Evaluate the implications of lower-bound proofs in computational complexity theory, using the comparison-based sorting lower bound of O(n log n) as an example.

Lower-bound proofs establish the minimum time complexity required for certain problem classes, guiding algorithm development. For comparison-based sorting, a proof shows that O(n log n) is the lower bound due to the necessity of comparing elements to determine order. This proof informs algorithm designers that no comparison-based sort can be faster than O(n log n), leading to the exploration of non-comparison sorts (e.g., radix sort) for potentially better performance in specific cases.