What question did this study set out to answer?

The aim is to define Tagma as a content-addressable structural primitive within Unicode for computing.

July 12, 20260 citationsOpen Access

Tagma: Content‑Addressable Structural Primitive Defined by the Hangul Syllabic Space

Key Points

The aim is to define Tagma as a content-addressable structural primitive within Unicode for computing.
Introduced the concept of Tagma and its relationship with Unicode and Hangul syllable blocks.
Described a RISC-V implementation that utilizes the Tagma primitive for encoding.
Explained the role of a software interface, known as the Projector layer, for translating coordinates.
Demonstrated that Tagma allows for direct identity derivation without the need for hash functions.
Showed that each Hangul syllable can function as both a 1-D address and a 3-D coordinate, enhancing computation efficiency.
Highlighted the reduced overhead in computing when utilizing structural properties instead of traditional hashing.

Abstract

Tagma is a structural identity primitive: the realization that a contiguous 16-bit Unicode block allocated to a three-axis writing system provides a collision-free, hash-less, structurally addressable coordinate space for computing. Computing standards are language-neutral and culture-neutral universal assets. Arabic numerals (0–9) belong to no single nation yet underpin every numerical operation in every instruction set. Unicode follows the same principle: it is an international standard that assigns each script a fixed address in a shared encoding space, treating all writing systems equally. Within this shared space, the Hangul syllable block (U+AC00–U+D7AF) occupies a contiguous 16-bit segment whose closed-form composition formula embeds three independent structural axes into every code point — a mathematical property absent from every other script on the Basic Multilingual Plane. This property elevates a cultural asset into a general-purpose computing primitive. Every content-addressable system in computing today generates identifiers through a hash function. This indirection layer imposes a predictable cost: gate area for the hash logic, cycle latency for computation, and storage overhead for the resulting identifier. Hash functions are a general solution but not the only one. When the identifier space has known structural properties, those properties can replace the hash function entirely. Any 16-bit value in this space is simultaneously a 1-D address (Unicode code point) and a 3-D coordinate (initial, medial, final), expressible as a Hangul syllable for debugging. One specification of this primitive is a gate-level combinatorial decoder that derives identity directly from value composition; a RISC-V implementation via the XIF coprocessor interface is provided as a reference. A coordinate can be displayed as a Hangul syllable for debugging, decomposed into its three axis values for assembly, or processed as a raw 16-bit value by the hardware. The Projector layer that performs these translations is a software interface and is not part of the decoder specification.

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