Coherence Engine Domain

Overview

The Coherence Engine domain provides mathematical AI interpretability capabilities for SPTFlo 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 SPTFlo 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:

// 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:

// 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:

// 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:

// 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:

// 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:

// 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
• Domain Model
• Integration Points
• ADR-006: Unified Memory Service
• ADR-022: AIDefence Integration