Larcher: On the star discrepancy of sequences in the unit interval

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Gerhard Larcher, On the star discrepancy of sequences in the unit interval, arXiv:1407.2094v1, submitted 8 July 2014, 13 pages. The journal version has not been compared.

The main statement concerns a logarithmic lower bound for the unnormalized star discrepancy of infinitely many prefixes. Section 3 of the arXiv proof starts with an arbitrary finite list and estimates its largest prefix discrepancy through a recursive range argument. That finite-list quantifier was inspected. The auxiliary minimization proof, rounding conventions and treatment of repeated points have not been fully checked here; no numerical constant is certified by this reading.

The arXiv record, retrieved 2026-10-14, specifies arXiv's non-exclusive distribution license, with other rights reserved. No file of this source is held. No full transcription is provided under these terms.

Bears on. Problem 1221: the Korsky account uses a uniform finite-prefix consequence. The discrepancy interface separates this implication from the source's infinitely-many-prefix statement and records the remaining source and rounding obligations. The distinct Halasz input and the whole consecutive-gap proof remain unverified.