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

Layer 5: Geometric manifolds - the shape of mathematical space

export interface GeometricManifolds {
    getMetric(a: bigint, b: bigint): number;
    findGeodesic(start: bigint, end: bigint): bigint[];
    getCurvature(n: bigint): CurvatureTensor;
}
export interface CurvatureTensor {
    scalar: number;
    ricci: number[][];
    sectional: Map<string, number>;
}
export interface PageManifold {
    basePoint: bigint;
    dimension: number;
    curvature: number;
    lagrangeWells: bigint[];
}
import type { FieldPattern } from '@uor-foundation/field-substrate';
export interface ExtendedFieldPattern {
    pattern: FieldPattern;
    activeFields: number[];
}
export interface FieldManifold {
    dimension: 8;
    points: ExtendedFieldPattern[];
    metric: (p1: ExtendedFieldPattern, p2: ExtendedFieldPattern) => number;
    curvature: CurvatureTensor;
    topology: 'torus';
}
export interface TangentSpace {
    basePoint: bigint;
    dimension: number;
    basis: TangentVector[];
    metric: RiemannianMetric;
}
export interface TangentVector {
    components: number[];
    magnitude: number;
}
export interface RiemannianMetric {
    tensor: number[][];
    determinant: number;
}
export interface UniversalBundle {
    base: 'NumberLine';
    fiber: 'FieldSpace';
    projection: (n: bigint, fields: ExtendedFieldPattern) => bigint;
    connection: FieldConnection;
}
export interface FieldConnection {
    parallelTransport: (v: TangentVector, path: bigint[]) => TangentVector;
    curvatureForm: number[][];
}
export * from './manifold';
export * from './metric';
export * from './geodesics';
export * from './field-space';
export * from './resonance-surface';
export * from './topology';
export * from './differential';
export * from './embedding';
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