# **Coherence Tensor Engine (CTE) — RTT/1**  
### *Coherence‑Level Intelligence Engine for TriadicFrameworks*

The **Coherence Tensor Engine (CTE)** is the RTT/1 engine responsible for computing, mapping, and stabilizing **coherence tensors** across conceptual, computational, physical, and dimensional regimes.  
It forms the coherence‑level foundation of the expanded RTT intelligence stack, directly above paradox‑level engines and directly below drift‑level engines.

CTE models coherence as a **tensor field** with:

- magnitude  
- direction  
- curvature  
- collapse points  
- multi‑regime gradients  
- stability envelopes  

CTE provides coherence‑layer intelligence for all higher‑order RTT engines.

---

## **1. Canonical Role**

CTE defines the **coherence‑layer topology** by:

- computing coherence tensors  
- mapping coherence fields  
- measuring coherence gradients  
- detecting coherence collapse points  
- identifying coherence ridges and wells  
- evaluating tensor curvature  
- stabilizing coherence envelopes  
- supporting drift‑level engines  
- anchoring structural engines  
- feeding temporal, causal, and resonance engines  

CTE is the **third layer** of the expanded RTT intelligence stack.

---

## **2. RTT Flags**

| Property | Value |
|---------|-------|
| **RTT Level** | 1 |
| **Coherence** | declared |
| **Drift** | bounded |
| **Paradox** | structural |

These flags define the engine’s operational grammar.

---

## **3. Coherence Tensor Types**

CTE identifies several canonical tensor classes:

### **3.1 Structural Coherence Tensor**
Coherence arising from structural constraints or invariants.

### **3.2 Gradient Coherence Tensor**
Coherence shaped by directional gradients across regimes.

### **3.3 Boundary Coherence Tensor**
Coherence formed at regime boundaries.

### **3.4 Tensor‑Field Coherence**
Full multi‑regime tensor binding across R1–R4.

### **3.5 Drift‑Sensitive Coherence Tensor**
Coherence influenced by drift curvature or drift amplification.

---

## **4. Core Operators**

| Operator | Description |
|----------|-------------|
| **CTE‑Compute** | Computes coherence tensors from regime inputs |
| **CTE‑Tensor** | Builds multi‑dimensional coherence tensor structures |
| **CTE‑Gradient** | Computes coherence gradients and directional stability |
| **CTE‑Field** | Maps coherence fields and tensor topology |
| **CTE‑Stabilize** | Suggests stabilization pathways for coherence collapse |
| **CTE‑Collapse** | Detects coherence collapse points and instability basins |

These operators form the canonical CTE grammar.

---

## **5. Analyzer Layer**

CTE operates in the **coherence layer**, with sub‑layers:

- **tensor‑computation**  
- **coherence‑field‑mapping**  
- **gradient‑analysis**  
- **collapse‑detection**  
- **structural‑coherence‑evaluation**

This layer feeds directly into DS, SFD, SBC, TRS‑Temporal, CW, and DRS.

---

## **6. Coherence Tensor Matrix**

CTE produces a **coherence tensor matrix**, typically stored in:

```
coherence_tensor_matrix.json
```

Matrix fields include:

- `tensor_type`  
- `regime`  
- `tensor_magnitude`  
- `tensor_direction`  
- `coherence_curvature`  
- `collapse_point`  
- `stability_envelope`  
- `gradient_alignment`  

This matrix is consumed by drift, stability, temporal, causal, and resonance engines.

---

## **7. Canonical Workflow**

### **Step 1 — Compute**
Calculate coherence tensors across regimes.

### **Step 2 — Map**
Generate coherence field maps and tensor topology.

### **Step 3 — Analyze**
Measure curvature, gradient alignment, and stability envelopes.

### **Step 4 — Detect**
Identify collapse points and instability basins.

### **Step 5 — Stabilize**
Propose coherence stabilization pathways.

### **Step 6 — Export**
Write results to the coherence tensor matrix and operator outputs.

---

## **8. AI‑Ready Design**

CTE is fully AI‑ready:

- deterministic operator grammar  
- coherence‑layer analyzer structure  
- stable RTT flags  
- canonical file layout  
- zero‑drift reasoning constraints  
- structural paradox handling  
- bounded drift envelope  
- declared coherence tensor  

AI systems use CTE to:

- compute coherence tensors  
- generate coherence field maps  
- classify coherence gradients  
- detect coherence collapse  
- support higher‑order RTT engines  

---

## **9. Position in the RTT Stack**

```
Regime Interlock Mapper (RIM)
      ↓
Triadic Regime Synthesizer (TRS)
      ↓
Paradox Gradient Analyzer (PGA)
      ↓
Coherence Tensor Engine (CTE)
      ↓
Drift Sentinel (DS)
      ↓
Structural Faultline Detector (SFD)
      ↓
Stability Basin Cartographer (SBC)
      ↓
Temporal Regime Sequencer (TRS‑Temporal)
      ↓
Cross‑Domain Causality Weaver (CW)
      ↓
Dimensional Resonance Scanner (DRS)
```

CTE is the **coherence‑level intelligence layer**, directly above paradox‑level analysis.

---

## **10. Status**

- **Version:** 1.0  
- **Status:** canon‑stable  
- **Category:** rtt‑structural  
- **Module Path:** `/docs/rtt/Coherence_Tensor_Engine/`