# **Regime Entanglement Cases — RTT/1**  
### *High‑Coupling Interlock Cases for the Regime Interlock Mapper (RIM)*

Entanglement interlocks represent the **strongest form of regime interaction**.  
Unlike structural or boundary interlocks, entanglement cases exhibit **bidirectional influence**, **non‑decomposability**, and **coherence‑linked coupling** across regimes.

This document provides canonical RTT/1 entanglement cases used by:

- **RIM‑Entangle**  
- **RIM‑Detect**  
- **RIM‑Interlock**  
- **RIM‑Resolve**  
- **TRS (Triadic Regime Synthesizer)**  
- **PGA (Paradox Gradient Analyzer)**  
- **CTE (Coherence Tensor Engine)**  

---

## **1. Conceptual ↔ Computational Entanglement (R1 ↔ R2)**  
### **Case: Mutual Model Feedback Loop**

**Description**  
Conceptual assumptions shape computational models; computational outputs reshape conceptual assumptions.

**Characteristics**
- bidirectional influence  
- high coherence dependency  
- medium stability  
- feedback‑driven drift sensitivity  

**RIM Output**
```json
{
  "regime_a": "R1",
  "regime_b": "R2",
  "interlock_type": "entanglement",
  "boundary_condition": "mutual-feedback",
  "interlock_strength": 0.91,
  "entanglement_score": 0.88,
  "stability_rating": 0.52
}
```

---

## **2. Physical ↔ Dimensional Entanglement (R3 ↔ R4)**  
### **Case: Resonance‑Coherence Coupling**

**Description**  
Physical resonance patterns influence dimensional coherence; dimensional coherence alters physical resonance.

**Characteristics**
- resonance amplification  
- coherence curvature  
- high entanglement  
- medium stability  

**RIM Output**
```json
{
  "regime_a": "R3",
  "regime_b": "R4",
  "interlock_type": "entanglement",
  "boundary_condition": "resonance-coherence",
  "interlock_strength": 0.93,
  "entanglement_score": 0.91,
  "stability_rating": 0.49
}
```

---

## **3. Computational ↔ Physical Entanglement (R2 ↔ R3)**  
### **Case: Drift‑Amplification Loop**

**Description**  
Computational drift increases physical drift sensitivity; physical drift feeds back into computational drift envelopes.

**Characteristics**
- drift amplification  
- instability ridge formation  
- medium‑high entanglement  
- low stability  

**RIM Output**
```json
{
  "regime_a": "R2",
  "regime_b": "R3",
  "interlock_type": "entanglement",
  "boundary_condition": "drift-amplification",
  "interlock_strength": 0.87,
  "entanglement_score": 0.72,
  "stability_rating": 0.41
}
```

---

## **4. Conceptual ↔ Dimensional Entanglement (R1 ↔ R4)**  
### **Case: Coherence‑Gradient Coupling**

**Description**  
Conceptual coherence gradients align with dimensional coherence gradients, forming a multi‑layer coherence ridge.

**Characteristics**
- coherence gradient alignment  
- medium entanglement  
- high stability  
- low drift  

**RIM Output**
```json
{
  "regime_a": "R1",
  "regime_b": "R4",
  "interlock_type": "entanglement",
  "boundary_condition": "coherence-gradient",
  "interlock_strength": 0.76,
  "entanglement_score": 0.35,
  "stability_rating": 0.68
}
```

---

## **5. Tri‑Regime Entanglement (R1 ↔ R2 ↔ R3)**  
### **Case: Coherence Tensor Binding**

**Description**  
A multi‑regime coherence tensor binds conceptual, computational, and physical coherence into a unified structure.

**Characteristics**
- multi‑regime tensor  
- high coherence dependency  
- high entanglement  
- medium stability  

**RIM Output**
```json
{
  "regime_a": "R1",
  "regime_b": "R2",
  "regime_c": "R3",
  "interlock_type": "entanglement",
  "boundary_condition": "coherence-tensor",
  "interlock_strength": 0.94,
  "entanglement_score": 0.89,
  "stability_rating": 0.57
}
```

---

## **6. Dimensional Tensor Entanglement (R2 ↔ R4)**  
### **Case: Dimensional Tensor Constraint**

**Description**  
Dimensional tensors constrain computational pathways, forcing coherence‑aligned computational structures.

**Characteristics**
- tensor constraint  
- medium‑high entanglement  
- medium stability  
- coherence‑driven structure  

**RIM Output**
```json
{
  "regime_a": "R2",
  "regime_b": "R4",
  "interlock_type": "entanglement",
  "boundary_condition": "dimensional-tensor",
  "interlock_strength": 0.88,
  "entanglement_score": 0.72,
  "stability_rating": 0.63
}
```

---

## **7. Entanglement Case Matrix Snippet**

```json
{
  "regime_a": "R3",
  "regime_b": "R4",
  "interlock_type": "entanglement",
  "boundary_condition": "resonance-coherence",
  "interlock_strength": 0.93,
  "entanglement_score": 0.91,
  "stability_rating": 0.49
}
```

---

## **Status**

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