content(app-G): 补全局部可辨识与时间退化解释

复用实切空间投影，说明有限距离模型中的幅相及未知 rate 消元。给出单有效采样和双采样单帧退化，保留 IP 块内斜率与不同帧时刻的恢复条件。

扩展现有 NumPy 确定性检查；SyncTeX 编译通过，无断引用。例子不替代实际配置验收，不增加 MC。

check_finite_range_bearing.py

@@ -224,7 +224,46 @@ def main():
     mixed_jac = np.linalg.lstsq(DESIGN, [
         mixed_motion(x, t, 1)[9]-mixed_motion(x, t, 0)[9] for t in TIMES], rcond=None)[0]
     check("mixed fixed-design OLS Jacobian", mixed_jac, finite_difference(mixed_coeff, x))
-    print("PASS: synthetic local formula checks; code-side geometry and CP/IP acceptance still required.")
+    # Appendix G: independent block phases remove constants, not intra-block slopes.
+    for nodes, starts, expected_rank in [([0.], [0., 3.], 0),
+                                         ([0., 2.], [0.], 1),
+                                         ([0., 2.], [0., 3.], 2),
+                                         ([0., 2.], [0., 3e-4], 2)]:
+        blocks, weights, centers = [], [], []
+        n = np.array(nodes)
+        for ell in range(2):
+            f, rate = z[2:]+coefficients(x, ell)[0]
+            for start in starts:
+                w = geometry(x, start, ell)[0]
+                a = np.exp(-2j*np.pi*ARRAY@w/WAVELENGTH)
+                mu = np.kron(np.exp(2j*np.pi*((f+rate*start)*n+.5*rate*n*n)), a)
+                J = np.column_stack((1j*np.repeat(n, len(a))*mu,
+                                     1j*np.repeat(start*n+.5*n*n, len(a))*mu))
+                projected = J-mu[:, None]*(mu.conj()@J/(mu.conj()@mu))[None, :]
+                expected = np.column_stack((
+                    1j*np.repeat(n-n.mean(), len(a))*mu,
+                    1j*np.repeat(start*(n-n.mean())+.5*(n*n-(n*n).mean()), len(a))*mu))
+                check("IP centered temporal scores", projected, expected)
+                blocks.append(projected)
+                weights.append(2*np.linalg.norm(projected[:, 0])**2)
+                centers.append(start+(n[-1]/2))
+        J = np.vstack(blocks)
+        real_J = np.vstack((J.real, J.imag))*np.sqrt(2)
+        assert np.linalg.matrix_rank(real_J, tol=1e-10) == expected_rank
+        if len(n) == 2:
+            weights, centers = np.array(weights), np.array(centers)
+            I = real_J.T@real_J
+            vectors = np.column_stack((np.ones(len(centers)), centers))
+            check("two-sample temporal information", I, vectors.T@(weights[:, None]*vectors))
+            residual = real_J[:, 0]-real_J[:, 1]*(I[1, 0]/I[1, 1])
+            check("real rate Schur complement", residual@residual,
+                  I[0, 0]-I[0, 1]**2/I[1, 1])
+            if expected_rank == 1:
+                check("single-frame exact frequency/rate cancellation", J@np.array([1., -1.]),
+                      np.zeros(len(J)))
+            elif starts[-1] < 1e-3:
+                assert 0 < residual@residual/I[0, 0] < 1e-7
+    print("PASS: synthetic local formula and temporal-rank checks; code-side geometry and CP/IP acceptance still required.")
 
 
 if __name__ == "__main__":