# **SBC Operators — RTT/1**  
### *Operator Grammar for the Stability Basin Cartographer (SBC)*

The **Stability Basin Cartographer (SBC)** defines the stability‑layer intelligence of RTT.  
Its operators map stability basins, compute basin gradients, identify stability fields, detect collapse zones, and propose stabilization strategies.

These operators feed directly into:

- **TRS‑Temporal** — Temporal Regime Sequencer  
- **CW** — Cross‑Domain Causality Weaver  
- **DRS** — Dimensional Resonance Scanner  

---

## **1. SBC‑Map**  
### *Map stability basins and stability topology*

**Purpose**  
Identify stability basins, stability fields, basin boundaries, collapse zones, and stability topology across R1–R4.

**Capabilities**  
- maps stability basins  
- identifies basin boundaries  
- detects stability fields  
- detects collapse zones  
- evaluates stability topology  

**Output Fields**  
- `basin_map`  
- `boundary_map`  
- `field_map`  
- `collapse_map`  
- `topology_map`  

---

## **2. SBC‑Basin**  
### *Analyze basin magnitude, direction, and curvature*

**Purpose**  
Compute basin magnitude, direction, curvature, envelope boundaries, and stability flow.

**Capabilities**  
- computes basin magnitude  
- computes basin direction  
- computes basin curvature  
- computes envelope boundaries  
- computes stability flow  

**Output Fields**  
- `basin_magnitude`  
- `basin_direction`  
- `basin_curvature`  
- `envelope_boundary`  
- `stability_flow`  

---

## **3. SBC‑Gradient**  
### *Compute basin gradients and directional stability flow*

**Purpose**  
Evaluate gradient magnitude, gradient direction, gradient curvature, and gradient‑driven stability flow.

**Capabilities**  
- computes gradient magnitude  
- computes gradient direction  
- computes gradient curvature  
- evaluates gradient stability flow  
- detects gradient inversion  

**Output Fields**  
- `gradient_magnitude`  
- `gradient_direction`  
- `gradient_curvature`  
- `gradient_flow`  
- `gradient_inversion`  

---

## **4. SBC‑Field**  
### *Map stability fields and stability curvature*

**Purpose**  
Generate stability‑field maps showing wells, ridges, basins, tensor‑level fields, and multi‑regime stability topology.

**Capabilities**  
- maps stability fields  
- maps stability wells  
- maps stability ridges  
- maps stability basins  
- maps multi‑regime stability topology  

**Output Fields**  
- `field_map`  
- `ridge_map`  
- `basin_map`  
- `well_map`  
- `topology_map`  

---

## **5. SBC‑Collapse**  
### *Detect basin collapse and instability onset*

**Purpose**  
Identify collapse zones, collapse‑point seams, collapse curvature, and collapse‑driven instability.

**Capabilities**  
- detects collapse zones  
- computes collapse curvature  
- detects collapse‑point seams  
- evaluates collapse stability  
- identifies collapse‑driven instability  

**Output Fields**  
- `collapse_zone`  
- `collapse_curvature`  
- `collapse_seam`  
- `collapse_stability`  
- `collapse_instability`  

---

## **6. SBC‑Stabilize**  
### *Propose stability reinforcement pathways*

**Purpose**  
Provide stabilization strategies for stability basins, stability fields, collapse zones, and multi‑regime stability tensors.

**Capabilities**  
- proposes stability reinforcement  
- proposes basin alignment  
- proposes gradient reduction  
- proposes collapse mitigation  
- proposes field stabilization  

**Output Fields**  
- `stabilization_pathway`  
- `basin_alignment`  
- `gradient_reduction`  
- `collapse_mitigation`  
- `field_stabilization`  

---

## **7. Operator Interaction Grammar**

### **Map → Basin → Gradient → Field → Collapse → Stabilize**

1. **SBC‑Map**  
   Identifies stability basins, fields, boundaries, and collapse zones.

2. **SBC‑Basin**  
   Computes basin magnitude, direction, curvature, and envelope boundaries.

3. **SBC‑Gradient**  
   Computes gradient magnitude, direction, curvature, and stability flow.

4. **SBC‑Field**  
   Maps stability fields, wells, ridges, basins, and topology.

5. **SBC‑Collapse**  
   Detects collapse zones, collapse curvature, and collapse‑point seams.

6. **SBC‑Stabilize**  
   Produces stabilization pathways and stability‑alignment strategies.

This grammar ensures deterministic stability‑layer behavior.

---

## **8. Operator Matrix Snippet**

```json
{
  "operator": "SBC-Gradient",
  "gradient_magnitude": 0.83,
  "gradient_direction": "R1↔R4",
  "gradient_curvature": 0.51,
  "gradient_flow": 0.69,
  "gradient_inversion": 0.22
}
```

---

## **Status**

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