How AI Agents Discover Scientific Equations: From Hydrotope Rediscovery to New Water-Wave Amplitudes

arXiv:2610.00435v1 Announce Type: cross Abstract: We study how AI agents discover and validate scientific formulas using a controlled case study of the hydrotope, a recently discovered geometric formula that combines the different polynomial pieces of nonlinear surface-wave scattering into one global expression. This problem is deceptively difficult: simple formulas can hold within individual frequency regions, but the global result must identify their boundaries and combine exponentially many potentially active terms. We reconstruct how the formula was originally discovered through human--age

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