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If \\phi is the volume, then g_{K,\\phi} is the covariogram, extensively studied in various sources. When \\phi is a quermassintegral (e.g., surface area or mean width) g_{K,\\phi} has been introduced by Nagel.\n  We study various properties of \\phi -covariograms, mostly in the case n=2 and under the assumption that \\phi is transla"},"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":"1307.1529","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-07-05T06:30:38Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"682a8e467709e799b68e80c6149865463b669feb8432eb34b07cfb9a9db2b234","abstract_canon_sha256":"3b7ab11b424059248fea84b4b1ae305bfb5882f05bb263b8e87fa87871bb101c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:03.083792Z","signature_b64":"BthyDXggviVChnCIop10jni/4DX/5scjweGTZUlKNZN+crMsYc3LlLxvrxLtkZKTw0nvvcDbzJsfxYboZh95DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63603a9dd1a2ea19eb75c19a53b137b666130a2f7cb181f3381431d30c5c3e6a","last_reissued_at":"2026-05-18T01:16:03.083170Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:03.083170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Covariograms generated by valuations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.MG","authors_text":"Gabriele Bianchi, Gennadiy Averkov","submitted_at":"2013-07-05T06:30:38Z","abstract_excerpt":"Let \\phi be a real-valued valuation on the family of compact convex subsets of \\mathbb{R}^n and let K be a convex body in \\mathbb{R}^n. 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