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Notes on Kozma and Nitzan's proof of θ(pc)=0
Abstract
We present a human intelligible proof of the conjectures of Kozma and Nitzan, that they used to show θ(pc)=0. The proof was recently found by AI, but was very poorly written. Our version is much shorter as it completely skips the horizontal term and its long estimate.
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BibTeX
@misc{blancrenaudie2026notes,
title = {{Notes on Kozma and Nitzan's proof of $θ(p_c)=0$}},
author = {Arthur Blanc-Renaudie},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10502},
eprint = {2610.10502},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05829500v1},
}
RIS
TY - UNPB
TI - Notes on Kozma and Nitzan's proof of θ(p_c)=0
AU - Arthur Blanc-Renaudie
PY - 2026
DA - 2026/10/07
PB - HAL
DO - 10.48550/arxiv.2610.10502
UR - https://hal.science/hal-05829500v1
AB - We present a human intelligible proof of the conjectures of Kozma and Nitzan, that they used to show θ(p_c)=0. The proof was recently found by AI, but was very poorly written. Our version is much shorter as it completely skips the horizontal term and its long estimate.
ER -