router: seed EnergyRouter centers from data quantiles instead of a fixed linspace

The 2026-07-22 rollout benchmark's router_gating diagnostic showed the
10-expert EnergyRouter's default linspace(-2, 2, n_experts) init assumes a
roughly uniform z-normalized energy distribution, leaving experts heavily
overlapping instead of partitioning the range. Add an optional
centers_init kwarg (backward compatible, defaults to the old linspace) and
have giant train estimate it from a reservoir sample of the real energy
column, collected during the existing normalizer-fitting pass.

tests/test_router.py

@@ -97,6 +97,42 @@ def test_build_router_ignores_unrecognized_kwargs():
     assert router.temperature == 0.3
 
 
+def test_energy_router_default_centers_are_linspace():
+    router = EnergyRouter(n_experts=4)
+    torch.testing.assert_close(router.centers, torch.linspace(-2.0, 2.0, 4))
+
+
+def test_energy_router_centers_init_overrides_default():
+    centers_init = [-1.0, 0.0, 0.5, 3.0]
+    router = EnergyRouter(n_experts=4, centers_init=centers_init)
+    torch.testing.assert_close(router.centers, torch.tensor(centers_init))
+
+
+def test_energy_router_centers_init_wrong_length_raises():
+    try:
+        EnergyRouter(n_experts=4, centers_init=[0.0, 1.0])
+    except ValueError:
+        return
+    raise AssertionError("expected ValueError for centers_init length mismatch")
+
+
+def test_energy_router_centers_init_respects_learn_centers_flag():
+    learned = EnergyRouter(
+        n_experts=3, centers_init=[-1.0, 0.0, 1.0], learn_centers=True
+    )
+    fixed = EnergyRouter(
+        n_experts=3, centers_init=[-1.0, 0.0, 1.0], learn_centers=False
+    )
+    assert isinstance(learned.centers, torch.nn.Parameter)
+    assert not isinstance(fixed.centers, torch.nn.Parameter)
+
+
+def test_build_router_threads_centers_init_through_energy_router():
+    centers_init = [-1.5, -0.5, 0.5, 1.5]
+    router = build_router("energy", 4, centers_init=centers_init)
+    torch.testing.assert_close(router.centers, torch.tensor(centers_init))
+
+
 def test_build_router_unknown_type_raises():
     try:
         build_router("nonexistent", 4)