{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7QKKM7OM3BYANEJ6VRA5EMNCUX","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":"772d598b8e0886805c637f14d16efb72f3de64e2517daf056af991c03910e9e2","cross_cats_sorted":["cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-08-20T22:51:21Z","title_canon_sha256":"05eeaaf0dc087e65b3aec2d235a83b99eadd8a90a66432b96e0d3d916a237a59"},"schema_version":"1.0","source":{"id":"1508.05143","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.05143","created_at":"2026-05-18T01:17:37Z"},{"alias_kind":"arxiv_version","alias_value":"1508.05143v2","created_at":"2026-05-18T01:17:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.05143","created_at":"2026-05-18T01:17:37Z"},{"alias_kind":"pith_short_12","alias_value":"7QKKM7OM3BYA","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7QKKM7OM3BYANEJ6","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7QKKM7OM","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:e6a43a082a6b3e092ffadb8979bf52744712668f4e0602c041cff9016903f04c","target":"graph","created_at":"2026-05-18T01:17:37Z","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 consider the well-studied cake cutting problem in which the goal is to identify a fair allocation based on a minimal number of queries from the agents. The problem has attracted considerable attention within various branches of computer science, mathematics, and economics. Although, the elegant Selfridge-Conway envy-free protocol for three agents has been known since 1960, it has been a major open problem for the last fifty years to obtain a bounded envy-free protocol for more than three agents. We propose a discrete and bounded envy-free protocol for four agents.","authors_text":"Haris Aziz, Simon Mackenzie","cross_cats":["cs.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-08-20T22:51:21Z","title":"A Discrete and Bounded Envy-free Cake Cutting Protocol for Four Agents"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.05143","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:c597a408c90063484e0a4cb381aaf9795d17a14bc1cbaabdb568da87ee73513b","target":"record","created_at":"2026-05-18T01:17:37Z","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":"772d598b8e0886805c637f14d16efb72f3de64e2517daf056af991c03910e9e2","cross_cats_sorted":["cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-08-20T22:51:21Z","title_canon_sha256":"05eeaaf0dc087e65b3aec2d235a83b99eadd8a90a66432b96e0d3d916a237a59"},"schema_version":"1.0","source":{"id":"1508.05143","kind":"arxiv","version":2}},"canonical_sha256":"fc14a67dccd87006913eac41d231a2a5c43ef26bb961d22f1c50b26828d6b794","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc14a67dccd87006913eac41d231a2a5c43ef26bb961d22f1c50b26828d6b794","first_computed_at":"2026-05-18T01:17:37.289446Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:37.289446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5t1HYRPZv5TL8+FZEo0lE7pBOgTpBqsovEa6YoGMBus+Q9vZesDQRHDeucsLijnpGl5JjcXO7IYXobEG/NICBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:37.290050Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.05143","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c597a408c90063484e0a4cb381aaf9795d17a14bc1cbaabdb568da87ee73513b","sha256:e6a43a082a6b3e092ffadb8979bf52744712668f4e0602c041cff9016903f04c"],"state_sha256":"f6ca8fb6541d6f9f2467f20fec47191e82c3a65e6445f18efe8188219ccdcf82"}