When the newly discovered equation “≡ 0 (mod 7)” is connected to the “≡ 0 (mod 19)” equation in the 19 numerical coding systems discovered before with “**AND**” logic, the probability of encoding reduce from (5.26%) 1/19 to (0.75%) 1/7 x 1/19 = 1 / 133. The (%0,75) 1/133 probability value creates a much more delicate discrimination than (%5,26) 1/19. Since the range of motion of the system decreases as the probability value decreases, we see that these two equivalents are connected with the “**OR**” logic when needs. When these two equivalents are connected with the “**OR**” logic, the probability value formed is 1/7 + 1/19 = 26/133 (19.55%) and this probability value is greater than (14.29%) 1/7.

In our opinion; Equivalence of the remainder 2, “≡ 2 (mode 7) and ≡ 2 (mode 19)” and the remainder of the 7, “≡ 7 (mode 19)” are considered without increasing the probability values of the encodings (without negatively affecting them), **increasing the options of the system, increasing the options of the needs or developing solutions. It would be the right approach to finding a solution.** If we calculate the probability value using the “**AND**” logic, 2/7 x 3/19 = 0.0451, the value 4.51% is less than (5.26%) 1/19. As a result, the probability value according to 1/19 is not increased or even decreased slightly.

*Systems that have been developed considering the remainder of zero use only integers. However, the development of systems will be towards real numbers and then to transcendental numbers such as π and e numbers. Imagine, if your PIN code is π number, who can break this code?!! Considering the remainder using modular arithmetic should be considered as a transition to real numbers.*

There is no mathematical (statistical) basis for insisting only on the remainder of zero (0) and the number 19 “≡ 0 (mode 19)”, as well as we think that it is very unnecessary to try to base this insistence on verses. Because the discovery process of numerical coding system continues. The weaknesses of the “≡ 0 (mod 19)” equivalence of the 19 numerical coding system have clearly emerged as a result of the developments.

It has become unable to respond to many numerical data. Unfortunately, the system and the Qur’an suffered great damage in order to answer to developments and the corrections, cancellations and denials of verses in the Qur’an were reached. **However, the systems that we have are those that do not have “Error Correction Code” and “Error Detection Code”, only those systems that can detect the original and extraordinary structure.** *(Spelling errors and Elif letter additions are excluded from this definition because spelling mistakes can be corrected according to spelling rules.)* Using this systems, we conclude that the Qur’an is original, preserved and extraordinary, based on these results. The scientific method we use is the deductive method. This method does not allow you to interfere with or alter the entire structure of the research subject. When you change something, such an approach takes you out of the scientific method. The gains of the research lose their scientificity and are not taken into consideration by the scientific community. As a matter of fact, the studies of numerical coding system of the Qur’an unfortunately has been brought into this situation today. The aim of our study is to ensure that the scientific errors are eliminated from the studies of numerical coding systems of the Qur’an that the system is developed in accordance with the needs, developed within a scientific framework and accepted by the scientific community or providing support all kind of studies.

As a result of our observations, the equivalents ≡ 0 (mode 7) and ≡ 0 (mode 19) generally confirm the authenticity of the system by operating on separate branches. One equivalence gives approval to one part of the phenomenon, while the other can give approval to another part of the phenomenon. This provides a very effective selectivity and a new option. We see it as a very clear development. When applied in this form, it does not negatively affect the probability of coding.

Our proposition “≡ 2 (mod 7)” and “≡ 2 (mode 19)” should be used only the fundamental data of the Qur’an, such as Surah number 114, Numbered Verse number (6234), un-numbered Basmalah number (112), special group Verse number (2) and their derivatives (Index data) as “≡ 2 (mod 7) and / or ≡ 2 (mod 7)”. Other numerical data of the Qur’an should be used as a support, that is, not in a negative way, but in a positive way. In other words, the equivalences we propose should be used as supporting, not determinative.

**“≡ 0 (mod 7) and ≡ 2 (mod 19)”** , **“≡ 2 (mod 7) and ≡ 0 (mod 19)”**

“≡ 7(mod 19)” equivalence should be preferred as a supportive rather than a determinant, as I mentioned above.

## System Basic Data and Numeric Encodings:

Mathematics, which is the language in which the universe is written, shows itself in the Qur’an with a poetic expression. You can see that the system does not leave an open point, covers all the basic data and there is no “remaining”.

All numbers with basic data are appropriate to the system.

