# Layer 2, Operative Trilateral Composition

> **Status:** Empirically complete · 2,285 / 2,288 trilaterals graded (99.87%) · 100% native composition
> **Date:** 2026-05-13/14
> **Computational implementation:** `Juthoor-Linguistic-Genealogy/`
> **Methodology spec:** [`Juthoor-Linguistic-Genealogy/docs/LAYER_2_V2_METHODOLOGY.md`](../../Juthoor-Linguistic-Genealogy/docs/LAYER_2_V2_METHODOLOGY.md)
> **Interactive dashboard:** [`Juthoor-Linguistic-Genealogy/outputs/audits/layer_2_dashboard_v2.html`](../../Juthoor-Linguistic-Genealogy/outputs/audits/layer_2_dashboard_v2.html)

## The finding

Every Arabic trilateral root in Jabal's lexicon is interpretable as:

> **(binary nucleus) does X to (third letter's charge as material)**

Where X is one of **12 relationship modes** in a finite operative grammar. The framing is empirical, reproducible, and 100% of native trilaterals find a coherent mode without forcing.

This closes the bottom-up part of the genealogy: **letters → binaries → trilaterals** is now grounded.

## The reframe (v1 → v2)

| Frame | Composition rule | Result |
|-------|------------------|--------|
| **v1** (additive) | binary + L3 = compound, L3 modifies the binary | ~95% fit, 10 "doesn't fit" cases per high-freq letter |
| **v2** (operative) | binary is the *agent*; L3 is the *material* acted upon | **100% native**, the failures dissolved |

The v1 failures were a category error. قصر ("preventing spread") wasn't broken; the question was wrong. Once reframed as "قص-cutting-precision BLOCKS the flow (ر)," the root is perfectly coherent.

## The 12-mode taxonomy

The verb-grammar of binary-on-L3 relationships, grouped by stance:

### POSITIVE (binary co-acts with L3), 55.2% of all roots

| Mode | Meaning | Canonical example |
|------|---------|-------------------|
| **CARRY** | binary carries L3-material forward/out | ورد: و-bind carries د-fixity → arriving |
| **HOLD** | binary contains/encloses L3-material | بلد: بل-wet holds د-fixity → ground, settled-place |
| **RELEASE** | binary lets L3-material burst out | فتح: فت-loose releases ح-warmth → opening |
| **PROJECT** | binary extends L3 outward as feature | حدد: ح-edge projects د-fixity → boundary |
| **INTENSIFY** | doubled or amplified L3 | جمد: ج-gather amplifies د-fixity → freezing solid |

### NEGATIVE (binary opposes L3), 11.5%

| Mode | Meaning | Canonical example |
|------|---------|-------------------|
| **BLOCK** | binary stops/seals/walls off L3-material | سدد: س-flow blocked → sealing, stopping |
| **DRAIN** | binary gradually depletes L3-material | فقد: فق-void drains د-fixity → losing |

### TRANSFORM (binary reshapes L3), 33.3%

| Mode | Meaning | Canonical example |
|------|---------|-------------------|
| **CHANNEL** | binary directs/shapes the L3's path | جرى: جر-pull channels ى-flow → running |
| **OPERATE** | binary modifies L3 via squeeze/fold/cut | حسم: حس-feel operates on م-mass → cutting decisively |
| **MIX** | blends the binary with L3 | روب: رو-going mixes ب-attach → curdled milk |
| **REVERT** | circles back / oscillates L3 | ردد: ر-flow reverts د-fixity → returning |

### EXCEPTION

| Mode | Meaning |
|------|---------|
| **LOANWORD** | non-native composition (1/2,285 in current dataset) |

## Global distribution

| Mode | Count | % |
|------|------:|---:|
| OPERATE | 558 | 24.4% |
| HOLD | 373 | 16.3% |
| PROJECT | 268 | 11.7% |
| INTENSIFY | 267 | 11.7% |
| RELEASE | 208 | 9.1% |
| CARRY | 146 | 6.4% |
| BLOCK | 132 | 5.8% |
| DRAIN | 130 | 5.7% |
| CHANNEL | 122 | 5.3% |
| REVERT | 66 | 2.9% |
| MIX | 14 | 0.6% |
| LOANWORD | 1 | 0.0% |

## Structural-signature tests (predicted patterns confirmed)

| Test | Prediction | Observed |
|------|-----------|---------:|
| Doubled-final roots (XYY, e.g., بدد · ردد · جدد) | INTENSIFY+OPERATE dominate | **66.9%** of 405 roots |
| Redoubled XY-XY roots (e.g., دردر · جمجم) | OPERATE+INTENSIFY dominate | **66.9%** of 251 roots |
| Letters with flow charge (ر · ل · ن · ع) | Skew positive (CARRY · CHANNEL · PROJECT · RELEASE) | Confirmed |
| Letters with mass charge (د · م · ق · ك · ص) | OPERATE + HOLD dominate | Confirmed |

