My proof for P vs NP Draft One, Variant One

DISCLAIMER:(Read This NOW Before you read my Proof!){I cannot emphasize this!}
Please do recognize that this is very tentative work. I would like you to read it with caution but not skepticism. This is also presented in an unadulterated fashion as this is my first draft and so constitutes my first variant If you do not have anything nice to say in the comments, don’t say it. Thank you for your time.

A solution for the P versus NP Problem
By: Nunghead

Abstract:

In this proof, I will outline a solution to the P versus NP Question. The main result of this proof is that Berman’s Theorem is proven in the positive implying P=NP as a corollary by the explicit construction of a unary language with the property that it is NP Complete

Axiom 1.0 (Garey and Johnson):
Any NP Complete problem’s corresponding binary language is also NP Complete.

Lemma 1.1 (Wikipedia):
Every binary language has a more compact unary version.

Proof of Lemma 1.1:
Since the universe of strings over any finite alphabet is a countable set, every language can be mapped to a unique set A of natural numbers; thus, every language has a unary version {1k | k in A}.

Theorem 1.0 (Berman)
If there exist a unary language that is NP Complete then P=NP

Remark 1.0:
We shall restrict ourselves to Strongly NP Complete languages as their complexity doesn’t vary with the changing encoding scheme i.e from binary to unary. Suppose, if we had used the Weakly-NP Complete language SUBSET SUM instead of using any Strongly-NP Complete language we would have unnaturally converted our problem from displaying exponential time in the worst case for large input values leading to its unary variant being in P but binary variant is not in P.

Proof of Theorem 1.0[1]
Final Proof:
Due to the fact that every Strongly NP Complete problem’s language is also Strongly NP Complete, we may pick any Strongly NP Complete language for the task ahead. We will pick Bin-Packing as the Strongly-NP Complete language to be specific. Now by applying Lemma 1.1 we know that Bin-Packing has a corresponding unary language .So now we can conclude there exists a corresponding unary language for Bin-Packing that is NP Complete, thereby proving P=NP via Berman’s Theorem i.e Theorem 1.0. Q.E.D

References:
Book, R.V., Wrathall, C., Selman, A.L. et al. Math. Systems Theory (1977) 11: 1. https://doi.org/10.1007/BF01768464
Relationship between density and deterministic complexity of NP-complete languages ,Piotr Berman
https://en.wikipedia.org/wiki/Unary_language,
https://complexityzoo.uwaterloo.ca/Complexity_Zoo:T
http://cgi.di.uoa.gr/~sgk/teaching/grad/handouts/karp.pdf
Michael R. Garey and David S. Johnson. 1990. Computers and Intractability; a Guide to the Theory of Np-Completeness. W. H. Freeman & Co., New York, NY, USA.

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[1] The proof is presented in Berman’s paper Relationship between density and deterministic complexity of NP-complete languages , theorems 1 and 2.