{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:CGKQDOGYIMA2SIRBMNM4SAHXKX","short_pith_number":"pith:CGKQDOGY","canonical_record":{"source":{"id":"1306.2741","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-06-12T08:22:37Z","cross_cats_sorted":[],"title_canon_sha256":"3a4a802cd1c1b4df3128fd7c396c94b6b98f3e56f76cb1a191141e14b02df74f","abstract_canon_sha256":"c45d5ef426a59098fedcf65829a6d64b37cf8cde2b802f643f89f829bb5d4ce7"},"schema_version":"1.0"},"canonical_sha256":"119501b8d84301a922216359c900f755f078716f6fab10b7e77f4b9d0c199183","source":{"kind":"arxiv","id":"1306.2741","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:CGKQDOGYIMA2SIRBMNM4SAHXKX","target":"record","payload":{"canonical_record":{"source":{"id":"1306.2741","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-06-12T08:22:37Z","cross_cats_sorted":[],"title_canon_sha256":"3a4a802cd1c1b4df3128fd7c396c94b6b98f3e56f76cb1a191141e14b02df74f","abstract_canon_sha256":"c45d5ef426a59098fedcf65829a6d64b37cf8cde2b802f643f89f829bb5d4ce7"},"schema_version":"1.0"},"canonical_sha256":"119501b8d84301a922216359c900f755f078716f6fab10b7e77f4b9d0c199183","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:58.524774Z","signature_b64":"zk65TpLLjqTrcumUJLKDdJwlAMMjP34M15IlyjT36zNUidy8sZbwzDt1GvcEk8EYZfqAgjtEX7pBhgNUS2KEDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"119501b8d84301a922216359c900f755f078716f6fab10b7e77f4b9d0c199183","last_reissued_at":"2026-05-18T00:44:58.524314Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:58.524314Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.2741","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:44:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"19f/SUuqCq5Xi4TVssgmjqYxJm3dJ53EljZtNJpWMM1tjGhd85los12cy4gyc2/FzrYRkhkg0i7EVT4VAVBABQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T13:53:19.305105Z"},"content_sha256":"af4623072bf9fabb6c6df06deb2cb68826b97c63ae9b371f254e8aee25c7a411","schema_version":"1.0","event_id":"sha256:af4623072bf9fabb6c6df06deb2cb68826b97c63ae9b371f254e8aee25c7a411"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:CGKQDOGYIMA2SIRBMNM4SAHXKX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convex Equipartitions: The Spicy Chicken Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Alfredo Hubard, Boris Aronov, Roman Karasev","submitted_at":"2013-06-12T08:22:37Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2741","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:44:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gELMTdMdDmWLiERHla14yXDvhiF+bX+ROWvBMWrzJENcwjnb1gRoMdNgXVxBL7IznciQ3hbw5c+erejJtJ1BBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T13:53:19.305519Z"},"content_sha256":"fd1306bad00c83354a8c93d04f948b71f03724d3cc7e60fdc3a81e7b2260bf02","schema_version":"1.0","event_id":"sha256:fd1306bad00c83354a8c93d04f948b71f03724d3cc7e60fdc3a81e7b2260bf02"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CGKQDOGYIMA2SIRBMNM4SAHXKX/bundle.json","state_url":"https://pith.science/pith/CGKQDOGYIMA2SIRBMNM4SAHXKX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CGKQDOGYIMA2SIRBMNM4SAHXKX/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-22T13:53:19Z","links":{"resolver":"https://pith.science/pith/CGKQDOGYIMA2SIRBMNM4SAHXKX","bundle":"https://pith.science/pith/CGKQDOGYIMA2SIRBMNM4SAHXKX/bundle.json","state":"https://pith.science/pith/CGKQDOGYIMA2SIRBMNM4SAHXKX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CGKQDOGYIMA2SIRBMNM4SAHXKX/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uLQa5A8KIZ+wNeu4UiqX4ISQxUsnk9co/fe50z7f4e4m4wstq5xOYobabbo6eTdkgUNwCGgcQzbIDiLReLwnCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T13:53:19.308753Z","bundle_sha256":"441011228e119a637b1e1fc76fe0966c9169d29e14a3ecfe382eaf219dde4b0d"}}