# nex-tagma

Standard reference implementation that consumes the Tagma coordinate space on top of neXus FIH storage

Author

Affiliation

SSCCS Foundation [](mailto:contact@ssccs.org)

[SSCCS Foundation](https://ssccs.org)

Published

July, 2026

Abstract

nex-tagma is the nexus-tagma hub, a standard reference implementation that bridges the Tagma three-axis coordinate space and the neXus FIH three-dimensional storage. It demonstrates that the O(1) direct addressing, collision-free uniqueness, axis decomposition, and proximity search properties of the Tagma syllabic coordinate system form an isomorphic mapping with the Fact-Inference-Hint three-dimensional cube. Every valid Hangul syllable becomes a first-class coordinate in FIH storage.

nex-tagma serves as a bridge and an experimental ground for neXus core refactoring. Design decisions and structural insights gained here flow directly into formalize FIH coordinate system. The rationale for refactoring the current hash-based multi-index storage model into a native 3D cube addressing scheme is supplied by the empirical data—latency benchmarks, collision properties, and axis slicing performance—generated at each evolutionary stage of nex-tagma.

Source

[Github](https://github.com/ssccsorg/nexus/tree/main/apps/nex-tagma)

Reference

[Nexus Apps](index.llms.md)

[Tagma Project](../../../projects/tagma)

Other Formats

[LLMs](https://docs.ssccs.org/projects/nexus/apps/tagma.llms.md)

## Identity

nex-tagma is a bridge that applies the three-axis coordinate system of Tagma to the FIH (Fact-Inference-Hint) three-dimensional storage structure of neXus. Design decisions and insights obtained here grow directly into the rationale for refactoring the nex core (Issue \#139 – formalize FIH coordinate system).

Identity flow across three layers:

![](tagma_files/figure-html/fig-identity-output-1.svg)

Figure 1: Identity flow: tagma-core provides the coordinate space, nex-tagma connects it to FIH storage, and insights feed back into nex refactoring

The linguistic equation is no coincidence: *co-ordinare* (to arrange together) = *syn-tagma* (that which is arranged together) declares that the Tagma project is the necessary realization of the Coord mechanism.

## Three-Dimensional Structure Mapping

The correspondence of the three Tagma axes to the three FIH dimensions is structural, not metaphorical:

| Tagma Axis         | FIH Dimension | Question              |
|--------------------|---------------|-----------------------|
| initial (choseong) | Fact          | What fact is it?      |
| medial (jungseong) | Inference     | What inference is it? |
| final (jongseong)  | Hint          | What hint is it?      |

Every valid (F, I, H) combination is encoded as one Tagma coordinate, mapped directly into an O(1) slot of the three-dimensional cube. This is structurally superior to the existing hash-based multi-index approach (by_fact ∩ by_origin ∩ by_semantic → O(N)), because the coordinate space guarantees constant-time addressing without index maintenance.

The mapping uses the entire Hangul syllabic space: 19 onsets × 21 nuclei × 28 codas = 11,172 addressable coordinates. Each coordinate is a native Unicode scalar value, not an opaque hash, and the axis decomposition property is embedded in the encoding itself.

## Property Transfer

The structural properties of the Tagma coordinate space transfer directly to FIH storage:

| Property | Tagma Coordinate | FIH Storage Application |
|----|----|----|
| O(1) direct addressing | `C(i,m,f) = BASE + 588i + 28m + f` | `storage[F][I][H]` |
| Collision-free | coordinate = uniqueness guarantee | same (F,I,H) combination always the same slot |
| Axis decomposition | `to_axes()` → individual fields | extract Fact only, extract Inference only, etc. |
| Proximity search | `hamming_distance()` | similar fact/inference/hint O(1) exploration |
| Built-in validation | valid coordinate range embedded in type system | invalid FIH combinations structurally impossible |

All fact/inference/hint combinations map to a single three-dimensional cube, and the cube’s O(1) access + axis decomposition + proximity search connect directly to the detection tasks of the OODA scheduler (gap identification, contradiction detection, state-change sensing).

![](tagma_files/figure-html/fig-property-output-1.svg)

Figure 2: Property transfer: each Tagma structural property maps isomorphically to an FIH storage operation

## Evolution Stages

nex-tagma evolves in stages, with each stage building on the previous and simultaneously feeding insights back to the nex core:

| Stage | Content | Status |
|----|----|----|
| 1 | Independent PoC – own `coord.rs`, SHA256 comparison benchmarks | Complete (#150) |
| 2 | tagma-core dependency – reuse Coord type, remove own coord.rs | Planned |
| 3 | nex storage integration – consume Tagma coordinates on FIH storage | Planned |
| 4 | 3D cube storage structure experiments – axis slicing, proximity search, OODA integration | Planned |
| 5 | Insight feedback → nex refactoring (#139 FIH coordinate system formalization) | Planned |

Stage 1 (complete) established the baseline: it proved that for a single syllable, a Tagma coordinate is 227× faster than SHA256 and provides native axis decomposition and collision-free properties. Stage 2 depends directly on `tagma-core`, eliminating code duplication. Stage 3 connects the coordinate model to actual FIH storage. Stage 4 experiments with cube-level operations. Stage 5 closes the loop: insights from all prior stages are formalized into the nex FIH coordinate system specification.