{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7SGOA2IAVOBN2VCO6IA7YVGX7B","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":"fe4a694fa42f3071e3a32cd1433bcd6dfa1d709cbb9c7931e72797d8dfedce9c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-02-02T15:02:37Z","title_canon_sha256":"c406ae4a7f2601156e437c18e6f30086981519661650dcf0933425490b8e41b6"},"schema_version":"1.0","source":{"id":"1602.00959","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.00959","created_at":"2026-05-18T01:21:24Z"},{"alias_kind":"arxiv_version","alias_value":"1602.00959v1","created_at":"2026-05-18T01:21:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.00959","created_at":"2026-05-18T01:21:24Z"},{"alias_kind":"pith_short_12","alias_value":"7SGOA2IAVOBN","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7SGOA2IAVOBN2VCO","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7SGOA2IA","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:e13e2056b5d867584708013186db9260594465372ea6713373b8a16bd85daaaa","target":"graph","created_at":"2026-05-18T01:21:24Z","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":"Barker and Larman asked the following. Let $K' \\subset {\\Bbb{R}}^d$ be a convex body, whose interior contains a given convex body $K \\subset {\\Bbb{R}}^d$, and let, for all supporting hyperplanes $H$ of $K$, the $(d-1)$-volumes of the intersections $K' \\cap H$ be given. Is $K'$ then uniquely determined? Yaskin and Zhang asked the analogous question when, for all supporting hyperplanes $H$ of $K$, the $d$-volumes of the \"caps\" cut off from $K'$ by $H$ are given. We give local positive answers to both of these questions, for small $C^2$-perturbations of $K$, provided the boundary of $K$ is $C^2_+","authors_text":"E. Makai, H. Martini, Jr.","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-02-02T15:02:37Z","title":"Unique local determination of convex bodies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00959","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":"sha256:52377a923348113bda54b07f67b4e4944eb4653ed3872067d19be8dc15f5b36c","target":"record","created_at":"2026-05-18T01:21:24Z","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":"fe4a694fa42f3071e3a32cd1433bcd6dfa1d709cbb9c7931e72797d8dfedce9c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-02-02T15:02:37Z","title_canon_sha256":"c406ae4a7f2601156e437c18e6f30086981519661650dcf0933425490b8e41b6"},"schema_version":"1.0","source":{"id":"1602.00959","kind":"arxiv","version":1}},"canonical_sha256":"fc8ce06900ab82dd544ef201fc54d7f84059fb49aea990ad7cd63e89f42844ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc8ce06900ab82dd544ef201fc54d7f84059fb49aea990ad7cd63e89f42844ee","first_computed_at":"2026-05-18T01:21:24.165245Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:24.165245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AdelC3AjCxxBTh16Rx3tEZHMRj4tlZFoNE588B+nW5jt+t7SHQKbEaTUdttYPpuSaym9WGVVJ68ks6mNwbbCAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:24.165889Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.00959","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52377a923348113bda54b07f67b4e4944eb4653ed3872067d19be8dc15f5b36c","sha256:e13e2056b5d867584708013186db9260594465372ea6713373b8a16bd85daaaa"],"state_sha256":"de5b35c35165d5872b93d024cc9ea8227cf675da28a59d4d6463f1ef9f09ce99"}