The virtual quantum computer (VQC) is a grid made of infinite yet constructable sets that follow a known pattern. Like a quantum spreadsheet.
The grid is the superposition. The collapse of that superposition will be two input parameters, d and e which can be calculated easily for all integers, c, where c is the difference of two squares. Its purpose and our goal is to learn and show the TRUTH, one of them being P=NP. Cracking RSA will be a consequence.
When the integers that are the difference of two squares are arranged into the grid and their corresponding properties are shown, a pattern emerges that shows calculation instead of searching is possible.
Glossary
Column
All cells for a given e.
Row
All cells for a given n
The grid is indexed using e, n, and t, where e is the rows, n is the columns, and t is the specific element in the cell.
Entry, record, element
one set of variables that represents one factorization for a number.
an entry = {e:n:d:x:a:b} (e, n, t)
{1:5:12:7:5:29} (1, 5, 4) is a record AKA an element AKA an entry.
ab record, nontrivial factorization, prime record
the element that contains the factorization of c that is not 1*c, hence, nontrivial.
1c record, trivial factorization
the element generated from setting a=1 and b=c
Cell
All entries for a given e,n (not to be confused with an entry itself.)
Genesis cell
e,1
Remainder Tree
The remainder tree is the result of treating d and e as c's recursively until 1 is reached, creating a tree with several to many branches.
Functions
na transform
a movement from a record in (e, n) into (e,1) where n becomes 1 and a becomes a times the n of the (e,n) record. It has also been used to refer to moving n*a records down in a cell.
T
T of number or T(input) is the triangle number function. If our input is 7, T(7) returns the 7th triangle number
T-1, inverse T
the inverse function of the triangle number function that returns the index of a given triangle number. If our input is the 7th triangle number, the function returns 7.
Variables
The map's legend is {e:n:d:x:a:b}, where c is any number that is the difference of two squares, so odd numbers are included. It is the number you want to factor. It is the number that the a and b in an entry multiply to make.
a and b are, to reiterate, the factors of c. a is the smaller factor of c, and b is the larger one.
d is the integer square root of c
e is the remainder of taking the integer square root of c. Unless c is a perfect square, a remainder will be left over.
i is the root of the large square. it is the same thing as (d+n)
j is the root of the small square. it is the same thing as (x+n). i^2 - j^2, difference of squares.
n is what you add to d to be exactly halfway between a and b, and it is the root of the large square. So it takes you from d to the large square.
x is what you add to a to make d. When added to n it makes the root of the small square.
f is what you add to c to make a square. (e is what you subtract from c to make the square below it, f adds to make the square above c.)
g is the square root of c with decimals, opposed to d, which discards decimals.
t is the third coordinate in the VQC, it is a function of x.
u is the base of a triangle that helps us calculate (x+n) for certain c values. simply put, it is a representation of (x+n). 8 times the triangle number of u plus one is x+n.
s was a variable used to demonstrate patterns in (e, 1). See "(e, 1)."
When capitalized versions of the variables are used in comparison to lowercase versions, the capitalized versions refer to the variable's value for the trivial record, and the lowercase variables refer to the values for the nontrivial record.
{e:N:d:X:A:B} (e, N, T) is the trivial element.
{e:n:d:x:a:b} (e, n, t) in this context is the nontrivial element, the prime factorization of c.