Evolutionary Ontology API

kernel-spec.md

Prime Kernel Evolutionary Ontology Specification

Version: 1.0.0
Status: Reference Implementation
Author: The UOR Foundation
Date: March 2025

1. Foundational Principles

The Prime Kernel is the foundational Evolutionary Ontology that implements the four axioms of the Prime Framework, providing core infrastructure for all other ontologies to build upon. It serves as both a runtime environment and a meta-ontology that enables the coherent evolution of knowledge structures.

1.1 Axiom Implementation

1.1.1 Reference Manifold (M)

The kernel implements a smooth, connected, orientable manifold M equipped with a nondegenerate metric tensor g. This manifold serves as the universal arena for embedding all ontological structures.

interface ReferenceManifold {
  dimension: number;
  metric: MetricTensor;
  atlas: Map<ChartID, Chart>;
  tangentSpace(point: ManifoldPoint): TangentSpace;
  normalSpace(point: ManifoldPoint): NormalSpace;
  exponentialMap(point: ManifoldPoint, tangentVector: TangentVector): ManifoldPoint;
  logarithmicMap(point1: ManifoldPoint, point2: ManifoldPoint): TangentVector;
  geodesic(point1: ManifoldPoint, point2: ManifoldPoint): Curve;
  parallelTransport(vector: TangentVector, curve: Curve): TangentVector;
  christoffelSymbols(point: ManifoldPoint): ChristoffelSymbols;
  riemannianCurvature(point: ManifoldPoint): RiemannianCurvatureTensor;
}

1.1.2 Algebraic Fibers (C_x)

At each point x ∈ M, the kernel attaches an associative algebra C_x (typically a Clifford algebra) that embeds ontological elements with their full mathematical structure.

interface AlgebraicFiber {
  dimension: number;
  basePoint: ManifoldPoint;
  product(a: FiberElement, b: FiberElement): FiberElement;
  sum(a: FiberElement, b: FiberElement): FiberElement;
  scalarMultiply(scalar: number, element: FiberElement): FiberElement;
  exponential(element: FiberElement): FiberElement;
  logarithm(element: FiberElement): FiberElement;
  embed(value: any): FiberElement;
  extract(element: FiberElement): any;
  createBasis(): FiberBasis;
  decompose(element: FiberElement, basis: FiberBasis): FiberCoordinates;
  reconstruct(coordinates: FiberCoordinates, basis: FiberBasis): FiberElement;
  grade(element: FiberElement): Map<number, FiberElement>;
}

1.1.3 Symmetry Group Action (G)

The kernel implements a Lie group G that acts on M by isometries and lifts to each fiber C_x as algebra automorphisms, ensuring consistency of representations across transformations.

interface SymmetryGroup {
  dimension: number;
  identity: GroupElement;
  multiply(a: GroupElement, b: GroupElement): GroupElement;
  inverse(element: GroupElement): GroupElement;
  lieAlgebra: LieAlgebra;
  exponentialMap(algebraElement: LieAlgebraElement): GroupElement;
  logarithmicMap(groupElement: GroupElement): LieAlgebraElement;
  act(element: GroupElement, point: ManifoldPoint): ManifoldPoint;
  liftToFiber(element: GroupElement, fiber: AlgebraicFiber): FiberAutomorphism;
  generateSubgroup(generators: GroupElement[]): SymmetrySubgroup;
  orbit(point: ManifoldPoint, subgroup: SymmetrySubgroup): ManifoldPoint[];
  isInvariant(element: FiberElement, transformation: GroupElement): boolean;
}

1.1.4 Coherence Inner Product

The kernel establishes a G-invariant, positive-definite inner product ⟨·,·⟩_c on each fiber C_x, inducing the coherence norm that selects canonical (minimal-norm) ontological representations.

interface CoherenceInnerProduct {
  evaluate(a: FiberElement, b: FiberElement): number;
  norm(element: FiberElement): number;
  distance(a: FiberElement, b: FiberElement): number;
  orthogonalize(elements: FiberElement[]): FiberElement[];
  project(element: FiberElement, subspace: FiberElement[]): FiberElement;
  gramMatrix(elements: FiberElement[]): Matrix;
  minimize(element: FiberElement, constraints: Constraint[]): FiberElement;
  isOrthogonal(a: FiberElement, b: FiberElement): boolean;
  decompose(element: FiberElement): OrthogonalDecomposition;
}

2. Kernel Architecture

2.1 Core Components

┌─────────────────────────────────────────────────────────────────────┐
│                          Prime Kernel                                │
│                                                                     │
│  ┌─────────────────┐  ┌─────────────────┐  ┌─────────────────────┐  │
│  │  Mathematical   │  │   Ontological   │  │  Evolutionary       │  │
│  │  Foundation     │  │   Registry      │  │  Engine             │  │
│  │                 │  │                 │  │                     │  │
│  │ • Manifold      │  │ • Concept Store │  │ • Crossover         │  │
│  │ • Fiber Algebra │  │ • Relation Maps │  │ • Mutation          │  │
│  │ • Symmetry      │  │ • Process Flow  │  │ • Selection         │  │
│  │ • Coherence     │  │ • Meta Registry │  │ • Fitness           │  │
│  └─────────────────┘  └─────────────────┘  └─────────────────────┘  │
│                                                                     │
│  ┌─────────────────┐  ┌─────────────────┐  ┌─────────────────────┐  │
│  │  Communication  │  │   Persistence   │  │  Security           │  │
│  │  Bus            │  │   Layer         │  │  Sandbox            │  │
│  │                 │  │                 │  │                     │  │
│  │ • Event System  │  │ • State Manager │  │ • Permission Model  │  │
│  │ • Message Queue │  │ • Serialization │  │ • Isolation         │  │
│  │ • RPC Channel   │  │ • Versioning    │  │ • Verification      │  │
│  │ • Subscriptions │  │ • Transactions  │  │ • Cryptography      │  │
│  └─────────────────┘  └─────────────────┘  └─────────────────────┘  │
│                                                                     │
│  ┌───────────────────────────────────────────────────────────────┐  │
│  │                  Plugin Management System                      │  │
│  │                                                               │  │
│  │  • Lifecycle Management  • Dependency Resolution              │  │
│  │  • Interface Registry    • Version Compatibility              │  │
│  └───────────────────────────────────────────────────────────────┘  │
└─────────────────────────────────────────────────────────────────────┘

2.2 Component Descriptions

2.2.1 Mathematical Foundation

Implements the four Prime Framework axioms as computational structures with precise mathematical properties. This component provides the fundamental operations for embedding, transforming, and evaluating ontological structures.

