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Lee, Vindas-Mel\\'endez, and Wang (2026) conjectured that the Ehrhart $h^*$-polynomials of these order polytopes are real-rooted. We prove this conjecture using a connection between these $h^*$-polynomials and non-nesting rook polynomials, which were recently introduced by Alexandersson and Jal (2024+) in connection with $P$-Eulerian polynomials for width two"},"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":"2607.00922","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-01T13:24:51Z","cross_cats_sorted":[],"title_canon_sha256":"ca8b75ff243ddc7616025a7806c03b8db6596f83802c54d6baca1d6126d54603","abstract_canon_sha256":"0cd47ccb649a30844ff90b9f63a7f42a8573d45a7f4ec7060975e6b39e14383c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-02T01:18:23.655049Z","signature_b64":"4pffArqPG6+USTBoPEFl90uxs7qdQzoRW34WvXamB+YGUkeQ9AuG3Le6ymGpJOzEuFE33b5ibsQjv+1g4WImCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f561c90834b82a1e2f66909d876a520a5ee41a01120221fdfaace4547962b414","last_reissued_at":"2026-07-02T01:18:23.654679Z","signature_status":"signed_v1","first_computed_at":"2026-07-02T01:18:23.654679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Order polytopes of generalized snake posets are $h^*$-real-rooted","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Aryaman Jal, Benjamin Braun","submitted_at":"2026-07-01T13:24:51Z","abstract_excerpt":"Order polytopes for generalized snake posets were recently studied by von Bell et al. 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