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If the family ${\\cal F}(\\Delta)$ defined by a Newton polyhedron $\\Delta$ consists of $(n-1)$-dimensional Calabi-Yau varieties, then the dual, or polar, polyhedron $\\Delta^*$ in the dual space defines another family ${\\cal F}(\\Delta^*)$ of Calabi-Yau varieties, so that we obtain t"},"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":"alg-geom/9310003","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"alg-geom","submitted_at":"1993-10-05T21:22:35Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"894edd898b5e24c2140dad9f2825c6d7fb7183bfc9a99e46e33943462fd9cd01","abstract_canon_sha256":"515e5e8f1ae4df100aa5c1b4ccc047e1c321d25d8bb73e00374f57ecaf553774"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:08:01.608031Z","signature_b64":"/mplZt7swDNT6rPwzQmSwRwJnU477fqz2F87s3rBgZ35VPM6P1RpDwKEiP+WUE6KYtEPIdX3K2unvbUkyhfWDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3005fb6dc036e8b83889be7d40c4bc3be44596e6c56a3a7f825e2e4ff5b90d2","last_reissued_at":"2026-07-04T15:08:01.607657Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:08:01.607657Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"alg-geom","authors_text":"Victor V. 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If the family ${\\cal F}(\\Delta)$ defined by a Newton polyhedron $\\Delta$ consists of $(n-1)$-dimensional Calabi-Yau varieties, then the dual, or polar, polyhedron $\\Delta^*$ in the dual space defines another family ${\\cal F}(\\Delta^*)$ of Calabi-Yau varieties, so that we obtain 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