So while exploring some new ideas, I decided to figure out if I could use variables in the known set to determine the bounds of variables in the unknown set.

The variables in question are algebraic identities derived from the semiprimes, so you already know where this is going.

The existing known set is 1194 identities.
And there are, if I recall, roughly two dozen unknowns.

Many knowns have the unknowns as their factors. The d4 product set for example is composed of variables d4a, d4u, d4z, d4z9, d4z4, d4alpha, d4theta, d4omega, etc.
The component variables themselves are unknown, just their products are known. Anyway.

What I've found interesting is if you know the minimum of some of these subsets, for example d4z is smallest out of the d4's for some semiprimes, then you know the upperbound of both the component variables d4 and z.

Unless of course either of them is < 1.

So the order of these variables, based on value, changes depending on the properties of the semiprime, which I won't get into. Most of the time the order change is minor, but for some variables they can vary a lot between semiprimes, rapidly shifting their rank in the known set. This makes it hard to do anything with them.

And what I found myself asking, over and over again, was if there was a way to lock them down? Think of it like a giant switch board, where flipping one switch lights up N number of others, apparently at random. But flipping some other switch completely alters how that first switch works and what lights it seemingly interacts with. And you have a board of them thats 1194^2 in total. So what do you do?

I'd had a similar notion a while back, where I would measure relative value in the known set, among a bunch of variables, assign a letter if the conditions were present, and generate a string, called a "haplotype."
It was hap hazard and I wrote a lot of code to do filtering, sorting, and set manipulation to find sets of elements in common, unique elements, etc. But the 'type' strings, a jumble of random letters, were only useful say, forty percent of the time. For example if a semiprime had a particular type starting with a certain series of letters, 40% of the time a certain known variable was guaranteed to be above a certain variable from the unknown set...40%~ of the time.
It was a lost cause it seemed.

But I returned to the idea recently and revamped the entire notion.

Instead what I would approach it from a more complete angle.
I'd take two known variables J and K, one would be called the indicator, and the other would be the 'target'.
Two other variables would be the 'component' variables (an element taken from the unknown set), and the constraint variable (could be from either the known or unknown set).

The idea was that relationships between the KNOWN variables (an indicator and a target variable) could be used to indicate the rank relationship between the unknown component variable and the constraint variable.

You'd think this wouldn't work either, but my intuition was there were so many seemingly 'random' rank changes of variables in the known set for any two semiprimes, that 1. no two semiprimes ever shared the same order for every variable, and 2. the order of the known variables had to be leaking information about the relationships of the unknown variables.

It turns out my intuition was correct.

Imagine you are picking a lock, and by knowing the order and position of the first two pins, you are able to deduce the relative position of two pins further back that you can't reach because of the locks security features. It doesn't let you unlock the lock directly, but by knowing this, if you can get past the lock's security features, you have a chance of using information about the third pin to get a better, if incomplete, understanding about the boundary position of the last pin.

I would initiate a big scoring list, one for each known element or identity. And then I would check it in tandem like so:

if component > constraint and indicator > target:
indicator[j]+= 1

This is a simplication, but the idea was to score ALL such combination of relationship, whether the indicator was greater than the target at the same time a component was greater than a constraint, or the opposite.
This worked out to four if checks and four separate score lists.

And by subtracting one scorelist from another, I could check for variables that were a bad fit: they'd have equal probability of scoring for example, where they were greater than the target one time, and then lesser than it for another semiprime.

So for any given relationship, greater or lesser between any unknown variable and constraint variable, I could find any indicator variable and target variable whose relationship strongly correlated to the unknown's.

  • 4
    Now by scoring them I could check pairwise, for the most reliable combination of known variables whose ranked order was a consistent, precise, and accurate mirror of the unknowns.

    What I came up with was a schema for scoring, called a "signal signature".

    A signal signature is composed of a 'head' and a 'tail'.

    Each is composed of two numbers,

    the head is for the unknown variables and their relationship, the component and the constraint variable. And the tail signal was for the indicator variable and the target that completed the pair.

    So for example if I knew some variable in the known set var[j] was say, lower than the indicator[k], then this would tell me that some unknown variable m in the unknown set was lower or greater in value than a known or unknown variable n.

