import { VecN } from '@holotope/core';
import { type EvaluateXpbdPotentialStateNOptions, type XpbdPotentialStateEvaluationN } from './xpbd-potential-state.js';
import { XpbdParticleN } from './xpbd-world.js';
export interface PredictXpbdInertialStateNOptions {
    readonly dimension: number;
    readonly particles: readonly XpbdParticleN[];
    readonly deltaTime: number;
    /** Constant RN gravity; defaults to zero. */
    readonly gravity?: VecN | ArrayLike<number>;
}
/** Non-mutating explicit prediction used as an optimization-time-step center. */
export interface XpbdInertialPredictionN {
    readonly dimension: number;
    readonly deltaTime: number;
    readonly positions: readonly VecN[];
    readonly accelerations: readonly VecN[];
}
export interface EvaluateXpbdIncrementalPotentialNOptions extends EvaluateXpbdPotentialStateNOptions {
    readonly deltaTime: number;
    /** Prescribed inertial centers paired one-to-one with `particles`. */
    readonly predictedPositions: readonly VecN[];
}
/**
 * Scaled Backward-Euler objective evidence at one RN candidate state.
 *
 * `objective = inertialObjective + deltaTime^2 * potentialEnergy`.
 * Gradients are restricted to free particles; fixed entries are zero.
 */
export interface XpbdIncrementalPotentialEvaluationN {
    readonly dimension: number;
    readonly deltaTime: number;
    readonly objective: number;
    readonly inertialObjective: number;
    readonly scaledConservativeObjective: number;
    readonly conservativePotentialEnergy: number;
    readonly gradients: readonly VecN[];
    readonly inertialGradients: readonly VecN[];
    readonly freeParticleMask: readonly boolean[];
    readonly freeParticleCount: number;
    readonly gradientNorm: number;
    readonly maximumParticleGradientNorm: number;
    /** Full conservative evidence, including gradients at prescribed particles. */
    readonly potential: XpbdPotentialStateEvaluationN;
}
/**
 * Predicts inertial centers from the current particle state without mutation.
 *
 * Registered conservative providers are intentionally absent: their energies
 * belong in the candidate objective. `particle.force` and gravity are treated
 * as explicit external accelerations, matching `XpbdWorldN` prediction.
 */
export declare function predictXpbdInertialStateN(options: PredictXpbdInertialStateNOptions): XpbdInertialPredictionN;
/**
 * Evaluates the scaled mass-plus-potential objective without writing live
 * particles or caller-owned prediction and candidate-position buffers.
 */
export declare function evaluateXpbdIncrementalPotentialN(options: EvaluateXpbdIncrementalPotentialNOptions): XpbdIncrementalPotentialEvaluationN;
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