The Sun (2,4,6,8) Binomial Representation Program

Project Overview & Series Context: This registration marks a major structural and computational update within the ongoing "Sun (2,4,6,8) Binomial Representation Program," a broader research series investigating the additive representability of integers via mixed-degree binomial coefficient sequences: n = C(w,2) + C(x,4) + C(y,6) + C(z,8) for w, x, y, z in Z_{>=2}. Abstract & Key Advances in Framework V13.1: This registration presents Framework V13.1, establishing a computationally audited structural foundation — the Triangular Witness–Gap Cascade Framework — exhaustively audited at the 10^7 scale: 1. Structural Decomposition: Establishes the exact witness index decomposition w*(n) = K(n) + \Delta(n) + 2, separating transition counting K(n) from gap deficiency \Delta(n). 2. Exhaustive Verification of Lemma C: Fully audits and proves the local residence bound B_j