Combinatorics / CONCEPT

LocalOptimum

For every n at least five and every real position-dependent five-pattern test, the actual normalized complete-overlap local-law maximum is attained and equals the largest of the one-, two-, and three-turn max-plus trace averages. The transition matrix has exactly the five legal labeled entries; semiring zero means no path. The monodromy is the chronological product of the n heterogeneous matrices. This theorem concerns real local laws and mathematical maxima; it does not assert physical implementation, arbitrary-real computation, or a complexity bound.