## Summary of Observations Pointing to a Proof of the Collatz Conjecture

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-- Summation of Path Densities During Initial Abstract Tree Development

-- Summation of L.d.a. Density Contributions After Complete Abstract
Tree Development

-- Regarding the L.d.a.s as Sieving Elements Would Cover Z+

-- Algorithm Locating Arbitrary Integers in the Abstract Tree ==>
All of Z+ is in the Abstract Tree

-- Directed Edges in Binary Predecessor Tree Ensure Reaching 1

-- Inductive Construction of the Predecessor Graph from its
Elements Can Result Only in a Binary Tree

-- 1:1:1 Mapping of (a)Unique Integers into (b)Unique Locations
in the Tree each with (c)Unique Paths to the Root
*(Thanks to Joe Parranto for this last.)***
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*Note: This is the last directly germane slide. The
following slides look at paradoxes, Feinstein's proof of
unprovability, and other oddments.*

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