/**
 * DOTS Vocabulary Types
 *
 * From the Double Operadic Theory of Systems (DOTS), this module provides
 * a minimal, domain-independent vocabulary for describing compositional systems.
 *
 * The MVP Cards architecture maps directly to DOTS:
 * - MCard → Carrier (the actual data/systems)
 * - PCard → Lens (tight) + Chart (loose)
 * - VCard → Arena + Action
 *
 * Reference: docs/WorkingNotes/Hub/Theory/Integration/DOTS Vocabulary as Efficient Representation for ABC Curriculum.md
 */
/**
 * DOTS Role enumeration
 *
 * These nine terms (seven structural + Action + Unit) form a complete,
 * compositional language for describing any system, interface, or interaction.
 */
export declare enum DOTSRole {
    /**
     * CARRIER - Category Car(S) of all actual data/systems
     *
     * MCard is the Carrier. Each MCard is an Object in the Carrier category;
     * each hash-link is a Morphism in Car(S).
     *
     * Polynomial Form: Objects = MCards, Morphisms = hash references
     */
    CARRIER = "Carrier",
    /**
     * LENS - Tight morphism (structure-preserving interface map)
     *
     * PCard's abstract_spec ↔ concrete_impl relationship is a Lens.
     * Ensures type safety: Abstract types match Concrete types.
     *
     * Lens = (get, put) pair with coherence laws
     */
    LENS = "Lens",
    /**
     * CHART - Loose morphism (behavioral interaction pattern)
     *
     * PCard's balanced_expectations (tests) describe the wiring.
     * Enables flexibility: same Abstract spec via different Concrete implementations.
     *
     * Chart = horizontal morphism in Target double category
     */
    CHART = "Chart",
    /**
     * ARENA - Interface type (what can interact)
     *
     * VCard is the Arena. It defines the subject_did, capabilities[],
     * and ExternalRef[]. An Arena is a pair of sets (Inputs, Outputs).
     *
     * Arena = (I, O) → Polynomial functor P(X) = Σ_{i∈I} X^{O(i)}
     */
    ARENA = "Arena",
    /**
     * ACTION - Module structure where interactions act on systems
     *
     * VCard enables Action: interactions (Charts/PCards) act on
     * systems (MCards/Carrier) to produce new systems.
     * The VCard authorization gate is the mechanism of this action.
     *
     * Action = Loose(I) ⊛ Car(S) → Car(S)
     */
    ACTION = "Action",
    /**
     * TARGET - Double category I of all interfaces and interactions
     *
     * The CLM design space. Contains all possible Arenas (objects),
     * Lenses (tight morphisms), and Charts (loose morphisms).
     */
    TARGET = "Target",
    /**
     * TIGHT - Vertical composition direction (strict)
     *
     * Prerequisites chains. Cannot skip foundational concepts.
     * Ensures type safety across compositions.
     *
     * Vertical = mandatory sequential dependency
     */
    TIGHT = "Tight",
    /**
     * LOOSE - Horizontal composition direction (flexible)
     *
     * Same concept via different interaction patterns.
     * Enables behavioral flexibility while preserving semantics.
     *
     * Horizontal = parallel/interchangeable alternatives
     */
    LOOSE = "Loose",
    /**
     * UNIT - Identity object for parallel composition
     *
     * Empty MCard / Root Namespace. The neutral element.
     * For any system S: Unit ⊗ S ≅ S
     */
    UNIT = "Unit"
}
/**
 * EOS (Experimental-Operational Symmetry) Role
 *
 * Each MVP Card type enforces a specific dimension of symmetry
 * to ensure environment-invariant correctness.
 */
export declare enum EOSRole {
    /**
     * INVARIANT_CONTENT - The Galois Root
     *
     * MCard: Hash(Content) is a pure function.
     * Same content in Dev = Same hash in Prod.
     * Environment-invariant identity.
     */
    INVARIANT_CONTENT = "InvariantContent",
    /**
     * GENERATIVE_LENS - Controlled Symmetry Breaking 1
     *
     * PCard: Pure function f(x)=y.
     * Invariant in definition, variant only in input.
     * The logic is environment-invariant.
     */
    GENERATIVE_LENS = "GenerativeLens",
    /**
     * SOVEREIGN_DECISION - Controlled Symmetry Breaking 2
     *
     * VCard: The Gap Junction.
     * Breaks symmetry by introducing Authority.
     * Decisional reality creation.
     */
    SOVEREIGN_DECISION = "SovereignDecision"
}
/**
 * Card Plane in the MVP Cards architecture
 *
 * Maps to SDN (Software-Defined Networking) plane separation:
 * Data Plane → Control Plane → Application Plane
 */
export declare enum CardPlane {
    /**
     * DATA_PLANE - MCard
     *
     * Immutable, content-addressable storage.
     * The monadic foundation that wraps effects.
     * CRD-only operations (Create, Retrieve, Delete).
     */
    DATA = "Data",
    /**
     * CONTROL_PLANE - PCard
     *
     * Polynomial functor composition.
     * Monadic execution via PTR.
     * Policy and logic gating.
     */
    CONTROL = "Control",
    /**
     * APPLICATION_PLANE - VCard
     *
     * Value exchange and authentication.
     * Side effect management (IO Monad).
     * Sovereign memory and authorization.
     */
    APPLICATION = "Application"
}
/**
 * Polynomial Functor Type
 *
 * The mathematical foundation for DOTS.
 * Every DOTS component is a polynomial functor of the form:
 * P(X) = Σ_{i∈I} X^{O(i)}
 */
export interface PolynomialFunctor {
    /** Positions (I) - input types, system states */
    positions: string[];
    /** Directions O(i) - output types per position */
    directions: Record<string, string[]>;
}
/**
 * DOTS metadata that can be attached to any card type
 */
export interface DOTSMetadata {
    /** Primary DOTS role (Carrier, Lens, Chart, Arena, Action) */
    role: DOTSRole;
    /** EOS symmetry role */
    eosRole?: EOSRole;
    /** Card plane (Data, Control, Application) */
    plane: CardPlane;
    /** Polynomial functor representation (optional) */
    polynomial?: PolynomialFunctor;
    /** Tight morphism references (prerequisite hashes) */
    tightRefs?: string[];
    /** Loose morphism references (alternative implementation hashes) */
    looseRefs?: string[];
}
/**
 * Create DOTS metadata for an MCard
 */
export declare function createMCardDOTSMetadata(tightRefs?: string[], looseRefs?: string[]): DOTSMetadata;
/**
 * Create DOTS metadata for a PCard (CLM)
 */
export declare function createPCardDOTSMetadata(isLens: boolean, tightRefs?: string[], looseRefs?: string[]): DOTSMetadata;
/**
 * Create DOTS metadata for a VCard
 */
export declare function createVCardDOTSMetadata(): DOTSMetadata;
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