nex-tagma
Standard reference implementation that consumes the Tagma coordinate space on top of neXus FIH storage
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.
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:
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).
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.