Mohs scale of mineral hardness finding the hardest material that the given material can scratch, or the softest material that can scratch the given material. For example, if some material is scratched by apatite but not by fluorite, its hardness on the Mohs scale would fall between 4 and 5. "Scratching" a material for the purposes of the Mohs scale means creating non-elastic dislocations visible to the naked eye. Frequently, materials that are lower on the Mohs scale can create microscopic, non-elastic dislocations on materials that have a higher Mohs number. While these microscopic dislocations are permanent and sometimes detrimental to the harder material's structural
Computational hardness assumption which is a computational hardness assumption about random instances of 3-SAT (sampled to maintain a specific ratio of clauses to variables). Average-case computational hardness assumptions are useful for proving average-case hardness in applications like statistics, where there is a natural distribution over inputs. Additionally, the planted clique hardness assumption has also been used to distinguish between polynomial and quasi-polynomial worst-case time complexity of other problems, similarly to the Exponential Time Hypothesis. The Unique Label Cover problem is a constraint satisfaction problem, where each constraint formula_60 involves two variables formula_77, and for each value of formula_26 there is a "unique" value