refactor: 将子模块转为普通目录，移除外部 git 依赖

- 移除 JEPA/lejepa-identifiability 子模块 gitlink
- 移除 research/multiply/MultiPLY 子模块 gitlink
- 删除 .gitmodules（不再有外部 URL 依赖）
- 两个目录内容作为普通文件纳入主仓库追踪
- 删除各自内部 .git 目录，消除嵌套 git 仓库

JEPA/lejepa-identifiability/lean/LeJEPA.lean

@@ -0,0 +1,65 @@
+import LeJEPA.Hermite
+import LeJEPA.Uniqueness
+import LeJEPA.Approx
+import LeJEPA.Dirichlet
+import LeJEPA.Planning
+
+/-!
+# LeJEPA Identifiability: Formal Verification in Lean 4
+
+Comprehensive formalization of the theoretical results in the paper.
+
+## Files
+
+- **`LeJEPA.Hermite`**: Main theorem (Theorem 4.1) via Hermite
+  polynomial spectral decomposition and the correlation bound.
+
+- **`LeJEPA.Uniqueness`**: Converse direction (Theorem 4.2), that
+  the Gaussian is the unique latent distribution yielding linear
+  identifiability under the Sturm–Liouville operator.
+
+- **`LeJEPA.Approx`**: Approximate identifiability bound
+  (Theorem 4.3) with D + (ε + D)² recovery error.
+
+- **`LeJEPA.Dirichlet`**: Alternative proof (Appendix D) via
+  Dirichlet energy, AM-GM / Jensen, and Mazur–Ulam.
+
+- **`LeJEPA.Planning`**: Planning equivalence corollary
+  (Corollary 4.5): under orthogonal identifiability, expected
+  costs, optimal values, and optimal plans coincide between the
+  learned latent and the true latent for any O(n)-invariant cost.
+
+## Verification Summary
+
+  | Component                            | Status      |
+  |--------------------------------------|-------------|
+  | Hermite basis & completeness         | axiomatized |
+  | Contraction lemma (ρᵈ decay)         | axiomatized |
+  | Mehler's formula                     | axiomatized |
+  | Correlation bound ≤ ρ                | VERIFIED    |
+  | Equality ⟺ w₁ = 1 (linearity)       | VERIFIED    |
+  | Loss lower bound 2(1−ρ)n             | VERIFIED    |
+  | Hermite theorem assembly h = Qz      | VERIFIED    |
+  | Affine eigenfunction → affine score  | VERIFIED    |
+  | Affine score → Gaussian density      | axiomatized |
+  | Gaussian → Hermite eigenfunctions    | axiomatized |
+  | Gaussian uniqueness biconditional    | VERIFIED    |
+  | Polar decomposition                  | axiomatized |
+  | Cross-degree Hermite orthogonality   | axiomatized |
+  | Spectral gap → W_nl ≤ D              | VERIFIED    |
+  | ‖M − Q‖²_F bound                     | VERIFIED    |
+  | Pythagorean decomposition            | axiomatized |
+  | Bound monotonicity                   | VERIFIED    |
+  | Approximate bound assembly           | VERIFIED    |
+  | Exact recovery (δ = ε = 0)           | VERIFIED    |
+  | AM-GM / Jensen                       | axiomatized |
+  | Mazur–Ulam                           | axiomatized |
+  | Orthogonal Jacobian → Lipschitz      | VERIFIED    |
+  | Bilipschitz → global isometry        | VERIFIED    |
+  | Dirichlet theorem assembly h = Qz    | VERIFIED    |
+  | Trajectory pushforward (stage/term)  | axiomatized |
+  | Per-step stage / terminal equiv.     | VERIFIED    |
+  | Planning equivalence (main step)     | VERIFIED    |
+  | Minimizer equivalence                | VERIFIED    |
+  | Value equivalence                    | VERIFIED    |
+-/