2.2.2 Ontological Registry

Manages the storage, indexing, and retrieval of all ontological elements. It maintains the structural integrity of the knowledge hierarchy and provides efficient query capabilities.

2.2.3 Evolutionary Engine

Implements the mechanisms for ontology evolution, including variation operators (crossover, mutation), selection mechanisms, and fitness evaluation functions.

2.2.4 Communication Bus

Provides a publish-subscribe event system and message-passing infrastructure for inter-ontology communication, enabling decoupled interaction patterns.

2.2.5 Persistence Layer

Manages the serialization, storage, and retrieval of ontological states, supporting versioning, transactional semantics, and state synchronization.

2.2.6 Security Sandbox

Enforces isolation boundaries, permission models, and verification mechanisms to ensure ontologies cannot compromise system integrity or access unauthorized resources.

2.2.7 Plugin Management System

Handles the complete lifecycle of Evolutionary Ontology plugins, from discovery and installation to initialization, updating, and termination.

3. Kernel API Specification

3.1 Mathematical Foundation API

3.1.1 Manifold Operations

interface ManifoldAPI {
  /**
   * Creates a point on the reference manifold
   * @param coordinates Coordinates in the default chart
   * @returns A manifold point
   */
  createPoint(coordinates: number[]): ManifoldPoint;
  
  /**
   * Calculates the geodesic distance between two manifold points
   * @param point1 First manifold point
   * @param point2 Second manifold point
   * @returns The distance between the points
   */
  distance(point1: ManifoldPoint, point2: ManifoldPoint): number;
  
  /**
   * Computes the tangent space at a specified point
   * @param point Manifold point
   * @returns The tangent space at the point
   */
  tangentSpace(point: ManifoldPoint): TangentSpace;
  
  /**
   * Creates a vector in the tangent space at a specified point
   * @param point Manifold point
   * @param components Vector components in the local basis
   * @returns A tangent vector
   */
  createTangentVector(point: ManifoldPoint, components: number[]): TangentVector;
  
  /**
   * Traces a geodesic curve from a point in the direction of a tangent vector
   * @param point Starting manifold point
   * @param vector Direction vector in the tangent space at point
   * @param distance Distance to travel along the geodesic
   * @returns The destination point
   */
  followGeodesic(point: ManifoldPoint, vector: TangentVector, distance: number): ManifoldPoint;
  
  /**
   * Creates a chart (local coordinate system) around a point
   * @param center Center point of the chart
   * @param radius Chart radius (in manifold distance)
   * @returns A chart ID
   */
  createChart(center: ManifoldPoint, radius: number): ChartID;
  
  /**
   * Converts point coordinates between charts
   * @param point Point to convert
   * @param sourceChart Source chart ID
   * @param targetChart Target chart ID
   * @returns Coordinates in the target chart
   */
  convertCoordinates(point: ManifoldPoint, sourceChart: ChartID, targetChart: ChartID): number[];
  
  /**
   * Computes the metric tensor at a specified point
   * @param point Manifold point
   * @returns The metric tensor at the point
   */
  metricTensor(point: ManifoldPoint): MetricTensor;
  
  /**
   * Computes the Christoffel symbols at a specified point
   * @param point Manifold point
   * @returns The Christoffel symbols at the point
   */
  christoffelSymbols(point: ManifoldPoint): ChristoffelSymbols;
  
  /**
   * Computes the Riemann curvature tensor at a specified point
   * @param point Manifold point
   * @returns The Riemann curvature tensor at the point
   */
  riemannTensor(point: ManifoldPoint): RiemannTensor;
}

3.1.2 Fiber Algebra Operations

interface FiberAlgebraAPI {
  /**
   * Creates an algebraic fiber at a specified manifold point
   * @param point Manifold point where the fiber is attached
   * @returns The algebraic fiber
   */
  createFiber(point: ManifoldPoint): AlgebraicFiber;
  
  /**
   * Retrieves the fiber at a specified manifold point
   * @param point Manifold point
   * @returns The algebraic fiber at the point
   */
  getFiber(point: ManifoldPoint): AlgebraicFiber;
  
  /**
   * Creates a basis for a fiber algebra
   * @param fiber The algebraic fiber
   * @param type Type of basis (standard, orthogonal, custom)
   * @returns A basis for the fiber
   */
  createBasis(fiber: AlgebraicFiber, type?: BasisType): FiberBasis;
  
  /**
   * Embeds a value in the fiber algebra
   * @param fiber The algebraic fiber
   * @param value Value to embed
   * @param embeddingType Type of embedding to use
   * @returns The embedded element
   */
  embed(fiber: AlgebraicFiber, value: any, embeddingType?: EmbeddingType): FiberElement;
  
  /**
   * Extracts a value from a fiber element
   * @param element Fiber element
   * @param extractionType Type of extraction to use
   * @returns The extracted value
   */
  extract(element: FiberElement, extractionType?: ExtractionType): any;
  
  /**
   * Performs the algebraic product operation
   * @param a First fiber element
   * @param b Second fiber element
   * @returns The product element
   */
  product(a: FiberElement, b: FiberElement): FiberElement;
  
  /**
   * Performs the algebraic sum operation
   * @param a First fiber element
   * @param b Second fiber element
   * @returns The sum element
   */
  sum(a: FiberElement, b: FiberElement): FiberElement;
  
  /**
   * Performs scalar multiplication
   * @param scalar Scalar value
   * @param element Fiber element
   * @returns The scaled element
   */
  scalarMultiply(scalar: number, element: FiberElement): FiberElement;
  
  /**
   * Computes the grade decomposition of a fiber element
   * @param element Fiber element
   * @returns Map from grade to component
   */
  gradeDecomposition(element: FiberElement): Map<number, FiberElement>;
  
  /**
   * Extracts the k-grade component of a fiber element
   * @param element Fiber element
   * @param grade Grade to extract
   * @returns The k-grade component
   */
  extractGrade(element: FiberElement, grade: number): FiberElement;
  
  /**
   * Computes the exponential of a fiber element
   * @param element Fiber element
   * @returns The exponential
   */
  exponential(element: FiberElement): FiberElement;
  
  /**
   * Computes the logarithm of a fiber element
   * @param element Fiber element
   * @returns The logarithm
   */
  logarithm(element: FiberElement): FiberElement;
}

3.1.3 Symmetry Group Operations

interface SymmetryGroupAPI {
  /**
   * Creates a symmetry group element from generators
   * @param generators List of generating elements
   * @returns The constructed group element
   */
  createGroupElement(generators: GroupGeneratorParams[]): GroupElement;
  
