Combinatorial decision problems and optimisation problems are related to search in exponential data using the Riemann Hypothesis and the net result is tractable algorithms--the result if valid is useful in Physics, Operations Research,Cryptography,Mathematics, Engineering and many other areas

1. Christmas/New Year-2017
PENGUIN EXPLAINS THE TRACTABILITY OF THE NP-
COMPLETE DECISION PROBLEM AND RELATES IT TO
THE SIMPLICITY OF THE RIEMANN HYPOTHESIS
WARNING TO STUDENTS!!
The views and results expressed here are not generally accepted and
so should not be used for any formal or informal educational or
training purposes. The study is exploratory in nature.

2. “The reasonable man adapts himself to the world; the unreasonable persists in trying to adapt the
world to himself. Therefore all progress depends on the unreasonable.”-G B Shaw
[PDF]The P=?NP Poll - Cs.umd.edu
https://www.cs.umd.edu/~gasarch/papers/poll.pdf
Anil Nerode:(Cornell, Math) What techniques? Pure combinatorics
if P=NP, Calculus estimates as in Hilbert’s solution of Waring’s
problem if P!=NP.
Being attached to a speculation is not a good guide to research
planning. One should always try both directions of every problem.
Prejudice has caused famous mathematicians to fail to solve
famous problems whose solution was opposite to their expectations,
even though they had developed all the methods required.
One should pay great attention to the Grand Sages and place a lot
of reliance on their Vision. It turns out the P=NP is valid and the
solution is merely a simple application of Pure Combinatorics.

3. Let us consider an example problem from the solution of
simultaneous equations from the area of Numerical Methods. A
solution that looks neat is Cramer’s method. However just like the
seeds of the Inquisition the determinant carries with it the seeds of
the exponential and we end up with an algorithm of exponential
time complexity. If we ‘chuck away’ determinants and use
Gaussian elimination then we end up with a polynomial time
complexity algorithm.
In the area of Combinatorial decision (or optimisation) problems we
use tend to use the traditional permutations and combinations.
Like the seeds of the Inquisition permutations and combinations
carry with them the seeds of the exponential and we end up with
algorithms of exponential time complexity with severe non-ending
Tom and Jerry shows and end up with an auto de fa announcing
exponential or sub-exponential time complexity. We have to redo
traditional combinatorics without using permutations and
combinations. How do we do this?
[PDF]The P=?NP Poll - Cs.umd.edu
https://www.cs.umd.edu/~gasarch/papers/poll.pdf
Moshe Vardi:(Rice)
The main argument in favour of P ≠ NP is the total lack of
fundamental progress in the area of exhaustive search.

4. The solution lies in obtaining a polynomial time complexity
algorithm for a search in exponential data. Consider the NP-
complete decision problem as searching for a steel needle in a
haystack. We monotonically number each strand/stalk/bit of hay
(and the steel needle) by successive terms from the Harmonic
series. Then we use a function known as the Lumpy function to
obtain the position of Tigger balancing on Pooh. The position of
Tigger varies from 0..1 and tells us how many houses ahead of
Pooh is Tigger’s position.
The base of the Hump is the range 0..1. For each strand/stalk/bit of
hay (and the steel needle) we compute the position of Tigger. Then
we use curve fitting on the positions of Tigger and find we end up
with humps like on a camel’s back.

5. Now if Tigger can balance himself exactly on the peak of the hump
at ½ then we have a solution to the combinatorial decision problem.
As we move away from the solution Tigger position closest to the
peak of a hump becomes more and more monotonically. This
property facilitates a binary search to determine where Tigger is
exactly on the peak of a hump and that is a solution to the
combinatorial decision problem obtained in polynomial time as
only repeated binary search is involved.
What is in the Hump?
The Hump is exactly the one we find in the x-rays of the Riemann
xi function.

6. The peak of a Hump is a zero of the Riemann zeta function and
corresponds to Tigger being exactly(sic) half a house ahead of Pooh
in a Pooh-Tigger cake distribution race.
It turns out that we do not need something as complex as the
Riemann zeta or xi function to describe and obtain the zeroes of the
Riemann zeta function. Just as a cup of tea remains a cup of tea
whether we consume it in a hut or a pushcart vendor, or a seven star
hotel or in a palace the zeroes of the Riemann zeta function are the
zeroes of the Lumpy function. A zero of the Riemann zeta
function can be related to the plain vanilla Harmonic series or to
the more sophisticated Euler zeta functions or the still more ‘jazzy’
Riemann zeta function. A zero of the Riemann zeta function
corresponds uniquely to a pair (a composite integer, a factor of the
composite integer). As there are an infinite number of such pairs
there are an infinite number of zeroes of the Riemann zeta
function. Between the zeroes is a point which corresponds to a

7. prime. As the primes are sparse as we go to larger and larger integer
the zeroes are densely populated as we go higher up the y-axis.
We have dispensed with permutations and combinations in the
search for a solution to the combinatorial decision problems along
with them the seeds of exponential time complexity they carry. This
allows polynomial time complexity algorithms for integer
factorisation(Piglet, Lumpy), discrete logarithms(Lumpy,Kanga),
elliptic curve discrete logarithms(Lumpy, Eeyore), sum of subsets
problem(Owl), NP-complete problems(Bees, Heffalump), travelling
salesman problem(Bees), Hamiltonian cycle problem(Bees), Eight
Queens problem (Gopher), Deadlock in operating systems(Gopher)
etc. etc.
For a description of the Lumpy function (see here) and for a
description of the Piglet Transform (see here).
As per the traditional practice in the Information Technology
industry Pooh would like to offer the algorithm (i.e. the Lumpy
function) to Yahoo! as Pooh is one of their oldest customers.

8. However Pooh says, “Oh, bother! I do not know where the front door
of Yahoo! is. In any case the hermit does not go to the King, the
King comes to the hermit. They can come over to my house. This is
the House at Pooh Corner”.
So it turns out that the solution to integer factorisation is a trivial
problem using the mighty mathematician Euler’s results. We are
lucky today to have the technology to reliably compute with high
precision numbers in any nook and corner of the world. The cost of
computation is negligible! The absence and lack of access to such
technology made the mighty mathematicians Euler, Gauss,
Riemann, Hilbert and others feel that integer factorisation and
later on the Riemann hypothesis are beyond human beings to
resolve. In the last century mighty mathematicians like
Ramanujam and Nash found the Riemann hypothesis jinxed as

9. they could not compute beyond 20 digits precision. The RSA-768
requires 450 digit precision in Pooh-Tigger cake distribution races.
Even with the availability of modern technology the Great Sage
Lenstra warned that numbers like RSA-768 and above are jinxed.
This is because if we use permutations and combinations to tackle
large number integer factorisation by traditional methods the
large numbers behave like vicious, vemenous serpents, because of
the exponential blow up of permutations and combinations. One
can easily end up ‘zapped’ with traditional ways of tackling
integer factorisation and the Riemann Hypothesis!
TOOLS TO TACKLE THE RIEMANN
HYPOTHESIS AND COMBINATORIAL
DECISION PROBLEMS
THE PIGLET COMPUTER& BINARY SEARCH