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As a consequence we bound the largest integer $d$ (the postulation number) for which the Hilbert polynomial $HP(C^\\alpha(\\mathcal{P}),d)$ disagrees with the Hilbert function $HF(C^\\alpha(\\mathcal{P}),d)=\\dim C^\\alpha(\\mathcal{P})_d$. The polynomial $HP(C^\\alpha(\\mathcal{P}),d)$ has been computed in [DiPasquale 2014], building on [McDonald-Schenck 09] and [Geramita-Schenck 98]. Hence the regularity bounds obtained indicate when a known pol"},"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":"1411.2176","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-11-08T23:59:08Z","cross_cats_sorted":[],"title_canon_sha256":"aecae13b14eaaf482fcf65cd7effa8c6c82cd01922166a23704421366fbb9cb6","abstract_canon_sha256":"9fb1f2dec20e4158b57633e321f26de01252389330e665a0d5d06f97cc126e49"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:08.268235Z","signature_b64":"KXjxSHksHrYuHjhBILqTWpSvN85yP3KsOc4dFS905WeXQZL25O0P7fDGB8YcTAvGm9jc6f86CAVhJkpUUdzxBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"958c1a85b0dfac324115227f042a3b083310bd470d6d9125a0dc7982ffb5b22e","last_reissued_at":"2026-05-18T02:38:08.267718Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:08.267718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Regularity of Mixed Spline Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Michael DiPasquale","submitted_at":"2014-11-08T23:59:08Z","abstract_excerpt":"We derive bounds on the regularity of the algebra $C^\\alpha(\\mathcal{P})$ of mixed splines over a central polytopal complex $\\mathcal{P}\\subset\\mathbb{R}^3$. 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