diff --git a/ROADMAP.md b/ROADMAP.md
index 391840b..da91b37 100644
--- a/ROADMAP.md
+++ b/ROADMAP.md
@@ -116,7 +116,7 @@
   - [ ] Closest pair of points solver for geometry toolkit
 
 ## Milestone 0.6.0 – Fold Barrier Physics Suite (Planned)
-- [ ] Align Fold barrier scope with the paper and define shared constraint interfaces in `src/physics/fold`
+- [x] Align Fold barrier scope with the paper and define shared constraint interfaces in `src/physics/fold`
 - **Barrier primitives** (each item: runtime module + `docs/index.d.ts` entry + Vitest coverage + runnable example when feasible)
   - [ ] Cubic barrier potential (energy, gradient, Hessian evaluation)
   - [ ] Stiffness design principle for frozen barrier stiffness
diff --git a/docs/index.d.ts b/docs/index.d.ts
index ba76c62..723aa36 100644
--- a/docs/index.d.ts
+++ b/docs/index.d.ts
@@ -115,6 +115,9 @@ export const examples: {
     readonly lz77Compress: 'examples/lz77.ts';
     readonly lz77Decompress: 'examples/lz77.ts';
   };
+  readonly physics: {
+    readonly createFoldConstraintRegistry: 'examples/foldSetup.ts';
+  };
   readonly performance: {
     readonly debounce: 'examples/requestDedup.ts';
     readonly throttle: 'examples/requestDedup.ts';
@@ -3285,6 +3288,80 @@ export function bresenhamLine(start: Point, end: Point): Point[];
 export interface ClosestPairResult { distance: number; pair: [Point, Point] | null }
 export function closestPair(points: ReadonlyArray<Point>): ClosestPairResult;
 
+// ============================================================================
+// ⚙️ PHYSICS & FOLD BARRIERS
+// ============================================================================
+
+/**
+ * Registry for Fold constraint factory implementations.
+ * Use for: hooking cubic/contact/wall barrier evaluators into the solver.
+ * Import: physics/fold/index.ts
+ */
+export function createFoldConstraintRegistry(): FoldConstraintRegistry;
+
+export type FoldConstraintType =
+  | 'cubic-barrier'
+  | 'contact-barrier'
+  | 'pin-barrier'
+  | 'wall-barrier'
+  | 'strain-barrier'
+  | 'friction'
+  | 'assembly'
+  | 'gap-evaluator';
+
+export interface FoldConstraintState {
+  gap: number;
+  maxGap: number;
+  stiffness: number;
+  direction: Vector3D;
+  extendedDirection?: Vector3D;
+  effectiveMass?: number;
+  metadata?: Record<string, unknown>;
+}
+
+export interface FoldComputationContext {
+  deltaTime: number;
+  iteration?: number;
+  time?: number;
+}
+
+export interface FoldConstraintEvaluation {
+  energy: number;
+  gradient: Vector3D;
+  hessian: Matrix3x3;
+}
+
+export interface FoldConstraint<TState = FoldConstraintState, TResult = FoldConstraintEvaluation> {
+  readonly type: FoldConstraintType;
+  readonly id?: string;
+  enabled: boolean;
+  evaluate(state: TState, context: FoldComputationContext): TResult;
+}
+
+export interface FoldConstraintFactory<TConfig, TState = FoldConstraintState, TResult = FoldConstraintEvaluation> {
+  readonly type: FoldConstraintType;
+  create(config: TConfig): FoldConstraint<TState, TResult>;
+}
+
+export interface FoldConstraintRegistry {
+  register<TConfig>(factory: FoldConstraintFactory<TConfig>): void;
+  get(type: FoldConstraintType): FoldConstraintFactory<unknown> | undefined;
+  list(): ReadonlyArray<FoldConstraintFactory<unknown>>;
+}
+
+export interface FoldSolverSettings {
+  maxIterations: number;
+  tolerance: number;
+  allowEarlyExit?: boolean;
+}
+
+export interface FoldSystemState {
+  positions: Array<Vector3D>;
+  velocities: Array<Vector3D>;
+  constraints: Array<FoldConstraint>;
+  settings: FoldSolverSettings;
+}
+
 /**
  * Common easing curves for animation.
  * Use for: UI transitions, motion design, data viz.
@@ -3717,6 +3794,12 @@ export interface Vector3D {
   z: number;
 }
 
