meta-log-db/dist/extensions/homology/types.d.ts

Native database package for Meta-Log (ProLog, DataLog, R5RS)

/**
 * Chain Complex and Homology Types
 *
 * Types for algebraic topology chain complexes and homology validation
 */
/**
 * Cell in a chain complex
 * @template N - Dimension (0, 1, 2, 3, or 4)
 */
export interface Cell<N extends 0 | 1 | 2 | 3 | 4> {
    id: string;
    dim: N;
    boundary: string[];
    data: any;
}
/**
 * Chain Complex structure
 *
 * A chain complex is a sequence of abelian groups (C₀, C₁, C₂, C₃, C₄)
 * connected by boundary operators (∂₁, ∂₂, ∂₃, ∂₄)
 *
 * Property: ∂_{n-1} ∘ ∂_n = 0 (boundary of boundary is zero)
 */
export interface ChainComplex {
    C0: Cell<0>[];
    C1: Cell<1>[];
    C2: Cell<2>[];
    C3: Cell<3>[];
    C4: Cell<4>[];
    boundary: Map<string, string[]>;
}
/**
 * Homology validation result
 */
export interface HomologyResult {
    valid: boolean;
    betti: number[];
    eulerCharacteristic: number;
    violations?: string[];
}
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