{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:CMH7D5LMS5FCMPLBVLFXXOUABA","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":"e33a2ac9bf31943e63f2ec94db0beecad24f59a7966ede618251804c366f560d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.GT","submitted_at":"2025-02-19T08:49:57Z","title_canon_sha256":"6ac1822787b5ed5bf0ab4aa50ce8841531c7807a8fc905eec2eb0d08ce33df04"},"schema_version":"1.0","source":{"id":"2502.13541","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.13541","created_at":"2026-07-05T10:16:48Z"},{"alias_kind":"arxiv_version","alias_value":"2502.13541v1","created_at":"2026-07-05T10:16:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.13541","created_at":"2026-07-05T10:16:48Z"},{"alias_kind":"pith_short_12","alias_value":"CMH7D5LMS5FC","created_at":"2026-07-05T10:16:48Z"},{"alias_kind":"pith_short_16","alias_value":"CMH7D5LMS5FCMPLB","created_at":"2026-07-05T10:16:48Z"},{"alias_kind":"pith_short_8","alias_value":"CMH7D5LM","created_at":"2026-07-05T10:16:48Z"}],"graph_snapshots":[{"event_id":"sha256:4cfba0997407dccfe5d4e4495e4f8b195639197c9dc04371c50e017970788d87","target":"graph","created_at":"2026-07-05T10:16:48Z","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/2502.13541/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider fair allocation of $m$ indivisible items to $n$ agents of equal entitlements, with submodular valuation functions. Previously, Seddighin and Seddighin [{\\em Artificial Intelligence} 2024] proved the existence of allocations that offer each agent at least a $\\frac{1}{c \\log n \\log\\log n}$ fraction of her maximin share (MMS), where $c$ is some large constant (over 1000, in their work). We modify their algorithm and improve its analysis, improving the ratio to $\\frac{1}{14 \\log n}$.\n  Some of our improvement stems from tighter analysis of concentration properties for the value of any ","authors_text":"Shengyu Huang, Uriel Feige","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.GT","submitted_at":"2025-02-19T08:49:57Z","title":"Concentration and maximin fair allocations for subadditive valuations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.13541","kind":"arxiv","version":1},"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":"sha256:33c3a2a78efcd8bd8edf0f2919ce6918bf0e5ededcf506bb4204c19fd68aefc5","target":"record","created_at":"2026-07-05T10:16:48Z","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":"e33a2ac9bf31943e63f2ec94db0beecad24f59a7966ede618251804c366f560d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.GT","submitted_at":"2025-02-19T08:49:57Z","title_canon_sha256":"6ac1822787b5ed5bf0ab4aa50ce8841531c7807a8fc905eec2eb0d08ce33df04"},"schema_version":"1.0","source":{"id":"2502.13541","kind":"arxiv","version":1}},"canonical_sha256":"130ff1f56c974a263d61aacb7bba800814166644e461a7e81e71016c86a84f78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"130ff1f56c974a263d61aacb7bba800814166644e461a7e81e71016c86a84f78","first_computed_at":"2026-07-05T10:16:48.890117Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:16:48.890117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jBv6eZYKyqpEv/+cSsAW+GItLNngSDKEBKne/7gtW/moyyTRUYe+TLnnnWJsPCTbyVbL7KC5JDyvtVj3THDZBA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:16:48.890551Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.13541","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33c3a2a78efcd8bd8edf0f2919ce6918bf0e5ededcf506bb4204c19fd68aefc5","sha256:4cfba0997407dccfe5d4e4495e4f8b195639197c9dc04371c50e017970788d87"],"state_sha256":"7bbafeda6c62f7b144419b1a7b7ef1987d591a46a0ccf7e7734261432ada43cf"}