Number–Wave Framework II: HABIT: The Structural Law of Spectrum Intersections

This article introduces HABIT as the structural law governing intersections of spectra in the Number--Wave Framework. It studies how two spectrum counts combine when their waves have common, parallel, or independent phase relations. The central idea is that an intersection is not controlled only by the independent product of the parent sizes. It also contains structural corrections from identical waves and parallel waves. These corrections isolate the internal dependency of the intersection. For an intersection $$T=A\cap B,$$ HABIT writes the finite structure in the form $$T(n)=\frac{H(n)A(n)B(n)}{I(n)}.$$ Here \(I(n)\) represents the identical-wave correction, while \(H(n)\) represents the remaining parallel-wave correction. The associated vibration term measures the residual dependency after the structural corrections have been separated. This article provides the structural foundation for later applications of the Number--Wave Framework to prime-pair spectra, especially twin-prime and Goldbach counting functions.