/** A provenance-driven assignment of one parameter to each source object. */
export interface Decoration<Source, Parameter> {
    readonly id: string;
    parameter(source: Source): Parameter;
}
export interface Decorated<Source, Parameter> {
    readonly source: Source;
    readonly parameter: Parameter;
}
/** Evaluate a decoration while retaining the source provenance beside its parameter. */
export declare function applyDecoration<Source, Parameter>(decoration: Decoration<Source, Parameter>, sources: readonly Source[]): readonly Decorated<Source, Parameter>[];
export interface DecorationEquivarianceGenerator<Source, Parameter> {
    readonly id: string;
    actOnSource(source: Source): Source;
    actOnParameter(parameter: Parameter): Parameter;
}
export interface DecorationEquivarianceMismatch {
    readonly generator: string;
    readonly sourceIndex: number;
    readonly targetKey: string;
    readonly reason: 'missing-target' | 'parameter-mismatch';
}
export interface DecorationEquivarianceReport {
    readonly decoration: string;
    readonly generatorCount: number;
    readonly sourceCount: number;
    readonly checked: number;
    readonly matched: number;
    readonly mismatches: readonly DecorationEquivarianceMismatch[];
    readonly equivariant: boolean;
}
export interface DecorationEquivarianceOptions<Source, Parameter> {
    readonly sources: readonly Source[];
    readonly decoration: Decoration<Source, Parameter>;
    readonly generators: readonly DecorationEquivarianceGenerator<Source, Parameter>[];
    /** Exact stable key for the finite source orbit. */
    sourceKey(source: Source): string;
    /** Equality in the parameter representation; exact decorations should use exact equality. */
    parameterEquals(left: Parameter, right: Parameter): boolean;
}
/**
 * Check `c(g·x) = g~·c(x)` on a finite source orbit.
 *
 * The source key turns every generator action into an explicit permutation.
 * Missing images and parameter failures are reported separately so a clipped
 * sample cannot masquerade as a failed intertwining law.
 */
export declare function checkDecorationEquivariance<Source, Parameter>({ sources, decoration, generators, sourceKey, parameterEquals }: DecorationEquivarianceOptions<Source, Parameter>): DecorationEquivarianceReport;
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