{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MMT5JC4X4MSINHUQDRJT6P2X2H","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":"d05da905cc61d9b7f33b7e5447924a886769de97e435bc63ae269fb62075508d","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-29T01:10:46Z","title_canon_sha256":"9612628cf3a780b21b2c0921856c099d3e35e8faa1d3683ae9cbf02f10ca63ae"},"schema_version":"1.0","source":{"id":"1810.00127","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.00127","created_at":"2026-05-17T23:40:13Z"},{"alias_kind":"arxiv_version","alias_value":"1810.00127v2","created_at":"2026-05-17T23:40:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.00127","created_at":"2026-05-17T23:40:13Z"},{"alias_kind":"pith_short_12","alias_value":"MMT5JC4X4MSI","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MMT5JC4X4MSINHUQ","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MMT5JC4X","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:9e3ad1fb46e9d159d3202f029c311ea1209fbe2c9ee2a2f1262da74a4d19bf82","target":"graph","created_at":"2026-05-17T23:40:13Z","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":"We consider the class of $\\lambda$-concave bodies in $\\mathbb R^{n+1}$; that is, convex bodies with the property that each of their boundary points supports a tangent ball of radius $1/\\lambda$ that lies locally (around the boundary point) inside the body. In this class we solve a reverse isoperimetric problem: we show that the convex hull of two balls of radius $1/\\lambda$ (a sausage body) is a unique volume minimizer among all $\\lambda$-concave bodies of given surface area. This is in a surprising contrast to the standard isoperimetric problem for which, as it is well-known, the unique maxim","authors_text":"Kateryna Tatarko, Kostiantyn Drach, Roman Chernov","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-29T01:10:46Z","title":"A sausage body is a unique solution for a reverse isoperimetric problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00127","kind":"arxiv","version":2},"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":"sha256:17aa53847b4279d99a287cceab0f9056ec02791f6adcea8037eb7781ec911cab","target":"record","created_at":"2026-05-17T23:40:13Z","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":"d05da905cc61d9b7f33b7e5447924a886769de97e435bc63ae269fb62075508d","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-29T01:10:46Z","title_canon_sha256":"9612628cf3a780b21b2c0921856c099d3e35e8faa1d3683ae9cbf02f10ca63ae"},"schema_version":"1.0","source":{"id":"1810.00127","kind":"arxiv","version":2}},"canonical_sha256":"6327d48b97e324869e901c533f3f57d1d69859df011786eab4e1b4395a529571","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6327d48b97e324869e901c533f3f57d1d69859df011786eab4e1b4395a529571","first_computed_at":"2026-05-17T23:40:13.971742Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:13.971742Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r4q3obf1Swzp71t0ElqZ4uG/FEYBnozDvry65BwJBfZWJFDFFx/Oy+YzwRhQMXdUwcF/m/KbaUJR1OVNeRc5DQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:13.972866Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.00127","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:17aa53847b4279d99a287cceab0f9056ec02791f6adcea8037eb7781ec911cab","sha256:9e3ad1fb46e9d159d3202f029c311ea1209fbe2c9ee2a2f1262da74a4d19bf82"],"state_sha256":"0cd2bd07a44497b9d641e7e94bb7c065cd0da1b618986bbca247db3fd36b78ba"}