{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:42H7E4YNG2F7NM5OMDIQYRCX4Z","short_pith_number":"pith:42H7E4YN","canonical_record":{"source":{"id":"1307.2908","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-07-10T20:02:18Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"2c9f1981b8842d78cf7a6a4c4d688bda0b62ec573c0f8e258da56077987464a0","abstract_canon_sha256":"de90d5f2867543ac3b6b3fd86629c98881fb74a6528988c478b3db1c290d31d6"},"schema_version":"1.0"},"canonical_sha256":"e68ff2730d368bf6b3ae60d10c4457e653fe4481a0c907b0bc2cbc9bf4381547","source":{"kind":"arxiv","id":"1307.2908","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.2908","created_at":"2026-05-18T03:08:46Z"},{"alias_kind":"arxiv_version","alias_value":"1307.2908v3","created_at":"2026-05-18T03:08:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.2908","created_at":"2026-05-18T03:08:46Z"},{"alias_kind":"pith_short_12","alias_value":"42H7E4YNG2F7","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"42H7E4YNG2F7NM5O","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"42H7E4YN","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:42H7E4YNG2F7NM5OMDIQYRCX4Z","target":"record","payload":{"canonical_record":{"source":{"id":"1307.2908","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-07-10T20:02:18Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"2c9f1981b8842d78cf7a6a4c4d688bda0b62ec573c0f8e258da56077987464a0","abstract_canon_sha256":"de90d5f2867543ac3b6b3fd86629c98881fb74a6528988c478b3db1c290d31d6"},"schema_version":"1.0"},"canonical_sha256":"e68ff2730d368bf6b3ae60d10c4457e653fe4481a0c907b0bc2cbc9bf4381547","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:46.900799Z","signature_b64":"+vXnIHo/hn/SkesJ7nrD5pfIqNT/gIPOidB7QJGq8jgS6ck1Cviv+UDixZCFpecvBApixpj1IkqzYy6x91vBBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e68ff2730d368bf6b3ae60d10c4457e653fe4481a0c907b0bc2cbc9bf4381547","last_reissued_at":"2026-05-18T03:08:46.900207Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:46.900207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.2908","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:08:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0BgeTqbLSWrbsmKpsLyTeCvFZ+dHF8inrNvNDEPhSTEZCvN6iHox2abCw1e/j94K17s26fQhPx+jgmcRyJuwCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:27:09.380528Z"},"content_sha256":"81aeb259a96b5b2ae440abadbe2decc54e869ab4fdb58f4c27a35438a650b5ad","schema_version":"1.0","event_id":"sha256:81aeb259a96b5b2ae440abadbe2decc54e869ab4fdb58f4c27a35438a650b5ad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:42H7E4YNG2F7NM5OMDIQYRCX4Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cake Cutting Algorithms for Piecewise Constant and Piecewise Uniform Valuations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.GT","authors_text":"Chun Ye, Haris Aziz","submitted_at":"2013-07-10T20:02:18Z","abstract_excerpt":"Cake cutting is one of the most fundamental settings in fair division and mechanism design without money. In this paper, we consider different levels of three fundamental goals in cake cutting: fairness, Pareto optimality, and strategyproofness. In particular, we present robust versions of envy-freeness and proportionality that are not only stronger than their standard counter-parts but also have less information requirements. We then focus on cake cutting with piecewise constant valuations and present three desirable algorithms: CCEA (Controlled Cake Eating Algorithm), MEA (Market Equilibrium"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2908","kind":"arxiv","version":3},"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":"2026-05-18T03:08:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xztS6Z1U3FWYxrRfgpA40r7ei/jh3UbFIgI4XfHB8pb9ph1ntepaj3MSrxLXWO6V6fMaLEo/9Ode4F/3n+WDAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:27:09.381165Z"},"content_sha256":"89a88ee18c5c1bb4854496824fb55676cbb7edb4bf30b27f39d9eb60826ff4f3","schema_version":"1.0","event_id":"sha256:89a88ee18c5c1bb4854496824fb55676cbb7edb4bf30b27f39d9eb60826ff4f3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/42H7E4YNG2F7NM5OMDIQYRCX4Z/bundle.json","state_url":"https://pith.science