  /**
   * Retrieves the identity element of the symmetry group
   * @returns The identity element
   */
  getIdentity(): GroupElement;
  
  /**
   * Computes the product of two group elements
   * @param a First group element
   * @param b Second group element
   * @returns The product element
   */
  multiply(a: GroupElement, b: GroupElement): GroupElement;
  
  /**
   * Computes the inverse of a group element
   * @param element Group element
   * @returns The inverse element
   */
  inverse(element: GroupElement): GroupElement;
  
  /**
   * Applies a group element to a manifold point
   * @param element Group element
   * @param point Manifold point
   * @returns The transformed point
   */
  applyToPoint(element: GroupElement, point: ManifoldPoint): ManifoldPoint;
  
  /**
   * Lifts a group element to act on a fiber
   * @param element Group element
   * @param fiber Algebraic fiber
   * @returns A fiber automorphism
   */
  liftToFiber(element: GroupElement, fiber: AlgebraicFiber): FiberAutomorphism;
  
  /**
   * Applies a lifted group element to a fiber element
   * @param automorphism Fiber automorphism
   * @param element Fiber element
   * @returns The transformed element
   */
  applyToFiberElement(automorphism: FiberAutomorphism, element: FiberElement): FiberElement;
  
  /**
   * Creates a one-parameter subgroup from a Lie algebra element
   * @param algebraElement Lie algebra element
   * @returns Function mapping parameter to group element
   */
  createOneParameterSubgroup(algebraElement: LieAlgebraElement): (t: number) => GroupElement;
  
  /**
   * Checks if an element is invariant under a transformation
   * @param element Fiber element
   * @param transformation Group element
   * @returns True if the element is invariant
   */
  isInvariant(element: FiberElement, transformation: GroupElement): boolean;
  
  /**
   * Computes the orbit of a point under a subgroup
   * @param point Manifold point
   * @param subgroup Symmetry subgroup
   * @param maxPoints Maximum number of points to generate
   * @returns Array of orbit points
   */
  computeOrbit(point: ManifoldPoint, subgroup: SymmetrySubgroup, maxPoints?: number): ManifoldPoint[];
}

3.1.4 Coherence Operations

interface CoherenceAPI {
  /**
   * Computes the coherence inner product of two fiber elements
   * @param a First fiber element
   * @param b Second fiber element
   * @returns The inner product value
   */
  innerProduct(a: FiberElement, b: FiberElement): number;
  
  /**
   * Computes the coherence norm of a fiber element
   * @param element Fiber element
   * @returns The coherence norm
   */
  norm(element: FiberElement): number;
  
  /**
   * Computes the coherence distance between two fiber elements
   * @param a First fiber element
   * @param b Second fiber element
   * @returns The coherence distance
   */
  distance(a: FiberElement, b: FiberElement): number;
  
  /**
   * Finds the minimal-norm element satisfying given constraints
   * @param fiber Algebraic fiber
   * @param constraints List of constraints
   * @param initialGuess Initial guess for the solution
   * @returns The minimal-norm element
   */
  findMinimalNormElement(
    fiber: AlgebraicFiber, 
    constraints: CoherenceConstraint[], 
    initialGuess?: FiberElement
  ): FiberElement;
  
  /**
   * Performs gradient descent to minimize coherence norm
   * @param element Initial fiber element
   * @param constraints List of constraints
   * @param options Optimization options
   * @returns The optimized element
   */
  minimizeCoherence(
    element: FiberElement, 
    constraints: CoherenceConstraint[], 
    options?: OptimizationOptions
  ): FiberElement;
  
  /**
   * Computes the gradient of the coherence norm
   * @param element Fiber element
   * @returns The gradient vector
   */
  coherenceGradient(element: FiberElement): FiberElement;
  
  /**
   * Orthogonalizes a set of fiber elements
   * @param elements Array of fiber elements
   * @returns Orthogonalized elements
   */
  orthogonalize(elements: FiberElement[]): FiberElement[];
  
  /**
   * Projects an element onto a subspace
   * @param element Fiber element
   * @param subspaceBasis Basis of the subspace
   * @returns The projected element
   */
  project(element: FiberElement, subspaceBasis: FiberElement[]): FiberElement;
  
  /**
   * Checks if an element is coherence-minimal
   * @param element Fiber element
   * @param tolerance Tolerance for minimality check
   * @returns True if the element is minimal
   */
  isCoherenceMinimal(element: FiberElement, tolerance?: number): boolean;
}

3.2 Ontological Registry API

interface OntologyRegistryAPI {
  /**
   * Registers a new ontology with the kernel
   * @param ontology The evolutionary ontology to register
   * @returns The assigned ontology ID
   */
  register(ontology: EvolutionaryOntology): OntologyID;
  
  /**
   * Retrieves an ontology by ID
   * @param id Ontology ID
   * @returns The ontology or undefined if not found
   */
  get(id: OntologyID): EvolutionaryOntology | undefined;
  
  /**
   * Lists all registered ontologies
   * @param filter Optional filter criteria
   * @returns Array of ontology IDs matching the filter
   */
  list(filter?: OntologyFilter): OntologyID[];
  
  /**
   * Unregisters an ontology
   * @param id Ontology ID
   * @returns True if successful
   */
  unregister(id: OntologyID): boolean;
  
  /**
   * Resolves dependencies for an ontology
   * @param id Ontology ID
   * @returns Map of dependency IDs to ontologies
   */
  resolveDependencies(id: OntologyID): Map<OntologyID, EvolutionaryOntology>;
  
  /**
   * Creates a concept element
   * @param params Concept parameters
   * @returns The created concept element
   */
  createConcept(params: ConceptParams): ConceptElement;
  
  /**
   * Creates a relation element
   * @param params Relation parameters
   * @returns The created relation element
   */
  createRelation(params: RelationParams): RelationElement;
  
  /**
   * Creates a process element
   * @param params Process parameters
   * @returns The created process element
   */
  createProcess(params: ProcessParams): ProcessElement;
  
  /**
   * Creates a context element
   * @param params Context parameters
   * @returns The created context element
   */
  createContext(params: ContextParams): ContextElement;
  
  /**
   * Creates a meta-element
   * @param params Meta-element parameters
   * @returns The created meta-element
   */
  createMetaElement(params: MetaElementParams): MetaElement;
  
  /**
   * Queries for elements matching specific criteria
   * @param query Query specification
   * @returns Query results
   */
  query(query: OntologyQuery): QueryResult;
  
