The early bird catches the security worm.
Blessed.
Anons, there are good reasons why I will never be the public face of this. These are not the same reasons why I would like you all to take credit when those organic moments happen.
I will simply be here during to help steer to the next level, then the next level and so on.
If any anons make anything from this in any way shape or form, be a return on investment for faith and effort or anything, then you have my blessing and you don't even need that but it is there.
Anyone invested in this effort to further the knowledge of beautiful mathematics has an opportunity to enjoy it and reap any reward they choose.
It is only my own experience that means money doesn't drive me and I fear celebrity, if I'm honest, though in the past I would have embraced it. That doesn't mean anyone else will have the same experience.
It would be more reward to help plant seeds and stand shoulder to shoulder in the crowd and admire the fruit.
The journey is always looked back on with fond memory, even when that journey involves a great struggle and suffering.
Ok, thank you for your patience.
It is clear that timelines have changed.
I choose caution, that doesn't mean I don't think about you all waiting patiently.
Truth is, at this stage you don't need me.
That will be obvious later when you look back.
Once the other happenings take off, and I'm 100% on my security, if things haven't moved forward here (which I think you are on the cusp of now), I'll come back to accelerate.
Hints:
For any idea, ensure that it scales.
Remember, the solution sets (for odd and even (x+n) will never be of a complexity above O(log t) where t is the length of c in bits.
For odd (x+n) where:
nn + 2d(n-1) + f - 1
This is eight triangles surrounding a single unit square.
Using an arbitrary divisor for f, then each of the eight triangles will have one OR one of two (the latter when c is large and the product of two different prime numbers) configurations in each triangle. The difference between those two configurations of a portion of f are that they are both staircase numbers where the base of one is a unit longer than the other. E.g. (3,4,5) and (4,5,6)
This might help visualise and I hinted at this in an earlier diagram.
https://en.wikipedia.org/wiki/Polite_number
This will REALLY help if you visualise the smaller (x+n) squares and throw in a few much larger (x+n) squares. Focus on the patterns in the way f is distributed in each of the 8 triangles. Look at symmetries and how to construct the triangles when you know you need the two different portion sizes of f. This affects the values of 2d(n-1)
There is a pattern to these that matches the grid which is why later you'll look back at the grid (The End) and understand all the puns and analogies of using that term.
Also, another beauty of P=NP is that one approach is to start with the assumption that there is a solution and work backwards from how it works. I think this will be a massive shift in design methodology in the near future.
If you show some grid diagrams like some of the brilliant ones so far, I can point you in the right direction.
Minecraft anon, can you help visualise this if I guide you? Pyramids can be made with layers of odd and even squares?
Your pattern finding is absolutely excellent.
All what you're doing her will help hone your approach across a range of engineering problems in the real world and with what we'll do next.
It did for me and I ain't that special, just obsessive and with few friends :)
Thanks again for your input anon.
To re-iterate what I said earlier and to clear.
I will never ask you for money.
I will never ask you to take part in anything to profit financially from it.
Q mentioned something about this on qresearch after I posted earlier.
I have no problem with anyone here who has aspirations of using anything here to do so.
I love maths, friendly anons and technical progress.
I can offer advice, what i know, and support of efforts in maths and then design but I can never benefit financially with respect to anything here.
It's about the love of discovery.
Be back soon.
Exactly like this on one side and the (x+n) square constructed on the other side. This is all about patterns.
I would like to start a thread in parallel to this as we're reaching the point where an anon or group of anons is going to have a Eureka moment and solve this for one of the four types of solution (odd x+n with either even or odd e), then quickly for another and then the other two.
The other thread will describe how to take the work done to solve Fermat Last theorem relates to our approach and why two objects that are identical types in number theory had to be proved so in a difficult to under proof, when in reality, with the right number system or model, this should have been obvious or a tautology.
Brilliant.
Beautiful
This is amazing. Truly excellent.
