{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:P2JBTPYGIPSLPPC2GAVKMBEX2Z","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":"a64734b31808485d36c332563ba262ecc063c2692ecee24b62c3947bd3b2d268","cross_cats_sorted":["math.MG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2021-12-27T11:55:10Z","title_canon_sha256":"cad13b9b023c0534cea309acc40e1e31cfd08bb56c3d98a2eb24f2bcf30250a9"},"schema_version":"1.0","source":{"id":"2112.13622","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.13622","created_at":"2026-07-05T07:12:45Z"},{"alias_kind":"arxiv_version","alias_value":"2112.13622v4","created_at":"2026-07-05T07:12:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.13622","created_at":"2026-07-05T07:12:45Z"},{"alias_kind":"pith_short_12","alias_value":"P2JBTPYGIPSL","created_at":"2026-07-05T07:12:45Z"},{"alias_kind":"pith_short_16","alias_value":"P2JBTPYGIPSLPPC2","created_at":"2026-07-05T07:12:45Z"},{"alias_kind":"pith_short_8","alias_value":"P2JBTPYG","created_at":"2026-07-05T07:12:45Z"}],"graph_snapshots":[{"event_id":"sha256:97cddd2d3a55d55baceb714db6b19e7caae387be65a425f11263511df6e8fc19","target":"graph","created_at":"2026-07-05T07:12:45Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2112.13622/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the algorithmic complexity of fair division problems with a focus on minimizing the number of queries needed to find an approximate solution with desired accuracy. We show for several classes of fair division problems that under certain natural conditions on sets of preferences, a logarithmic number of queries with respect to accuracy is sufficient.","authors_text":"Alexandr Grebennikov, Andrei V. Malyutin, Mikhail Mikhailov, Oleg R. Musin, Xenia Isaeva","cross_cats":["math.MG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2021-12-27T11:55:10Z","title":"Logarithmic algorithms for fair division problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.13622","kind":"arxiv","version":4},"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:f9d1a4f09306289737e16171564e5a143fd372110f62973a5232e29e46616a75","target":"record","created_at":"2026-07-05T07:12:45Z","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":"a64734b31808485d36c332563ba262ecc063c2692ecee24b62c3947bd3b2d268","cross_cats_sorted":["math.MG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2021-12-27T11:55:10Z","title_canon_sha256":"cad13b9b023c0534cea309acc40e1e31cfd08bb56c3d98a2eb24f2bcf30250a9"},"schema_version":"1.0","source":{"id":"2112.13622","kind":"arxiv","version":4}},"canonical_sha256":"7e9219bf0643e4b7bc5a302aa60497d67dca823d74691c832568b915b8bd47f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e9219bf0643e4b7bc5a302aa60497d67dca823d74691c832568b915b8bd47f7","first_computed_at":"2026-07-05T07:12:45.833090Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:12:45.833090Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GV692ESd4jtm4wtSkhaU87erR9viQWm8tgt1XTt0dyazUvVNPu/gpg1crybLGv6GTx2aZs2PnMRUd7yUJuNKAg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:12:45.833500Z","signed_message":"canonical_sha256_bytes"},"source_id":"2112.13622","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9d1a4f09306289737e16171564e5a143fd372110f62973a5232e29e46616a75","sha256:97cddd2d3a55d55baceb714db6b19e7caae387be65a425f11263511df6e8fc19"],"state_sha256":"4cbbcd103dbdf2d1e5d03ec92ef2959b4751a619d82b07bec67f156aad0d6afb"}