+export type Matrix3x3 = [
+  [number, number, number],
+  [number, number, number],
+  [number, number, number]
+];
+
 export interface Rect {
   x: number;
   y: number;
diff --git a/examples/foldSetup.ts b/examples/foldSetup.ts
new file mode 100644
index 0000000..1ad66bb
--- /dev/null
+++ b/examples/foldSetup.ts
@@ -0,0 +1,27 @@
+import { createFoldConstraintRegistry } from '../src/index.js';
+
+const registry = createFoldConstraintRegistry();
+
+registry.register({
+  type: 'cubic-barrier',
+  create(config: { stiffness: number }) {
+    return {
+      type: 'cubic-barrier',
+      enabled: true,
+      evaluate(state) {
+        const stiffness = config.stiffness;
+        return {
+          energy: stiffness * state.gap ** 2,
+          gradient: { x: 0, y: 0, z: 0 },
+          hessian: [
+            [stiffness, 0, 0],
+            [0, stiffness, 0],
+            [0, 0, stiffness],
+          ],
+        };
+      },
+    };
+  },
+});
+
+console.log(registry.list().length);
diff --git a/src/index.ts b/src/index.ts
index 33ce7a6..dd16494 100644
--- a/src/index.ts
+++ b/src/index.ts
@@ -113,6 +113,9 @@ export const examples = {
     lz77Compress: 'examples/lz77.ts',
     lz77Decompress: 'examples/lz77.ts',
   },
+  physics: {
+    createFoldConstraintRegistry: 'examples/foldSetup.ts',
+  },
   performance: {
     debounce: 'examples/requestDedup.ts',
     throttle: 'examples/requestDedup.ts',
@@ -1180,6 +1183,24 @@ export { bresenhamLine } from './geometry/bresenham.js';
 export { closestPair } from './geometry/closestPair.js';
 export type { ClosestPairResult } from './geometry/closestPair.js';
 
+// ============================================================================
+// ⚙️ PHYSICS & FOLD BARRIERS
+// ============================================================================
+
+export { createFoldConstraintRegistry } from './physics/fold/index.js';
+
+export type {
+  FoldConstraintType,
+  FoldConstraintState,
+  FoldComputationContext,
+  FoldConstraintEvaluation,
+  FoldConstraint,
+  FoldConstraintFactory,
+  FoldConstraintRegistry,
+  FoldSolverSettings,
+  FoldSystemState,
+} from './physics/fold/index.js';
+
 // ============================================================================
 // 🎨 VISUAL & ANIMATION
 // ============================================================================
diff --git a/src/physics/fold/index.ts b/src/physics/fold/index.ts
new file mode 100644
index 0000000..d470296
--- /dev/null
+++ b/src/physics/fold/index.ts
@@ -0,0 +1 @@
+export * from './types.js';
diff --git a/src/physics/fold/types.ts b/src/physics/fold/types.ts
new file mode 100644
index 0000000..e156269
--- /dev/null
+++ b/src/physics/fold/types.ts
@@ -0,0 +1,90 @@
+import type { Matrix3x3, Vector3D } from '../../types.js';
+
+export type FoldConstraintType =
+  | 'cubic-barrier'
+  | 'contact-barrier'
+  | 'pin-barrier'
+  | 'wall-barrier'
+  | 'strain-barrier'
+  | 'friction'
+  | 'assembly'
+  | 'gap-evaluator';
+
+export interface FoldConstraintState {
+  /** Signed distance or constraint gap value. */
+  gap: number;
+  /** Maximum admissible distance before penalties engage. */
+  maxGap: number;
+  /** Effective stiffness (frozen) for this evaluation. */
+  stiffness: number;
+  /** Primary constraint direction or normal. */
+  direction: Vector3D;
+  /** Optional extended direction used by Fold contact formulations. */
+  extendedDirection?: Vector3D;
+  /** Effective mass or mass-like term used for stiffness design. */
+  effectiveMass?: number;
+  /** Optional metadata bag for constraint-specific state. */
+  metadata?: Record<string, unknown>;
+}
+
+export interface FoldComputationContext {
+  /** Current simulation time step. */
+  deltaTime: number;
+  /** Iteration index inside the solver/integrator. */
+  iteration?: number;
+  /** Optional absolute time for schedule dependent systems. */
+  time?: number;
+}
+
+export interface FoldConstraintEvaluation {
+  energy: number;
+  gradient: Vector3D;
+  hessian: Matrix3x3;
+}
+
+export interface FoldConstraint<TState = FoldConstraintState, TResult = FoldConstraintEvaluation> {
+  readonly type: FoldConstraintType;
+  readonly id?: string;
+  enabled: boolean;
+  evaluate(state: TState, context: FoldComputationContext): TResult;
+}
+
+export interface FoldConstraintFactory<TConfig, TState = FoldConstraintState, TResult = FoldConstraintEvaluation> {
+  readonly type: FoldConstraintType;
+  create(config: TConfig): FoldConstraint<TState, TResult>;
+}
+
+export interface FoldConstraintRegistry {
+  register<TConfig>(factory: FoldConstraintFactory<TConfig>): void;
+  get(type: FoldConstraintType): FoldConstraintFactory<unknown> | undefined;
+  list(): ReadonlyArray<FoldConstraintFactory<unknown>>;
+}
+
+export function createFoldConstraintRegistry(): FoldConstraintRegistry {
+  const factories = new Map<FoldConstraintType, FoldConstraintFactory<unknown>>();
+
+  return {
+    register<TConfig>(factory: FoldConstraintFactory<TConfig>) {
+      factories.set(factory.type, factory as FoldConstraintFactory<unknown>);
+    },
+    get(type: FoldConstraintType) {
+      return factories.get(type);
+    },
+    list() {
+      return Array.from(factories.values());
+    },
+  };
+}
+
+export interface FoldSolverSettings {
+  maxIterations: number;
+  tolerance: number;
+  allowEarlyExit?: boolean;
+}
+
+export interface FoldSystemState {
+  positions: Array<Vector3D>;
+  velocities: Array<Vector3D>;
+  constraints: Array<FoldConstraint>;
+  settings: FoldSolverSettings;
+}
diff --git a/src/types.ts b/src/types.ts
index 553fbbb..650e1ba 100644
--- a/src/types.ts
+++ b/src/types.ts
@@ -18,6 +18,12 @@ export interface Vector3D {
   z: number;
 }
 
