{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:OQNMQ4WMW3LFPYN3AJYOLLCUJY","short_pith_number":"pith:OQNMQ4WM","canonical_record":{"source":{"id":"1904.02502","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-04-04T11:59:00Z","cross_cats_sorted":[],"title_canon_sha256":"2d7b6bad06978596289d63124bacd013f07b3ce36a7af032545c6af01aff044d","abstract_canon_sha256":"cd794ebeab17190a9df0611970c8155ddd61cb520e8668869ca3257e40006afb"},"schema_version":"1.0"},"canonical_sha256":"741ac872ccb6d657e1bb0270e5ac544e3fea0e965012d6daceb0761e46d899ff","source":{"kind":"arxiv","id":"1904.02502","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.02502","created_at":"2026-05-17T23:49:23Z"},{"alias_kind":"arxiv_version","alias_value":"1904.02502v1","created_at":"2026-05-17T23:49:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.02502","created_at":"2026-05-17T23:49:23Z"},{"alias_kind":"pith_short_12","alias_value":"OQNMQ4WMW3LF","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"OQNMQ4WMW3LFPYN3","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"OQNMQ4WM","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:OQNMQ4WMW3LFPYN3AJYOLLCUJY","target":"record","payload":{"canonical_record":{"source":{"id":"1904.02502","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-04-04T11:59:00Z","cross_cats_sorted":[],"title_canon_sha256":"2d7b6bad06978596289d63124bacd013f07b3ce36a7af032545c6af01aff044d","abstract_canon_sha256":"cd794ebeab17190a9df0611970c8155ddd61cb520e8668869ca3257e40006afb"},"schema_version":"1.0"},"canonical_sha256":"741ac872ccb6d657e1bb0270e5ac544e3fea0e965012d6daceb0761e46d899ff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:23.461351Z","signature_b64":"QTQo2+RixKHMt/1xe53FQKYyYjjakNT7ltxGVbbbdcWIgREaF6jXIaNkOJQPyKjw5yzUd21Vms/0hklaDRU9Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"741ac872ccb6d657e1bb0270e5ac544e3fea0e965012d6daceb0761e46d899ff","last_reissued_at":"2026-05-17T23:49:23.460880Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:23.460880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.02502","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:49:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UdDI1VjlstRUiHfkFZuvfd3w0PWTwFn2CCEfVI7aqcgxBHVQyrgJgswgm2kWQwRAeQ5kQLiuDieqwW8DBPYfBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:41:28.307442Z"},"content_sha256":"aaa29b386273053f2573757004074ecd1b25e10a79bca6651e5f6ea44576d16b","schema_version":"1.0","event_id":"sha256:aaa29b386273053f2573757004074ecd1b25e10a79bca6651e5f6ea44576d16b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:OQNMQ4WMW3LFPYN3AJYOLLCUJY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharing a pizza: bisecting masses with two cuts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Alexander Pilz, Luis Barba, Patrick Schnider","submitted_at":"2019-04-04T11:59:00Z","abstract_excerpt":"Assume you have a pizza consisting of four ingredients (e.g., bread, tomatoes, cheese and olives) that you want to share with your friend. You want to do this fairly, meaning that you and your friend should get the same amount of each ingredient. How many times do you need to cut the pizza so that this is possible? We will show that two straight cuts always suffice. More formally, we will show the following extension of the well-known Ham-sandwich theorem: Given four mass distributions in the plane, they can be simultaneously bisected with two lines. That is, there exist two oriented lines wit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.02502","kind":"arxiv","version":1},"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":"2026-05-17T23:49:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/flp/eFNdLkGkFU0NgZv8BtboKph+k/WmfG1UW1Sa0778ghJm6OC5yHb6eJg2AIGCpfTR0+4/Zs1otyvCeFtDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:41:28.308142Z"},"content_sha256":"a5021f81f10c10eec14a82cf510912a689ffbd109de8886054a2def4929acb09","schema_version":"1.0","event_id":"sha256:a5021f81f10c10eec14a82cf510912a689ffbd109de8886054a2def4929acb09"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OQNMQ4WMW3LFPYN3AJYOLLCUJY/bundle.json","state_url":"https://pith.