# Coherence Engine Domain

## Overview

The Coherence Engine domain provides mathematical AI interpretability capabilities for Claude Flow V3 through the `prime-radiant` plugin. It enables rigorous coherence validation, spectral stability analysis, and causal reasoning using advanced mathematical frameworks including Sheaf Cohomology, Spectral Graph Theory, and Do-Calculus.

## Strategic Design

### Domain Vision

> Ensure mathematical coherence and stability across all AI operations through rigorous validation gates that prevent contradictions, detect hallucinations, and verify multi-agent consensus.

### Core Subdomains

```
Coherence Engine Domain
├── Coherence Validation (Core)       # Sheaf Laplacian contradiction detection
├── Spectral Analysis (Core)          # Stability and clustering analysis
├── Causal Inference (Supporting)     # Do-calculus interventional queries
├── Consensus Verification (Core)     # Multi-agent agreement validation
├── Topology Analysis (Supporting)    # Quantum topology features
└── Type Theory (Generic)             # HoTT proofs and verification
```

### Subdomain Classification

| Subdomain | Type | Complexity | Business Value |
|-----------|------|------------|----------------|
| Coherence Validation | Core | High | Critical |
| Spectral Analysis | Core | High | High |
| Causal Inference | Supporting | High | Medium |
| Consensus Verification | Core | Medium | Critical |
| Topology Analysis | Supporting | High | Medium |
| Type Theory | Generic | High | Low |

## Context Map

```
┌─────────────────────────────────────────────────────────────────────────────────┐
│                           Coherence Engine Domain                                │
├─────────────────────────────────────────────────────────────────────────────────┤
│                                                                                  │
│                        ┌─────────────────────────┐                               │
│                        │   Coherence Gate        │                               │
│                        │   (Central Validator)   │                               │
│                        └───────────┬─────────────┘                               │
│                                    │                                             │
│        ┌───────────────────────────┼───────────────────────────┐                 │
│        │                           │                           │                 │
│        ▼                           ▼                           ▼                 │
│  ┌───────────────┐         ┌───────────────┐         ┌───────────────┐          │
│  │ Cohomology    │         │ Spectral      │         │ Causal        │          │
│  │ Engine        │         │ Engine        │         │ Engine        │          │
│  ├───────────────┤         ├───────────────┤         ├───────────────┤          │
│  │ • Sheaf       │         │ • Eigenvalue  │         │ • Do-calculus │          │
│  │   Laplacian   │         │   computation │         │ • Confounders │          │
│  │ • Energy      │         │ • Spectral    │         │ • Backdoor    │          │
│  │   calculation │         │   gap         │         │   paths       │          │
│  └───────────────┘         └───────────────┘         └───────────────┘          │
│        │                           │                           │                 │
│        └───────────────────────────┼───────────────────────────┘                 │
│                                    │                                             │
│                                    ▼                                             │
│                        ┌─────────────────────────┐                               │
│                        │   Supporting Services   │                               │
│                        ├─────────────────────────┤                               │
│                        │ • Quantum Engine        │                               │
│                        │ • Category Engine       │                               │
│                        │ • HoTT Engine           │                               │
│                        └─────────────────────────┘                               │
│                                                                                  │
└─────────────────────────────────────────────────────────────────────────────────┘
                                     │
                    Integration with Claude Flow V3
                                     │
        ┌────────────────────────────┼────────────────────────────┐
        │                            │                            │
        ▼                            ▼                            ▼
┌───────────────┐          ┌───────────────┐          ┌───────────────┐
│ Memory        │          │ Coordination  │          │ Security      │
│ Domain (V3)   │          │ Domain (V3)   │          │ Domain (V3)   │
├───────────────┤          ├───────────────┤          ├───────────────┤
│ Shared Kernel │          │ Shared Kernel │          │ Conformist    │
│ (Pre-storage  │          │ (Consensus    │          │ (Input        │
│  coherence    │          │  verification)│          │  validation)  │
│  gate)        │          │               │          │               │
└───────────────┘          └───────────────┘          └───────────────┘
```

