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For a set of vectors $\\mathcal P$, we call its {\\em dual} a set of vectors ${\\mathcal P}^*$ such that $\\langle p,q\\rangle\\in\\{0,\\pm 1\\}$ for all $p\\in{\\mathcal P}$ and $q\\in{\\mathcal P}^*$. We prove that Minkowski sum of a Voronoi parallelotope $P(a)$ and a segment is a Voronoi parallelotope $P(a+a_e)$ if and only if this segment is parallel to a vector $e$ of the dual of the set of normal vectors of all facets of $P(a)$, where $a_e(p)"},"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":"1501.01212","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-01-06T15:55:23Z","cross_cats_sorted":[],"title_canon_sha256":"ea5c297c7fd1a3f0c4c0eaf73c8f9a7367607d37f3b2d1cfaf8192c1dffe0ee3","abstract_canon_sha256":"a4773797646968fd24dfc7fbb71493aa427d1455d09e56a5b1905242300d4101"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:00.090909Z","signature_b64":"LtTXurWzLH9CifM5ugSMwajUT6EpdetBFf39f4zb10UZLay+uygC8EpVd1rcxFWQbsOtfu+CMbF2R/CAW89cDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f1cc2272c07867dddb01e3d148ca2e73af06113a87abfbc972e104b19a114d5","last_reissued_at":"2026-05-18T02:30:00.090551Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:00.090551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minkowski sum of a Voronoi parallelotope and a segment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Robert Erdahl, Viacheslav Grishukhin","submitted_at":"2015-01-06T15:55:23Z","abstract_excerpt":"By a {\\em Voronoi parallelotope} $P(a)$ we mean a parallelotope determined by a non-negative quadratic form $a$. 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