Building upon Helfgott's 2014 proof of the three prime theorem, I reconstructed the explicit constant system of the minor-arc (marginal arc) portion, rearranging the explicit constants scattered across multiple inequalities into a structure of a one-dimensional supremum problem. Through this rewriting, all minor-arc contributions are explicitly written as explicit functions, their maximum values determining the final constants. By utilizing tail monotonicity and interval arithmetic, the steps that previously relied on manual estimation can be transformed into verifiable and reproducible numerical proofs. The core objective of this work is to organize the originally complex and difficult-to-fully-verify constant estimation into a complete system that can be machine-verified, revealing the main bottleneck limiting threshold descent under fixed parameters. Read the full article: hackmd.io@7C7W0vM5Ql2UqkP2SwnA8A/Proof-of-Ternary-Goldbach… A Rigorous Computational Reconstruction of the Minor-Arc Bound in Helfgott’s Proof of Ternary Goldbach — Mirror Tang