### Integration Relationships

| Coherence Context | V3 Domain | Relationship | Description |
|-------------------|-----------|--------------|-------------|
| Coherence Validation | Memory | Shared Kernel | Pre-storage coherence gate |
| Spectral Analysis | Coordination | Shared Kernel | Swarm stability metrics |
| Consensus Verification | Hive-Mind | Shared Kernel | Mathematical consensus check |
| Causal Inference | Security | Conformist | Attack pattern analysis |
| Topology Analysis | Memory | Customer-Supplier | Vector cluster analysis |

## Bounded Contexts

### 1. Coherence Validation Context

**Responsibility**: Detect contradictions using Sheaf Laplacian energy

**Core Concepts**:
- **Sheaf Laplacian**: Mathematical operator measuring local-to-global consistency
- **Coherence Energy**: Scalar value (0=coherent, 1=contradictory)
- **Violation Detection**: Identification of specific contradictory elements

**Ubiquitous Language**:
- **Coherent**: Energy < 0.3, no significant contradictions
- **Warning Zone**: Energy 0.3-0.7, minor inconsistencies
- **Contradictory**: Energy > 0.7, major contradictions
- **Coherence Gate**: Validation checkpoint before storage

**Key Operations**:
```typescript
// Check coherence of vector set
checkCoherence(vectors: Float32Array[]): CoherenceResult

// Validate memory entry against context
validate(entry: MemoryEntry, context: MemoryEntry[]): CoherenceValidation

// Batch validation with progressive context
validateBatch(entries: MemoryEntry[]): CoherenceValidation[]
```

### 2. Spectral Analysis Context

**Responsibility**: Analyze stability using spectral graph theory

**Core Concepts**:
- **Eigenvalues**: Characteristic values of adjacency matrix
- **Spectral Gap**: Difference between first and second eigenvalues
- **Stability Index**: Aggregate stability measure

**Ubiquitous Language**:
- **Spectrally Stable**: Positive spectral gap > 0.1
- **Clustering Tendency**: Low second eigenvalue indicates clusters
- **Connectivity**: First eigenvalue indicates overall connectivity

**Key Operations**:
```typescript
// Compute eigenvalues of adjacency matrix
computeEigenvalues(adjacencyMatrix: Float32Array): Float32Array

// Analyze stability of a system
analyzeSpectral(adjacencyMatrix: Float32Array): SpectralResult

// Detect clustering patterns
detectClusters(adjacencyMatrix: Float32Array): ClusterResult
```

### 3. Causal Inference Context

**Responsibility**: Do-calculus based causal reasoning

**Core Concepts**:
- **Causal Graph**: DAG representing causal relationships
- **Intervention**: do(X=x) operator for causal queries
- **Confounders**: Variables affecting both treatment and outcome
- **Backdoor Paths**: Non-causal paths creating spurious correlation

**Ubiquitous Language**:
- **Treatment**: Intervention variable
- **Outcome**: Effect variable to measure
- **Causal Effect**: True effect of intervention (vs correlation)
- **Valid Intervention**: No unblocked backdoor paths

**Key Operations**:
```typescript
// Estimate causal effect
estimateEffect(treatment: string, outcome: string, graph: CausalGraph): number

// Identify confounding variables
identifyConfounders(treatment: string, outcome: string, graph: CausalGraph): string[]

// Find backdoor paths
findBackdoorPaths(treatment: string, outcome: string, graph: CausalGraph): string[][]
```

### 4. Consensus Verification Context

**Responsibility**: Mathematical validation of multi-agent agreement

**Core Concepts**:
- **Agent State Vectors**: Embedding representations of agent positions
- **Agreement Ratio**: Fraction of agents in consensus
- **Coherence Check**: Cross-agent consistency validation

**Ubiquitous Language**:
- **Consensus Achieved**: Agreement ratio > threshold AND coherent
- **Verified Consensus**: Mathematically validated agreement
- **Byzantine Tolerance**: Resilience to faulty agents

