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.

James Harris