{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UCESTBHPS5GLIVWVNWDXASZODT","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":"eac0ddd9fb9e72c93bb581faf801f722b8dc917ed3b64bc1c8c442c687e24087","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-17T17:27:33Z","title_canon_sha256":"0a009ca000f2beed9e8d325161259790fa5b979849f0b35d0b89e754b4bb2f67"},"schema_version":"1.0","source":{"id":"1610.05221","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.05221","created_at":"2026-05-18T00:21:35Z"},{"alias_kind":"arxiv_version","alias_value":"1610.05221v3","created_at":"2026-05-18T00:21:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.05221","created_at":"2026-05-18T00:21:35Z"},{"alias_kind":"pith_short_12","alias_value":"UCESTBHPS5GL","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UCESTBHPS5GLIVWV","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UCESTBHP","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:d475c6c503017b062df21f73711f41a4b93047b49ad904b116d4f38d6b137b34","target":"graph","created_at":"2026-05-18T00:21:35Z","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 a higher-dimensional 'balls-into-bins' problem. An infinite sequence of i.i.d. random vectors is revealed to us one vector at a time, and we are required to partition these vectors into a fixed number of bins in such a way as to keep the sums of the vectors in the different bins close together; how close can we keep these sums almost surely? This question, our primary focus in this paper, is closely related to the classical problem of partitioning a sequence of vectors into balanced subsequences, in addition to having applications to some problems in computer science.","authors_text":"Alex Scott, Bhargav Narayanan, Juhan Aru, Ramarathnam Venkatesan","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-17T17:27:33Z","title":"Balancing sums of random vectors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05221","kind":"arxiv","version":3},"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":"sha256:7611c81177d48924bf7545f5828b00ca0bdda626f534f0af68e7c240bc61e171","target":"record","created_at":"2026-05-18T00:21:35Z","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":"eac0ddd9fb9e72c93bb581faf801f722b8dc917ed3b64bc1c8c442c687e24087","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-17T17:27:33Z","title_canon_sha256":"0a009ca000f2beed9e8d325161259790fa5b979849f0b35d0b89e754b4bb2f67"},"schema_version":"1.0","source":{"id":"1610.05221","kind":"arxiv","version":3}},"canonical_sha256":"a0892984ef974cb456d56d87704b2e1cee4a89c9ef86695da60fa14891c1cf1b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a0892984ef974cb456d56d87704b2e1cee4a89c9ef86695da60fa14891c1cf1b","first_computed_at":"2026-05-18T00:21:35.511824Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:35.511824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FqaTEgVqmWP9h0vij1FvHLzv2qnp1zy5TlZfqIsjjnrQhJrOAs7wm+JDeTwyRe2UiK95k328EbTMDhobg3iwAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:35.512531Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.05221","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7611c81177d48924bf7545f5828b00ca0bdda626f534f0af68e7c240bc61e171","sha256:d475c6c503017b062df21f73711f41a4b93047b49ad904b116d4f38d6b137b34"],"state_sha256":"bd7d0fea0687ddb8f53c85491417101ec318d721f5e5af3a0b39cdbbdb854c87"}