Collatz Conjecture — Frequency Reduction, Binary Potential, and a Conditional Appendix

This paper performs a precise problem reduction of the Collatz conjecture. The main result (Chapters 1–9) is: if the limit inferior of the frequency of d≥3 (plunge) states satisfies P3 > 0.2925, then the orbit necessarily converges. This is a sufficient condition. The paper also identifies three common logical traps, proves via the LTE lemma that a single plunge cannot linearly compensate for a surge, and includes a conditional appendix on binary potential and sparsity hypothesis as a possible future attack direction.