Are hidden constants in theoretical computer science really that large?

We use large language models to recover the hidden constants in theoretical computer science proofs, asking how large the constants are, why some become large, and how tighter analysis can improve the guarantees. We introduce ConstAble, which follows proof dependencies to derive explicit bounds and track their conditions. Our benchmark, ConstEval, evaluates bound recovery, proof validity, and error detection on 93 prepared instances and 93 paired variants with injected proof defects. Among 91 targets with numerical coefficients, 69 have representative coefficients below 1,000 under their stated resource models and parameter settings. The recovered proofs show how costs multiply across nested calls and why small leading coefficients can hide large costs at finite input sizes. The resulting bounds support comparisons at concrete input sizes, and our subsequent analysis tightens an earlier recovered three-distinctness bound without changing the algorithm. ConstAble improves bound completion over one-shot inference. With comparable median token use, it completes 65.6%–92.5% of targets, while baselines using additional generation or revision complete at most 9.68%.