**Key Operations**:
```typescript
// Verify consensus mathematically
verifyConsensus(agentStates: AgentState[]): ConsensusVerification

// Check vote coherence
checkVoteCoherence(votes: Vote[]): CoherenceResult

// Analyze agreement patterns
analyzeAgreement(agentStates: AgentState[]): AgreementAnalysis
```

### 5. Topology Analysis Context

**Responsibility**: Quantum topology for structural analysis

**Core Concepts**:
- **Betti Numbers**: Topological invariants (b0=components, b1=loops, b2=voids)
- **Persistence Diagram**: Birth-death pairs of topological features
- **Homology Classes**: Equivalence classes of cycles

**Ubiquitous Language**:
- **Connected Components**: Betti number b0
- **Cycles/Loops**: Betti number b1
- **Voids/Cavities**: Betti number b2
- **Persistent Feature**: Long-lived topological structure

**Key Operations**:
```typescript
// Compute Betti numbers
computeBettiNumbers(points: Float32Array[], dimension: number): number[]

// Generate persistence diagram
computePersistenceDiagram(points: Float32Array[]): [number, number][]

// Count homology classes
countHomologyClasses(points: Float32Array[], dimension: number): number
```

### 6. Type Theory Context

**Responsibility**: Homotopy Type Theory proofs and verification

**Core Concepts**:
- **Type**: Classification of values
- **Proof**: Evidence of proposition truth
- **Normal Form**: Canonical representation of term

**Ubiquitous Language**:
- **Type Judgment**: Statement that term has a type
- **Proof Verification**: Checking proof validity
- **Type Inference**: Deriving type from term structure

**Key Operations**:
```typescript
// Verify a proof
verifyProof(proposition: string, proof: string): boolean

// Infer type of a term
inferType(term: string): string

// Normalize a term
normalize(term: string): string
```

## Engine Inventory

### Total: 6 Mathematical Engines

| Engine | Purpose | Performance |
|--------|---------|-------------|
| CohomologyEngine | Sheaf Laplacian coherence | <5ms per check |
| SpectralEngine | Eigenvalue stability | <20ms for 100x100 |
| CausalEngine | Do-calculus inference | <10ms per query |
| QuantumEngine | Persistent homology | <50ms per computation |
| CategoryEngine | Functor/morphism ops | <5ms per operation |
| HottEngine | Type theory proofs | <10ms per verification |

## Memory Namespaces

All Coherence Engine data is stored under the `pr/` namespace prefix:

| Namespace | Purpose | Description |
|-----------|---------|-------------|
| `pr/coherence-checks` | Validation history | Records of coherence validations |
| `pr/stability-metrics` | Stability data | Swarm stability measurements |
| `pr/causal-models` | Causal graphs | Stored causal relationship models |
| `pr/topology-features` | Topological data | Computed topological features |

## Integration Points

### Memory Domain
- **Hook**: `pre-memory-store` - Coherence gate before storage
- **Service**: `CoherentMemoryService` - Extended memory with coherence

### Hive-Mind Domain
- **Hook**: `pre-consensus` - Consensus coherence validation
- **Hook**: `post-swarm-task` - Stability analysis after tasks
- **Service**: `CoherentHiveMind` - Extended hive-mind with verification

### Security Domain
- **Hook**: `pre-rag-retrieval` - Hallucination prevention
- **Integration**: Input validity checking via coherence

### AIDefence Domain
- **Extension**: Coherence-based threat detection
- **Integration**: Mathematical attack pattern analysis

## Related Documentation

- [ADR-031: Prime Radiant Integration](../../implementation/adrs/ADR-031-prime-radiant-integration.md)
- [Domain Model](./domain-model.md)
- [Integration Points](./integration-points.md)
- [ADR-006: Unified Memory Service](../../implementation/adrs/ADR-006-UNIFIED-MEMORY.md)
- [ADR-022: AIDefence Integration](../../implementation/adrs/ADR-022-aidefence-integration.md)
