{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JCZC3WXCWJAG7A63XCIHHEWH6U","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":"c72a569238980dca27d55d38ea3df7d3e22a486b7754eebbbba4c912f0fa5830","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-09-22T16:35:59Z","title_canon_sha256":"b3afad9cb5e7237b9ce3bb0596c48a334fd84f142900a0687d2755ba1207f18c"},"schema_version":"1.0","source":{"id":"1609.07056","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.07056","created_at":"2026-05-18T01:04:02Z"},{"alias_kind":"arxiv_version","alias_value":"1609.07056v2","created_at":"2026-05-18T01:04:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07056","created_at":"2026-05-18T01:04:02Z"},{"alias_kind":"pith_short_12","alias_value":"JCZC3WXCWJAG","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JCZC3WXCWJAG7A63","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JCZC3WXC","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:b5f1fcad26e3934f3981f9ae706c94283f618453bede48f4afe74ccda7a0422d","target":"graph","created_at":"2026-05-18T01:04:02Z","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":"We study the problem of allocating $m$ items to $n$ agents subject to maximizing the Nash social welfare (NSW) objective. We write a novel convex programming relaxation for this problem, and we show that a simple randomized rounding algorithm gives a $1/e$ approximation factor of the objective.\n  Our main technical contribution is an extension of Gurvits's lower bound on the coefficient of the square-free monomial of a degree $m$-homogeneous stable polynomial on $m$ variables to all homogeneous polynomials. We use this extension to analyze the expected welfare of the allocation returned by our","authors_text":"Amin Saberi, Mohit Singh, Nima Anari, Shayan Oveis Gharan","cross_cats":["cs.DM","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-09-22T16:35:59Z","title":"Nash Social Welfare, Matrix Permanent, and Stable Polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07056","kind":"arxiv","version":2},"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":"sha256:142224e354533a2d3f658f99aa428b8eeffae49177210ad62d25830a76172520","target":"record","created_at":"2026-05-18T01:04:02Z","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":"c72a569238980dca27d55d38ea3df7d3e22a486b7754eebbbba4c912f0fa5830","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-09-22T16:35:59Z","title_canon_sha256":"b3afad9cb5e7237b9ce3bb0596c48a334fd84f142900a0687d2755ba1207f18c"},"schema_version":"1.0","source":{"id":"1609.07056","kind":"arxiv","version":2}},"canonical_sha256":"48b22ddae2b2406f83dbb8907392c7f52c8eb98c9c2ad74f9c4585a02a7ec52c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"48b22ddae2b2406f83dbb8907392c7f52c8eb98c9c2ad74f9c4585a02a7ec52c","first_computed_at":"2026-05-18T01:04:02.165898Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:02.165898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QXqJMfY6Y+RvtNWc1H/axQbMKdfXweOKvOKJk/Ry9ZTdTXR5Jy8TkvbpHzQOAOmY4lnoKN2svpyIwq+4XS9BDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:02.167094Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.07056","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:142224e354533a2d3f658f99aa428b8eeffae49177210ad62d25830a76172520","sha256:b5f1fcad26e3934f3981f9ae706c94283f618453bede48f4afe74ccda7a0422d"],"state_sha256":"eb7f6ba69438285b3bbb44e8515f5cfe44565dadd2a70453c87205d1144c8443"}