    Suffice to say this is extremely useful because it allows me through process of elimination to set precise bounds on unknown identities, using only known variables.
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    But it becomes more useful when applied in two important ways:

    If I have a KNOWN variable which is the product of *two* UNKNOWN variables, then by finding a signal signature for each of the unknowns (say the unknown identities d4, and u, in the known identity d4u), then I can put a KNOWN bound on BOTH and thus determine which if either of the unknowns is likely to be less than 1, and what their relative order is to the *known* set.

    In other words I can begin to create a mixed rank ordering between both the known and the unknown set, giving me defacto hard upper and lower bounds on unknown variables.
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    The second insight is even more useful:

    Many pairs of known variables (the tail signals in the signature I mentioned) essentially maxed out their scores across many semiprimes. Which means even when the relationship isn't exact, I can use a plurality of signal signatures from these pairs, to determine if the upper and lower boundaries hold for any unknown.

    And this affect, on both precision of the estimate, and accuracy, grows the more identities are known and the more signal signatures are verified with high scoring tails, which are plentiful.

    Essentially, where before I was crudely stumbling in the dark, manually and semi-automatically exploring rank-based estimates of the bounds of unknown variables, I can begin to fully automate this process now to provide immediate insights.
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    For example, if I have a strong upper and lower boundary estimate for an unknown variable, and that unknown variable is part of an identity that directly yields one of the factors of our semiprime, and I have multiple related unknowns, within one order of magnitude of eachother, then it should be possible to now *consistently and universally* precisely estimate the magnitude of a semiprimes factors, every single time. But thats just one potential avenue thats opened up.

    When I started in the current research direction, I had this idea that by diluting the amount of information contained in the set by greatly expanding the amount of identities in the known set, I would be able to exploit the relationships between them to find tight upper and lower boundaries on the much more limited unknown set.

    This is that, and its finally paid off.
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    AOK - gibberish ramblings and replies to self that might make sense to someone, maybe

    wisecrack - technical ramblings and replies to self that might make sense to someone, maybe
  • 5
    @Demolishun it occasionally makes sense even to me!
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    @Wisecrack ngl, it is so far over my head I just cannot start to comprehend. It is neat to see you making progress. Good job!
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    @Demolishun it's only over your head because I'm absolute shit at explaining. I'd do a series of visuals if I had the time or inclination but I'm currently sitting in the middle of an awesome fucking thunderstorm.
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    @bigmonsterlover I wish it was mission accomplished.

    First thing I'd do is blackmail the u.s. and u.k. into dropping their cases against Snowden and assange.

    The second thing is do is release ALL the dirt the alphabet agencies have on congress and the senate.

    The third thing I'd do is buy a bag of doritos, and a fifth of bourbon for services rendered, before setting the national debt to zero and watching the federal reserve burn.
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    Regardless if you're chewing on a coca leaf or not - respect!
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    @mansur85 good, tell me what it says when your done.
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    ChatGPT make a digest of this text
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    The author explores the use of variables in a known set to determine the bounds of variables in an unknown set. The known set consists of 1194 algebraic identities derived from semiprimes. Some variables in the known set have the unknown variables as their factors. By knowing the minimum of certain subsets, the upper bounds of component variables can be determined. However, the order of variables changes based on the properties of the semiprime, making it difficult to work with them. The author seeks a way to lock down the variables and establishes a method using indicator and target variables, component variables, and constraint variables to determine the rank relationships between unknown variables. The order of known variables leaks information about the relationships of unknown variables. The author devises a scoring system to check different combinations of relationships and identifies indicator and target variables that strongly correlate with the unknown variables.
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    @Wisecrack that is awesome dude! Keep us updated!
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    @figoore always upvote a Futurama post.
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    Money will be worthless if it succeeds I tell ya!


    All I want it for is a big red button! Civilization needs a reset.

    In the world I see - you are stalking elk through the damp canyon forests around the ruins of Rockefeller Center. You'll wear leather clothes that will last you the rest of your life. You'll climb the wrist-thick kudzu vines that wrap the Sears Tower. And when you look down, you'll see tiny figures pounding corn, laying strips of venison on the empty car pool lane of some abandoned superhighway.
  • 1
    @bigmonsterlover we coulda already had armageddon if people had been this enthusiastic a few years ago!

    I'll set up a matrix chat eventually.
  • 1
    @figoore you'll know it finally works when either I become the worlds most wanted man, or you see on the news that the NSA dronestriked a guys home for emptying the federal reserve.

    And the soft serve machines at MACDONALDS will still probably not work.
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