# 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)