/**
 * CERTIFY — the Optimality Certificate. The thing no black-box optimizer ships: a falsifiable bound on
 * HOW FAR the best-found could be from the true global best.
 *
 * Every optimizer returns "here's the best I found". None tell you "and the true optimum cannot be more
 * than X% better than this" — so you never know if you stopped because it's good or because the optimizer
 * is bad. CERTIFY closes that: assuming the response surface changes no faster than a Lipschitz constant L
 * (ESTIMATED FROM YOUR OWN DATA, then held conservatively), the value at any unobserved point x is bounded
 * by min_i ( f(x_i) + L·‖x − x_i‖ ). Maximising that bound over a space-filling sweep gives a CERTIFIED
 * CEILING the global optimum cannot exceed. Your best vs that ceiling = a provable "within X% of the best
 * possible" — signable alongside the discovery trace.
 *
 * Honest by construction (DIAKRISIS): this is "certified UNDER a data-estimated Lipschitz bound", not an
 * unconditional proof — a black box can hide an arbitrarily sharp spike between samples. We estimate L from
 * the observed pairs and hold a conservative safety factor, and we STATE the assumption. The gauntlet
 * checks the honest, guaranteed properties (the ceiling never sits below what you already saw, it tightens
 * as you sample more, it is deterministic) and that on smooth, well-sampled surfaces the certified gap is
 * small — falsifiable, reproducible.
 */
import { type Space } from "./space.js";
import { type Observation, type Goal } from "./engine.js";
export interface OptimalityCertificate {
    n: number;
    bestObserved: number;
    certifiedCeiling: number;
    gap: number;
    withinPct: number;
    lipschitz: number;
    assumption: string;
}
/**
 * Certify how close the best-found is to the global optimum, under a data-estimated Lipschitz bound.
 * @param obs    the (experiment, value) history
 * @param space  the search space (for normalisation + the sweep)
 * @param goal   maximise | minimise
 * @param safety conservative multiplier on the estimated Lipschitz constant (>=1; default 1.5)
 * @param sweep  number of space-filling probe points for the ceiling (default 2000)
 */
export declare function certifyOptimality(obs: ReadonlyArray<Observation>, space: Space, goal?: Goal, safety?: number, sweep?: number): OptimalityCertificate;
export declare function certifyGauntlet(): Promise<{
    score: 0 | 100;
    checks: Array<{
        name: string;
        pass: boolean;
        detail: string;
    }>;
}>;
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