“The paper provides an example where the deterministic subcategory is the category of Stone spaces and the kernels correspond to a restricted class of Kleisli arrows for the Radon monad.”

“The paper introduces 'incremental certificate learning' to maximize work in sound linear relaxation and invoke exact piecewise-linear reasoning only when relaxations become inconclusive.”

“The distance-aware approach achieves higher accuracy on coarse grids (max. 60%p accuracy gain) with only a moderate verification overhead (approximately 1.4x), making zone encoding the key lever for efficient zero-knowledge spatial checks.”

“The paper provides "necessary and sufficient conditions for $\mathcal{A}$ to admit the structure of a model category whose cofibrant objects are $\mathcal{C}$ and whose fibrant objects are $\mathcal{F}$."”

“Think of it like this: Physics found its language in calculus. Circuit design found its language in Boolean logic. Pedro argues that AI has been missing its language - until now.”

“The article's primary focus is on the relationship between boolean circuits and neural networks.”