Deep Scientific Reasoning under Physical Constraints: Structure-Aware Spectrum Prediction for Electronic Density of States

Structured scientific spectra encode rich physical information while satisfying hard constraints such as conservation and spectral geometry. We study a canonical example, the electronic density of states (eDOS), whose accurate prediction is central to materials discovery. Prior methods often (i) decouple band gaps from eDOS, (ii) violate total-state conservation, or (iii) collapse crystals into global embeddings that obscure atom-projected contributions. We introduce \textbf{DeepSciReasoner}, a design paradigm for deep scientific reasoning under physical constraints. Instantiated for eDOS prediction, DeepSciReasoner combines structure-aware spectrum decoding with constraint-preserving physical reasoning, in this case, mass-conserving iterative refinement. It substantially improves eDOS accuracy while maintaining physical validity, enabling reliable high-throughput screening. Beyond eDOS, DeepSciReasoner offers a reusable blueprint for predicting structured scientific spectra under hard physical constraints.