{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:7QKKM7OM3BYANEJ6VRA5EMNCUX","short_pith_number":"pith:7QKKM7OM","schema_version":"1.0","canonical_sha256":"fc14a67dccd87006913eac41d231a2a5c43ef26bb961d22f1c50b26828d6b794","source":{"kind":"arxiv","id":"1508.05143","version":2},"attestation_state":"computed","paper":{"title":"A Discrete and Bounded Envy-free Cake Cutting Protocol for Four Agents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.GT"],"primary_cat":"cs.DS","authors_text":"Haris Aziz, Simon Mackenzie","submitted_at":"2015-08-20T22:51:21Z","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1508.05143","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-08-20T22:51:21Z","cross_cats_sorted":["cs.GT"],"title_canon_sha256":"05eeaaf0dc087e65b3aec2d235a83b99eadd8a90a66432b96e0d3d916a237a59","abstract_canon_sha256":"772d598b8e0886805c637f14d16efb72f3de64e2517daf056af991c03910e9e2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:37.290050Z","signature_b64":"5t1HYRPZv5TL8+FZEo0lE7pBOgTpBqsovEa6YoGMBus+Q9vZesDQRHDeucsLijnpGl5JjcXO7IYXobEG/NICBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc14a67dccd87006913eac41d231a2a5c43ef26bb961d22f1c50b26828d6b794","last_reissued_at":"2026-05-18T01:17:37.289446Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:37.289446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Discrete and Bounded Envy-free Cake Cutting Protocol for Four Agents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.GT"],"primary_cat":"cs.DS","authors_text":"Haris Aziz, Simon Mackenzie","submitted_at":"2015-08-20T22:51:21Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.05143","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1508.05143","created_at":"2026-05-18T01:17:37.289554+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.05143v2","created_at":"2026-05-18T01:17:37.289554+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.05143","created_at":"2026-05-18T01:17:37.289554+00:00"},{"alias_kind":"pith_short_12","alias_value":"7QKKM7OM3BYA","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"7QKKM7OM3BYANEJ6","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"7QKKM7OM","created_at":"2026-05-18T12:29:10.953037+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7QKKM7OM3BYANEJ6VRA5EMNCUX","json":"https://pith.science/pith/7QKKM7OM3BYANEJ6VRA5EMNCUX.json","graph_json":"https://pith.science/api/pith-number/7QKKM7OM3BYANEJ6VRA5EMNCUX/graph.json","events_json":"https://pith.science/api/pith-number/7QKKM7OM3BYANEJ6VRA5EMNCUX/events.json","paper":"https://pith.science/paper/7QKKM7OM"},"agent_actions":{"view_html":"https://pith.science/pith/7QKKM7OM3BYANEJ6VRA5EMNCUX","download_json":"https://pith.science/pith/7QKKM7OM3BYANEJ6VRA5EMNCUX.json","view_paper":"https://pith.science/paper/7QKKM7OM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.05143&json=true","fetch_graph":"https://pith.science/api/pith-number/7QKKM7OM3BYANEJ6VRA5EMNCUX/graph.json","fetch_events":"https://pith.science/api/pith-number/7QKKM7OM3BYANEJ6VRA5EMNCUX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7QKKM7OM3BYANEJ6VRA5EMNCUX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7QKKM7OM3BYANEJ6VRA5EMNCUX/action/storage_attestation","attest_author":"https://pith.science/pith/7QKKM7OM3BYANEJ6VRA5EMNCUX/action/author_attestation","sign_citation":"https://pith.science/pith/7QKKM7OM3BYANEJ6VRA5EMNCUX/action/citation_signature","submit_replication":"https://pith.science/pith/7QKKM7OM3BYANEJ6VRA5EMNCUX/action/replication_record"}},"created_at":"2026-05-18T01:17:37.289554+00:00","updated_at":"2026-05-18T01:17:37.289554+00:00"}