/** Dense reference policy for modifying provider-local potential curvature. */
export interface XpbdProviderLocalPsdCurvaturePolicyN {
    /** Explicit opt-in discriminator. */
    readonly kind: 'provider-local-psd';
    /** Relative tolerance used to audit reconstructed Hessian symmetry. */
    readonly symmetryTolerance?: number;
    /** Relative convergence tolerance forwarded to the dense eigensolver. */
    readonly eigensolverTolerance?: number;
    /** Maximum cyclic Jacobi sweeps per provider-local matrix. */
    readonly eigensolverMaximumSweeps?: number;
}
/** Dense reference policy for PSD-projecting provider-declared local blocks. */
export interface XpbdProviderBlockPsdCurvaturePolicyN {
    /** Explicit block-local opt-in discriminator. */
    readonly kind: 'provider-block-psd';
    /** Relative tolerance used to audit every reconstructed block's symmetry. */
    readonly symmetryTolerance?: number;
    /** Relative tolerance for raw block assembly against the aggregate HVP. */
    readonly decompositionTolerance?: number;
    /** Relative convergence tolerance forwarded to each dense eigensolve. */
    readonly eigensolverTolerance?: number;
    /** Maximum cyclic Jacobi sweeps for each local block. */
    readonly eigensolverMaximumSweeps?: number;
}
/**
 * Curvature used by analytic incremental-potential composition.
 *
 * `'exact'` is the default and preserves the providers' mathematical
 * Hessians. Provider-local PSD reconstructs one dense matrix per provider.
 * Provider-block PSD instead projects an exact provider-authored additive
 * decomposition, falling back visibly to one implicit provider block when no
 * finer decomposition exists.
 */
export type XpbdIncrementalPotentialCurvaturePolicyN = 'exact' | XpbdProviderLocalPsdCurvaturePolicyN | XpbdProviderBlockPsdCurvaturePolicyN;
/** Normalized policy name retained in result evidence. */
export type XpbdIncrementalPotentialCurvaturePolicyKindN = 'exact' | 'provider-local-psd' | 'provider-block-psd';
/** Evidence for one unchanged exact provider product. */
export interface XpbdConservativeExactCurvatureApplicationN {
    /** Confirms the mathematical provider HVP was used unchanged. */
    readonly kind: 'exact';
    /** One provider HVP evaluates the requested direction. */
    readonly operatorEvaluations: 1;
}
/** Evidence for one dense provider-local PSD projection. */
export interface XpbdConservativeProviderLocalPsdApplicationN {
    /** Confirms that negative local eigenvalues were clamped to zero. */
    readonly kind: 'provider-local-psd';
    /** Scalar variables in provider particle-major, axis-minor order. */
    readonly localVariableCount: number;
    /**
     * One provider HVP per local basis vector.
     *
     * A compiled fixed-coordinate operator may pay this construction once and
     * reuse it across several products.
     */
    readonly operatorEvaluations: number;
    /** Eigenvalues of the audited symmetric local Hessian, ascending. */
    readonly rawEigenvalues: Float64Array;
    /** `max(rawEigenvalues[i], 0)` in the same order. */
    readonly projectedEigenvalues: Float64Array;
    /** Number of strictly negative raw eigenvalues that were clamped. */
    readonly clippedEigenvalueCount: number;
    /** Maximum absolute skew divided by the local matrix scale. */
    readonly relativeSymmetryError: number;
    /** Largest eigensystem residual reported by the dense CPU reference. */
    readonly eigensystemMaxResidual: number;
    /** Maximum absolute entry of `VᵀV - I`. */
    readonly eigensystemOrthogonalityError: number;
}
/** Spectral evidence for one PSD-projected provider curvature block. */
export interface XpbdConservativePsdBlockApplicationN {
    /** Stable identity unique within the owning provider. */
    readonly blockId: string;
    /** Stable particle ids in block product order. */
    readonly particleIds: readonly string[];
    /** Scalar variables in block particle-major, axis-minor order. */
    readonly localVariableCount: number;
    /**
     * One exact block HVP per local basis vector, paid once by a compiled
     * fixed-coordinate operator.
     */
    readonly operatorEvaluations: number;
    /** Eigenvalues of the audited symmetric block Hessian, ascending. */
    readonly rawEigenvalues: Float64Array;
    /** `max(rawEigenvalues[i], 0)` in the same order. */
    readonly projectedEigenvalues: Float64Array;
    /** Number of strictly negative block eigenvalues that were clamped. */
    readonly clippedEigenvalueCount: number;
    /** Maximum absolute block skew divided by its matrix scale. */
    readonly relativeSymmetryError: number;
    /** Largest block eigensystem residual from the dense CPU reference. */
    readonly eigensystemMaxResidual: number;
    /** Maximum absolute entry of the block's `VᵀV - I`. */
    readonly eigensystemOrthogonalityError: number;
}
/** Evidence for PSD projection over declared or implicit provider blocks. */
export interface XpbdConservativeProviderBlockPsdApplicationN {
    /** Confirms block-local rather than whole-provider projection. */
    readonly kind: 'provider-block-psd';
    /** Whether the provider supplied a finer sum or formed one implicit block. */
    readonly decomposition: 'declared' | 'implicit-provider';
    /** Number of independently projected blocks. */
    readonly blockCount: number;
    /**
     * Sum of block-basis HVPs plus one exact aggregate audit HVP.
     *
     * Compilation may reuse the basis portion; the aggregate audit remains
     * direction-specific.
     */
    readonly operatorEvaluations: number;
    /** Relative norm error of raw block assembly against the aggregate HVP. */
    readonly rawAssemblyRelativeError: number;
    /** Source-ordered spectral evidence for every projected block. */
    readonly blocks: readonly XpbdConservativePsdBlockApplicationN[];
}
/** Provider-local curvature construction attached to product evidence. */
export type XpbdConservativeCurvatureApplicationN = XpbdConservativeExactCurvatureApplicationN | XpbdConservativeProviderLocalPsdApplicationN | XpbdConservativeProviderBlockPsdApplicationN;
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