  /**
   * Updates an existing ontological element
   * @param elementId Element ID
   * @param updates Changes to apply
   * @returns The updated element
   */
  updateElement(elementId: ElementID, updates: ElementUpdates): OntologyElement;
  
  /**
   * Deletes an ontological element
   * @param elementId Element ID
   * @returns True if successful
   */
  deleteElement(elementId: ElementID): boolean;
}

3.3 Evolutionary Engine API

interface EvolutionaryEngineAPI {
  /**
   * Performs crossover between two parent ontologies
   * @param parent1 First parent ontology
   * @param parent2 Second parent ontology
   * @param options Crossover options
   * @returns The offspring ontology
   */
  crossover(
    parent1: EvolutionaryOntology, 
    parent2: EvolutionaryOntology, 
    options?: CrossoverOptions
  ): EvolutionaryOntology;
  
  /**
   * Applies mutation to an ontology
   * @param ontology Ontology to mutate
   * @param mutationRate Mutation rate (0.0-1.0)
   * @param options Mutation options
   * @returns The mutated ontology
   */
  mutate(
    ontology: EvolutionaryOntology, 
    mutationRate?: number, 
    options?: MutationOptions
  ): EvolutionaryOntology;
  
  /**
   * Selects ontologies from a population based on fitness
   * @param population Population of ontologies
   * @param selectionCount Number of ontologies to select
   * @param options Selection options
   * @returns The selected ontologies
   */
  select(
    population: EvolutionaryOntology[], 
    selectionCount: number, 
    options?: SelectionOptions
  ): EvolutionaryOntology[];
  
  /**
   * Evaluates the fitness of an ontology
   * @param ontology Ontology to evaluate
   * @param criteria Fitness criteria
   * @returns The fitness score
   */
  evaluateFitness(
    ontology: EvolutionaryOntology, 
    criteria: FitnessCriteria
  ): number;
  
  /**
   * Evolves a population of ontologies
   * @param population Initial population
   * @param generations Number of generations to evolve
   * @param options Evolution options
   * @returns The evolved population
   */
  evolvePopulation(
    population: EvolutionaryOntology[], 
    generations: number, 
    options: EvolutionOptions
  ): EvolutionaryOntology[];
  
  /**
   * Checks if an ontology is viable (satisfies all constraints)
   * @param ontology Ontology to check
   * @returns True if the ontology is viable
   */
  isViable(ontology: EvolutionaryOntology): boolean;
  
  /**
   * Optimizes an ontology to improve coherence
   * @param ontology Ontology to optimize
   * @param options Optimization options
   * @returns The optimized ontology
   */
  optimizeCoherence(
    ontology: EvolutionaryOntology, 
    options?: OptimizationOptions
  ): EvolutionaryOntology;
  
  /**
   * Creates a variant of an ontology by modifying specific aspects
   * @param ontology Base ontology
   * @param variations Variations to apply
   * @returns The variant ontology
   */
  createVariant(
    ontology: EvolutionaryOntology, 
    variations: OntologyVariation[]
  ): EvolutionaryOntology;
}

3.4 Communication Bus API

interface CommunicationBusAPI {
  /**
   * Subscribes to an event
   * @param event Event name or pattern
   * @param callback Callback function
   * @returns Subscription ID
   */
  subscribe(event: EventName | EventPattern, callback: EventCallback): SubscriptionID;
  
  /**
   * Unsubscribes from an event
   * @param subscriptionId Subscription ID
   * @returns True if successful
   */
  unsubscribe(subscriptionId: SubscriptionID): boolean;
  
  /**
   * Publishes an event to all subscribers
   * @param event Event name
   * @param data Event data
   * @param options Publishing options
   * @returns True if delivered to at least one subscriber
   */
  publish(event: EventName, data: any, options?: PublishOptions): boolean;
  
  /**
   * Sends a message to a specific ontology
   * @param targetId Target ontology ID
   * @param message Message content
   * @param options Sending options
   * @returns Promise resolving to the response
   */
  sendMessage(targetId: OntologyID, message: any, options?: MessageOptions): Promise<any>;
  
  /**
   * Registers a handler for incoming messages
   * @param handler Message handler function
   * @returns Handler ID
   */
  registerMessageHandler(handler: MessageHandler): HandlerID;
  
  /**
   * Unregisters a message handler
   * @param handlerId Handler ID
   * @returns True if successful
   */
  unregisterMessageHandler(handlerId: HandlerID): boolean;
  
  /**
   * Creates a new event channel with isolated scope
   * @param name Channel name
   * @param options Channel options
   * @returns The created channel
   */
  createChannel(name: string, options?: ChannelOptions): EventChannel;
  
  /**
   * Sets up a remote procedure call endpoint
   * @param procedure Procedure name
   * @param implementation Procedure implementation
   * @param options RPC options
   * @returns Procedure ID
   */
  registerRpcProcedure(
    procedure: string, 
    implementation: RpcImplementation, 
    options?: RpcOptions
  ): ProcedureID;
  
  /**
   * Calls a remote procedure
   * @param ontologyId Target ontology ID
   * @param procedure Procedure name
   * @param params Procedure parameters
   * @returns Promise resolving to the result
   */
  callRpcProcedure(
    ontologyId: OntologyID, 
    procedure: string, 
    params: any[]
  ): Promise<any>;
}

3.5 Persistence Layer API

interface PersistenceAPI {
  /**
   * Persists an ontology state
   * @param ontology Ontology to persist
   * @param options Persistence options
   * @returns Promise resolving to the state ID
   */
  saveState(ontology: EvolutionaryOntology, options?: PersistenceOptions): Promise<StateID>;
  
  /**
   * Loads an ontology state
   * @param stateId State ID
   * @param options Loading options
   * @returns Promise resolving to the loaded ontology
   */
  loadState(stateId: StateID, options?: LoadOptions): Promise<EvolutionaryOntology>;
  
  /**
   * Lists available states for an ontology
   * @param ontologyId Ontology ID
   * @param filter Optional filter criteria
   * @returns Promise resolving to array of state metadata
   */
  listStates(ontologyId: OntologyID, filter?: StateFilter): Promise<StateMetadata[]>;
  
  /**
   * Deletes a persisted state
   * @param stateId State ID
   * @returns Promise resolving to true if successful
   */
  deleteState(stateId: StateID): Promise<boolean>;
  
  /**
   * Creates a new transaction
   * @param options Transaction options
   * @returns The created transaction
   */
  beginTransaction(options?: TransactionOptions): Transaction;
  
  /**
   * Serializes an ontology to a transferable format
   * @param ontology Ontology to serialize
   * @param format Serialization format
   * @returns The serialized ontology
   */
  serialize(ontology: EvolutionaryOntology, format?: SerializationFormat): SerializedOntology;
  
