Secret

a. The spin operator has an analogue to 3-vector direction (name the form $\sigma \cdot \hat{n}$) owing to how the basis of the state vectors are chosen (everything just alinear combination of spin up spin down state vectors), that allows them to as if split into 3 components for each spatial direction nicely as if it is a 3-vector
b. Postulate on why quantum mathematical formulation agree so well with experiment – The basis is chosen such that any significant experiment results just happens to pop up in the spectra of many Hermitian operators

$n(1-z_0) = t(p_2-p_1)$ is the constraint. In fact, this has some relationship with the twin primes conjecture
Starting with solving the equation $p_1x+p_2y=1$
If p1,p2 are twin primes and n is even, then the equation has solutions $(1,1)$ and solves the goldbach's conjecture
For the general goldbach conjecture which ask if every integer can be written as the sum of two primes, this only occurs if the prime gap is a multiple of the given integer
So the whole question resolves to, is there an integer for every gap between primes

**Lemma**
Proving that by the fundamental theorem of algebra, any product decomposition of integers is finite
- We have n, Suppose there is a m > n, n can said to be finite relative to m. Then
- By fundamental theorem of algebra, n can decompose into many factors
- We know that (-1)(-1) = 1
- The product of positive factors is a multivariable monotonically increasing function f, so f(x1,x2,x3,x4, ...) = n for given n exists
- 0n = 0, so to have nonzero n, all terms has to be positive or negative