Tuesday, February 26, 2008


JSH: In the neighborhood

Oddly enough to me the most fascinating find from surrogate factoring which has created the means to end the impasse is a remarkably simple result that follows from a relatively simple equation:

x^2 = y^2 + nT - (1 + α^2)(k_0^2 + 2pjk_0 + p^2*j^2) - (k_0 + pj)pr_2

That is the equation that comes from letting 2αx = k + pr_2, and z = x + αk, when

z^2 = y^2 + nT

and considering k = k_0 + pj, to see how

nT - (1 + α^2)(k_0^2 + 2pjk_0 + p^2*j^2)

behaves as you increment or decrement k with j.

So actually I just kind of expanded out the traditional difference of squares.

Um, that's what they call thinking out of the box.

And you have trivially that as j increments OR decrements, r_2 will tend to be negative to compensate, so

nT - (1 + α^2)(k_0^2 + 2pjk_0 + p^2*j^2)

will have a minima and change around that value as j increases which is just an incredibly powerful result as it allows you to to get an idea of the value of z.

So the approach to the factoring problem is really tackling finding how to get z, when

z^2 = y^2 + nT

and all those variables are just helpers in that task.

You're just trying to get in the neighborhood.

And it can be shown that if x, y and z are rational

k^2 = (1 + α^2)^{-1}(nT) mod p

so you can go looking for z by looking for k, where you can get k's residue modulo p, an odd prime.

Qualifications are few. Yes, for a given choice of p, x, y and z rational may not exist such that all equations are satisfied but you can try different primes. Um, there are, after all, a LOT of primes.

So you have prime numbers as helpers that disappear after helping you to factor, and you have a surprisingly simple result with a parabolic minima, and you get quadratic residues, and it's the factoring problem and I've been talking about this latest research for days, and still math society waits…

Um, could REAL mathematicians wait?

Would Gauss or Euler or Fermat? Archimedes?

My place in history is secure even though I know a lot more than most of you clearly know so I also know that there may not be much history left! Not human history at least.

But not understanding is what this situation is all about, as some people didn't understand that lying about math would invite the retribution of the math because they didn't believe in mathematics itself.

The poor field was overrun by people who hate math but found a way to work the system by lying. That's all. Nothing more.

But without advancement in mathematics, humanity has no future, so the Universe will just kill off the species as no longer of further use.

By stopping mathematical progress, these people removed a key element in the purpose of the continued existence of the entire species so the clock is ticking down faster than any of you can imagine because you're too dumb to realize that if YOU lied and got things wrong, why couldn't others have?

Guess at how many years are left, and I'm sure you'll be wrong.

Yup. The test of humanity was a subtle one but it was very fair.

It was all about mathematical absolutes.

[A reply to someone who described what James had written as “meaningless garbage”.]

Actually it is easily derived.

Let z^2 = y^2 + nT, where T is the target to be factored.

Further let 2αx = k + p*r_2, where I use r_2 for historical reasons since the full theory also has an r_1, and where p is an odd prime of your choice.

Then you let z = x+αk, and substitute, and finally you let

k= k_0 + pj

where j is an integer.

As I explained in my initial post you get a remarkable result that k_0 will be near the maximum k such that abs(nT - (1+α^2)k^2) is a minimum, which you can prove rigorously with

x^2 = y^2 + nT - (1 + α^2)(k_0^2 + 2pjk_0 + p^2*j^2) - (k_0 + pj)pr_2

so the circle is complete.

It IS a simple result that has profound consequences, but we live in a complex world, so the debate continues as I face people who have learned to just fight for one more day.

Their strategy is always just to fight for one more day, fooling the world, and each day they keep people from the truth is a victory for them.

I am just one person fighting against a society around the world that is firmly entrenched that has betrayed the public trust.

At this point smarter people can exploit the mathematics but unfortunately I am sure that there are people who will try to hide exploits.

So yes, if say, a bank gets invaded by hackers who are breaking RSA at will, I fear that will be hidden. If you lose all your money as a result they will tell you it's your fault and you will not get a penny back.

If you protest you will be ignored.

And then you will understand how powerful they truly are.

I wish I knew a better way. Some way to save innocents from the fall-out.

But with a betrayal of trust on this scale I am at a loss for a better answer.

They will fail with a big collapse I fear, when they can no longer hide the security breaches. And can no longer explain away the collapses in security.

Florida in the United States lost power today. Is it yet another demonstration that will be explained away by powerful people fighting to keep their control? Or are the official explanations given correct?

I don't know.

My main task is to preserve civilization. IN order to do so I am empowered to sacrifice whatever needs to be lost. There are probably already lost.

Unheard. Unappreciated, except by me. I will honor their memory even if no one else understands.

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