  /**
   * Deserializes an ontology from a transferable format
   * @param serialized Serialized ontology
   * @param options Deserialization options
   * @returns The deserialized ontology
   */
  deserialize(serialized: SerializedOntology, options?: DeserializationOptions): EvolutionaryOntology;
  
  /**
   * Computes the difference between two ontology states
   * @param base Base ontology
   * @param target Target ontology
   * @returns The computed difference
   */
  diff(base: EvolutionaryOntology, target: EvolutionaryOntology): OntologyDiff;
  
  /**
   * Applies a diff to an ontology
   * @param ontology Base ontology
   * @param diff Ontology diff to apply
   * @returns The resulting ontology
   */
  patch(ontology: EvolutionaryOntology, diff: OntologyDiff): EvolutionaryOntology;
  
  /**
   * Creates a new version of an ontology
   * @param ontology Ontology to version
   * @param versionInfo Version information
   * @returns Promise resolving to the version ID
   */
  createVersion(ontology: EvolutionaryOntology, versionInfo: VersionInfo): Promise<VersionID>;
  
  /**
   * Retrieves a specific version of an ontology
   * @param ontologyId Ontology ID
   * @param versionId Version ID
   * @returns Promise resolving to the versioned ontology
   */
  getVersion(ontologyId: OntologyID, versionId: VersionID): Promise<EvolutionaryOntology>;
}

3.6 Security Sandbox API

interface SecuritySandboxAPI {
  /**
   * Creates a security context for an ontology
   * @param ontologyId Ontology ID
   * @param permissions Initial permissions
   * @returns The created security context
   */
  createSecurityContext(ontologyId: OntologyID, permissions: Permission[]): SecurityContext;
  
  /**
   * Grants a permission to an ontology
   * @param ontologyId Ontology ID
   * @param permission Permission to grant
   * @returns True if successful
   */
  grantPermission(ontologyId: OntologyID, permission: Permission): boolean;
  
  /**
   * Revokes a permission from an ontology
   * @param ontologyId Ontology ID
   * @param permission Permission to revoke
   * @returns True if successful
   */
  revokePermission(ontologyId: OntologyID, permission: Permission): boolean;
  
  /**
   * Checks if an ontology has a specific permission
   * @param ontologyId Ontology ID
   * @param permission Permission to check
   * @returns True if the ontology has the permission
   */
  hasPermission(ontologyId: OntologyID, permission: Permission): boolean;
  
  /**
   * Executes code in a restricted sandbox
   * @param ontologyId Ontology ID
   * @param code Code to execute
   * @param options Execution options
   * @returns Promise resolving to the execution result
   */
  executeSandboxed(
    ontologyId: OntologyID, 
    code: SandboxedCode, 
    options?: SandboxOptions
  ): Promise<SandboxResult>;
  
  /**
   * Verifies the integrity of an ontology
   * @param ontology Ontology to verify
   * @returns Verification result
   */
  verifyIntegrity(ontology: EvolutionaryOntology): VerificationResult;
  
  /**
   * Creates a restricted API for an ontology
   * @param ontologyId Ontology ID
   * @param apiDefinition API definition
   * @returns The restricted API proxy
   */
  createRestrictedApi(ontologyId: OntologyID, apiDefinition: ApiDefinition): RestrictedApiProxy;
  
  /**
   * Signs data with the kernel's key
   * @param data Data to sign
   * @param options Signing options
   * @returns The signature
   */
  sign(data: any, options?: SigningOptions): Signature;
  
  /**
   * Verifies a signature
   * @param data Original data
   * @param signature Signature to verify
   * @param publicKey Public key (if not the kernel's)
   * @returns True if the signature is valid
   */
  verify(data: any, signature: Signature, publicKey?: PublicKey): boolean;
}

3.7 Plugin Management API

interface PluginManagementAPI {
  /**
   * Loads an ontology plugin from a source
   * @param source Plugin source location
   * @param options Loading options
   * @returns Promise resolving to the loaded ontology
   */
  loadPlugin(source: PluginSource, options?: LoadOptions): Promise<EvolutionaryOntology>;
  
  /**
   * Initializes a loaded plugin
   * @param ontologyId Ontology ID
   * @param options Initialization options
   * @returns Promise resolving when initialization is complete
   */
  initializePlugin(ontologyId: OntologyID, options?: InitOptions): Promise<void>;
  
  /**
   * Terminates a running plugin
   * @param ontologyId Ontology ID
   * @param options Termination options
   * @returns Promise resolving when termination is complete
   */
  terminatePlugin(ontologyId: OntologyID, options?: TerminateOptions): Promise<void>;
  
  /**
   * Updates a plugin to a new version
   * @param ontologyId Ontology ID
   * @param targetVersion Target version specification
   * @param options Update options
   * @returns Promise resolving to the updated ontology
   */
  updatePlugin(
    ontologyId: OntologyID, 
    targetVersion: VersionSpec, 
    options?: UpdateOptions
  ): Promise<EvolutionaryOntology>;
  
  /**
   * Resolves plugin dependencies
   * @param ontologyId Ontology ID
   * @param options Resolution options
   * @returns Promise resolving to resolved dependencies
   */
  resolveDependencies(
    ontologyId: OntologyID, 
    options?: ResolutionOptions
  ): Promise<Map<DependencyID, EvolutionaryOntology>>;
  
  /**
   * Validates a plugin against constraints
   * @param ontology Ontology to validate
   * @param constraints Validation constraints
   * @returns Validation result
   */
  validatePlugin(
    ontology: EvolutionaryOntology, 
    constraints: ValidationConstraints
  ): ValidationResult;
  
  /**
   * Gets the current status of a plugin
   * @param ontologyId Ontology ID
   * @returns The plugin status
   */
  getPluginStatus(ontologyId: OntologyID): PluginStatus;
  
  /**
   * Gets detailed information about a plugin
   * @param ontologyId Ontology ID
   * @returns Plugin information
   */
  getPluginInfo(ontologyId: OntologyID): PluginInfo;
  
  /**
   * Lists all loaded plugins
   * @param filter Optional filter criteria
   * @returns List of plugin information
   */
  listPlugins(filter?: PluginFilter): PluginInfo[];
}

4. Implementation Requirements

4.1 Core Requirements

1. Mathematical Rigor

   • All mathematical operations must preserve the algebraic properties defined by the Prime Framework
   • Numerical stability must be ensured through appropriate algorithms and error control

