feat: add threshold computation via binary search

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

model/test_density_evolution.py

@@ -50,3 +50,45 @@ class TestDensityEvolution:
         # Run one step
         beliefs = density_evolution_step(beliefs, msg_memory, ORIGINAL_STAIRCASE_PROFILE, z_pop)
         assert beliefs.shape == (n_base, z_pop), f"Shape changed after step: {beliefs.shape}"
+
+
+class TestThresholdComputation:
+    """Tests for threshold binary search."""
+
+    def test_threshold_original_staircase(self):
+        """Threshold for original staircase [7,2,2,2,2,2,2,1] should be ~3-6 photons."""
+        from density_evolution import compute_threshold_for_profile
+        np.random.seed(42)
+        threshold = compute_threshold_for_profile(
+            [7, 2, 2, 2, 2, 2, 2, 1], m_base=7, lam_b=0.1,
+            z_pop=10000, tol=0.5
+        )
+        assert 2.0 < threshold < 8.0, f"Expected threshold ~3-6, got {threshold}"
+
+    def test_threshold_peg_ring(self):
+        """PEG ring [7,3,3,3,2,2,2,2] should have lower or equal threshold than original."""
+        from density_evolution import compute_threshold_for_profile
+        np.random.seed(42)
+        thresh_orig = compute_threshold_for_profile(
+            [7, 2, 2, 2, 2, 2, 2, 1], m_base=7, lam_b=0.1,
+            z_pop=15000, tol=0.25
+        )
+        np.random.seed(123)
+        thresh_peg = compute_threshold_for_profile(
+            [7, 3, 3, 3, 2, 2, 2, 2], m_base=7, lam_b=0.1,
+            z_pop=15000, tol=0.25
+        )
+        assert thresh_peg <= thresh_orig, (
+            f"PEG threshold {thresh_peg} should be <= original {thresh_orig}"
+        )
+
+    def test_profile_to_hbase(self):
+        """build_de_profile should produce valid profile with correct column degrees."""
+        from density_evolution import build_de_profile
+        profile = build_de_profile([7, 3, 2, 2, 2, 2, 2, 2], m_base=7)
+        assert profile['n_base'] == 8
+        assert profile['m_base'] == 7
+        assert profile['vn_degrees'] == [7, 3, 2, 2, 2, 2, 2, 2]
+        # Every row should have at least 2 connections
+        for r, conns in enumerate(profile['connections']):
+            assert len(conns) >= 2, f"Row {r} has only {len(conns)} connections"