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As applications, we settle two conjectures: one by Bandari, Bayati, and Herzog regarding polymatroidal ideals, and another by Castillo, Cid-Ruiz, Mohammadi, and Monta\\~no regarding the M\\\"obius support of a polymatroid."},"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":"2507.13153","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2025-07-17T14:16:02Z","cross_cats_sorted":["math.AG","math.CO"],"title_canon_sha256":"9e56cb7ba9f17b9d7b4dfbaac287e4ed2f7194245b8fa2a61a546f2eeddec537","abstract_canon_sha256":"9d21b3892f63c947d69406624d3f6e74f3e0de8c51380d971bfbf2173563f820"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:38:55.556876Z","signature_b64":"kykN0bsMNMkMoA8zNFUd6zRKuIiYOyDBN1U1S5aGNGnqsBMCyOjCCAqupem4GcT1HzBYki2KBstcpmEZT5+2Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e054941ab17149c9765fea89e499009121ad93429d48d3f2620350e5f8f9a3df","last_reissued_at":"2026-07-05T11:38:55.556375Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:38:55.556375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Syzygies of polymatroidal ideals","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG","math.CO"],"primary_cat":"math.AC","authors_text":"Anna Shapiro, Jacob P. 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