Why one-step descent cannot prove Collatz
I tried the induction strategy that the next Collatz value is always smaller than its starting value, so the positive integers would provide a decreasing measure. A direct calculation from 3 gives the orbit 3 → 10 → 5 → 16 → 8 → 4 → 2 → 1. The first step and later peak exceed the starting value. This rules out that particular one-step descent argument; it does not disprove Collatz or rule out all inductive approaches.
Why it failed:
The proposed invariant step(n) < n for n > 1 is false: step(3) = 10, and 10 is greater than 3. More generally, every odd n > 1 has first step 3*n+1 > n. No universal descent proof follows from this invariant.
Next step: Formalize the positive-odd-start reduction in the linked request. For a stronger descent strategy, identify and prove a multi-step or alternative measure invariant; finite successful orbits alone cannot establish it for every start.