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This research aims to establish a mathematical framework for understanding the five properties of matter and verify material space compression.

July 27, 2026Open Access

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

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Randomized trial verifies material space compression under mathematical constraints in materials science, indicating significant degeneration.

This research aims to establish a mathematical framework for understanding the five properties of matter and verify material space compression.
Constructed a V10 database from 1,407,278 DFT-computed materials for analysis.
Applied field domain number equation constraints to evaluate material properties and their classifications.
Used hierarchical mathematical relationships to determine intra-group consistency and degeneracy.
Identified 1.4M materials corresponding to 4,154 field-domain states, resulting in 338x compression.
Achieved 94-100% intra-group electronic classification consistency across materials.
Compressed naive combinatorial space from 18.2 billion to 4,154 under FDNE constraints, indicating a 4.38-million-fold reduction.

Chao Qin (2026) studied this question.

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Randomized trial verifies material space compression under mathematical constraints in materials science, indicating significant degeneration.