# **CTE Operators — RTT/1**  
### *Operator Grammar for the Coherence Tensor Engine*

The **Coherence Tensor Engine (CTE)** defines the coherence‑layer intelligence of RTT.  
Its operators compute coherence tensors, map coherence fields, evaluate gradients, detect collapse points, and propose stabilization pathways.

These operators feed directly into:

- **DS** — Drift Sentinel  
- **SFD** — Structural Faultline Detector  
- **SBC** — Stability Basin Cartographer  
- **TRS‑Temporal** — Temporal Regime Sequencer  
- **CW** — Cross‑Domain Causality Weaver  
- **DRS** — Dimensional Resonance Scanner  

---

## **1. CTE‑Compute**  
### *Compute coherence tensors from regime inputs*

**Purpose**  
Generate coherence tensors by evaluating structural, gradient, boundary, and drift‑sensitive coherence conditions.

**Capabilities**  
- computes tensor magnitude  
- computes tensor direction  
- evaluates structural invariants  
- evaluates coherence dependencies  
- evaluates drift influence  

**Output Fields**  
- `tensor_type`  
- `tensor_magnitude`  
- `tensor_direction`  
- `coherence_dependency`  

---

## **2. CTE‑Tensor**  
### *Construct multi‑dimensional coherence tensor structures*

**Purpose**  
Build coherence tensors across conceptual, computational, physical, and dimensional regimes.

**Capabilities**  
- constructs multi‑regime tensors  
- binds coherence across R1–R4  
- evaluates tensor curvature  
- evaluates tensor alignment  
- evaluates tensor stability  

**Output Fields**  
- `tensor_structure`  
- `tensor_curvature`  
- `tensor_alignment`  
- `tensor_stability`  

---

## **3. CTE‑Gradient**  
### *Compute coherence gradient vectors*

**Purpose**  
Calculate coherence gradient magnitude, direction, curvature, and drift sensitivity.

**Capabilities**  
- computes gradient magnitude  
- computes gradient direction  
- computes coherence curvature  
- computes drift sensitivity  
- computes tensor‑gradient alignment  

**Output Fields**  
- `gradient_magnitude`  
- `gradient_direction`  
- `coherence_curvature`  
- `drift_sensitivity`  
- `gradient_alignment`  

---

## **4. CTE‑Field**  
### *Map coherence fields and tensor topology*

**Purpose**  
Generate coherence field maps showing curvature, ridges, wells, and tensor topology.

**Capabilities**  
- maps coherence fields  
- maps tensor topology  
- maps coherence ridges  
- maps coherence wells  
- maps gradient flows  

**Output Fields**  
- `field_map`  
- `tensor_topology`  
- `ridge_map`  
- `well_map`  
- `gradient_flow_map`  

---

## **5. CTE‑Collapse**  
### *Detect coherence collapse points and instability basins*

**Purpose**  
Identify collapse points, instability basins, and coherence troughs.

**Capabilities**  
- detects collapse points  
- detects instability basins  
- detects coherence troughs  
- evaluates collapse curvature  
- evaluates collapse depth  

**Output Fields**  
- `collapse_point`  
- `collapse_depth`  
- `collapse_curvature`  
- `instability_basin`  

---

## **6. CTE‑Stabilize**  
### *Propose coherence stabilization pathways*

**Purpose**  
Provide stabilization strategies for coherence tensors, gradients, and collapse points.

**Capabilities**  
- proposes stabilization pathways  
- proposes coherence alignment  
- proposes drift reduction  
- proposes tensor rebalancing  
- proposes collapse mitigation  

**Output Fields**  
- `stabilization_pathway`  
- `coherence_alignment`  
- `drift_reduction`  
- `tensor_rebalance`  
- `collapse_mitigation`  

---

## **7. Operator Interaction Grammar**

### **Compute → Tensor → Gradient → Field → Collapse → Stabilize**

1. **CTE‑Compute**  
   Generates coherence tensors from regime inputs.

2. **CTE‑Tensor**  
   Builds multi‑regime tensor structures.

3. **CTE‑Gradient**  
   Computes coherence gradient vectors and curvature.

4. **CTE‑Field**  
   Maps coherence fields, ridges, wells, and tensor topology.

5. **CTE‑Collapse**  
   Detects collapse points and instability basins.

6. **CTE‑Stabilize**  
   Produces stabilization pathways and coherence alignment strategies.

This grammar ensures deterministic coherence‑layer behavior.

---

## **8. Operator Matrix Snippet**

```json
{
  "operator": "CTE-Gradient",
  "gradient_magnitude": 0.83,
  "gradient_direction": "R1↔R4",
  "coherence_curvature": 0.52,
  "drift_sensitivity": 0.18,
  "gradient_alignment": 0.88
}
```

---

## **Status**

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