2. Performance Considerations

   • Performance-critical operations must be optimized for efficiency
   • Memory usage must be minimized, especially for large ontologies
   • Parallelization should be employed where appropriate

3. Fault Tolerance

   • The kernel must handle errors gracefully without compromising system stability
   • Recovery mechanisms must be provided for critical failures
   • Data integrity must be maintained at all times

4. Security

   • The kernel must enforce strict isolation between ontologies
   • Access to sensitive operations must be properly controlled
   • All external inputs must be validated and sanitized

5. Extensibility

   • The kernel must provide well-defined extension points
   • New mathematical structures must be addable without breaking existing functionality
   • Performance optimizations must not compromise the mathematical model

4.2 Concurrency Model

The Prime Kernel must implement a robust concurrency model that ensures:

1. Thread Safety

   • All public APIs must be thread-safe
   • Internal state must be protected against concurrent modifications
   • Deadlock prevention mechanisms must be implemented

2. Non-blocking Operations

   • Long-running operations should not block the main execution thread
   • Asynchronous APIs must be provided for potentially blocking operations
   • Concurrent access to shared resources must be managed efficiently

3. Event Processing

   • Events must be processed in a predictable order
   • Event processing must not block other kernel operations
   • Event delivery guarantees must be clearly defined and enforced

4.3 Error Handling

The kernel must implement a comprehensive error handling strategy:

1. Error Categories

   • Mathematical errors (e.g., singular matrices, divergent series)
   • Structural errors (e.g., invalid ontology structure)
   • Security errors (e.g., permission violations)
   • Resource errors (e.g., memory exhaustion)
   • External errors (e.g., network failures)

2. Error Reporting

   • Detailed error information must be provided for debugging
   • Error context must be captured to facilitate diagnosis
   • Error logging must be configurable

3. Error Recovery

   • Critical operations must be transactional when possible
   • Recovery strategies must be provided for common error scenarios
   • System integrity must be maintained after errors

4.4 Versioning and Compatibility

The kernel must implement a robust versioning strategy:

1. Semantic Versioning

   • Major version increments indicate breaking changes
   • Minor version increments indicate backwards-compatible enhancements
   • Patch version increments indicate backwards-compatible bug fixes

2. API Compatibility

   • Backward compatibility must be maintained within major versions
   • Deprecated APIs must be marked and supported for at least one major version
   • Migration paths must be provided for breaking changes

3. Data Format Compatibility

   • Serialization formats must include version information
   • Forward and backward compatibility of serialized data must be ensured
   • Version negotiation protocols must be implemented for interoperation

5. Operational Semantics

5.1 Kernel Initialization

1. Bootstrapping Process

   • Load core mathematical structures
   • Initialize fiber algebra infrastructure
   • Set up symmetry group generators
   • Create default reference manifold

2. Configuration Loading

   • Parse and validate configuration parameters
   • Apply system-specific optimizations
   • Set up security boundaries

3. Subsystem Initialization

   • Initialize persistence layer
   • Set up communication bus
   • Prepare evolutionary engine
   • Configure security sandbox

5.2 Ontology Lifecycle Management

1. Loading Phase

   • Parse ontology package
   • Validate structural integrity
   • Resolve dependencies
   • Create initial state

2. Initialization Phase

   • Call ontology initialization method
   • Register event handlers
   • Set up communication channels
   • Establish security context

3. Running Phase

   • Process events
   • Execute ontology logic
   • Manage state changes
   • Handle user interactions

4. Termination Phase

   • Notify dependent ontologies
   • Unregister event handlers
   • Save final state
   • Release resources

5.3 Evolution Process

1. Population Management

   • Create initial population
   • Maintain diversity
   • Track genealogy
   • Enforce population constraints

2. Selection Mechanism

   • Evaluate fitness
   • Rank individuals
   • Apply selection pressure
   • Handle special cases (elitism, etc.)

3. Variation Operators

   • Apply crossover
   • Perform mutation
   • Ensure viable offspring
   • Maintain coherence properties

4. Adaptation Control

   • Detect convergence
   • Adjust parameters dynamically
   • Respond to environmental changes
   • Prevent premature convergence

6. Security Model

6.1 Threat Model

The Prime Kernel's security model addresses the following threats:

1. Malicious Ontologies

   • Unauthorized resource access
   • Data exfiltration attempts
   • Denial-of-service attacks
   • Sandbox escape attempts

2. External Threats

   • Man-in-the-middle attacks
   • Data tampering
   • Replay attacks
   • Cryptographic attacks

3. Supply Chain Risks

   • Compromised ontology sources
   • Dependency attacks
   • Trojan code injection
   • Version manipulation

6.2 Permission System

The kernel implements a fine-grained permission system:

1. Permission Types

   • Resource access permissions
   • Communication permissions
   • Persistence permissions
   • Evolution permissions
   • System interaction permissions

2. Permission Granting

   • Static permissions defined at installation
   • Dynamic permissions granted during runtime
   • User-approved permissions
   • Capability-based security model

3. Permission Enforcement

   • Pre-execution checks
   • Runtime monitoring
   • Post-execution validation
   • Audit logging

6.3 Isolation Mechanisms

The kernel enforces strong isolation between ontologies:

1. Memory Isolation

   • Private memory spaces for each ontology
   • Controlled sharing through explicit APIs
   • Memory sanitization after use
   • Protection against side-channel attacks

2. Execution Isolation

   • Separate execution contexts
   • Resource quotas
   • CPU time limits
   • Priority management

3. State Isolation

   • Private state storage
   • Controlled state sharing
   • Transaction boundaries
   • Data access policies

7. Extension Points

7.1 Mathematical Extensions

The kernel supports extensions to its mathematical foundation:

1. Custom Manifolds

   • Define specialized geometry for specific domains
   • Implement domain-specific metrics
   • Create custom coordinate systems
   • Define specialized curvature properties

2. Extended Fiber Algebras

   • Add specialized algebra types
   • Implement domain-specific operations
   • Define custom embedding strategies
   • Create specialized extraction methods

3. Custom Symmetry Groups

   • Define domain-specific transformations
   • Implement specialized group structures
   • Create custom generators
   • Define specialized action patterns

7.2 Evolutionary Extensions

The kernel supports extensions to its evolutionary mechanisms:

1. Custom Crossover Operators

   • Implement domain-specific recombination
   • Create specialized exchange patterns
   • Define context-sensitive crossover
   • Implement multi-parent recombination

2. Custom Mutation Operators

   • Create targeted mutation strategies
   • Implement structural mutations
   • Define constraint-preserving mutations
   • Create diversity-enhancing mutations