science/pith/OQNMQ4WMW3LFPYN3AJYOLLCUJY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OQNMQ4WMW3LFPYN3AJYOLLCUJY/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":"2026-05-26T20:41:28Z","links":{"resolver":"https://pith.science/pith/OQNMQ4WMW3LFPYN3AJYOLLCUJY","bundle":"https://pith.science/pith/OQNMQ4WMW3LFPYN3AJYOLLCUJY/bundle.json","state":"https://pith.science/pith/OQNMQ4WMW3LFPYN3AJYOLLCUJY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OQNMQ4WMW3LFPYN3AJYOLLCUJY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:OQNMQ4WMW3LFPYN3AJYOLLCUJY","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":"cd794ebeab17190a9df0611970c8155ddd61cb520e8668869ca3257e40006afb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-04-04T11:59:00Z","title_canon_sha256":"2d7b6bad06978596289d63124bacd013f07b3ce36a7af032545c6af01aff044d"},"schema_version":"1.0","source":{"id":"1904.02502","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.02502","created_at":"2026-05-17T23:49:23Z"},{"alias_kind":"arxiv_version","alias_value":"1904.02502v1","created_at":"2026-05-17T23:49:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.02502","created_at":"2026-05-17T23:49:23Z"},{"alias_kind":"pith_short_12","alias_value":"OQNMQ4WMW3LF","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"OQNMQ4WMW3LFPYN3","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"OQNMQ4WM","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:a5021f81f10c10eec14a82cf510912a689ffbd109de8886054a2def4929acb09","target":"graph","created_at":"2026-05-17T23:49:23Z","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":"Assume you have a pizza consisting of four ingredients (e.g., bread, tomatoes, cheese and olives) that you want to share with your friend. You want to do this fairly, meaning that you and your friend should get the same amount of each ingredient. How many times do you need to cut the pizza so that this is possible? We will show that two straight cuts always suffice. More formally, we will show the following extension of the well-known Ham-sandwich theorem: Given four mass distributions in the plane, they can be simultaneously bisected with two lines. That is, there exist two oriented lines wit","authors_text":"Alexander Pilz, Luis Barba, Patrick Schnider","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-04-04T11:59:00Z","title":"Sharing a pizza: bisecting masses with two cuts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.02502","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:aaa29b386273053f2573757004074ecd1b25e10a79bca6651e5f6ea44576d16b","target":"record","created_at":"2026-05-17T23:49:23Z","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":"cd794ebeab17190a9df0611970c8155ddd61cb520e8668869ca3257e40006afb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-04-04T11:59:00Z","title_canon_sha256":"2d7b6bad06978596289d63124bacd013f07b3ce36a7af032545c6af01aff044d"},"schema_version":"1.0","source":{"id":"1904.02502","kind":"arxiv","version":1}},"canonical_sha256":"741ac872ccb6d657e1bb0270e5ac544e3fea0e965012d6daceb0761e46d899ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"741ac872ccb6d657e1bb0270e5ac544e3fea0e965012d6daceb0761e46d899ff","first_computed_at":"2026-05-17T23:49:23.460880Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:23.460880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QTQo2+RixKHMt/1xe53FQKYyYjjakNT7ltxGVbbbdcWIgREaF6jXIaNkOJQPyKjw5yzUd21Vms/0hklaDRU9Ag==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:23.461351Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.02502","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aaa29b386273053f2573757004074ecd1b25e10a79bca6651e5f6ea44576d16b","sha256:a5021f81f10c10eec14a82cf510912a689ffbd109de8886054a2def4929acb09"],"state_sha256":"42ea7ba9fe0acdbf9846094971b5d809fa4530dcc712f9be4f9b85e1faddedfc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FpxAz3IeyJyA8wZJOnC+BwdCoiL0YF+K/CNb3ShtGjKxL9VLDSnpgoJGX3dVFCZ9bbkOELyK5uP7oCw0ym0mBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T20:41:28.311838Z","bundle_sha256":"1266970f85c32bd8e8bc6afcab04f9ed6bb0904b2d07c079a55f3a642e8fd823"}}