First Functional Divergence Solved Case: Collatz Conjecture
Status: Logical Beauty Possession
The transition between the upward force of 3 and the downward capture of 2 is governed by the Logical Engineering Transitions (LET's):
These formulas define the internal quotients (Qi, Qj) that regulate the functional flow of the sequence across the 1D Array, neutralizing the "Infinity Marker" through structural regulation.
The definitive proof of Collatz Unicity is revealed through the Domain Analysis of the structural intersections between C.E.-1 and C.E.-2:
The Rational Lock:
This demonstration proves that all structural intersections between these formulas exist ONLY for Rationals. There is NOT ONE single intersection found within the Integers Domain (Z).
Conclusion: Because any secondary loop or infinite escape would require an intersection within the Integers, the Table2To3 geometry strictly forbids them. This Integer-Exclusion forces all whole numbers into the single, unique path of the Trivial Cycle (4-2-1).
"We do not count to infinity; we define the Rational boundaries that protect the Integer path."
By moving the problem from 'Time and Memory' to Logic Presence, the Murgu Collatz Unicity provides a permanent solution to the functional divergence of the 3n+1 problem.