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The family of $C$-coconvex sets is closed under the addition $\\oplus$ defined by $C\\setminus(A_1\\oplus A_2)= (C\\setminus A_1)+(C\\setminus A_2)$. We develop first steps of a Brunn--Minkowski theory for $C$-coconvex sets, which relates this addition to the notion of volume. In particular, we establish the equality conditions"},"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":"1706.03573","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-06-12T11:34:48Z","cross_cats_sorted":[],"title_canon_sha256":"5bc9e7aa7ef1996156b81289938fc41e8874fc1a9004c1a39f16097ab638d672","abstract_canon_sha256":"0d8f963eb28a2f4fa5c5c85345e366e0b510da2f36c50fed5f5d7120499694fb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:12.498761Z","signature_b64":"BNoiCkNt/yi3YwokNNnSmbZRwTk81SHTtGeB489QlyLZ6ki8fVgYT2jpmh37wlzMM4rbIeRwNq49KJjCEK98CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4308ad6151c09098167a7dc61b60a46b3f0aeee8176f2bf6a8c023d8676c191","last_reissued_at":"2026-05-18T00:31:12.498260Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:12.498260Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Brunn-Minkowski theory for coconvex sets of finite volume","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Rolf Schneider","submitted_at":"2017-06-12T11:34:48Z","abstract_excerpt":"Let $C$ be a closed convex cone in ${\\mathbb R}^n$, pointed and with interior points. 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