diff --git a/crates/ml-alpha/tests/integrated_trainer_smoke.rs b/crates/ml-alpha/tests/integrated_trainer_smoke.rs
index f792aa3cc..66f75a98c 100644
--- a/crates/ml-alpha/tests/integrated_trainer_smoke.rs
+++ b/crates/ml-alpha/tests/integrated_trainer_smoke.rs
@@ -105,16 +105,26 @@ fn integrated_trainer_step_with_lobsim_runs_without_panic() {
     assert!(stats.l_v.is_finite(), "l_v is not finite: {}", stats.l_v);
     assert!(stats.l_total.is_finite(), "l_total is not finite: {}", stats.l_total);
 
-    // λs sum to ~1.0 (loss-balance default before any controller fires).
-    let lambda_sum = stats.lambdas.bce
-        + stats.lambdas.q
-        + stats.lambdas.pi
-        + stats.lambdas.v
-        + stats.lambdas.aux;
-    assert!(
-        (lambda_sum - 1.0).abs() < 1e-4,
-        "loss-balance λs should sum to 1.0; got {lambda_sum}"
-    );
+    // Each λ is finite + positive. The per-head divide-by-5 happens
+    // at the trainer's loss-combine site (see `loss_balance.rs::Default`
+    // doc), so each λ defaults to 1.0 (sum 5.0) on first observation.
+    // Asserting the SUM equals a specific value locks the test against
+    // any future controller-driven re-weighting (canonical
+    // `pearl_tests_must_prove_not_lock_observations`); the invariant
+    // we actually care about is "every head has a finite positive
+    // weight so the encoder gets a real-valued gradient signal."
+    for (name, lam) in [
+        ("bce", stats.lambdas.bce),
+        ("q",   stats.lambdas.q),
+        ("pi",  stats.lambdas.pi),
+        ("v",   stats.lambdas.v),
+        ("aux", stats.lambdas.aux),
+    ] {
+        assert!(
+            lam.is_finite() && lam > 0.0,
+            "lambda[{name}] must be finite + positive; got {lam}"
+        );
+    }
 
     eprintln!(
         "R6 OK — step_with_lobsim end-to-end: l_bce={} l_q={} l_pi={} l_v={} l_aux={} l_total={}",
diff --git a/crates/ml-alpha/tests/r5_controllers_and_soft_update.rs b/crates/ml-alpha/tests/r5_controllers_and_soft_update.rs
index 5fd254639..ee21afe50 100644
--- a/crates/ml-alpha/tests/r5_controllers_and_soft_update.rs
+++ b/crates/ml-alpha/tests/r5_controllers_and_soft_update.rs
@@ -118,7 +118,13 @@ fn g3_per_step_controllers_move_isv_outputs_when_fed_real_emas() {
         (RL_KL_PI_EMA_INDEX, 0.1),                      // → rl_ppo_clip
         (RL_ENTROPY_OBSERVED_EMA_INDEX, 0.5),           // → rl_entropy_coef
         (RL_ADVANTAGE_VAR_RATIO_EMA_INDEX, 5.0),        // → rl_rollout_steps
-        (RL_TD_KURTOSIS_EMA_INDEX, 10.0),               // → rl_per_alpha
+        // td_kurtosis = 20.0 chosen so the per_α controller's target
+        // (0.4 + 0.2 × (20 − 3) / 7 = 0.886) is distinct from the
+        // bootstrap 0.6 — a fixture value of 10.0 mapped exactly to
+        // target = 0.6, making the Wiener blend produce 0.6 regardless
+        // of α and rendering the "moved off bootstrap" assertion
+        // unfalsifiable (canonical `pearl_tests_must_prove_not_lock_observations`).
+        (RL_TD_KURTOSIS_EMA_INDEX, 20.0),               // → rl_per_alpha
         (RL_MEAN_ABS_PNL_EMA_INDEX, 50.0),              // → rl_reward_scale
     ];
     for (slot, obs_val) in inputs {