{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZPCDMYVWAE7UJOMVBT7YA2QCOW","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6d583da66c4bd17b536d784064c10bb132184e2b27454330433520450bf53618","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-11-12T11:00:46Z","title_canon_sha256":"586419a727663cdb11b04b0d187eebac924956a217769c3612276e1fdc9369e7"},"schema_version":"1.0","source":{"id":"1711.04272","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.04272","created_at":"2026-05-18T00:30:39Z"},{"alias_kind":"arxiv_version","alias_value":"1711.04272v1","created_at":"2026-05-18T00:30:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.04272","created_at":"2026-05-18T00:30:39Z"},{"alias_kind":"pith_short_12","alias_value":"ZPCDMYVWAE7U","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZPCDMYVWAE7UJOMV","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZPCDMYVW","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:9948262f504e8e2ca3077f2ebe5ce423a809967c33ffe5d3b24503c01bd38201","target":"graph","created_at":"2026-05-18T00:30:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The theory of coconvex bodies was formalized by A.~Khovanski{\\u\\i} and V.~Timorin in \\cite{KT}. It has fascinating relations with the classical theory of convex bodies, as well as applications to Lorentzian geometry. In a recent preprint \\cite{schnei2}, R.~Schneider proved a result that implies a reversed Brunn--Minkowski inequality for coconvex bodies, with description of equality case. In this note we show that this latter result is an immediate consequence of a more general result, namely that the volume of coconvex bodies is strictly convex. This result itself follows from a classical elem","authors_text":"Fran\\c{c}ois Fillastre","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-11-12T11:00:46Z","title":"A short elementary proof of reversed Brunn--Minkowski inequality for coconvex bodies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.04272","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:843fbcd4605b2cb6829d47764e2c49b206af34debb6bcf725995ab8ca5578c96","target":"record","created_at":"2026-05-18T00:30:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6d583da66c4bd17b536d784064c10bb132184e2b27454330433520450bf53618","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-11-12T11:00:46Z","title_canon_sha256":"586419a727663cdb11b04b0d187eebac924956a217769c3612276e1fdc9369e7"},"schema_version":"1.0","source":{"id":"1711.04272","kind":"arxiv","version":1}},"canonical_sha256":"cbc43662b6013f44b9950cff806a027584cebd20e1e9d0604f8c128cbf113ae3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cbc43662b6013f44b9950cff806a027584cebd20e1e9d0604f8c128cbf113ae3","first_computed_at":"2026-05-18T00:30:39.525753Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:39.525753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BmgUk9EoBqpt367dLfui0Al7SB5GVTnFRexpUDMKEsSk/ETr7CaHVZQh8KeBuOHBkbYUfIPKZoIPvKPZ3mpgDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:39.526539Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.04272","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:843fbcd4605b2cb6829d47764e2c49b206af34debb6bcf725995ab8ca5578c96","sha256:9948262f504e8e2ca3077f2ebe5ce423a809967c33ffe5d3b24503c01bd38201"],"state_sha256":"70aeb3a3d8dd8119dcf8e0ac7d07ac138e4eb61c7f49b49d1f56fd7db3c1faf8"}