Collatz Conjecture proof

A proof of the Collatz Conjecture...

Abstract:
We present a complete structural proof of the Collatz Conjecture across the full
domain of natural numbers N. By partitioning N into evens, odd non-S elements,
and the base set S (n ≡1 (mod 4)), we establish deterministic mapping chains
that reduce all trajectories into S. Within S, we construct a multi-dimensional pe-
riodic lattice structure, termed the untwisted fishnet, governed by esid coordinates
and j-indexed linear polynomial transformations aj + b. Through nested modular
sparsifications of sibsets, we establish an inductive termination sweep and prove
a systemic deadlock contradiction: the existence of a single non-terminating tra-
jectory forces a global failure of termination across all of S, directly contradicting
known finite sinks. Furthermore, we prove that boundary transitions between S
and non-S regions possess a fundamental prime power asymmetry 3a != 2b, ruling
out boundary cycles. Together, these results restrict all trajectories in N to the
unique fixed point n = 1.

https://zenodo.org/records/21960729 contains Lean code (version 4.33.0) to verify the proof.