feat: add alpha optimization for normalized min-sum

Add optimize_alpha() function that sweeps hardware-friendly alpha
values to find the best DE threshold with normalized min-sum.
Add alpha-sweep CLI subcommand and --z/--cn-mode/--alpha options
to the full pipeline.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

model/test_density_evolution.py

@@ -281,3 +281,31 @@ class TestNormalizedMinSumDE:
         assert thresh_norm != thresh_offset, (
             f"Thresholds should differ: offset={thresh_offset}, normalized={thresh_norm}"
         )
+
+
+class TestAlphaOptimization:
+    """Tests for alpha sweep optimization."""
+
+    def test_optimize_alpha_returns_best(self):
+        """Alpha sweep for optimized degrees should find threshold < 3.5."""
+        from density_evolution import optimize_alpha
+        np.random.seed(42)
+        best_alpha, best_threshold = optimize_alpha(
+            [7, 4, 4, 4, 4, 3, 3, 3], m_base=7, lam_b=0.1,
+            z_pop=10000, tol=0.5
+        )
+        assert best_alpha is not None, "Should find a best alpha"
+        assert 0.5 <= best_alpha <= 1.0, f"Alpha {best_alpha} out of range"
+        # Normalized should be competitive with offset threshold (3.05)
+        assert best_threshold < 4.0, f"Best threshold {best_threshold} too high"
+
+    def test_alpha_sweep_range(self):
+        """All alpha values in range should produce valid thresholds."""
+        from density_evolution import optimize_alpha, build_de_profile, compute_threshold
+        np.random.seed(42)
+        profile = build_de_profile([7, 4, 4, 4, 4, 3, 3, 3], m_base=7)
+        alpha_range = [0.5, 0.75, 1.0]
+        for alpha in alpha_range:
+            t = compute_threshold(profile, lam_b=0.1, z_pop=5000, tol=1.0,
+                                  cn_mode='normalized', alpha=alpha)
+            assert 0.1 < t < 20.0, f"alpha={alpha}: threshold {t} out of valid range"