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Breakthrough Tracker record

Independent preprints claim a dimension-free Komlós discrepancy bound

Guo, Fang and Lu claim a universal 3√(2π) discrepancy bound for unit-norm columns; Karingula and Lovett give a separate elementary proof with constant 36; and an algorithmic follow-up claims polynomial-time constant discrepancy.

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Stable ID
math-komlos-log-quarter-bound-2026
Revision
math-komlos-log-quarter-bound-2026.v2
Field
Mathematics · Discrepancy theory, combinatorics and formal verification
Evidence
Tier 1 · Peer reviewed: No
Record state
Provisional · Provisional claimed proof with separate reproof
Last checked

AI role

The first constant-bound proof is attributed to the Odin Automatic AI Research Agent. Karingula and Lovett disclose ChatGPT 6 Astra assistance in refining the proof and writing. The algorithmic follow-up is by the original team.

Record details

Problem or result
The dimension-free Komlós discrepancy conjecture and an algorithmic construction
Authors
Shengtao Guo, Ethan X. Fang and Junwei Lu; Sankeerth Rao Karingula and Shachar Lovett
Institutions
Harvard T.H. Chan School of Public Health; Agentin AI; University of California, San Diego
Result date
Preprints submitted September 10–20 and revised through September 22, 2026

Why it matters

A universal constant is the conjectured threshold. The separate elementary proof provides meaningful technical corroboration, and the spectral follow-up claims a polynomial-time construction.

Limits

All three papers are unrefereed preprints. The reproof simplifies the original rather than peer-reviewing it, and the algorithm’s stated polynomial is very large rather than a practical benchmark. Ercan’s earlier log-quarter result remains valid historical progress.

Sources

  1. Primary: Ercan, a log-quarter bound for the Komlós problem
  2. Primary: Guo, Fang and Lu, a constant Komlós bound
  3. Independent preprint: Karingula and Lovett, an elementary Komlós proof
  4. Primary: Guo, Fang and Lu, algorithmic Komlós follow-up

Correction and revision history

  1. 2026-09-10 — Added after primary-source, scope, status, AI-role and limitation review.
  2. 2026-10-02 — Reclassified from best-bound progress to a provisional full-proof claim after a dimension-free bound, separate elementary reproof and algorithmic follow-up appeared.

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