{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CGKQDOGYIMA2SIRBMNM4SAHXKX","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":"c45d5ef426a59098fedcf65829a6d64b37cf8cde2b802f643f89f829bb5d4ce7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-06-12T08:22:37Z","title_canon_sha256":"3a4a802cd1c1b4df3128fd7c396c94b6b98f3e56f76cb1a191141e14b02df74f"},"schema_version":"1.0","source":{"id":"1306.2741","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.2741","created_at":"2026-05-18T00:44:58Z"},{"alias_kind":"arxiv_version","alias_value":"1306.2741v2","created_at":"2026-05-18T00:44:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.2741","created_at":"2026-05-18T00:44:58Z"},{"alias_kind":"pith_short_12","alias_value":"CGKQDOGYIMA2","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CGKQDOGYIMA2SIRB","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CGKQDOGY","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:fd1306bad00c83354a8c93d04f948b71f03724d3cc7e60fdc3a81e7b2260bf02","target":"graph","created_at":"2026-05-18T00:44:58Z","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 show that, for any prime power n and any convex body K (i.e., a compact convex set with interior) in Rd, there exists a partition of K into n convex sets with equal volumes and equal surface areas. Similar results regarding equipartitions with respect to continuous functionals and absolutely continuous measures on convex bodies are also proven. These include a generalization of the ham-sandwich theorem to arbitrary number of convex pieces confirming a conjecture of Kaneko and Kano, a similar generalization of perfect partitions of a cake and its icing, and a generalization of the Gromov-Bor","authors_text":"Alfredo Hubard, Boris Aronov, Roman Karasev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-06-12T08:22:37Z","title":"Convex Equipartitions: The Spicy Chicken Theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2741","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:af4623072bf9fabb6c6df06deb2cb68826b97c63ae9b371f254e8aee25c7a411","target":"record","created_at":"2026-05-18T00:44:58Z","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":"c45d5ef426a59098fedcf65829a6d64b37cf8cde2b802f643f89f829bb5d4ce7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-06-12T08:22:37Z","title_canon_sha256":"3a4a802cd1c1b4df3128fd7c396c94b6b98f3e56f76cb1a191141e14b02df74f"},"schema_version":"1.0","source":{"id":"1306.2741","kind":"arxiv","version":2}},"canonical_sha256":"119501b8d84301a922216359c900f755f078716f6fab10b7e77f4b9d0c199183","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"119501b8d84301a922216359c900f755f078716f6fab10b7e77f4b9d0c199183","first_computed_at":"2026-05-18T00:44:58.524314Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:58.524314Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zk65TpLLjqTrcumUJLKDdJwlAMMjP34M15IlyjT36zNUidy8sZbwzDt1GvcEk8EYZfqAgjtEX7pBhgNUS2KEDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:58.524774Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.2741","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af4623072bf9fabb6c6df06deb2cb68826b97c63ae9b371f254e8aee25c7a411","sha256:fd1306bad00c83354a8c93d04f948b71f03724d3cc7e60fdc3a81e7b2260bf02"],"state_sha256":"15e000e0c6f102343873056d5437600938ce51197568d1b3163a2d99cab399db"}