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We say that $\\mathcal{P}$ possesses the integer decomposition property if, for any integer $k = 1, 2, \\ldots$ and for any $\\alpha \\in k \\mathcal{P} \\cap \\mathbb{Z}^N$, there exist $\\alpha_{1}, \\ldots, \\alpha_k$ belonging to $\\mathcal{P} \\cap \\mathbb{Z}^N$ such that $\\alpha = \\alpha_1 + \\cdots + \\alpha_k$. A fundamental question is to determine the integers $k > 0$ for which the dilated polytope $k\\mathcal{P}$ possesses the i"},"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":"1211.5755","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-25T10:48:50Z","cross_cats_sorted":["math.AC","math.AG"],"title_canon_sha256":"950aeba573d47994131da15e64738e752b85dfea0b5ad5309b1ecd7e18ce83ad","abstract_canon_sha256":"9fb6e5e937a7e5ca10d783179cec752e011fc70e13810f9342816e350688f6d0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:48.375263Z","signature_b64":"CrsNXLHs8W0OoYTyJIOzNkcbBNv57cUS4fiXZE7RssNNdws0wX0/wlHfOnFFa/r17xqPNTKI6EtJ40icWwXEDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2ccfd567338e44822845441b405b09f67aee72f093f18cd49cffc84cad26c79","last_reissued_at":"2026-05-18T03:20:48.374539Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:48.374539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Integer decomposition property of dilated polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.AG"],"primary_cat":"math.CO","authors_text":"Akihiro Higashitani, Christian Haase, David A. 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