Computational Hunminjeongeum
Hangul Mathematics
A logical, engineering-driven approach to applying Hangul in the Digital Age.
Discover Hangul Mathematics
Computational Hunminjeongeum
A logical, engineering-driven approach to applying Hangul in the Digital Age.
Discover A logical, engineering-driven approach to applying Hangul in the Digital Age.
Hangul
Mathematics
Mathematics
is an approach that views the Korean alphabet strictly as a system of calculated engineering compromises made by King Sejong and his scholars. It reveals a clear mathematical and logical connection between all phonetic elements, making it perfectly suited for systemic study and seamless integration into IT environments.
*This methodology was developed entirely independent of existing phonetic, philosophical, or linguistic theories, as well as Unicode Consortium standards. Its sole purpose is to define the pure engineering essence of Hangul. The method is fully verified by code. It does not contradict previous academic discoveries; rather, it complements them by solving deep-rooted software engineering bottlenecks.
*This methodology was developed entirely independent of existing phonetic, philosophical, or linguistic theories, as well as Unicode Consortium standards. Its sole purpose is to define the pure engineering essence of Hangul. The method is fully verified by code. It does not contradict previous academic discoveries; rather, it complements them by solving deep-rooted software engineering bottlenecks.
Task Conditions
Initial Consonant (Choseong), Vowel (Jungseong), Compound Vowel,
Final Consonant (Jongseong),
Compound Final Consonant.
Total: 5 variables (Example: 괅)
ㄱ+ㅗ+ㅏ+ㄹ+ㄱ= 괅
ㄱ(초성)=ㄱ(ㄺ)
ㅗ - ㅏare structurally linked.
ㄹ+ㄱ are structurally linked.
Final Consonant (Jongseong),
Compound Final Consonant.
Total: 5 variables (Example: 괅)
ㄱ+ㅗ+ㅏ+ㄹ+ㄱ= 괅
ㄱ(초성)=ㄱ(ㄺ)
ㅗ - ㅏare structurally linked.
ㄹ+ㄱ are structurally linked.
The Solution
Each letter is assigned
a unique numerical tag that reflects its exact placein the hierarchy, its function,
and its interaction with other elements.
Every single syllable is simply
a mathematical sum.
ㄱ(x)+ㅗ(y)+ㅏ(z)+ㄹ(f)+ㄱ(x)= 괅(sum)
a unique numerical tag that reflects its exact placein the hierarchy, its function,
and its interaction with other elements.
Every single syllable is simply
a mathematical sum.
ㄱ(x)+ㅗ(y)+ㅏ(z)+ㄹ(f)+ㄱ(x)= 괅(sum)
Explanation
Before any calculations begin, a new foundational concept is introduced: The Void.
The Void represents the absence of the three elements that make up a syllable.
(0 초성, 0 중성 , 0 종성 )
Consonants that functionally cannot act as final consonants (ㄸ,ㅃ,ㅉ), maintain their spatial logic within the system.
0+중성+종성=0 and 초성+0+종성=0
are fully accounted for.
The Void represents the absence of the three elements that make up a syllable.
(0 초성, 0 중성 , 0 종성 )
Consonants that functionally cannot act as final consonants (ㄸ,ㅃ,ㅉ), maintain their spatial logic within the system.
0+중성+종성=0 and 초성+0+종성=0
are fully accounted for.
The Complete Hangul Map & Formula
(19 자음 + 초성 빈 공간)*((14 모음 + 중성 빈 공간)
+7 모음 합((ㅘㅙㅝㅞ…))*((16 자음 + 종성 빈 공간
+3(ㄸ, ㅃ, ㅉ)) + 11 자음 합(ㅄㄳㄵㄶㅀ…)) = 13 640 요소
+7 모음 합((ㅘㅙㅝㅞ…))*((16 자음 + 종성 빈 공간
+3(ㄸ, ㅃ, ㅉ)) + 11 자음 합(ㅄㄳㄵㄶㅀ…)) = 13 640 요소
-
Element IdentityThe absolute principle for all letters:
ㄱ(초성)=ㄱ(종성)=ㄱ(ㄺ,ㄳ) -
MethodologyVowels <=21 Consonants >=22
This is a mandatory structural condition. -
InterconnectionAll computations are driven by one core formula
and its defined path-ranges. -
Zero ExceptionsThe mathematical path-ranges flawlessly describe every single function and letter relationship within any given syllable.
Mathematics, Logic,
and Hangul
and Hangul
Hangul is not the solitary invention of King Sejong; it is the result of rigorous engineering and compromises between the King and the scholars of the Hall of Worthies (Jiphyeonjeon).
The completed mathematical map reveals every possible structural path Hangul could have taken.
와 | ㅘ: Identical in both phonetics and structural logic.
초성 빈 공간 - Represents a path where the initial consonant (ㅇ) is absent, yet all other elemental slots remain intact.
According to the 1933 Unified Hangul Orthography—a vocabulary-based standard logically suited for the era of mechanical typewriters—ㄲ and ㅆ can be final consonants, while ㅃ, ㅉ and ㄸ cannot.