3. Custom Selection Mechanisms

   • Implement specialized fitness functions
   • Create multi-objective selection
   • Define niching strategies
   • Implement co-evolutionary selection

7.3 Interface Extensions

The kernel supports extensions to its interfaces:

1. Custom Event Types

   • Define domain-specific events
   • Create specialized event patterns
   • Implement event transformation
   • Define event correlation rules

2. Custom RPC Mechanisms

   • Implement specialized call patterns
   • Create domain-specific protocols
   • Define extended parameter types
   • Implement specialized serialization

3. Custom Persistence Strategies

   • Create specialized storage patterns
   • Implement domain-specific serialization
   • Define versioning strategies
   • Create specialized indexing methods

8. Performance Considerations

8.1 Optimization Strategies

The kernel implements several optimization strategies:

1. Lazy Evaluation

   • Defer expensive computations until results are needed
   • Cache intermediate results for reuse
   • Implement incremental computation
   • Prioritize critical operations

2. Parallelization

   • Parallelize independent operations
   • Use worker pools for compute-intensive tasks
   • Implement task-stealing algorithms
   • Optimize for multi-core architectures

3. Memory Management

   • Use efficient data structures
   • Implement object pooling
   • Optimize memory layout
   • Minimize allocation/deallocation cycles

8.2 Scalability Considerations

The kernel is designed to scale across several dimensions:

1. Ontology Size Scaling

   • Efficient handling of large ontologies
   • Hierarchical indexing structures
   • Partial loading strategies
   • Specialized data structures for large collections

2. Ontology Count Scaling

   • Efficient management of many ontologies
   • Resource sharing mechanisms
   • Load balancing strategies
   • Prioritization mechanisms

3. Computation Scaling

   • Distributed computation capabilities
   • Workload partitioning
   • Computation offloading
   • Resource-aware scheduling

8.3 Benchmarking Requirements

The kernel includes benchmarking capabilities:

1. Performance Metrics

   • Operation throughput
   • Memory utilization
   • Latency distribution
   • Scalability characteristics

2. Benchmark Scenarios

   • Small ontology operations
   • Large ontology operations
   • Multi-ontology scenarios
   • Evolution-intensive scenarios

3. Profiling Tools

   • Operation profiling
   • Memory profiling
   • Lock contention analysis
   • Cache efficiency analysis

9. Reference Implementation

9.1 Technology Stack

A reference implementation of the Prime Kernel may use the following technology stack:

1. Core Language

   • TypeScript/JavaScript for portability
   • WebAssembly for performance-critical components
   • Web Workers for parallelization

2. Mathematical Libraries

   • Numeric.js for general numeric operations
   • Three.js/math for geometric operations
   • Custom implementation of Clifford algebra

3. Storage

   • IndexedDB for browser persistence
   • Custom serialization for efficiency
   • JSON for interchange format

4. UI Integration

   • Custom renderer for ontology visualization
   • React for components
   • Responsive design for multi-device support

9.2 Deployment Models

The reference implementation supports multiple deployment models:

1. Browser Deployment

   • Single-page application
   • Progressive web app
   • Browser extension

2. Server Deployment

   • Node.js runtime
   • Docker containerization
   • Microservice architecture

3. Hybrid Deployment

   • Local computation with remote synchronization
   • Edge computing with central coordination
   • Distributed peer-to-peer network

9.3 Integration Patterns

The reference implementation supports several integration patterns:

1. API Integration

   • RESTful API for remote access
   • WebSocket for real-time communication
   • GraphQL for flexible queries

2. Plugin Integration

   • Web Component standards
   • JavaScript modules
   • Custom module formats

3. Data Integration

   • Standard formats (JSON, XML)
   • Custom binary formats
   • Stream processing

10. Summary

The Prime Kernel Evolutionary Ontology specification defines a comprehensive implementation of the Prime Framework's axioms as a computational system. It provides the foundation for an extensible, secure, and mathematically rigorous platform for evolutionary ontologies.

Key features include:

1. Mathematical Foundation: Implementations of manifolds, fiber algebras, symmetry groups, and coherence inner products.

2. Ontological Registry: Management of ontology elements with query capabilities.

3. Evolutionary Engine: Mechanisms for ontology evolution through crossover, mutation, and selection.

4. Communication Bus: Event system for inter-ontology communication.

5. Persistence Layer: Storage and retrieval of ontology states.

6. Security Sandbox: Isolation and permission enforcement.

7. Plugin Management: Lifecycle management for ontology plugins.

This specification serves as the definitive guide for implementing the Prime Kernel as the foundation of an Evolutionary Ontology system.

spec-overview.md

Evolutionary Ontology Framework Specification

Overview

An Evolutionary Ontology (EO) framework based on the Prime Framework that enables domain knowledge structures to evolve, adapt, and maintain coherence across domains. This document outlines the architecture for a plugin-based dashboard system where each plugin is an Evolutionary Ontology.

Core Architecture

┌─────────────────────────────────────────────────────────────┐
│                     Prime Dashboard                          │
│                                                             │
│  ┌─────────────────────────────────────────────────────┐   │
│  │               Prime Framework Kernel                 │   │
│  └─────────────────────────────────────────────────────┘   │
│                                                             │
│  ┌───────────┐ ┌───────────┐ ┌───────────┐ ┌───────────┐   │
│  │ Identity  │ │  Storage  │ │  Styling  │ │   Other   │   │
│  │ Ontology  │ │  Ontology │ │  Ontology │ │ Ontologies│   │
│  └───────────┘ └───────────┘ └───────────┘ └───────────┘   │
│                                                             │
│  ┌─────────────────────────────────────────────────────┐   │
│  │          Imported Evolutionary Ontologies            │   │
│  └─────────────────────────────────────────────────────┘   │
└─────────────────────────────────────────────────────────────┘

Principles

1. Modularity - Even the kernel is a plugin (the base Evolutionary Ontology)
2. Separation of Concerns - Ontologies define structure and function, not styling
3. Interoperability - Ontologies can communicate through the kernel
4. Coherence - All ontologies maintain mathematical coherence per Prime Framework principles
5. Evolvability - Ontologies can adapt through well-defined evolutionary operations

