Mathematical Framework and Degeneracy Verification of the Five Properties of Matter: Material Space Compression Under the Field Domain Number Equation Constraint

This paper presents the five-property framework of matter (FC field coherence, FF field frequency, R prime field capacity, PC polymorphic coupling, B4F boundary four-forces), established on the mathematical constraints of the Field Domain Number Equation (FDNE). The framework comprises four hierarchical layers of mathematical relationships: FDNE substrate constraints, PC ratio-chain coupling, boundary four-force parameterization, and bridge mapping to process quantities. A V10 database was constructed from 1,407,278 DFT-computed materials for full-scale verification, revealing that material space is highly degenerate under the five-property constraints: 1.4M materials correspond to only 4,154 field-domain states (integer precision, 338x compression), with an average of 4.3 materials sharing the same 7-dimensional fingerprint per group. Intra-group electronic classification consistency reaches 94-100%, while the traditional metal/semiconductor/insulator classification spans multiple categories in 65.7% of R prime states. The naive combinatorial space (18.2 billion) is compressed to 4,154 under FDNE constraints - a 4.38-million-fold compression. A flashlight model is proposed to explain the material naming inflation mechanism. Both Chinese and English versions are included.