import { VecN } from '@holotope/core';
export interface AnalyzeLinearSimplexOrientationNOptions {
    /** Non-degenerate full-dimensional N-simplex defining positive material orientation. */
    readonly restPositions: readonly VecN[];
    /** Particle positions at normalized trajectory time zero. */
    readonly startPositions: readonly VecN[];
    /** Particle positions at normalized trajectory time one. */
    readonly endPositions: readonly VecN[];
    /** Required signed current/rest measure ratio. Zero detects collapse/inversion. */
    readonly minimumSignedMeasureRatio: number;
    /** Smallest unresolved normalized-time interval. Default 2^-30. */
    readonly timeTolerance?: number;
    /** Hard de Casteljau subdivision depth. Default 48. */
    readonly maximumDepth?: number;
    /** Relative Bernstein-coefficient tolerance. Default 256 * Number.EPSILON. */
    readonly relativeCoefficientTolerance?: number;
}
/**
 * Evidence shared by every outcome of one linear orientation analysis.
 *
 * Unlike measure, the signed ratio carries a sign, so crossing the threshold
 * means the simplex inverted rather than merely flattened. The fields record
 * the polynomial analysed along the trajectory and the tolerances used, so an
 * outcome can be reproduced from the record without re-deriving it.
 */
export interface LinearSimplexOrientationAnalysisBaseN {
    /** Euclidean dimension shared by the simplex vertices. */
    readonly dimension: number;
    /** Degree of the signed-ratio polynomial in normalized time. */
    readonly degree: number;
    /** Required signed current/rest measure ratio, as authored. */
    readonly minimumSignedMeasureRatio: number;
    /** Signed measure ratio at normalized time zero. */
    readonly startSignedMeasureRatio: number;
    /** Signed measure ratio at normalized time one. */
    readonly endSignedMeasureRatio: number;
    /** Coefficients of `signedRatio(t) - minimumSignedMeasureRatio` in powers of t. */
    readonly monomialCoefficients: Float64Array;
    /** The same threshold polynomial in the Bernstein basis on [0,1]. */
    readonly bernsteinCoefficients: Float64Array;
    /** Smallest normalized-time interval the subdivision will not split. */
    readonly timeTolerance: number;
    /** Hard de Casteljau subdivision depth, bounding the search regardless. */
    readonly maximumDepth: number;
    /** Bernstein-coefficient tolerance relative to the coefficient scale. */
    readonly relativeCoefficientTolerance: number;
    /** Absolute Bernstein-coefficient tolerance derived from that scale. */
    readonly absoluteCoefficientTolerance: number;
}
export interface LinearSimplexOrientationSafeN extends LinearSimplexOrientationAnalysisBaseN {
    readonly status: 'safe';
    /** Conservative positive lower bound assembled from accepted Bernstein leaves. */
    readonly minimumMarginLowerBound: number;
}
export interface LinearSimplexOrientationInitialViolationN extends LinearSimplexOrientationAnalysisBaseN {
    readonly status: 'initial-violation';
    readonly initialMargin: number;
}
export interface LinearSimplexOrientationPossibleViolationN extends LinearSimplexOrientationAnalysisBaseN {
    readonly status: 'possible-violation';
    /** Earliest conservative normalized-time enclosure that could meet the threshold. */
    readonly timeBracket: readonly [number, number];
    readonly candidateTime: number;
    readonly marginAtBracketStart: number;
    readonly marginAtBracketEnd: number;
    readonly bernsteinBounds: readonly [number, number];
    readonly reason: 'negative-enclosure' | 'resolution-limit';
}
export type LinearSimplexOrientationAnalysisN = LinearSimplexOrientationSafeN | LinearSimplexOrientationInitialViolationN | LinearSimplexOrientationPossibleViolationN;
/**
 * Conservatively checks a linear full-dimensional simplex trajectory.
 *
 * `det(A + tB)` is assembled exactly with respect to the chosen Float64
 * determinant routine by multilinearity over column subsets. Bernstein convex
 * hull bounds and left-to-right de Casteljau subdivision then exclude the
 * complete interval or return its earliest unresolved threshold enclosure.
 *
 * The reference coefficient construction costs O(2^N N^3). It is intended as
 * an auditable small-N golden path, not a high-dimensional performance backend.
 */
export declare function analyzeLinearSimplexOrientationN(options: AnalyzeLinearSimplexOrientationNOptions): LinearSimplexOrientationAnalysisN;
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