Kernel API

interface PrimeKernel {
  // Core Prime Framework functionality
  manifold: {
    createPoint(coordinates: number[]): ManifoldPoint;
    calculateMetric(point1: ManifoldPoint, point2: ManifoldPoint): number;
    // Other manifold operations
  };
  
  fiber: {
    createAlgebraicFiber(point: ManifoldPoint): AlgebraicFiber;
    embedValue(fiber: AlgebraicFiber, value: any): EmbeddedValue;
    applyOperation(fiber: AlgebraicFiber, operation: Operation): AlgebraicFiber;
    // Other fiber operations
  };
  
  symmetry: {
    createGroupAction(parameters: GroupParameters): SymmetryGroupAction;
    applyTransformation(action: SymmetryGroupAction, element: EmbeddedValue): EmbeddedValue;
    // Other symmetry operations
  };
  
  coherence: {
    calculateCoherenceNorm(element: EmbeddedValue): number;
    minimizeCoherence(element: EmbeddedValue): EmbeddedValue;
    // Other coherence operations
  };
  
  // Ontology management
  ontology: {
    register(ontology: EvolutionaryOntology): OntologyID;
    import(source: string): Promise<EvolutionaryOntology>;
    get(id: OntologyID): EvolutionaryOntology;
    list(): OntologyID[];
    unregister(id: OntologyID): boolean;
  };
  
  // Event system for inter-ontology communication
  events: {
    subscribe(event: string, callback: (data: any) => void): SubscriptionID;
    publish(event: string, data: any): void;
    unsubscribe(id: SubscriptionID): boolean;
  };
  
  // Evolution operations
  evolution: {
    crossover(parent1: EvolutionaryOntology, parent2: EvolutionaryOntology): EvolutionaryOntology;
    mutate(ontology: EvolutionaryOntology, rate?: number): EvolutionaryOntology;
    select(population: EvolutionaryOntology[], criteria: SelectionCriteria): EvolutionaryOntology[];
  };
}

Plugin (Evolutionary Ontology) API

interface EvolutionaryOntology {
  // Metadata
  id: string;
  name: string;
  version: string;
  description: string;
  dependencies: string[]; // IDs of other ontologies this one depends on
  
  // Structure
  conceptElements: ConceptElement[];
  relationElements: RelationElement[];
  processElements: ProcessElement[];
  contextElements: ContextElement[];
  metaElements: MetaElement[];
  
  // Core lifecycle methods
  initialize(kernel: PrimeKernel): Promise<void>;
  terminate(): Promise<void>;
  
  // Interaction methods
  handleAction(action: Action): Promise<ActionResult>;
  getInterface(): OntologyInterface; // Public API exposed to other ontologies
  
  // Evolutionary methods
  getFitness(): number;
  getCoherenceNorm(): number;
  adapt(environment: Environment): Promise<void>;
  
  // Rendering (structure only, not styling)
  getRenderTree(): RenderNode;
}

interface RenderNode {
  type: string;
  properties: Record<string, any>;
  children: RenderNode[];
  ontologyHooks?: OntologyHook[]; // Points where styling can attach
}

interface OntologyInterface {
  // Methods and properties exposed to other ontologies
  // Defined by each individual ontology
  [key: string]: any;
}

Styling Ontology API

interface StylingOntology extends EvolutionaryOntology {
  // Apply styles to render tree nodes
  applyStyles(renderTree: RenderNode): StyledRenderNode;
  
  // Register style components
  registerStyleComponent(component: StyleComponent): void;
  
  // Get available themes
  getThemes(): Theme[];
  
  // Set active theme
  setTheme(themeId: string): void;
}

interface StyleComponent {
  selector: string; // How to target render nodes
  styles: Record<string, any>; // Style properties
  priority: number; // For style cascade resolution
}

interface Theme {
  id: string;
  name: string;
  variables: Record<string, any>; // Theme variables
  components: StyleComponent[];
}

Built-in Core Ontologies

1. Kernel Ontology

   • Implements the Prime Framework fundamentals
   • Manages ontology registration and communication
   • Provides evolution operations

2. Identity Ontology

   • User authentication and authorization
   • Profile management
   • Permission control

3. Storage Ontology

   • Browser persistent storage
   • Remote storage integration
   • Data synchronization

4. Styling Ontology

   • Theme management
   • Component styling
   • Responsive design

5. Import Ontology

   • Remote ontology discovery
   • Ontology package validation
   • Version management

Implementation Best Practices

1. Ontology Structure

   • Each ontology should be a self-contained package with clear dependencies
   • Structure should follow the Prime Framework's axioms
   • Include manifest.json describing the ontology's properties and dependencies

2. Coherence Maintenance

   • Regularly calculate and minimize coherence norms
   • Handle coherence violations gracefully
   • Log coherence metrics for debugging

3. Evolution Approach

   • Implement crossover, mutation, and selection carefully
   • Define fitness functions appropriate to the domain
   • Preserve historical versions for rollback if needed

4. Interoperability

   • Use the event system for loose coupling
   • Document public interfaces thoroughly
   • Handle missing dependencies gracefully

5. Rendering

   • Separate structure from presentation completely
   • Use ontology hooks to mark style attachment points
   • Ensure render trees are serializable

Getting Started Example

// Define a simple Evolutionary Ontology
const myOntology: EvolutionaryOntology = {
  id: "com.example.my-ontology",
  name: "My Example Ontology",
  version: "1.0.0",
  description: "A simple example ontology",
  dependencies: ["com.prime.styling"],
  
  conceptElements: [
    { id: "concept1", name: "Example Concept", properties: {...} }
  ],
  
  relationElements: [
    { id: "relation1", source: "concept1", target: "concept1", type: "self-reference" }
  ],
  
  // Other elements...
  
  async initialize(kernel) {
    // Setup code
    await kernel.ontology.get("com.prime.styling");
    kernel.events.subscribe("user-action", this.handleUserAction);
  },
  
  async terminate() {
    // Cleanup code
  },
  
  async handleAction(action) {
    // Handle user or system actions
    return { success: true };
  },
  
  getInterface() {
    return {
      doSomething: () => { /* Implementation */ }
    };
  },
  
  getFitness() {
    return 0.95; // Example fitness score
  },
  
  getCoherenceNorm() {
    return 0.05; // Example coherence norm (lower is better)
  },
  
  async adapt(environment) {
    // Adaptation logic
  },
  
  getRenderTree() {
    return {
      type: "container",
      properties: { id: "main-container" },
      children: [
        {
          type: "header",
          properties: { title: "My Ontology" },
          children: [],
          ontologyHooks: ["header-styling"]
        }
        // More render nodes...
      ]
    };
  }
};

// Register with the dashboard
const kernel = getPrimeKernel();
const ontologyId = await kernel.ontology.register(myOntology);

This specification provides a foundation for building an Evolutionary Ontology framework based on the Prime Framework. It separates structure from styling, allows for interoperability between ontologies, and enables evolutionary adaptation while maintaining coherence.