Has anyone read Ken Conrow's Collatz Conjecture website?

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http://www-personal.ksu.edu/~kconrow/" [Broken]

I mean really read it, to where they understand it, not just
to the point where their eyes glaze over?

I see his site cited quite frequently, but I don't know if
I've ever seen any critique. I admit, I was intimiitaded by
his site at first. But over the years, I'm become increasingly
skeptical, especially now (Jul 2009) that he thinks he's finally
worked out the proof. He's still asking for help to formalize
his proof into a publishable format and I can't help him there.
We have corresponded by e-mail frequently in the past and I've
helped him with little things over the years like fixing his
faulty state machines.

But I can't see the validity of this interger density thing.
And he seems reluctant to talk about my objections. I would like
to think my point devastates his theory so much he's speechless,
but maybe he thinks it's so trivially wrong he won't waste his
time (although with the help I've given in the past, you would
think he would have the courtesy to tell me what's wrong).

So I'm soliciting other opinions since Ken seems reluctant to
offer his.

I'll try to keep this as concise as possible, I hope I get it
right.

Let's start with the basis of Ken's proof, the Left Descent
Assemblies (LDA). Ken breaks up his Collatz graph into branches
that start with odd numbers 0 (mod 3) and ends them on the
first place an odd number is followed by 3 consecutive evens.
This odd number is called the LDA Header. After an LDA Header,
the sequence merges into other LDAs until they all eventually
merge to 1. Ken points out that all LDA Headers are 5 (mod 8)
and if all LDA Headers are gathered into a set and used as the
root of something he calls the Abstract Predecessor Tree (APT),
he can prove that this tree has an integer density of 1 which
he claims proves that every positive integer is on the Trivia
Collatz Graph, thus, proving it.

Now, I don't have any problem with this integre density thing.
If Collatz is true, of course the Collatz graph contains all the
integers.

But he's not using the Collatz graph, he's using the APT.

And this is the nub of my gist. I say the truth of Collatz does
not follow from integer density 1 of the APT even if it's true.

Suppose I use 3n+7 instead of 3n+1.

Now, we know 3n+7 fails the conjecture, it's Collatz graph has
multiple disjoint pieces and any number not on the Trivial Graph
is a counterexample.

We know its LDA Headers are 3 (mod 8).

We know that all the disjoint graph pieces have LDA Headers.

So, collecting LDA Headers into a set must necessarily include
the counterexamples on the APT.

All APTs for all 3n+C systems must have an integer density of 1,
there's no where else for an integer to be. It simply does not
follow that Collatz is true just because its APT has an integer
density of 1, since 3n+7 has and it isn't true.

I say Ken has abstracted away the very thing he's trying to
prove, that integer density of the APT does not prove the
graph components of the underlying Collatz graph are not
disjoint.

Does any of this sound right?
 
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Answers and Replies

  • #2
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Hello,
I am a freshman at UNCC who has taken interest in the Conjecture and studied independently since August of last year. I recently attempted to make contact with Mr. Conrow in hopes of clarification, and unfortunately that attempt failed. I read his work to the best of my ability, however I believe I do not have the credentials or the experience with mathematics to understand his work, much less make an educated argument or criticism. If you are still interested in the Collatz conjecture, I would love to learn more about his work and share what I know about the Conjecture. His worked grabbed my attention because I recognized the binary graph and thought of my own research.
Thank you for your contributions towards the Conjecture!
 
  • #3
DrClaude
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This thread is from 2009, and the OP hasn't been here since 2013.

Thread closed.
 

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