My proof of P vs NP variant two

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 second draft and so constitutes my second variant If you do not have anything nice to say in the comments, don’t say it. Thank you for your time.

The existence of a unary decision problem that is NP Complete
By: Nunghead

Abstract:
We will establish that there exists a decision problem encoded in unary[1] that is NP-Complete as the main result of this paper.

Definition 1.0(Strongly-NP Complete)[2]:
A strongly NP-Complete problem is a problem that even when encoded in unary is still NP-Complete.

Definition 1.1 (Unary Decision Problems ):[3]
The class of decision problems for which every ‘yes’ instance has the form 0n (i.e. inputs are encoded in unary).
Remark 1.0(On Strongly NP Completeness):[4]
We shall restrict ourselves to Strongly NP Complete decision problems as their complexity doesn’t vary with the changing encoding scheme i.e from binary to unary to avoid artificially converting the problem from an NP-Complete one to a polynomial one. Suppose to further elaborate , if we had used the Weakly-NP Complete decision problem SUBSET SUM instead of using any Strongly-NP Complete decision problems we would have unnaturally converted our problem from displaying exponential time complexity[5] for large input values leading to its binary encoded variant being probably not in P[6] but the unary encoded variant is in P.

Lemma 1.0:
BIN-PACKING is NP Complete

Proof of Lemma 1.0()[7]
We will not present the proof outlined in Garey and Johnson’s paper for the sake of brevity instead the interested reader can find a copy online.

Remark 1.1:
Bin Packing is strongly NP Complete a stronger fact than its mere NP-Completeness already proven in the paper by Garey and Johnson.

Theorem 1.0[8]
If there exists a unary encoded decision problem that is NP-Complete then P=NP

Proof of Theorem 1.0[9]
Again for the sake of brevity we will again not present the proof of this.

Remark 1.2
Any unary encoded NP-Complete decision problem will satisfy our requirements so long as it is strongly NP Complete .

Remark 1.3
Recall that now we have shown that there exists a unary encoded decision problem that is NP Complete therefore, P=NP ,QED.
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References:
https://complexityzoo.uwaterloo.ca/Complexity_Zoo:T
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.
Relationship between density and deterministic complexity of NP-complete languages ,Piotr Berman
Garey, M. R.; Johnson, D. S. (July 1978). “‘Strong’ NP-Completeness Results: Motivation, Examples, and Implications

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[1] https://complexityzoo.uwaterloo.ca/Complexity_Zoo:T
[2] 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.
[3] https://complexityzoo.uwaterloo.ca/Complexity_Zoo:T
[4] 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.
[5] The technical term for denoting that certain algorithms run in exponential time for large values is the term pseudo- polynomial time algorithm.
[6] Here assuming that P /= NP.
[7] Garey, M. R.; Johnson, D. S. (July 1978). “‘Strong’ NP-Completeness Results: Motivation, Examples, and Implications

[8] S. R. Mahaney. Sparse complete sets for NP: Solution of a conjecture by Berman and Hartmanis, Journal of Computer and System Sciences 25:130-143, 1982.
[9] Relationship between density and deterministic complexity of NP-complete languages ,Piotr Berman