@uor-foundation/geometry/dist/topology.d.ts

Layer 5: Geometric manifolds - the shape of mathematical space

import type { PageTopology } from '@uor-foundation/topology';
import type { FieldSubstrate } from '@uor-foundation/field-substrate';
export interface Loop {
    basePoint: bigint;
    path: bigint[];
    isClosed: boolean;
    windingNumber: number;
}
export interface HomologyGroup {
    dimension: number;
    rank: number;
    torsion: number[];
    generators: Loop[][];
}
export interface FundamentalGroup {
    basePoint: bigint;
    generators: Loop[];
    relations: string[];
}
export interface EulerCharacteristic {
    vertices: number;
    edges: number;
    faces: number;
    chi: number;
}
export declare class TopologicalInvariants {
    private topology;
    private fieldSubstrate;
    private fieldSpaceGeometry;
    constructor(topology: PageTopology, fieldSubstrate: FieldSubstrate);
    computeFundamentalGroup(basePoint: bigint, radius: bigint): FundamentalGroup;
    findLoopGenerators(basePoint: bigint, _radius: bigint): Loop[];
    createFieldCycleLoop(basePoint: bigint): Loop | null;
    createLagrangeLoop(basePoint: bigint, lagrangePoint: bigint): Loop | null;
    createPageBoundaryLoop(basePoint: bigint): Loop | null;
    computeHomologyGroups(maxDimension: number): HomologyGroup[];
    private computeH0;
    private computeH1;
    private computeH2;
    computeEulerCharacteristic(region: bigint[]): EulerCharacteristic;
    computeBettiNumbers(maxDimension: number): number[];
    isContractible(loop: Loop): boolean;
    simplifyLoop(loop: Loop): Loop;
    computeGenus(): number;
    detectHoles(region: bigint[]): bigint[][];
    private findRelations;
    private computeCommutator;
    private getPageNumber;
    private findLagrangePointsInPage;
    private patternsEqual;
    private createPath;
    private computeWindingNumber;
    private createFieldDimensionLoop;
    private createPageCycleLoop;
    private areAdjacent;
    private countFaces;
    private getSampleRegion;
    private findBoundary;
    private findConnectedComponents;
    private exploreComponent;
}
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