Functions in Goldbach Space

Here's a short list of the most important functions in Goldbach Space.

\forall f \in BelowList, we will say \forall x,y \in People, we will definite f likewise:

I. The Goldbach Relation - the particular and binary instance of the Metric

    R(x,y)==

       0-y is not in x's Goldbach set

       1- y is in x's Goldbach set

**Let's note that since R is an anti-transitive, and symmetric relation, which is anti-reflexive over the Lawmaker single-tone {Lawmaker}. As official provers, we are working towards improving R to R', a relation, which is anti-reflexive over every set of people, in other words:

\forall X \in P(People) \forall x \in X    (x,x) \notin R'

 

II. The Metric-d(x,y) - the general and metric instance of the Goldbach Relation:  

    d(x,y)==

      0-if x=y

      3-if x doesn't know y

      2- if x knows y but y isn't in x's Goldbach set

      1- if y is in x's Goldbach set

III. The Lawmaker Number-D(Lawmaker, x) 

    A. The Weak Lawmaker Number-distance in proofs and meetings:

          D_W(Lawmaker,x)=

      

         if (d(x, Lawmaker))>1

                { 
                 1+\sum_{i,j \in Goldbach_{Lawmaker}}d(x_i,x_j)+|{k: \exists i \in G_{Lawmaker}:          d(x_i,x_k)=1}|; 
                 }

         if (d(x, Lawmaker)==1)

                 { 
                 1;

                  }

  

    B. The Strong Lawmaker Number-distance in proofs:

             D_S(Lawmaker,x)=

           if (d(x,Lawmaker))>1:  
                 {
                   1+\sum_{i, j \in Goldbach_{Lawmaker}}d(x_i,x_j);  
                   "Note: This number can be א0";
                 }           

            if (d(x,Lawmaker)==1)
                  {
                    1
                   }
            if (x==Lawmaker)
                   {
                    0
                    }  

IV. The Lawmaker's Validity Function V:
Let's note that the Validity Function is a very complicated function, that depends on many variables and functions. Therefore, there's no way to accurately write the validity function in a countable number of symbols in exponential time. Anyways, here are some of the variables and functions that the Lawmaker's Validity Function depends on:
      A. P: t \rightarrow (p(x_1),p(x_2),p(x_3))
          P(t) was discovered a number of days ago by signer 110.10011, and therefore little is known about this function. We don't even know how to approximate it. All what we really know about this function is one property.
           Interesting Property:
             \sum_{t \in DomP}Pt=\sum_{i=1}^{3}(Max((\frac{d}{dx_i})(p(x_i)))^{2}

           The Lawmaker will greatly thank anyone who discovers more properties about the P function.
  
      B. Frequency Variable - \lambda 
      C. Control Function - D(t,p,s,b)
           Very little is known about the Control Function - we don't even know if the control function depends on t,p,s,b only. All what we know is that the Control Function has a maximum point, and that:
                    \lim_{b \rightarrow \pm \infty}D(t,p,s,b)=0 

            In addition, at this maximum point:
                   p \rightarrow \infty
                   s \rightarrow \infty
  
      D. Lesson Function - L(t, I, f, o)
           Note: The Lesson Function is a very complicated function with many variables, and therefore the function written below is only an approximation, of undetermined accuracy.
           L(t,l,f,o)=\frac{I}{t}+f^{oI} (information_freq+formality^{information_order})
                When the information frequency function is:
                        inf_freq=\frac{I}{t} 
           Let's note that L is maximal when:
                  I= \infty
                 o= \infty
                 f= \infty   
                 t=0
           Obviously, such a situation cannot exist in our universe, but we can take a limit. :)

           Since the Lesson Function is probably the largest (in absolute value) distribution to the Validity Function, it's integral that signers take the above variables to a limit, as to optimize the Proof's Validity. :)

     E. The Liquid Function - A(t,c,l,q)
          Note: This is only an approximation.
          A(t,c,l,q)=(t_0-t)(c-c_0)lq^{100c} (time*concentration*Liter*quality^{100concentration})

     F. The Space and Heat Functions - S,H:(w,-w) \rightarrow {0,1,-1}
           \forall x \in (-w,w): S(x),H(x)==
                     if (x is unoccupied)
                         {
                         0
                          }      
                     if (x==Lawmaker)
                          {
                          1
                           }
                      if (x==Signer)
                           {
                            -1
                            } 
              Note: The Validity Function is maximal when the Space and Heat Functions are maximal.
                        

As signers, you are all obligated to discover more functions for the Lawmaker, so that she can formalize them, and get o(\frac{1}{n}) much closer to proving Goldbach's Conjecture, as well as other open problems in mathematics. A signer that discovers a new function or new properties of an existing function will be rewarded.

Valid Proof!!!
Goldbach's Lawmaker Cat (Meow!) ^_^