The Type-C Integer-Gap Lemma for Periodic Collatz Blocks

Abstract

This record fixes the Type-C local rigidity component used in the author’s ongoing research toward a proof of the Collatz conjecture.The paper establishes an exact block decomposition, exact block transport, the Type U / Type C / Type D classification, and proves the Type-C Integer-Gap Lemma. As a consequence, every Type-C block is shown to be strictly descending except for the trivial fixed point. This work is intended as a reusable component for subsequent global analysis and does not claim a complete proof of the Collatz conjecture.