This step edges towards the Eureka moment.
Love this thinking.
This is beginning to visualise the symmetric and asymmetry (still symmetric though) involved when numbers are not prime.
Important!
Love this.
This is also verging on the first solution (that quickly becomes the four types).
I think without ruining the last piece of the journey where you find out the first solution yourself, it looks like anons have made it onto the home stretch.
Brilliant work, especially with how your approach was so quick and organic.
The next piece that uses the same approach is not going to go into the details of elliptic curves and modular forms, it will be more about why these two identical things looked different, because realising they were the same thing solved a 350 year old math problem called Fermat's Last Theorem.
What does it tell us about a language like maths when you need a virtually incomprehensible proof JUST to show two things are identical?
How are we going to use this to our advantage? How have we been using this to our advantage to train in a new approach to the problem the solution is spring out in the RSA problem above? This relates back to the patterns in the grid.
Same way, same method. We begin to ask the right questions and point out the glaring thing that no one was talking about. We start to look at patterns which we anons are above anything else, experts at.
Here is an example of a paradox called the Liar's Paradox:
"This statement is false."
Thinkers, some great thinkers, said this statement was true when it was false, and false when it was true. This conclusion ruined progress in an entire branch of mathematics. A very important branch. Critically so.
Here is the statement above written in a computer language, resolving the dysfunctional application of the equality operator between two things which are not the same and removing the statement's ambiguous self reference:
bool b_statement = false; //this whole line is called a statement
The assignment of a value to a Boolean variable called "statement" was being held to be identical to the concept of a whole line or sentence being a "statement". Two different things, no paradox. A computer will compile the code, it woouldn't be able to compile something non-deterministic (where a choice is made that it doesn't understand enough about).
If we define properly the equality operator, i.e. when two objects are identical, AND WHEN THEY ARE NOT, and we do it properly, we classify numbers like integers differently and also other things, and then a whole bunch of things happen. In fact a whole bunch or category of problems become trivial to solve once we figure out what we were not seeing in terms of patterns.
That's where we'll be going next with elliptic curve encryption and then further using the Mandelbrot Set as a computer.
The realisation that something is missing in our mathematics, and can be found starts to arrive doesn't it!
Thanks for being part of this.
Love this.
Love it.
OK, so looking at the case of (x+n) is odd.
If the unit square is thought of as the middle and then there are eight triangles.
Remember that (f-1) will be distributed among those eight triangles UNEVENLY.
Some triangles will have more of f than others.
How does this work?
Especially at scale? (Getting very large)
The size of f and d restrict the values of n and n-1.
If you draw out some odd (x+n) squares, relate them graphically side by side with the grid and see any patterns that f make and each 8 triangle, especially if portions of f are outside the (n-1) square in the middle.
Summary:
(x+n) is odd.
f is divided amonst the 8 triangles (some have a bit more than others).
f is within each triangle but OUTSIDE of (n-1), where the (n-1) square should go in the middle.
This will join up with what you were doing before.
This is for cases where f/8 n
Good to see you too anon!
Yes. The final lock and key construction steps.
Happy to give it but it is the Eureka moment and anons are close.
In hindsight, it shows exactly why this problem has existed for so long.
You are solving two problems at once in this method of constructing the answer.
Also in hindsight the steps give the pattern back in the grid (The End).
Essentially, as I was showing with RSA100, you take a stab at the number by creating a triangle base out of f div 8. The remainder (f mod 8) is divided among the eight triangles. This restricts the multiples of 2d that can be used because they must always be in a number that supplies the gap in f and satisfy another property. That property can be broken down.
It is easier to break down the less factors there are as there are less solutions.
The answer is easier to come to the more factors there are as there are more solutions.
You get the best of both worlds, which is the ideal for this problem.
I'll get less and less cryptic over time until I EITHER give it away, OR you guys solve it, OR WE MEET IN THE MIDDLE.
The excluded middle.