Creation Moment 7/20/2025 - The "Groaning": Even down to the level of Chrystals

For we know that the whole creation groaneth and travaileth in pain together until now. Romans 8:22

"Researchers at the University of Osaka have developed new mathematical models that offer new insights into the behavior of crystal defects.

Crystals are widely admired 

for their striking appearance and symmetry. 

However, beneath their polished surfaces lies a complex internal structure that poses significant challenges for scientists attempting to describe them with mathematical precision.
--In theory, a flawless crystal would have atoms arranged in a

perfectly repeating pattern. 

--But in reality, nearly all crystals exhibit irregularities. 

These structural flaws might include a missing atom or an additional bond, and while they may seem minor, they can have serious mechanical effects.
“Defects come in many forms,” explains lead author of the study Shunsuke Kobayashi. “For example, there are so-called dislocations associated with the breaking of translational symmetry and disclinations associated with the breaking of rotational symmetry. Capturing all of these kinds of defects in a single mathematical theory is not straightforward.”
Using the formalism of Riemann–Cartan manifolds, the research team was able to elegantly encapsulate the topological properties of defects and rigorously prove the relationship between dislocations and disclinations; previously, only empirical observations existed, and their rigorous mathematical forms were a mystery. " SciTechDaily