{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:EJZ7QF7VHAFOYSCZTZCN5OREHX","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":"807cdf2c9faa26a91d68afe83da6f49ec1f573a5d2ab1bc47363199487aed09b","cross_cats_sorted":["cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-07-28T21:33:26Z","title_canon_sha256":"049e1e0594cd8d99f3eaee4da2810e0cac96fe367f5354a022703cc1858f3a2e"},"schema_version":"1.0","source":{"id":"1507.08497","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.08497","created_at":"2026-05-18T01:34:54Z"},{"alias_kind":"arxiv_version","alias_value":"1507.08497v2","created_at":"2026-05-18T01:34:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.08497","created_at":"2026-05-18T01:34:54Z"},{"alias_kind":"pith_short_12","alias_value":"EJZ7QF7VHAFO","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EJZ7QF7VHAFOYSCZ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EJZ7QF7V","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:ff96bd23633c56e27136d5fbec3592a159ae7cbeca496a9017665527fbdc16c3","target":"graph","created_at":"2026-05-18T01:34:54Z","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":"A division of a cake by n people is envy free if everyone thinks they got the biggest pieces. Note that peoples tastes can differ. There is a discrete protocol for envy free division for n=3 which takes at most 5 cuts. For n=4 and beyond there is a protocol but the number of cuts it takes is unbounded. In particular the number of cuts depends on peoples tastes. Given any number N peoples tastes can be set so that the algorithm takes over N cuts. There are three such algorithms known. Which is better?\n  We have devised a way to measure the number of cuts even though it is unbounded. We use ordi","authors_text":"William Gasarch","cross_cats":["cs.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-07-28T21:33:26Z","title":"Which Unbounded Protocol for Envy Free Cake Cutting is Better?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08497","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":"sha256:2d46b32d3b75b690b52b34311e780d7847698c453f0bd9a57565649a8d996bde","target":"record","created_at":"2026-05-18T01:34:54Z","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":"807cdf2c9faa26a91d68afe83da6f49ec1f573a5d2ab1bc47363199487aed09b","cross_cats_sorted":["cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-07-28T21:33:26Z","title_canon_sha256":"049e1e0594cd8d99f3eaee4da2810e0cac96fe367f5354a022703cc1858f3a2e"},"schema_version":"1.0","source":{"id":"1507.08497","kind":"arxiv","version":2}},"canonical_sha256":"2273f817f5380aec48599e44deba243de7fa7a8ad5e384c6aae9d062551955f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2273f817f5380aec48599e44deba243de7fa7a8ad5e384c6aae9d062551955f0","first_computed_at":"2026-05-18T01:34:54.291478Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:54.291478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XmfPD4x4jg8As1lmTjryDWssec3MzlWkbhkAVkeLUwGT5e+PKqn4npFWcIqSiHN4yYxGdf9N2CEUZYFnf6CuBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:54.292130Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.08497","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d46b32d3b75b690b52b34311e780d7847698c453f0bd9a57565649a8d996bde","sha256:ff96bd23633c56e27136d5fbec3592a159ae7cbeca496a9017665527fbdc16c3"],"state_sha256":"acc603f77412d6871ef85b47957f605c20949af695859cf8e4cb390b21148c4c"}