# **Coherence Tensor Profiles — RTT/1**  
### *Profile Dictionary for the Coherence Tensor Engine (CTE)*

Coherence tensor profiles define the **canonical shapes, behaviors, stability envelopes, and collapse geometries** of coherence tensors across conceptual, computational, physical, and dimensional regimes.

These profiles are used by:

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

Each profile includes:

- **definition**  
- **tensor signature**  
- **field behavior**  
- **gradient behavior**  
- **collapse geometry**  
- **stability envelope**  
- **canonical CTE output pattern**

---

## **1. Structural Coherence Profiles**

### **Profile: Structural Invariant Tensor**
**Definition**  
Coherence arising from structural invariants (symmetry, conservation, monotonicity).

**Tensor Signature**
- medium‑high magnitude  
- stable direction  
- low curvature  

**Field Behavior**
- narrow field  
- shallow coherence ridge  

**Gradient Behavior**
- low drift sensitivity  
- high alignment  

**Collapse Geometry**
- no collapse point  
- rigid boundary  

**Stability Envelope**
- high stability  

---

### **Profile: Structural Constraint Tensor**
**Definition**  
Coherence enforced by computational or physical constraints.

**Tensor Signature**
- medium magnitude  
- constraint‑aligned direction  
- medium curvature  

**Field Behavior**
- moderate field width  
- constraint ridge  

**Gradient Behavior**
- medium drift sensitivity  

**Collapse Geometry**
- shallow collapse basin  

**Stability Envelope**
- medium‑high stability  

---

## **2. Gradient Coherence Profiles**

### **Profile: Coherence Gradient Alignment**
**Definition**  
Coherence gradients across regimes align, forming a coherence ridge.

**Tensor Signature**
- high magnitude  
- bidirectional vector  
- medium curvature  

**Field Behavior**
- wide field  
- ridge formation  

**Gradient Behavior**
- high alignment  
- medium drift sensitivity  

**Collapse Geometry**
- no collapse point  

**Stability Envelope**
- high stability  

---

### **Profile: Drift‑Sensitive Coherence Gradient**
**Definition**  
Drift curvature influences coherence gradients.

**Tensor Signature**
- medium‑high magnitude  
- drift‑aligned direction  
- high curvature  

**Field Behavior**
- medium‑wide field  
- drift ridge  

**Gradient Behavior**
- high drift sensitivity  

**Collapse Geometry**
- medium collapse basin  

**Stability Envelope**
- medium stability  

---

## **3. Boundary Coherence Profiles**

### **Profile: Abstraction‑Boundary Tensor**
**Definition**  
Coherence forms at the boundary between conceptual abstraction and physical measurement.

**Tensor Signature**
- medium magnitude  
- abstraction → measurement direction  
- medium curvature  

**Field Behavior**
- narrow field  
- boundary ridge  

**Gradient Behavior**
- medium alignment  

**Collapse Geometry**
- shallow basin  

**Stability Envelope**
- medium‑high stability  

---

### **Profile: Gradient‑Boundary Tensor**
**Definition**  
Aligned gradients across regimes produce boundary coherence.

**Tensor Signature**
- high magnitude  
- aligned direction  
- medium curvature  

**Field Behavior**
- wide field  
- alignment ridge  

**Gradient Behavior**
- high alignment  

**Collapse Geometry**
- medium‑deep basin  

**Stability Envelope**
- medium stability  

---

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

### **Profile: Multi‑Regime Coherence Tensor**
**Definition**  
A multi‑regime tensor binds coherence across R1–R3 or R1–R4.

**Tensor Signature**
- very high magnitude  
- tensor direction  
- high curvature  

**Field Behavior**
- wide field  
- tensor topology  

**Gradient Behavior**
- high alignment  
- medium drift sensitivity  

**Collapse Geometry**
- deep basin  

**Stability Envelope**
- high stability  

---

### **Profile: Dimensional Tensor Constraint**
**Definition**  
Dimensional tensors constrain computational coherence pathways.

**Tensor Signature**
- high magnitude  
- dimensional → computational direction  
- medium‑high curvature  

**Field Behavior**
- medium‑wide field  
- tensor trough  

**Gradient Behavior**
- medium alignment  

**Collapse Geometry**
- medium‑deep basin  

**Stability Envelope**
- medium‑high stability  

---

## **5. Collapse‑Point Coherence Profiles**

### **Profile: Coherence Collapse Basin**
**Definition**  
Drift amplification creates a coherence collapse basin.

**Tensor Signature**
- very high magnitude  
- drift‑aligned direction  
- high curvature  

**Field Behavior**
- wide field  
- collapse basin  

**Gradient Behavior**
- high drift sensitivity  

**Collapse Geometry**
- deep collapse basin  
- instability ridge  

**Stability Envelope**
- low stability  

---

### **Profile: Coherence Collapse Ridge**
**Definition**  
Coherence decreases in one regime while sensitivity increases in another.

**Tensor Signature**
- medium‑high magnitude  
- inversion direction  
- medium‑high curvature  

**Field Behavior**
- medium field  
- collapse ridge  

**Gradient Behavior**
- medium drift sensitivity  

**Collapse Geometry**
- medium‑deep basin  

**Stability Envelope**
- medium stability  

---

## **6. Canonical CTE Output Pattern**

```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/`