## Relation to the vault

This vault contains the upstream theoretical inputs that made Layer 2 v2 possible:

- **Layer 0** ([`consensus-letter-charges.md`](../03-scholar-extracts/consensus-letter-charges.md)), 28-letter dual-face charges; the v2 dataset uses exactly these charges as the L3-material readings.
- **Layer 1** ([`jabal-letters.html`](../03-scholar-extracts/jabal-letters.html)), 453 binary nuclei tested under the unified word-evidence test; v2 inherits the validated binary readings.
- **Architecture spec** ([`lv1-architecture.md`](lv1-architecture.md)), predicted >60% trilateral prediction accuracy for Layer 2. The operative reframe achieved 100% interpretive coverage (a different target than predictive accuracy, see Limits below).

## Where this lives in the codebase

```
Juthoor-Linguistic-Genealogy/
├── docs/LAYER_2_V2_METHODOLOGY.md           ← full methodology (9 sections)
├── scripts/layer_2/
│   ├── README.md                            ← batch-script guide
│   ├── __manifest_v2.py                     ← schema, L3_CHARGES table, append_results()
│   ├── batch_<letter>_v2.py × 13            ← per-letter verdict files
│   ├── batch_combined_*_v2.py × 2           ← combined low-frequency batches
│   ├── build_dashboard_v2.py                ← dashboard generator
│   ├── sample_for_irr.py                    ← stratified IRR sampler
│   └── compute_irr.py                       ← Cohen's κ + confusion matrix
└── outputs/audits/
    ├── layer_2_results_v2.jsonl             ← 2,285 verdicts (one JSON per line)
    ├── layer_2_manifest_v2.json             ← per-batch progress tracker
    └── layer_2_dashboard_v2.html            ← 316 KB interactive dashboard
```

## Coverage, why 453 / 507 nuclei, not 784?

Arabic has 28 letters → 28² = 784 mathematically possible ordered binary pairs. Jabal's lexicon attests only ~453 nuclei; the trilateral decomposition shows 507 unique binaries appearing as L1+L2. Where did the other 277 go?

**Answer:** they're filtered, not missing. Full decomposition in [`Juthoor-Linguistic-Genealogy/outputs/audits/layer_2_coverage_gap.md`](../../Juthoor-Linguistic-Genealogy/outputs/audits/layer_2_coverage_gap.md) (auto-generated):

| Filter | Pairs removed | Reason |
|--------|--------------:|--------|
| alif-initial (ا as L1) | 28 | ا is a vowel marker, cannot begin a root |
| identical XX | 25 | Obligatory Contour Principle, repeated consonant blocked |
| same-articulator-class | 107 | Soft OCP, articulator hygiene |
| **Genuine lexical gaps** | **155** | **Phonologically allowed but unused by Arabic** |

Of 277 missing pairs, **160 (58%) are phonotactically blocked** and only **155 (20% of all 784 possibilities)** are true lexical gaps. The 100% native-composition result is honestly bounded: every trilateral that *exists* in Arabic gets a coherent operative reading. Whether the model can predict charges for the 155 lexical-gap binaries is the natural next test.

## Limits & open questions

- **Interpretive, not generative.** Given an arbitrary L1·L2·L3, the model does not yet *predict* the mode; the rater reads the actual root meaning and chooses the operative reading that fits. A future classifier could test mode-from-charges predictability, and the 155 lexical-gap pairs above are the natural held-out set.
- **Single-rater dataset.** All 2,285 verdicts come from one rater (Opus). Inter-rater κ checking tooling is in place (`sample_for_irr.py`, `compute_irr.py`) but the κ has not yet been computed against a second rater.
- **Loanwords undercounted.** Only 1/2,285 was tagged LOANWORD. Many candidates (e.g., فردوس, سندس, سنبل) are arguably native compositions under the operative model. A focused audit of suspected loanwords is warranted.
- **Quadrilateral and quintilateral roots.** The schema generalises (binary-on-L3, then ternary-on-L4) but has not been formalised. Roots like قنطر, زنجبيل, طمأن are sketched as "X holds/operates on then Y" in the reasons but lack a dedicated framework.

## Citation

```
Temessek, Y. (2026). Operative Composition of Arabic Trilateral Roots.
Layer 2 v2, 2,285 trilaterals graded under 12-mode operative grammar.
The Arabic Tongue (nature-genome-application) + Juthoor-Linguistic-Genealogy.
```