{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:RZHOZM2SUKTOTTQJDKO7FLGP7T","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":"51c3c49efcaa5d19399360e548a1feca8051c5c570109918c7b1d2a8f0478a9a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2023-08-02T20:01:11Z","title_canon_sha256":"d623c8169a94f81c4d959ca83a662158e8d6d43b729f89ef2f1a77b077297960"},"schema_version":"1.0","source":{"id":"2308.01406","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.01406","created_at":"2026-07-05T06:37:17Z"},{"alias_kind":"arxiv_version","alias_value":"2308.01406v1","created_at":"2026-07-05T06:37:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.01406","created_at":"2026-07-05T06:37:17Z"},{"alias_kind":"pith_short_12","alias_value":"RZHOZM2SUKTO","created_at":"2026-07-05T06:37:17Z"},{"alias_kind":"pith_short_16","alias_value":"RZHOZM2SUKTOTTQJ","created_at":"2026-07-05T06:37:17Z"},{"alias_kind":"pith_short_8","alias_value":"RZHOZM2S","created_at":"2026-07-05T06:37:17Z"}],"graph_snapshots":[{"event_id":"sha256:38b9fe7a4a506bd368f6731bc2485a197a3ffe044abfc74487cae2f7796267b7","target":"graph","created_at":"2026-07-05T06:37:17Z","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/2308.01406/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that there exists an online algorithm that for any sequence of vectors $v_1,\\ldots,v_T \\in \\mathbb{R}^n$ with $\\|v_i\\|_2 \\leq 1$, arriving one at a time, decides random signs $x_1,\\ldots,x_T \\in \\{ -1,1\\}$ so that for every $t \\le T$, the prefix sum $\\sum_{i=1}^t x_iv_i$ is $10$-subgaussian. This improves over the work of Alweiss, Liu and Sawhney who kept prefix sums $O(\\sqrt{\\log (nT)})$-subgaussian, and gives a $O(\\sqrt{\\log T})$ bound on the discrepancy $\\max_{t \\in T} \\|\\sum_{i=1}^t x_i v_i\\|_\\infty$. Our proof combines a generalization of Banaszczyk's prefix balancing result to t","authors_text":"Janardhan Kulkarni, Thomas Rothvoss, Victor Reis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2023-08-02T20:01:11Z","title":"Optimal Online Discrepancy Minimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.01406","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:df7f59d17039e38bf491f061b37aaa4671446864188c64765a37dcfaae5d939a","target":"record","created_at":"2026-07-05T06:37:17Z","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":"51c3c49efcaa5d19399360e548a1feca8051c5c570109918c7b1d2a8f0478a9a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2023-08-02T20:01:11Z","title_canon_sha256":"d623c8169a94f81c4d959ca83a662158e8d6d43b729f89ef2f1a77b077297960"},"schema_version":"1.0","source":{"id":"2308.01406","kind":"arxiv","version":1}},"canonical_sha256":"8e4eecb352a2a6e9ce091a9df2accffcd279222a1a2dcd1a7ac65fb0032337a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e4eecb352a2a6e9ce091a9df2accffcd279222a1a2dcd1a7ac65fb0032337a1","first_computed_at":"2026-07-05T06:37:17.954796Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:37:17.954796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mv5rdgZKxnLITBuuM2Mfrd5H1P+/7uDGu6imkPVGBf4vgSG6Qso5vL4XyeVvq1t3s0uRSdlCJ987pXDIciofCg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:37:17.955269Z","signed_message":"canonical_sha256_bytes"},"source_id":"2308.01406","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df7f59d17039e38bf491f061b37aaa4671446864188c64765a37dcfaae5d939a","sha256:38b9fe7a4a506bd368f6731bc2485a197a3ffe044abfc74487cae2f7796267b7"],"state_sha256":"82afa962a6688d5af74e716f001a3d6952f99fee6e69a94f13e4243a702e7b5d"}