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It is known that, when $d$ grows, the maximum volume of the simplices $T \\in \\cT^d(1)$ becomes extremely large. We improve and refine bounds on the size of $T \\in \\mathcal{T}^d(1)$ (where by the size we mean the volume or the number of lattice points). It is shown that each $T \\in \\mathcal{T}^d(1)$ can be decompo"},"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":"1103.0629","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-03-03T09:41:28Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"8e96bbad4efbd71758c5598e83212fa26ab7eec5904310001f69f96c56f74845","abstract_canon_sha256":"53241bf41af34549127c77be01c835a9a0fd6d9bd43c641286d2cade4e8acc5d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:00:15.955473Z","signature_b64":"IyU4BPbqQx/KsVGKt7uKoauY8A9QgpXm9pkRIo4V3gDiI22ckj0q48zJQIZ27nqhP6oHlkyr4uw+YH9Zu5ZCCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ddce7adf3a26c252271de593e48bee8a3bed72992ea5b2082aa733203e5da2b","last_reissued_at":"2026-05-18T04:00:15.954637Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:00:15.954637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the size of lattice simplices with a single interior lattice point","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"Gennadiy Averkov","submitted_at":"2011-03-03T09:41:28Z","abstract_excerpt":"Let $\\mathcal{T}^d(1)$ be the set of all $d$-dimensional simplices $T$ in $\\real^d$ with integer vertices and a single integer point in the interior of $T$. 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