@uor-foundation/geometry/dist/resonance-surface.d.ts

Layer 5: Geometric manifolds - the shape of mathematical space

import type { ResonanceDynamics } from '@uor-foundation/resonance';
import type { PageTopology } from '@uor-foundation/topology';
export interface ResonanceSurface {
    center: bigint;
    radius: bigint;
    values: Map<bigint, number>;
    criticalPoints: CriticalPoint[];
}
export interface CriticalPoint {
    position: bigint;
    value: number;
    type: 'minimum' | 'maximum' | 'saddle';
    hessian: number;
}
export interface EnergyLandscape {
    bounds: {
        min: bigint;
        max: bigint;
    };
    resolution: bigint;
    potential: Map<bigint, number>;
    gradientField: Map<bigint, number>;
    flowLines: FlowLine[];
}
export interface FlowLine {
    start: bigint;
    path: bigint[];
    endpoint: bigint;
    endpointType: 'minimum' | 'boundary';
}
export declare class ResonanceSurfaceAnalyzer {
    private resonance;
    private topology;
    constructor(resonance: ResonanceDynamics, topology: PageTopology);
    computeResonanceSurface(center: bigint, radius: bigint): ResonanceSurface;
    findCriticalPoints(surface: Map<bigint, number>): CriticalPoint[];
    computeEnergyLandscape(min: bigint, max: bigint, resolution?: bigint): EnergyLandscape;
    computeFlowLines(potential: Map<bigint, number>, gradientField: Map<bigint, number>, min: bigint, max: bigint, resolution: bigint): FlowLine[];
    followGradientFlow(start: bigint, gradientField: Map<bigint, number>, min: bigint, max: bigint, resolution: bigint): FlowLine;
    findBasinsOfAttraction(landscape: EnergyLandscape): Map<bigint, bigint[]>;
    computePotentialBarrier(from: bigint, to: bigint): number;
    private findOptimalPath;
    visualizeSlice(surface: ResonanceSurface): string;
    computeMorseComplex(landscape: EnergyLandscape): MorseComplex;
    private findMorseConnections;
}
interface MorseComplex {
    criticalPoints: CriticalPoint[];
    connections: Array<[bigint, bigint]>;
    dimension: number;
}
export {};
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