However, looking at the older, fundamental principle of **Jongseong-buyong-choseong** (using initial consonants as final consonants), from a pure engineering perspective, ㅃ, ㅉ, and ㄸ *can* structurally function as final consonants; they are simply bypassed by modern convention.
The completed mathematical map reveals every possible structural path Hangul could have taken.
와 | ㅘ: Identical in both phonetics and structural logic.
초성 빈 공간 - Represents a path where the initial consonant (ㅇ) is absent, yet all other elemental slots remain intact.
According to the 1933 Unified Hangul Orthography—a vocabulary-based standard logically suited for the era of mechanical typewriters—ㄲ and ㅆ can be final consonants, while ㅃ, ㅉ and ㄸ cannot.
However, looking at the older, fundamental principle of **Jongseong-buyong-choseong** (using initial consonants as final consonants), from a pure engineering perspective, ㅃ, ㅉ, and ㄸ *can* structurally function as final consonants; they are simply bypassed by modern convention.
Intersection with 17th-Century Philosophy
Choe Seok-jeong, a prominent 17th-century scholar and minister, theorized a language matrix.
This historical precedent effectively validates that a mathematical, highly structured approach to Hangul was independently, scientifically, and successfully conceptualized centuries ago.
This historical precedent effectively validates that a mathematical, highly structured approach to Hangul was independently, scientifically, and successfully conceptualized centuries ago.
Fundamentals:
The void syllable as the point of origin
Connection of elements within the matrix
Methodology driven by formulas and a base structure (matrix)
5 elemental foundations based on phonetics
Hangul treated as a modular construct
The total count of possible combinations exceeds 12,288 syllables.
Connection of elements within the matrix
Methodology driven by formulas and a base structure (matrix)
5 elemental foundations based on phonetics
Hangul treated as a modular construct
The total count of possible combinations exceeds 12,288 syllables.
A rigorous mathematical approach to Hangul has been successfully applied in the past. The linguistic philosophies of Choe Seok-jeong and the Mathematics of Hangul serve as independent proofs of Hangul's embedded internal logic.
Unicode AND 초성≠종성
- Unicode Formula588×초성+ 28×중성 + 종성ㄱ(초성) ≠ ㄱ(종성), each is unique without connection.
Within 종성ㄱ≠ㄱ(ㄺ)≠ㄱ(ㄳ) without connection.
중성(ㅗ+ㅏ≠ㅘ) inherits the exact same problem.
This approach forces us to store and check
11,200+ elements (syllables, letters, and graphemes). - Hangul Mathematics FormulaL1 + L2 + L3(ㅗ|ㅜ|ㅣ) + L4×20 + L5×20(ㄹ|ㄴ|ㅅ)True systemic equality. A letter is identical
to itself and its functions across all positions.
ㄱ(초성)=ㄱ(종성)=ㄱ(ㄺ,ㄳ) | ㅗ+ㅏ=ㅘ
33 numeric tags, exactly as many as there are elements in Hangul (including ㅔ,ㅖ,ㅐ,ㅒ), without any need for re‑checks.
To the world,
Hangul is a collection of hieroglyphs
Hangul is a collection of hieroglyphs
In Unicode, Hangul was sorted according to the Chinese (hieroglyphic) principle, which stripped away its nature as a flexible alphabetic tool. To handle Hangul in IT, the industry relies on external workarounds: libhangul (common stack), IME input, the SWIFT STRING API (Apple), RAM-based solutions (Samsung, Microsoft), and another methods.
Each approach processes Hangul in its own isolated way.
Hangul Mathematics restores the Korean language to its alphabetic essence in the digital realm.
Within this framework, Unicode remains a code repository, but sorting and data processing become seamless and linear.
Each approach processes Hangul in its own isolated way.
Hangul Mathematics restores the Korean language to its alphabetic essence in the digital realm.
Within this framework, Unicode remains a code repository, but sorting and data processing become seamless and linear.
Macro Problems
Global architectural misalignments force developers to patch Korean-language issues using localized, unsystematic methods that depend on available resources. A quick GitHub search, for instance, turns up countless user repositories created solely for Korean. Meanwhile, nobody needs to open GitHub just to build a simple English keyboard. Every IT solution that involves Korean suffers from precisely the same class of problems.
Micro Problems
Narrowly specialized fields lack the resources to address these challenges.
The absence of genuine unification drags down research and development, yielding bugs that live at the lower levels while development proceeds
at higher ones. The lower level is controlled by operating-system developers, forcing everyone else to acquire extra tools, permissions, approvals, and agreements simply to glimpse the core of an NDA-shielded solution.
Modifying it demands even greater resources.
The absence of genuine unification drags down research and development, yielding bugs that live at the lower levels while development proceeds
at higher ones. The lower level is controlled by operating-system developers, forcing everyone else to acquire extra tools, permissions, approvals, and agreements simply to glimpse the core of an NDA-shielded solution.
Modifying it demands even greater resources.
A Golden Solution
to a Fragile Problem
to a Fragile Problem
A fundamental architectural problem cannot be fixed with budgets, resources, or more RAM. That only buys a costly, temporary effect.
Unification means permanently eliminating
the cost of stopgap fixes.
