{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:QWKQP3AUPBF2UYS57Z7IQDHDXG","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":"51a203cce3b08e8222f359cb29b66ef5a28de459e7efb50ade01f997260649d9","cross_cats_sorted":["cs.DM","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-03-16T08:54:29Z","title_canon_sha256":"2508fde1c5bdeb17d4e71592dc73891cc34529fcd08d38fc45a4bedfe8106238"},"schema_version":"1.0","source":{"id":"1903.06898","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.06898","created_at":"2026-07-05T01:17:56Z"},{"alias_kind":"arxiv_version","alias_value":"1903.06898v2","created_at":"2026-07-05T01:17:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.06898","created_at":"2026-07-05T01:17:56Z"},{"alias_kind":"pith_short_12","alias_value":"QWKQP3AUPBF2","created_at":"2026-07-05T01:17:56Z"},{"alias_kind":"pith_short_16","alias_value":"QWKQP3AUPBF2UYS5","created_at":"2026-07-05T01:17:56Z"},{"alias_kind":"pith_short_8","alias_value":"QWKQP3AU","created_at":"2026-07-05T01:17:56Z"}],"graph_snapshots":[{"event_id":"sha256:f8ceef31cbf3d33643a7cc5ca525c8f3b4b3b2b3fb028c1985b8341bfd17452f","target":"graph","created_at":"2026-07-05T01:17:56Z","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/1903.06898/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider an online vector balancing game where vectors $v_t$, chosen uniformly at random in $\\{-1,+1\\}^n$, arrive over time and a sign $x_t \\in \\{-1,+1\\}$ must be picked immediately upon the arrival of $v_t$. The goal is to minimize the $L^\\infty$ norm of the signed sum $\\sum_t x_t v_t$. We give an online strategy for picking the signs $x_t$ that has value $O(n^{1/2})$ with high probability. Up to constants, this is the best possible even when the vectors are given in advance.","authors_text":"Joel H. Spencer, Nikhil Bansal","cross_cats":["cs.DM","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-03-16T08:54:29Z","title":"On-Line Balancing of Random Inputs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.06898","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:cc9a2b94cd022df4190f31907e56a7fcb66196c60b9e89def50dfc1aa8c56632","target":"record","created_at":"2026-07-05T01:17:56Z","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":"51a203cce3b08e8222f359cb29b66ef5a28de459e7efb50ade01f997260649d9","cross_cats_sorted":["cs.DM","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-03-16T08:54:29Z","title_canon_sha256":"2508fde1c5bdeb17d4e71592dc73891cc34529fcd08d38fc45a4bedfe8106238"},"schema_version":"1.0","source":{"id":"1903.06898","kind":"arxiv","version":2}},"canonical_sha256":"859507ec14784baa625dfe7e880ce3b9bffa425ae71e71a43f9efac196462a3c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"859507ec14784baa625dfe7e880ce3b9bffa425ae71e71a43f9efac196462a3c","first_computed_at":"2026-07-05T01:17:56.377393Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:17:56.377393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pQAd8sZo+HQKunu+i3kXFo1zM8eVC/AKq9i3/23WRaUlttULCG98VE+Dc2nGrSA3iOOqv68gbwNlzKV2IrNdBg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:17:56.377822Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.06898","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc9a2b94cd022df4190f31907e56a7fcb66196c60b9e89def50dfc1aa8c56632","sha256:f8ceef31cbf3d33643a7cc5ca525c8f3b4b3b2b3fb028c1985b8341bfd17452f"],"state_sha256":"129cdf1c2f8dfcb975e83b2e7a9615377537c5b5a3f0ec11d9939ef1d58be0fc"}