"The P versus NP problem is a major unsolved problem in computer science. It asks whether every problem whose solution can be quickly verified (technically, verified in polynomial time) can also be solved quickly (again, in polynomial time)."
"Consider Sudoku, a game where the player is given a partially filled-in grid of numbers and attempts to complete the grid following certain rules. Given an incomplete Sudoku grid, of any size, is there at least one legal solution? Any proposed solution is easily verified, and the time to check a solution grows slowly (polynomially) as the grid gets bigger. However, all known algorithms for finding solutions take, for difficult examples, time that grows exponentially as the grid gets bigger. So, Sudoku is in NP (quickly checkable) but does not seem to be in P (quickly solvable)."
https://en.wikipedia.org/wiki/P_versus_NP_problem
Proof:
t= units of time
1. P = 10t, NP = 1t
Each problem takes ten minutes to solve. Each problem takes 1 minute to check.
2. P = 10t > NP = 1t
The problem occurs that it takes longer to solve the problem than to check it.
3. (P ˄ NP) = 11t
Solving and Checking the problem requires 11 minutes total.
4. A paradox results: The problem is not solved until it is checked as the checking process is part of the solution itself. Checking the problem requires solving it again, thus fractals/fractions occur. P variates into NP where P ∋ (P/NP).
5. NP is a fractal/fraction of P. It is a fractal as a replication of the time line, as a time line composed of further fractals is a time line. It is a fraction as each time line is a quantity of 1, that relative to an underlying timeline that represents a potential unity as a singularity is a ratio of timelines.
6. P effectively replicates itself into a fractal/fraction state through NP → ((P → (1/10 = NP) ˅ P = (10P)). But this in itself is a further paradox as NP necessitates that P changes its value from a solvable time of 10 minutes into 1. Finding the solution of the problem always requires the manifestation of a timeline. It effectively creates time.
7. The solving of the problem, the first time, results in the problem being checked (or rechecked) in correspondingly shorter and shorter times. So where P 10t → P1t → P1/10t → P 1/100t → P (n → 0)= ∞ what we observe is that all problems as dynamically being solved are timelines. A problem that is equivalent to:
(P 10t ∧ Np 1t) = P11.111111111....
8. NP is just a value inversion of P, but is inherent within P as the solution to the problem requires the checking of the problem as a replication of the solving of the problem. Each dynamic solving of the problem effectively replicates itself in time through the checking of the Problem but this occurs in a progressive reoccurance of fractions/fractal time lines considering both P and NP are timelines. For each time NP occurs the dynamic process of P becomes shorter in one respect and longer in another. The original time line of the problem becomes shorter but is added onto the problem.
Thus the nature of solving a problem is grounded in recursion where "finding the solution" observes a process of definition.
8a. P, with NP as a fractal/fraction of P, is thus expanding time in one respect as P is a problem of time.
8b. In a seperate respect to increase NP to a ratio where the solution of the problem is the same as checking the problem causes a point 0 or singularity where problem solving is the same as checking in the time lines. As the problem is solved it is checked.
9. The N Versus NP problem falls under a contradiction as considering if the problem is to be solved it must be checked, thus causing the paradox to replicate itself and N Versus NP. If checked according to a computer infinitely creates the problem by replicating its solution into smaller and smaller variations. If check by standard human awareness, it continues following the same nature.
N versus NP can never be checked, therefore it can never be solved in its standard context.
N Versus NP negates itself as a problem and observes itself as inherent process within the nature of reasoning and computation. The problem ceases to exist and solves itself as a process of definition. Problems are the creation of definition.
Thus, using a soduku puzzle as an example, the framework of the puzzle is actually created according to the process of answering it as the puzzle is an inversion. This inversion can be pictured where all numbers are empty spaces and all empty spaces are numbers.
Now the Sudoku puzzle as solved, empirically exists relative to other Sudoku puzzles which are solved but these puzzles form a much larger problem of all Sudoku puzzles as one Sudoku, which cannot be solved as it is a continuum of puzzle creation.
10. P Vs. NP is its own solution to its own problem as a process of definition.
P Vs. NP Presented Solution
Re: P Vs. NP Presented Solution
"As a process of definition" I never said P = NP.
It takes 10 minutes to solve P
1 minute to check NP
NP observes a rate of change in how long it takes to solve P.
P took ten minutes to solve, then 1 minute to .1 minute (second NP considering prior NP is still P relative to new NP) to .01 minute, etc.
Checking is repeated solving where the solving occurs at a specific rate for each time it occurs.
P vs. NP observes a progressive change in rates of the ability to solve.