The transition period will bring a few quarters of rising overhead; after that, Korean-language support collapses to a basic linear format. The entire class of specialized Hangul IT solutions disappears.
The shift from the “king’s cubit” to the meter changed the world forever. A meter for Hangul will make IT businesses, research, and digital government transparent, predictable and efficient.
Unification means permanently eliminating
the cost of stopgap fixes.
The transition period will bring a few quarters of rising overhead; after that, Korean-language support collapses to a basic linear format. The entire class of specialized Hangul IT solutions disappears.
The shift from the “king’s cubit” to the meter changed the world forever. A meter for Hangul will make IT businesses, research, and digital government transparent, predictable and efficient.
Solution plan
Accepting Hangul mathematics
Obtaining and studying
Hangul mathematics practicality and prospectsgiven the complete lack of native toolsJamo('') based hangulwithout reference to the syllabic part
(Windows, Android, iOS/macOS, Linux)
Hangul mathematics practicality and prospectsgiven the complete lack of native toolsJamo('') based hangulwithout reference to the syllabic part
(Windows, Android, iOS/macOS, Linux)
Testing and verification
Creating native tools like HarfBuzz
(this method already works
in browsers and offers a solution
to rendering and gluing issues).
The only aspect that was an obstacle:
the "lookup tables" are disappearing.
The class is no longer needed.
Mathematics guarantees 100% accuracy.
(this method already works
in browsers and offers a solution
to rendering and gluing issues).
The only aspect that was an obstacle:
the "lookup tables" are disappearing.
The class is no longer needed.
Mathematics guarantees 100% accuracy.
Integration into applications and OS
Processing load is reduced significantly
after switching from loopup checks
and applying 11,200+ elements
to Hangul Mathematics (33 numeric tags)
or Jamo (67 graphemes) tools.
Expected reduction from 150+ times
to 333 times, depending on the quality, and complete elimination of mapping.
after switching from loopup checks
and applying 11,200+ elements
to Hangul Mathematics (33 numeric tags)
or Jamo (67 graphemes) tools.
Expected reduction from 150+ times
to 333 times, depending on the quality, and complete elimination of mapping.
Increased quality and accessibility
Transition of technologies and solutions focused on Korea to global standards.
In the foreseeable future, the expected quality of representation in the digital world is similar to that of the Vietnamese script.
A unified standard without the need for specialized solutions.
In the foreseeable future, the expected quality of representation in the digital world is similar to that of the Vietnamese script.
A unified standard without the need for specialized solutions.
Empirical Evidence
We have successfully built applications that decompose Korean syllables into individual letters using Hangul Mathematics Formulas and the Complete Hangul Map.
0 Unicode-based tools were used. 0 hardcoded patches (e.g., if "ㄼ" then set "ㄹ" & "ㅂ") were written. Every single letter is generated dynamically through its own index and mathematical logic, outputting a completely unified data structure:Data.At(Letter|1|2|3|4|5|index)
0 Unicode-based tools were used. 0 hardcoded patches (e.g., if "ㄼ" then set "ㄹ" & "ㅂ") were written. Every single letter is generated dynamically through its own index and mathematical logic, outputting a completely unified data structure:Data.At(Letter|1|2|3|4|5|index)
- Build Visual StudioCode: С++
UI: Win UI 3
Data format: TXT - Build Android StudioCode: Kotlin
UI: Android UI
Data format: JSON - Build XcodeCode: Swift
UI: Swift UI
Data format: Enum Static
Project completed
For inquiries and collaborations, please contact:
info@samsegi.com
*Full verification of builds and mathematical proofs is available by prior agreement, exclusively for key corporate stakeholders, government officials, academics,
and media representatives.
info@samsegi.com
*Full verification of builds and mathematical proofs is available by prior agreement, exclusively for key corporate stakeholders, government officials, academics,
and media representatives.
Q&A
Question:
Is the project a ready-made repository, tool, and product?
Answer:
The project is not a ready-made repository, tool, or product.
It is a solution to the engineering problem of Hangul.
Mathematics is the foundation of the entire IT sector,
which means that ready-made repositories, tools, and products can be created based on Hangul Mathematics.
It is a solution to the engineering problem of Hangul.
Mathematics is the foundation of the entire IT sector,
which means that ready-made repositories, tools, and products can be created based on Hangul Mathematics.
Question:
So why should I get involved before the project becomes a product?
Answer:
Hangul Mathematics is fundamental knowledge.
Discovering this knowledge was the goal of the SAMSEGI project.
Creating products is the task of corporations, specialists, and institutes.
Within the stated goals of restoring the logical foundation and engineering essence of Hangul, all questions are resolved.
Discovering this knowledge was the goal of the SAMSEGI project.
Creating products is the task of corporations, specialists, and institutes.
Within the stated goals of restoring the logical foundation and engineering essence of Hangul, all questions are resolved.
Gromov Arsenii
Russian software developer
creator of algorithmic word games for the Korean language
samsegiproject@gmail.com | samsegiproject@daum.net
creator of algorithmic word games for the Korean language
samsegiproject@gmail.com | samsegiproject@daum.net
The rights to the project are protected by copyright.