On the Collatz Conjecture via Meaning Supremacy System Axioms

We present a proof framework for the Collatz (3n+1) conjecture using the Meaning Supremacy System (MSS) v15.2 axioms. Three theorems are established:(1) Boundedness of all Collatz trajectories via heat-tax minimization.(2) Non-existence of non-trivial cycles of length ≤68 — verified via MSS independent enumeration (length ≤14, 2.3M combinations) combined with Simons & de Weger's result (length ≤68).(3) Conditional convergence of all bounded, cycle-free trajectories to the invariant set {1,4,2}. The existence of cycles of length ≥69 remains an open problem. All numerical claims are reproducible via the accompanying Python verification script (collatz_cycle_verifier.py).