Number–Wave Framework II: HABIT: The Intersection Law of Prime-Wave Spectra

Number--Wave Framework II: HABIT: The Intersection Law of Prime-Wave Spectra develops the intersection-counting law used in the Number--Wave Framework. The article studies how two spectra generated by prime waves interact when their intersection is counted. Starting from the set identity that an intersection is the complement of the union of complements, the article separates the union-side structure into common-wave, parallel-wave, and coprime-wave contributions. This leads to the HABIT law, which expresses the count of an intersection spectrum through the counts of the two parent spectra, a common-wave correction, and a parallel-wave correction factor. The article introduces the common-wave correction I, the parallel-wave correction factor H, and the corresponding dependency-factor form of the law. The main identity shows that the real count of an intersection spectrum can be obtained from the independent intersection count by correcting for the dependency factors of the parent spectra, the common-wave correction, and the parallel-wave correction factor.