import { z } from 'zod';
/**
 * Zod schema for backward algorithm result
 */
export declare const BackwardResultSchema: z.ZodObject<{
    beta: z.ZodArray<z.ZodArray<z.ZodNumber>>;
}, z.core.$strip>;
/**
 * TypeScript types derived from Zod schemas
 */
export type BackwardResult = z.infer<typeof BackwardResultSchema>;
/**
 * Validated type after parsing
 */
export type BackwardResultValidated = z.output<typeof BackwardResultSchema>;