Independent developer Charlie Reams, assisted by Claude Code, has completed a formal proof of the ternary Goldbach conjecture, producing a cumulative 194,000 lines of Lean 4 code with zero "sorry" placeholders, all of which were strictly machine-verified. During the process, the AI autonomously identified 11 issues in Harald Helfgott's original 2013 proof—including incorrectly written constants, invalid inequalities, discrepancies in cited data, and confusion of main arc scales—and completed the necessary repairs. Subsequently, the two reduced the external additional assumptions on which the proof depended from five to just two existing publicly verified numerical results, significantly advancing the rigor and completeness of the proof. This development has also prompted the mathematics community to shift its criteria for deeming a proof "complete" toward machine-verifiable formalization.