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

Layer 5: Geometric manifolds - the shape of mathematical space

import type { FieldSubstrate } from '@uor-foundation/field-substrate';
import type { ResonanceDynamics } from '@uor-foundation/resonance';
import type { PageTopology } from '@uor-foundation/topology';
import type { ArithmeticOperators } from '@uor-foundation/operators';
import type { AlgebraicStructures } from '@uor-foundation/algebra';
import type { GeometricManifolds, CurvatureTensor, PageManifold, FieldManifold, TangentSpace, UniversalBundle } from './index';
export declare class MathematicalManifold implements GeometricManifolds {
    private fieldSubstrate;
    private resonance;
    private topology;
    private _operators;
    private _algebra;
    constructor(fieldSubstrate: FieldSubstrate, resonance: ResonanceDynamics, topology: PageTopology, _operators: ArithmeticOperators, _algebra: AlgebraicStructures);
    getMetric(a: bigint, b: bigint): number;
    findGeodesic(start: bigint, end: bigint): bigint[];
    getCurvature(n: bigint): CurvatureTensor;
    getPageManifold(pageNumber: bigint): PageManifold;
    getFieldManifold(): FieldManifold;
    getTangentSpace(n: bigint): TangentSpace;
    getUniversalBundle(): UniversalBundle;
    private fieldSpaceDistanceSquared;
    private resonanceBarrierSquared;
    private topologicalDistanceSquared;
    private getNeighbors;
    private computeRicciCurvature;
    private computeSectionalCurvature;
    private computeFieldSpaceCurvature;
    private computeMetricTensor;
    private computeDeterminant;
    private getMinor;
    private computeConnection;
    private applyConnection;
    private computeCurvatureForm;
}
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