**7 Coding number_1 ≡ 0 (mod 7) **

**19 Coding number_2 ≡ 0 (mod 19) **

**2 number of special group verses ≡ 2 (mod 7) and/or ≡ 2 (mod 19)**

**Only number 2 is a special prime number as Even number**

**The sum of the coding numbers is 19.**

**7 **+** 1 **+** 9 **+** 2 **=** 19**

** 114 Surah number **

** 6555 Sum of Surah numbers **

** 6348 Sum of Verse numbers **

** 6346 Sum of Verse numbers (without special group verses) **

** 112 Un-numbered Basmalah **

** 6236 Sum of Numbered verses **

** 6234 Sum of Numbered verses (without special group verses) **

** 7 19 114 6236 112 ≡ 0 (mod 19)**

** 7 19 6234 112 2 ≡ 0 (mod 19) and ≡ 0 (mod 7)**

** 6555 6346 ≡ 0 (mod 19)**

** 6555 114 ≡ 0 (mod 19)**

** 114 6555 ≡ 0 (mod 19)**

** 114 6346 ≡ 0 (mod 19)**

** 6555 ≡ 0 (mod 19)**

** 6346 ≡ 0 (mod 19)**

** 114 ≡ 0 (mod 19)**

** 114 6236 ≡ 0 (mod 7)**

** 114 6348 ≡ 0 (mod 7)**

** 112 ≡ 0 (mod 7)**

** 114 = 2 + 112**

** 6348 = 2 + 6346**

** 6236 = 2 + 6234**

** 6348 = 2 + 6234 + 112**

** 6348 ≡ 2 (mod 19)**

** 6234 ≡ 2 (mod 19)**

** 114 6348 ≡ 2 (mod 19)**

** 6555 6348 ≡ 2 (mod 19)**

** 6555 6234 ≡ 2 (mod 19)**

** 6555 6234 ≡ 2 (mod 7)**

** 6555 6346 ≡ 2 (mod 7)**

** 114 ≡ 2 (mod 7)**

**The Coding structure of 6348 verses in 114 surahs is 114 ≡ 2 (mod 7) and 6348 ≡ 2 (mod 19) **

**114 6348 ≡ 0 (mod 7) and ≡ 2 (mod 19) , 6348 = 6346+2 , 114 6346 ≡ 0 (mod 19)**

## About the system method:

- The basic method for introducing systems is the deductive method. In defining the numerical coding system, the equivalence of mathematical results and the data grouping structure were considered the best way to protect the Qur’an.
- Symbolic expressions should be logical and meaningful. The ordering and use of symbols should not be taken out of their natural structure.
- All the symbolic structures that provide equivalence or that have equality and similarity are suitable for the system. It shows that the structure is preserved and extraordinary and that is Allah’s word.
- The group of 6348 verses in the Qur’an; Number 6234 numbered verses, 112 un-numbered Basmalah s and 2 special groups should be used as a verse.
- The word counts in the Qur’an should be regarded as singular and not suffixed.
- Word counts should be made only on numbered verses, the last two verses of At-Tawbah surah and the un-numbered Basmalah group are not included in the word counts.
- Letter counts all verses should be included in the system. (6348 verses)
- Data groups or subcomponents must provide equivalences. During the separation of data into sub-components / groups, structures with the same characteristics should be collected in the same sub-groups.
- “ ≡ 0 (mod 7) and/or ≡ 0 (mod 19) “ this equivalence spreads entire of the Qur’an.
- The group of private verses must verify the numerical system.
- The number of special verses that we associate with the number 2 “≡ 2 (mod 7) and/or ≡ 2 (mod 19)” equivalents in the basic data of the Qur’an “≡ 2 (mod 7) and/or ≡ 2 (mod 19)” should be used, because 2 special verses come to the forefront where they find meaning in the Qur’an is the basic numerical data (114 Surah and 6348 verses).
- “ ≡ 2 (mod 7) and/or ≡ 2 (mod 19) ” When the equivalents are used in verses of Qur’an, should be used like this, “≡ 2 (mod 7) and ≡ 2 (mod 19)” , “≡ 0 (mod 7) and ≡ 2 (mod 19)” , “≡ 2 (mod 7) and ≡ 0 (mod 19)”

“≡ 2 (mod 7) and ≡ 7 (mod 19)” , “≡ 0 (mod 7) and ≡ 7 (mod 19)” as a supportive, not decisive.

- When using the equivalence “= 7 (mod 19)” containing the numbers 7 and 19, it should be used as a supportive rather than a determinant.

Note: We cannot say that the method has been completed and will continue to improve.

## An epistemological experiment to understand the system well:

- Let’s say we are enumerating sections of a book, 604 pages, 114 chapters, 6348 paragraphs in this book, the name of the leading character and adjectives belonging to this character, the mathematical discipline and coding structure given above as the method is included in the book.
- Let us assume that the numerical cluster totals of the division and paragraph numbers are adapted to the mathematical system given above.
- In addition; Let us consider that there are Even and Odd numerical symmetry in the numerical cluster formed by the division and paragraph numbers and the sum of the sub-number clusters that make up this symmetry is in mathematical discipline in accordance with the method given above.
- Finally, let us assume that the chapters and paragraphs that make up this book have been formed in 23 years as pieces of a small piece of a puzzle and formed into books.

*To learn the landing details of the verses, please refer to Unit-3 / Additional information or search on the Internet as “descent order of verse groups in the Qur’an”.*

* *http://www.hakveadalet.com/wp-content/uploads/Nuzul.pdf

There are many more details about the mathematical structure, but even the ones we’ve mentioned above will shed light on how we sould understand the incredibly complex event is, how it protects the original structure against changes and tampering and that it cannot be done by a human 1400 years ago.

The mathematical structure that we tried to express in the Qur’an; it contains a clarity that can be measured, physically based on findings. We want to express this mathematical structure as the mathematical miracle of the Qur’an.

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