+export type Matrix3x3 = [
+  [number, number, number],
+  [number, number, number],
+  [number, number, number]
+];
+
 export interface Rect {
   x: number;
   y: number;
diff --git a/tests/fold.test.ts b/tests/fold.test.ts
new file mode 100644
index 0000000..4cad3da
--- /dev/null
+++ b/tests/fold.test.ts
@@ -0,0 +1,72 @@
+import { describe, expect, expectTypeOf, it } from 'vitest';
+
+import {
+  createFoldConstraintRegistry,
+  type FoldConstraint,
+  type FoldConstraintEvaluation,
+  type FoldConstraintState,
+  type FoldConstraintType,
+} from '../src/physics/fold/index.js';
+
+const testConstraint: FoldConstraint = {
+  type: 'cubic-barrier',
+  enabled: true,
+  evaluate(state) {
+    return {
+      energy: state.gap ** 2,
+      gradient: { x: 0, y: 0, z: 0 },
+      hessian: [
+        [1, 0, 0],
+        [0, 1, 0],
+        [0, 0, 1],
+      ],
+    };
+  },
+};
+
+const registry = createFoldConstraintRegistry();
+registry.register({
+  type: 'cubic-barrier',
+  create: () => testConstraint,
+});
+
+describe('Fold constraint registry', () => {
+  it('registers and retrieves factories', () => {
+    expect(registry.get('cubic-barrier')).toBeDefined();
+    expect(registry.list()).toHaveLength(1);
+  });
+
+  it('evaluates through registered constraint', () => {
+    const factory = registry.get('cubic-barrier');
+    expect(factory).toBeDefined();
+    if (!factory) return;
+
+    const instance = factory.create({} as unknown);
+    const evaluation = instance.evaluate(
+      {
+        gap: 0.1,
+        maxGap: 1,
+        stiffness: 10,
+        direction: { x: 0, y: 0, z: 1 },
+      },
+      { deltaTime: 1 }
+    );
+
+    expect(evaluation.energy).toBeTypeOf('number');
+  });
+
+  it('provides type safety helpers', () => {
+    expectTypeOf<FoldConstraintType>().toEqualTypeOf<
+      | 'cubic-barrier'
+      | 'contact-barrier'
+      | 'pin-barrier'
+      | 'wall-barrier'
+      | 'strain-barrier'
+      | 'friction'
+      | 'assembly'
+      | 'gap-evaluator'
+    >();
+
+    expectTypeOf<FoldConstraint>().toMatchTypeOf<FoldConstraint<FoldConstraintState, FoldConstraintEvaluation>>();
+  });
+});
diff --git a/tests/index.test.ts b/tests/index.test.ts
index c64928b..341ff08 100644
--- a/tests/index.test.ts
+++ b/tests/index.test.ts
@@ -57,6 +57,7 @@ describe('package entry point', () => {
     expect(examples.spatial.buildBvh).toBe('examples/bvh.ts');
     expect(examples.spatial.queryBvh).toBe('examples/bvh.ts');
     expect(examples.spatial.raycastBvh).toBe('examples/bvh.ts');
+    expect(examples.physics.createFoldConstraintRegistry).toBe('examples/foldSetup.ts');
   });
 
   it('provides strong typing for example categories and names', () => {
@@ -71,6 +72,7 @@ describe('package entry point', () => {
       | 'gameplay'
       | 'graph'
       | 'geometry'
+      | 'physics'
       | 'visual'
     >();
 
@@ -195,6 +197,10 @@ describe('package entry point', () => {
       | 'closestPair'
     >();
 
+    expectTypeOf<ExampleName<'physics'>>().toEqualTypeOf<
+      'createFoldConstraintRegistry'
+    >();
+
     expectTypeOf<ExampleName<'ai'>>().toEqualTypeOf<
       | 'seek'
       | 'flee'