/pith/42H7E4YNG2F7NM5OMDIQYRCX4Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/42H7E4YNG2F7NM5OMDIQYRCX4Z/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":"2026-05-27T10:27:09Z","links":{"resolver":"https://pith.science/pith/42H7E4YNG2F7NM5OMDIQYRCX4Z","bundle":"https://pith.science/pith/42H7E4YNG2F7NM5OMDIQYRCX4Z/bundle.json","state":"https://pith.science/pith/42H7E4YNG2F7NM5OMDIQYRCX4Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/42H7E4YNG2F7NM5OMDIQYRCX4Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:42H7E4YNG2F7NM5OMDIQYRCX4Z","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":"de90d5f2867543ac3b6b3fd86629c98881fb74a6528988c478b3db1c290d31d6","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-07-10T20:02:18Z","title_canon_sha256":"2c9f1981b8842d78cf7a6a4c4d688bda0b62ec573c0f8e258da56077987464a0"},"schema_version":"1.0","source":{"id":"1307.2908","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.2908","created_at":"2026-05-18T03:08:46Z"},{"alias_kind":"arxiv_version","alias_value":"1307.2908v3","created_at":"2026-05-18T03:08:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.2908","created_at":"2026-05-18T03:08:46Z"},{"alias_kind":"pith_short_12","alias_value":"42H7E4YNG2F7","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"42H7E4YNG2F7NM5O","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"42H7E4YN","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:89a88ee18c5c1bb4854496824fb55676cbb7edb4bf30b27f39d9eb60826ff4f3","target":"graph","created_at":"2026-05-18T03:08:46Z","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":"Cake cutting is one of the most fundamental settings in fair division and mechanism design without money. In this paper, we consider different levels of three fundamental goals in cake cutting: fairness, Pareto optimality, and strategyproofness. In particular, we present robust versions of envy-freeness and proportionality that are not only stronger than their standard counter-parts but also have less information requirements. We then focus on cake cutting with piecewise constant valuations and present three desirable algorithms: CCEA (Controlled Cake Eating Algorithm), MEA (Market Equilibrium","authors_text":"Chun Ye, Haris Aziz","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-07-10T20:02:18Z","title":"Cake Cutting Algorithms for Piecewise Constant and Piecewise Uniform Valuations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2908","kind":"arxiv","version":3},"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":"sha256:81aeb259a96b5b2ae440abadbe2decc54e869ab4fdb58f4c27a35438a650b5ad","target":"record","created_at":"2026-05-18T03:08:46Z","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":"de90d5f2867543ac3b6b3fd86629c98881fb74a6528988c478b3db1c290d31d6","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-07-10T20:02:18Z","title_canon_sha256":"2c9f1981b8842d78cf7a6a4c4d688bda0b62ec573c0f8e258da56077987464a0"},"schema_version":"1.0","source":{"id":"1307.2908","kind":"arxiv","version":3}},"canonical_sha256":"e68ff2730d368bf6b3ae60d10c4457e653fe4481a0c907b0bc2cbc9bf4381547","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e68ff2730d368bf6b3ae60d10c4457e653fe4481a0c907b0bc2cbc9bf4381547","first_computed_at":"2026-05-18T03:08:46.900207Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:08:46.900207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+vXnIHo/hn/SkesJ7nrD5pfIqNT/gIPOidB7QJGq8jgS6ck1Cviv+UDixZCFpecvBApixpj1IkqzYy6x91vBBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:08:46.900799Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.2908","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81aeb259a96b5b2ae440abadbe2decc54e869ab4fdb58f4c27a35438a650b5ad","sha256:89a88ee18c5c1bb4854496824fb55676cbb7edb4bf30b27f39d9eb60826ff4f3"],"state_sha256":"ac500b97c396a922ed70a2786ff858ce079213d7c47f9983a1d31d08034e73b6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4TPSrLyfX0PDBbZ6O75q5Muu0jpLbeHPCp9WxfbGC3ZeEVCMBs541Cht2SM8YpySaLhaECBvH6lM5utzWHD1Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T10:27:09.384548Z","bundle_sha256":"7511884a076bd4d80bb4e6d44d2e31330caf381f4223bd8548c9e785d81d3353"}}