{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:XISZIXHFCOC3KDG7HUJ2JD2QAW","short_pith_number":"pith:XISZIXHF","schema_version":"1.0","canonical_sha256":"ba25945ce51385b50cdf3d13a48f5005b7c3802fcb9b7a7a95f13616a0e936da","source":{"kind":"arxiv","id":"2506.05613","version":1},"attestation_state":"computed","paper":{"title":"Beating the Logarithmic Barrier for the Subadditive Maximin Share Problem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Masoud Seddighin, Saeed Seddighin","submitted_at":"2025-06-05T21:55:07Z","abstract_excerpt":"We study the problem of fair allocation of indivisible goods for subadditive agents. While constant-\\textsf{MMS} bounds have been given for additive and fractionally subadditive agents, the best existential bound for the case of subadditive agents is $1/O(\\log n \\log \\log n)$. In this work, we improve this bound to a $1/O((\\log \\log n)^2)$-\\textsf{MMS} guarantee. To this end, we introduce new matching techniques and rounding methods for subadditive valuations that we believe are of independent interest and will find their applications in future work."},"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":"2506.05613","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.GT","submitted_at":"2025-06-05T21:55:07Z","cross_cats_sorted":[],"title_canon_sha256":"0324edbdfc18ab44c44b2bcf7ba41ded009d8e1a20a913cf94d3b9e8e2786dcb","abstract_canon_sha256":"6d2180cd98a78bbfa64eb8c5a5be90979ae683f2cb7198ed1d78f1851a013f26"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:17:06.888766Z","signature_b64":"x2LW2vkQJxpjaJfhY4wnyi9nYP5Xpgz+Ijgk5fVa0G+eNuN/9Xknpo64MKT/UuDFfQ+3WdkgPb9m3u3cIYl0Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba25945ce51385b50cdf3d13a48f5005b7c3802fcb9b7a7a95f13616a0e936da","last_reissued_at":"2026-07-05T11:17:06.888143Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:17:06.888143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Beating the Logarithmic Barrier for the Subadditive Maximin Share Problem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Masoud Seddighin, Saeed Seddighin","submitted_at":"2025-06-05T21:55:07Z","abstract_excerpt":"We study the problem of fair allocation of indivisible goods for subadditive agents. While constant-\\textsf{MMS} bounds have been given for additive and fractionally subadditive agents, the best existential bound for the case of subadditive agents is $1/O(\\log n \\log \\log n)$. In this work, we improve this bound to a $1/O((\\log \\log n)^2)$-\\textsf{MMS} guarantee. To this end, we introduce new matching techniques and rounding methods for subadditive valuations that we believe are of independent interest and will find their applications in future work."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.05613","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.05613/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2506.05613","created_at":"2026-07-05T11:17:06.888216+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.05613v1","created_at":"2026-07-05T11:17:06.888216+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.05613","created_at":"2026-07-05T11:17:06.888216+00:00"},{"alias_kind":"pith_short_12","alias_value":"XISZIXHFCOC3","created_at":"2026-07-05T11:17:06.888216+00:00"},{"alias_kind":"pith_short_16","alias_value":"XISZIXHFCOC3KDG7","created_at":"2026-07-05T11:17:06.888216+00:00"},{"alias_kind":"pith_short_8","alias_value":"XISZIXHF","created_at":"2026-07-05T11:17:06.888216+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.21493","citing_title":"From multi-allocations to allocations, with subadditive valuations","ref_index":15,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XISZIXHFCOC3KDG7HUJ2JD2QAW","json":"https://pith.science/pith/XISZIXHFCOC3KDG7HUJ2JD2QAW.json","graph_json":"https://pith.science/api/pith-number/XISZIXHFCOC3KDG7HUJ2JD2QAW/graph.json","events_json":"https://pith.science/api/pith-number/XISZIXHFCOC3KDG7HUJ2JD2QAW/events.json","paper":"https://pith.science/paper/XISZIXHF"},"agent_actions":{"view_html":"https://pith.science/pith/XISZIXHFCOC3KDG7HUJ2JD2QAW","download_json":"https://pith.science/pith/XISZIXHFCOC3KDG7HUJ2JD2QAW.json","view_paper":"https://pith.science/paper/XISZIXHF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.05613&json=true","fetch_graph":"https://pith.science/api/pith-number/XISZIXHFCOC3KDG7HUJ2JD2QAW/graph.json","fetch_events":"https://pith.science/api/pith-number/XISZIXHFCOC3KDG7HUJ2JD2QAW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XISZIXHFCOC3KDG7HUJ2JD2QAW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XISZIXHFCOC3KDG7HUJ2JD2QAW/action/storage_attestation","attest_author":"https://pith.science/pith/XISZIXHFCOC3KDG7HUJ2JD2QAW/action/author_attestation","sign_citation":"https://pith.science/pith/XISZIXHFCOC3KDG7HUJ2JD2QAW/action/citation_signature","submit_replication":"https://pith.science/pith/XISZIXHFCOC3KDG7HUJ2JD2QAW/action/replication_record"}},"created_at":"2026-07-05T11:17:06.888216+00:00","updated_at":"2026-07-05T11:17:06.888216+00:00"}