Seonbin Kim | Search arXiv

arXiv2026

OPRD-Imp: a dataset of experimentally observed impurities and side products in multi-step pharmaceutical syntheses

Predicting reaction impurities is a critical yet persistently data-limited challenge in pharmaceutical process chemistry. While machine learning models for reaction outcome prediction have advanced rapidly, benchmarking their ability to predict impurities remains impractical due to the absence of curated, publicly accessible datasets. We present OPRD-Imp, a dataset of 229 organic reactions drawn from 62 publications in Organic Process Research & Development, each annotated with experimentally observed impurities and their mechanistic origins. A total of 784 impurity entries is provided, classified into four origin categories. Reactions are represented as reaction SMILES and impurities as individual SMILES strings, with multi-step synthetic route connectivity preserved. All data were manually extracted from the source publications by trained chemists following a standardized extraction protocol, with expert chemical validation and manual structure drawing. OPRD-Imp is intended to serve as a benchmark resource for evaluating models that predict reaction impurities, providing experimentally reported impurity annotations and mechanistic origin labels that are not systematically represented in conventional reaction datasets.

physics.chem-ph↗

arXiv2026

Polychromatic blocks and explicit lower bounds for multicolour van der Waerden numbers

Let $W(r,k)$ be the least $N$ such that every $r$-colouring of $\{1,\dots,N\}$ contains a monochromatic $k$-term arithmetic progression. Many of the best lower bounds for $W(r,k)$ with $r\ge3$ come from blow-up recurrences of Blankenship, Cummings and Taranchuk and of Xu, in which a known colouring is lengthened by a periodic block. Call an $h$-colouring of $Z_q$ $k$-polychromatic if every $k$-term progression with nonzero common difference meets each of the $h$ colours. The argument behind these recurrences shows that such a colouring gives $W(r,k)>q(W(r-\lceil r/h\rceil,k)-1)$ for all $r\ge h$. We show that cubic, quartic, quintic and sextic residue colourings give $k$-polychromatic blocks with $q$ much larger than $k$ (e.g. $q=1,376,317$ for $h=3$ and $k=28$), and use them to get explicit lower bounds. For three colours and $9\le k\le28$ we improve on every published bound we know of, among them $W(3,9)>4,002,705$ and $W(3,28)>159,594,201,561,100,726$. For $3\le r\le6$ and $9\le k\le28$, $77$ of the $80$ cases improve on what the published bounds give under these recurrences and the other three tie. For $r=5$ and $12\le k\le15$ the best values come from palettes that are cyclic intervals of colours indexed by quintic residues. We checked every block by exhaustive enumeration and every base colouring by computer. We also prove that the block modulus is at most $(W(2,k)-1)/(k-1)$, so the method does not improve the asymptotics. For large $k$ the largest cubic block modulus lies between $k^{4-\varepsilon}$ and $k^2 4^k$.

math.CO↗