Cross-Domain Mathematical Structures in Physics: Automated Discovery of Equation Equivalences Across Subfields

Automated analysis of 1,143 arXiv papers across 9 physics subfield pairs identified 4 novel cross-domain equation equivalences and validated 6 known connections from 90,516 extracted equations. Novel findings: (1) Noncommutative quantum oscillator evolution is structurally analogous to weak turbulence mode coupling — zero prior papers. (2) Porous media homogenization cell problems share mathematical structure with harmonic maps from differential geometry — zero prior papers. (3) The Batalin-Vilkovisky gauge theory action maps to fluid helicity conservation — zero prior papers connecting BV formalism to helicity specifically. (4) SYK scrambling time integrals share quadratic spectral structure with non-Hermitian fluctuation response — specific instance is new, general scrambling-FDT principle is known. Validated connections include three independent detections of Martin-Siggia-Rose formalism, the membrane paradigm, an exact JT gravity/Klein-Gordon equivalence (score 0.95), and dilaton dimensional reduction. Quality filtering reduced 658 raw structural matches to 10 genuine findings through six physics-specific gates and multi-level equivalence evaluation. All findings require expert evaluation.