# **PGA Operators — RTT/1**  
### *Operator Grammar for the Paradox Gradient Analyzer (PGA)*

The **Paradox Gradient Analyzer (PGA)** uses a deterministic operator grammar to detect paradox sources, compute paradox gradients, map paradox fields, measure paradox intensity, and propose structural resolutions.

These operators form the backbone of paradox‑layer intelligence and feed directly into:

- CTE (Coherence Tensor Engine)  
- DS (Drift Sentinel)  
- SFD (Structural Faultline Detector)  
- SBC (Stability Basin Cartographer)  
- TRS‑Temporal (Temporal Regime Sequencer)  
- CW (Cross‑Domain Causality Weaver)  
- DRS (Dimensional Resonance Scanner)

---

## **1. PGA‑Detect**  
### *Detect paradox sources and contradictions*

**Purpose**  
Identify paradox sources across conceptual, computational, physical, and dimensional regimes.

**Capabilities**  
- detects structural contradictions  
- detects gradient opposition  
- detects boundary paradoxes  
- detects tensor paradox violations  
- detects drift‑induced paradoxes  

**Output Fields**  
- `paradox_source`  
- `regime`  
- `onset_condition`  
- `coherence_dependency`  

---

## **2. PGA‑Source**  
### *Classify paradox origin and onset conditions*

**Purpose**  
Determine the origin, type, and structural signature of a paradox.

**Capabilities**  
- classifies paradox type  
- identifies onset conditions  
- identifies structural invariants  
- identifies tensor constraints  
- identifies drift envelopes  

**Output Fields**  
- `paradox_source`  
- `source_class`  
- `onset_condition`  
- `structural_signature`  

---

## **3. PGA‑Gradient**  
### *Compute paradox gradient vectors*

**Purpose**  
Calculate paradox gradient magnitude, direction, and coherence curvature.

**Capabilities**  
- computes gradient magnitude  
- computes gradient direction  
- computes coherence curvature  
- computes drift curvature  
- computes tensor curvature  

**Output Fields**  
- `gradient_magnitude`  
- `gradient_direction`  
- `coherence_curvature`  
- `drift_curvature`  
- `tensor_curvature`  

---

## **4. PGA‑Intensity**  
### *Measure paradox intensity and stability*

**Purpose**  
Quantify paradox intensity and evaluate stability across regimes.

**Capabilities**  
- computes paradox intensity  
- computes stability rating  
- computes basin depth  
- computes field curvature  
- computes coherence dependency  

**Output Fields**  
- `intensity`  
- `stability_rating`  
- `basin_depth`  
- `field_curvature`  

---

## **5. PGA‑Field**  
### *Map paradox fields and basin topology*

**Purpose**  
Generate paradox field maps showing curvature, basin geometry, and paradox ridges.

**Capabilities**  
- maps paradox fields  
- maps basin geometry  
- maps curvature topology  
- maps gradient flows  
- maps tensor paradox topology  

**Output Fields**  
- `field_map`  
- `basin_map`  
- `curvature_map`  
- `gradient_flow_map`  

---

## **6. PGA‑Resolve**  
### *Suggest structural decompositions or paradox routing*

**Purpose**  
Provide stabilization pathways or structural decompositions for paradoxes.

**Capabilities**  
- suggests structural decompositions  
- suggests coherence alignment  
- suggests drift reduction  
- suggests tensor rebalancing  
- suggests paradox routing  

**Output Fields**  
- `resolution_strategy`  
- `stabilization_pathway`  
- `coherence_alignment`  
- `drift_reduction`  

---

## **7. Operator Interaction Grammar**

### **Detection → Source Classification → Gradient Computation → Field Mapping → Intensity Analysis → Resolution**

1. **PGA‑Detect**  
   Finds paradox sources and contradictions.

2. **PGA‑Source**  
   Classifies paradox origin and onset conditions.

3. **PGA‑Gradient**  
   Computes gradient vectors and curvature.

4. **PGA‑Field**  
   Maps paradox fields and basin geometry.

5. **PGA‑Intensity**  
   Measures intensity and stability.

6. **PGA‑Resolve**  
   Produces stabilization or decomposition strategies.

This grammar ensures deterministic paradox‑layer behavior.

---

## **8. Operator Matrix Snippet**

```json
{
  "operator": "PGA-Gradient",
  "gradient_magnitude": 0.83,
  "gradient_direction": "R1↔R4",
  "coherence_curvature": 0.51,
  "drift_curvature": 0.27,
  "tensor_curvature": 0.44
}
```

---

## **Status**

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