern intersection polynomials on Richardson varieties in ordinary and Lagrangian Grassmannians. We then obtain that $\\mathcal N(s_{\\lambda/\\mu})$, $\\mathcal N(P_{\\lambda/\\mu})$, $\\mathcal N(Q_{\\lambda/\\mu})$ are realizable volume polynomials. This settles the skew-Schur and Schur-$P$ Lorentzian conjectures of Huh--Matherne--M\\'esz\\'aros--St.~Dizier and strengthens the latter to arbitrary skew $P/Q$-functions.\n  The construction extends to cycle transforms attached to arbitrary irreducible subvarieties"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.10516","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/2608.10516/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":"2608.10516","created_at":"2026-08-12T01:22:39.182073+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.10516v1","created_at":"2026-08-12T01:22:39.182073+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.10516","created_at":"2026-08-12T01:22:39.182073+00:00"},{"alias_kind":"pith_short_12","alias_value":"SSDHO677T5JW","created_at":"2026-08-12T01:22:39.182073+00:00"},{"alias_kind":"pith_short_16","alias_value":"SSDHO677T5JW2I4A","created_at":"2026-08-12T01:22:39.182073+00:00"},{"alias_kind":"pith_short_8","alias_value":"SSDHO677","created_at":"2026-08-12T01:22:39.182073+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SSDHO677T5JW2I4AYVSSGOATSG","json":"https://pith.science/pith/SSDHO677T5JW2I4AYVSSGOATSG.json","graph_json":"https://pith.science/api/pith-number/SSDHO677T5JW2I4AYVSSGOATSG/graph.json","events_json":"https://pith.science/api/pith-number/SSDHO677T5JW2I4AYVSSGOATSG/events.json","paper":"https://pith.science/paper/SSDHO677"},"agent_actions":{"view_html":"https://pith.science/pith/SSDHO677T5JW2I4AYVSSGOATSG","download_json":"https://pith.science/pith/SSDHO677T5JW2I4AYVSSGOATSG.json","view_paper":"https://pith.science/paper/SSDHO677","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.10516&json=true","fetch_graph":"https://pith.science/api/pith-number/SSDHO677T5JW2I4AYVSSGOATSG/graph.json","fetch_events":"https://pith.science/api/pith-number/SSDHO677T5JW2I4AYVSSGOATSG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SSDHO677T5JW2I4AYVSSGOATSG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SSDHO677T5JW2I4AYVSSGOATSG/action/storage_attestation","attest_author":"https://pith.science/pith/SSDHO677T5JW2I4AYVSSGOATSG/action/author_attestation","sign_citation":"https://pith.science/pith/SSDHO677T5JW2I4AYVSSGOATSG/action/citation_signature","submit_replication":"https://pith.science/pith/SSDHO677T5JW2I4AYVSSGOATSG/action/replication_record"}},"created_at":"2026-08-12T01:22:39.182073+00:00","updated_at":"2026-08-12T01:22:39.182073+00:00"}