@uor-foundation/geometry/dist/field-space.d.ts

Layer 5: Geometric manifolds - the shape of mathematical space

import type { FieldSubstrate } from '@uor-foundation/field-substrate';
import type { FieldManifold } from './index';
export interface FieldCoordinate {
    pattern: boolean[];
    index: number;
    activeCount: number;
}
export interface FieldNeighborhood {
    center: FieldCoordinate;
    neighbors: FieldCoordinate[];
    radius: number;
}
export declare class FieldSpaceGeometry {
    private fieldSubstrate;
    private readonly dimension;
    private readonly totalPatterns;
    constructor(fieldSubstrate: FieldSubstrate);
    getFieldCoordinate(n: bigint): FieldCoordinate;
    patternToIndex(pattern: boolean[]): number;
    indexToPattern(index: number): boolean[];
    hammingDistance(p1: boolean[], p2: boolean[]): number;
    fieldSpaceDistance(coord1: FieldCoordinate, coord2: FieldCoordinate): number;
    getNeighborhood(coord: FieldCoordinate, radius: number): FieldNeighborhood;
    getFieldPath(start: FieldCoordinate, end: FieldCoordinate): FieldCoordinate[];
    getOrthogonalBasis(coord: FieldCoordinate): boolean[][];
    getFieldVolume(region: FieldCoordinate[]): number;
    isConnected(region: FieldCoordinate[]): boolean;
    getGrayCodePath(): FieldCoordinate[];
    getHypercubeEmbedding(): Map<number, number[]>;
    getFieldManifold(): FieldManifold;
    private computeHypercubeCurvature;
    projectToLowerDimension(coord: FieldCoordinate, dimensions: number[]): boolean[];
    liftFromLowerDimension(lowDimPattern: boolean[], dimensions: number[]): FieldCoordinate;
    getSymmetryGroup(): string[];
    applySymmetry(coord: FieldCoordinate, symmetry: string): FieldCoordinate;
}
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