Finite Propagation and Signed-Path Interference in the Gilbreath Difference Triangle

I studied the iterated absolute-difference triangle generated by the primes, with emphasis on boundary propagation, parity, and the arithmetic role of consecutive prime gaps. The investigation includes finite observations of small-value returns, including occurrences involving the values 2 and 3, but does not treat these observations as an infinite theorem. We prove a finite dependency bound and an amplitude inequality, describe the adjacent-XOR parity evolution, and derive an exact signed-path expansion for the normalized interior triangle. The path coefficients satisfy a zero-sum identity. These results reduce the proposed interference approach to a sharply parameterized open problem concerning the prime-gap-weighted path sum; they do not prove the classical Gilbreath conjecture.