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The next frontier for artificial general intelligence is tackling unresolved scientific problems, calling for benchmarks that assess progress beyond established knowledge. We introduce OpenProblemBench, a benchmark of 82 unresolved problems drawn from the mathematics and theoretical physics literature. Each problem sup...
Differentiable programming connects scientific computation with gradient-based inference, learning and design. Extending these capabilities across a heterogeneous software ecosystem requires specialized effort to implement derivatives, integrate interfaces and evaluate quality. AI coding agents can accelerate this tran...
The crossover from long-range (LR) to short-range (SR) criticality in percolation has remained unsettled because previous renormalization-group (RG) analysis within the $\epsilon'=3\sigma-d$ expansion fixes the anomalous dimension at $\eta=2-\sigma$, whereas SR percolation has $\eta_{\rm SR}<0$ near $d=6$. Sak's matchi...
We study the one-dimensional long-range self-avoiding walk in the grand-canonical ensemble where the statistical weight of a jump of length $r$ decays algebraically as $r^{-(d+\sigma)}$. Using large-scale Monte Carlo simulations with an efficient irreversible update scheme, we obtain high-precision estimates of the cri...
We study the two-dimensional XY model with the nonanalytic pair potential $2[(1-\cos\delta)/2]^{p}$, whose small-angle law $\propto|\delta|^{2p}$ carries a cusp for $p<1$ and a flat bottom for $p>1$, invalidating the harmonic spin-wave expansion. Two questions arise: the nature of the low-temperature ($T$) phase and of...
State-of-the-art models are far more proficient in scientific coding than SciCode has suggested---the bottleneck was not model capability, but the quality of the evaluation instrument.
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