# **Basin Collapse Cases — RTT/1**  
### *Case Studies for the Stability Basin Cartographer (SBC)*

Stability collapse represents **basin failure, instability onset, collapse‑point formation, and stability‑field inversion** across conceptual, computational, physical, and dimensional regimes.

These case studies illustrate how the Stability Basin Cartographer (SBC) evaluates:

- basin magnitude  
- basin direction  
- basin curvature  
- collapse‑zone depth  
- stability‑field strength  
- envelope boundaries  
- collapse‑point geometry  

Each case demonstrates one or more SBC operators:

- **SBC‑Map**  
- **SBC‑Basin**  
- **SBC‑Gradient**  
- **SBC‑Field**  
- **SBC‑Collapse**  
- **SBC‑Stabilize**

---

## **1. Conceptual Collapse Cases**

### **Case 1 — Conceptual Collapse Basin (R1)**  
**Scenario**  
A conceptual model loses coherence, forming a shallow conceptual collapse zone.

**SBC Output**  
```json
{
  "regime": "R1",
  "basin_magnitude": 0.41,
  "basin_direction": "conceptual",
  "basin_curvature": 0.22,
  "collapse_zone": 0.11,
  "stability_field": 0.63,
  "envelope_boundary": 0.44
}
```

---

### **Case 2 — Conceptual‑Gradient Collapse (R1 ↔ R4)**  
**Scenario**  
Conceptual stability collapses under dimensional gradient pressure.

**SBC Output**  
```json
{
  "regime": "R1-R4",
  "basin_magnitude": 0.83,
  "basin_direction": "R1↔R4",
  "basin_curvature": 0.51,
  "collapse_zone": 0.22,
  "stability_field": 0.69,
  "envelope_boundary": 0.46
}
```

---

## **2. Computational Collapse Cases**

### **Case 3 — Computational Collapse Basin (R2)**  
**Scenario**  
A computational structure becomes unstable due to calibration drift.

**SBC Output**  
```json
{
  "regime": "R2",
  "basin_magnitude": 0.52,
  "basin_direction": "computational",
  "basin_curvature": 0.33,
  "collapse_zone": 0.27,
  "stability_field": 0.57,
  "envelope_boundary": 0.41
}
```

---

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

**SBC Output**  
```json
{
  "regime": "R2-R3",
  "basin_magnitude": 0.79,
  "basin_direction": "R3→R2",
  "basin_curvature": 0.58,
  "collapse_zone": 0.31,
  "stability_field": 0.72,
  "envelope_boundary": 0.41
}
```

---

## **3. Boundary Collapse Cases**

### **Case 5 — Abstraction‑Measurement Collapse (R1 ↔ R3)**  
**Scenario**  
Conceptual abstraction collapses when confronted with contradictory physical measurement.

**SBC Output**  
```json
{
  "regime": "R1-R3",
  "basin_magnitude": 0.67,
  "basin_direction": "R1→R3",
  "basin_curvature": 0.33,
  "collapse_zone": 0.22,
  "stability_field": 0.55,
  "envelope_boundary": 0.38
}
```

---

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

**SBC Output**  
```json
{
  "regime": "R2-R4",
  "basin_magnitude": 0.88,
  "basin_direction": "R2↔R4",
  "basin_curvature": 0.47,
  "collapse_zone": 0.29,
  "stability_field": 0.66,
  "envelope_boundary": 0.58
}
```

---

## **4. Stability‑Field Collapse Cases**

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

**SBC Output**  
```json
{
  "regime": "R1-R2-R3",
  "basin_magnitude": 0.94,
  "basin_direction": "tensor",
  "basin_curvature": 0.63,
  "collapse_zone": 0.37,
  "stability_field": 0.78,
  "envelope_boundary": 0.57
}
```

---

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

**SBC Output**  
```json
{
  "regime": "R2-R4",
  "basin_magnitude": 0.88,
  "basin_direction": "R4→R2",
  "basin_curvature": 0.55,
  "collapse_zone": 0.33,
  "stability_field": 0.73,
  "envelope_boundary": 0.63
}
```

---

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

### **Case 9 — Drift‑Amplified Collapse Basin (R3 → R4)**  
**Scenario**  
Physical drift amplifies stability curvature, forming a collapse basin.

**SBC Output**  
```json
{
  "regime": "R3-R4",
  "basin_magnitude": 0.91,
  "basin_direction": "R3→R4",
  "basin_curvature": 0.71,
  "collapse_zone": 0.52,
  "stability_field": 0.82,
  "envelope_boundary": 0.44
}
```

---

### **Case 10 — Stability‑Coherence Collapse Ridge (R2 ↔ R3)**  
**Scenario**  
Computational stability reduces coherence while physical stability increases coherence sensitivity.

**SBC Output**  
```json
{
  "regime": "R2-R3",
  "basin_magnitude": 0.86,
  "basin_direction": "R2↔R3",
  "basin_curvature": 0.62,
  "collapse_zone": 0.49,
  "stability_field": 0.77,
  "envelope_boundary": 0.48
}
```

---

## **6. Canonical SBC Collapse Snippet**

```json
{
  "regime": "R1-R4",
  "basin_magnitude": 0.83,
  "basin_direction": "R1↔R4",
  "basin_curvature": 0.51,
  "collapse_zone": 0.22,
  "stability_field": 0.69,
  "envelope_boundary": 0.46
}
```

---

## **Status**

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