# **Causal Discontinuity Cases — RTT/1**  
### *Case Studies for the Cross‑Domain Causality Weaver (CW)*

Causal discontinuities represent **breaks in causal flow, polarity inversions, discontinuity boundaries, causal fractures, and cross‑domain causal collapse** across conceptual, computational, physical, and dimensional regimes.

These case studies illustrate how the Cross‑Domain Causality Weaver (CW) evaluates:

- causal magnitude  
- causal direction  
- causal curvature  
- discontinuity depth  
- propagation rate  
- stability envelope  
- causal‑fracture geometry  

Each case demonstrates one or more CW operators:

- **CW‑Signature**  
- **CW‑Vector**  
- **CW‑Field**  
- **CW‑Discontinuity**  
- **CW‑Weave**  
- **CW‑Stabilize**

---

## **1. Conceptual Discontinuity Cases**

### **Case 1 — Conceptual Causal Break (R1)**  
**Scenario**  
A conceptual model loses coherence, forming a shallow causal discontinuity.

**CW Output**  
```json
{
  "regime": "R1",
  "causal_magnitude": 0.41,
  "causal_direction": "conceptual",
  "causal_curvature": 0.22,
  "discontinuity_depth": 0.11,
  "propagation_rate": 0.33,
  "stability_envelope": 0.63
}
```

---

### **Case 2 — Conceptual‑Dimensional Discontinuity (R1 ↔ R4)**  
**Scenario**  
Conceptual causality collapses under dimensional polarity pressure.

**CW Output**  
```json
{
  "regime": "R1-R4",
  "causal_magnitude": 0.83,
  "causal_direction": "R1↔R4",
  "causal_curvature": 0.52,
  "discontinuity_depth": 0.22,
  "propagation_rate": 0.33,
  "stability_envelope": 0.69
}
```

---

## **2. Computational Discontinuity Cases**

### **Case 3 — Computational Causal Break (R2)**  
**Scenario**  
A computational structure becomes unstable due to calibration drift, forming a causal fracture.

**CW Output**  
```json
{
  "regime": "R2",
  "causal_magnitude": 0.52,
  "causal_direction": "computational",
  "causal_curvature": 0.33,
  "discontinuity_depth": 0.27,
  "propagation_rate": 0.27,
  "stability_envelope": 0.57
}
```

---

### **Case 4 — Computational‑Physical Discontinuity (R2 ↔ R3)**  
**Scenario**  
Computational causality collapses under physical measurement sensitivity.

**CW Output**  
```json
{
  "regime": "R2-R3",
  "causal_magnitude": 0.79,
  "causal_direction": "R3→R2",
  "causal_curvature": 0.58,
  "discontinuity_depth": 0.31,
  "propagation_rate": 0.27,
  "stability_envelope": 0.72
}
```

---

## **3. Boundary Discontinuity Cases**

### **Case 5 — Abstraction‑Measurement Causal Discontinuity (R1 ↔ R3)**  
**Scenario**  
Conceptual abstraction contradicts physical measurement, forming a causal discontinuity boundary.

**CW Output**  
```json
{
  "regime": "R1-R3",
  "causal_magnitude": 0.67,
  "causal_direction": "R1→R3",
  "causal_curvature": 0.33,
  "discontinuity_depth": 0.22,
  "propagation_rate": 0.38,
  "stability_envelope": 0.55
}
```

---

### **Case 6 — Gradient‑Boundary Causal Discontinuity (R2 ↔ R4)**  
**Scenario**  
Aligned gradients across computational and dimensional regimes collapse into causal instability.

**CW Output**  
```json
{
  "regime": "R2-R4",
  "causal_magnitude": 0.88,
  "causal_direction": "R2↔R4",
  "causal_curvature": 0.47,
  "discontinuity_depth": 0.29,
  "propagation_rate": 0.33,
  "stability_envelope": 0.66
}
```

---

## **4. Causal‑Field Discontinuity Cases**

### **Case 7 — Multi‑Regime Causal Field Collapse (R1 ↔ R2 ↔ R3)**  
**Scenario**  
A multi‑regime causal field collapses under tensor‑level instability.

**CW Output**  
```json
{
  "regime": "R1-R2-R3",
  "causal_magnitude": 0.94,
  "causal_direction": "tensor",
  "causal_curvature": 0.63,
  "discontinuity_depth": 0.37,
  "propagation_rate": 0.41,
  "stability_envelope": 0.78
}
```

---

### **Case 8 — Dimensional Causal Collapse (R2 ↔ R4)**  
**Scenario**  
Dimensional constraints collapse computational causal pathways.

**CW Output**  
```json
{
  "regime": "R2-R4",
  "causal_magnitude": 0.88,
  "causal_direction": "R4→R2",
  "causal_curvature": 0.55,
  "discontinuity_depth": 0.33,
  "propagation_rate": 0.29,
  "stability_envelope": 0.73
}
```

---

## **5. Drift‑Sensitive Discontinuity Cases**

### **Case 9 — Drift‑Amplified Causal Discontinuity (R3 → R4)**  
**Scenario**  
Physical drift amplifies causal curvature, forming a drift‑sensitive discontinuity.

**CW Output**  
```json
{
  "regime": "R3-R4",
  "causal_magnitude": 0.91,
  "causal_direction": "R3→R4",
  "causal_curvature": 0.71,
  "discontinuity_depth": 0.52,
  "propagation_rate": 0.44,
  "stability_envelope": 0.82
}
```

---

### **Case 10 — Stability‑Coherence Causal Ridge (R2 ↔ R3)**  
**Scenario**  
Computational stability reduces coherence while physical stability increases coherence sensitivity, forming a causal ridge.

**CW Output**  
```json
{
  "regime": "R2-R3",
  "causal_magnitude": 0.86,
  "causal_direction": "R2↔R3",
  "causal_curvature": 0.62,
  "discontinuity_depth": 0.49,
  "propagation_rate": 0.48,
  "stability_envelope": 0.77
}
```

---

## **6. Canonical CW Discontinuity Snippet**

```json
{
  "regime": "R1-R4",
  "causal_magnitude": 0.83,
  "causal_direction": "R1↔R4",
  "causal_curvature": 0.52,
  "discontinuity_depth": 0.22,
  "propagation_rate": 0.33,
  "stability_envelope": 0.69
}
```

---

## **Status**

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