Researchers tackled the problem of finding an optimal tokenizer—a vocabulary that minimizes token count for a fixed size. Normally, byte-pair encoding (BPE) does this greedily, but it can fall within 1% of optimal only. Tempus et al. recast tokenization as an integer linear program: one binary “color” variable per possible substring (whether it’s in the vocab), edge variables for each occurrence, plus flow constraints to ensure a valid parse. They relax the ILP to a continuous LP, solve it, then round the color variables to get a feasible but suboptimal tokenizer, using the LP’s objective as a lower bound and the rounded solution as an upper bound. Building on TSP solvers’ cutting‐plane methods, the author asked OpenAI’s Codex to generate valid cuts for the tokenization LP. A cut is a linear constraint that all integral solutions satisfy but the current fractional solution violates. Instead of manually crafting cuts, they brute‐forced small projections: pick pairs or triplets of words where color variables were fractional, set up auxiliary LPs to maximize violation, then add those constraints back into the main LP. This raised the lower bound and improved the rounded tokenizer’s performance. Pretokenization (splitting text into words and merging repeats) remains a limiting assumption. It slashes variable count—crucial for tractability—but means the solution is only optimal under that pretokenizer. Removing it could yield true global optimality but would balloon the LP’s size. Future work might explore cutting planes that work on raw byte sequences or find more efficient heuristics to guide Codex’s search for violated constraints.