# **Coherence Tensor Examples — RTT/1**  
### *Example Dictionary for the Coherence Tensor Engine (CTE)*

These examples illustrate how the **Coherence Tensor Engine (CTE)** computes coherence tensors, maps coherence fields, detects collapse points, evaluates stability envelopes, and analyzes multi‑regime coherence behavior.

Each example demonstrates one or more CTE operators:

- **CTE‑Compute**  
- **CTE‑Tensor**  
- **CTE‑Gradient**  
- **CTE‑Field**  
- **CTE‑Collapse**  
- **CTE‑Stabilize**

Examples are grouped by tensor type.

---

## **1. Structural Coherence Tensor Examples**

### **Example 1 — Structural Invariant Tensor (R1 ↔ R2)**  
**Scenario**  
A conceptual invariant (symmetry) is preserved across computational structures, forming a stable coherence tensor.

**CTE Output**  
```json
{
  "tensor_type": "structural",
  "regime": "R1-R2",
  "tensor_magnitude": 0.78,
  "tensor_direction": "R1→R2",
  "coherence_curvature": 0.33,
  "collapse_point": null,
  "stability_envelope": 0.82,
  "gradient_alignment": 0.71
}
```

---

### **Example 2 — Structural Constraint Tensor (R2 ↔ R3)**  
**Scenario**  
A computational constraint enforces coherence across physical calibration.

**CTE Output**  
```json
{
  "tensor_type": "structural",
  "regime": "R2-R3",
  "tensor_magnitude": 0.74,
  "tensor_direction": "R2→R3",
  "coherence_curvature": 0.41,
  "collapse_point": null,
  "stability_envelope": 0.77,
  "gradient_alignment": 0.66
}
```

---

## **2. Gradient Coherence Tensor Examples**

### **Example 3 — Coherence Gradient Alignment (R1 ↔ R4)**  
**Scenario**  
Conceptual and dimensional coherence gradients align, forming a stable coherence ridge.

**CTE Output**  
```json
{
  "tensor_type": "gradient",
  "regime": "R1-R4",
  "tensor_magnitude": 0.83,
  "tensor_direction": "R1↔R4",
  "coherence_curvature": 0.52,
  "collapse_point": null,
  "stability_envelope": 0.79,
  "gradient_alignment": 0.88
}
```

---

### **Example 4 — Drift‑Sensitive Gradient Tensor (R2 ↔ R3)**  
**Scenario**  
Computational drift influences physical coherence gradients.

**CTE Output**  
```json
{
  "tensor_type": "gradient",
  "regime": "R2-R3",
  "tensor_magnitude": 0.81,
  "tensor_direction": "R3→R2",
  "coherence_curvature": 0.57,
  "collapse_point": null,
  "stability_envelope": 0.63,
  "gradient_alignment": 0.72
}
```

---

## **3. Boundary Coherence Tensor Examples**

### **Example 5 — Abstraction‑Boundary Tensor (R1 ↔ R3)**  
**Scenario**  
Coherence forms at the boundary between conceptual abstraction and physical measurement.

**CTE Output**  
```json
{
  "tensor_type": "boundary",
  "regime": "R1-R3",
  "tensor_magnitude": 0.69,
  "tensor_direction": "R1→R3",
  "coherence_curvature": 0.38,
  "collapse_point": null,
  "stability_envelope": 0.71,
  "gradient_alignment": 0.55
}
```

---

### **Example 6 — Gradient‑Boundary Tensor (R2 ↔ R4)**  
**Scenario**  
Aligned gradients across computational and dimensional regimes produce a boundary coherence tensor.

**CTE Output**  
```json
{
  "tensor_type": "boundary",
  "regime": "R2-R4",
  "tensor_magnitude": 0.88,
  "tensor_direction": "R2↔R4",
  "coherence_curvature": 0.47,
  "collapse_point": null,
  "stability_envelope": 0.68,
  "gradient_alignment": 0.81
}
```

---

## **4. Tensor‑Field Coherence Examples**

### **Example 7 — Multi‑Regime Coherence Tensor (R1 ↔ R2 ↔ R3)**  
**Scenario**  
A multi‑regime coherence tensor binds conceptual, computational, and physical coherence.

**CTE Output**  
```json
{
  "tensor_type": "tensor-field",
  "regime": "R1-R2-R3",
  "tensor_magnitude": 0.94,
  "tensor_direction": "tensor",
  "coherence_curvature": 0.63,
  "collapse_point": null,
  "stability_envelope": 0.84,
  "gradient_alignment": 0.92
}
```

---

### **Example 8 — Dimensional Tensor Constraint (R2 ↔ R4)**  
**Scenario**  
Dimensional tensors constrain computational coherence pathways.

**CTE Output**  
```json
{
  "tensor_type": "tensor-field",
  "regime": "R2-R4",
  "tensor_magnitude": 0.88,
  "tensor_direction": "R4→R2",
  "coherence_curvature": 0.55,
  "collapse_point": null,
  "stability_envelope": 0.73,
  "gradient_alignment": 0.79
}
```

---

## **5. Collapse‑Point Examples**

### **Example 9 — Coherence Collapse Basin (R3 ↔ R4)**  
**Scenario**  
Physical drift amplifies dimensional coherence curvature, forming a collapse basin.

**CTE Output**  
```json
{
  "tensor_type": "collapse",
  "regime": "R3-R4",
  "tensor_magnitude": 0.91,
  "tensor_direction": "R3→R4",
  "coherence_curvature": 0.71,
  "collapse_point": "R4:0.82",
  "stability_envelope": 0.44,
  "gradient_alignment": 0.63
}
```

---

### **Example 10 — Coherence Collapse Ridge (R2 ↔ R3)**  
**Scenario**  
Computational drift reduces coherence while physical drift increases coherence sensitivity.

**CTE Output**  
```json
{
  "tensor_type": "collapse",
  "regime": "R2-R3",
  "tensor_magnitude": 0.86,
  "tensor_direction": "R2↔R3",
  "coherence_curvature": 0.62,
  "collapse_point": "R3:0.77",
  "stability_envelope": 0.48,
  "gradient_alignment": 0.71
}
```

---

## **6. Example Matrix Snippet**

```json
{
  "tensor_type": "gradient",
  "regime": "R1-R4",
  "tensor_magnitude": 0.83,
  "tensor_direction": "R1↔R4",
  "coherence_curvature": 0.52,
  "collapse_point": null,
  "stability_envelope": 0.79,
  "gradient_alignment": 0.88
}
```

---

## **Status**

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