diff --git a/fusion_accounting_followup/tests/__init__.py b/fusion_accounting_followup/tests/__init__.py
index 76912615..583b044b 100644
--- a/fusion_accounting_followup/tests/__init__.py
+++ b/fusion_accounting_followup/tests/__init__.py
@@ -14,3 +14,4 @@ from . import test_followup_controller
 from . import test_followup_adapter
 from . import test_followup_tools
 from . import test_followup_cron
+from . import test_engine_property
diff --git a/fusion_accounting_followup/tests/test_engine_property.py b/fusion_accounting_followup/tests/test_engine_property.py
new file mode 100644
index 00000000..99b6679d
--- /dev/null
+++ b/fusion_accounting_followup/tests/test_engine_property.py
@@ -0,0 +1,92 @@
+"""Property-based invariants for follow-up services."""
+
+from datetime import date, timedelta
+
+from hypothesis import given, settings, strategies as st, HealthCheck
+from odoo.tests.common import TransactionCase
+from odoo.tests import tagged
+
+from odoo.addons.fusion_accounting_followup.services.overdue_aging import (
+    compute_aging, BUCKETS,
+)
+from odoo.addons.fusion_accounting_followup.services.risk_scorer import score_partner
+from odoo.addons.fusion_accounting_followup.services.tone_selector import select_tone
+
+
+@tagged('post_install', '-at_install', 'property_based')
+class TestAgingInvariants(TransactionCase):
+
+    @given(
+        as_of=st.dates(min_value=date(2020, 1, 1), max_value=date(2030, 12, 31)),
+        amounts=st.lists(
+            st.tuples(
+                st.integers(min_value=-180, max_value=180),
+                st.floats(min_value=0.01, max_value=100000,
+                          allow_nan=False, allow_infinity=False),
+            ),
+            min_size=0, max_size=20,
+        ),
+    )
+    @settings(max_examples=80, deadline=2000,
+              suppress_health_check=[HealthCheck.function_scoped_fixture])
+    def test_buckets_sum_equals_total(self, as_of, amounts):
+        lines = [
+            {'date_maturity': as_of + timedelta(days=offset),
+             'amount_residual': round(amt, 2)}
+            for offset, amt in amounts
+        ]
+        report = compute_aging(move_lines=lines, as_of=as_of)
+        bucket_sum = sum(b.amount for b in report.buckets)
+        self.assertAlmostEqual(bucket_sum, report.total_amount, places=1)
+
+    @given(
+        as_of=st.dates(min_value=date(2020, 1, 1), max_value=date(2030, 12, 31)),
+        days_overdue=st.integers(min_value=1, max_value=365),
+        amount=st.floats(min_value=0.01, max_value=10000,
+                         allow_nan=False, allow_infinity=False),
+    )
+    @settings(max_examples=50, deadline=2000,
+              suppress_health_check=[HealthCheck.function_scoped_fixture])
+    def test_overdue_amount_excludes_current(self, as_of, days_overdue, amount):
+        lines = [
+            {'date_maturity': as_of - timedelta(days=days_overdue),
+             'amount_residual': round(amount, 2)},
+            {'date_maturity': as_of + timedelta(days=10),
+             'amount_residual': 100.0},
+        ]
+        report = compute_aging(move_lines=lines, as_of=as_of)
+        self.assertAlmostEqual(report.total_overdue_amount, round(amount, 2), places=1)
+
+    @given(
+        invoices=st.integers(min_value=0, max_value=100),
+        late=st.integers(min_value=0, max_value=100),
+        days_late=st.floats(min_value=0, max_value=180,
+                            allow_nan=False, allow_infinity=False),
+    )
+    @settings(max_examples=80, deadline=2000,
+              suppress_health_check=[HealthCheck.function_scoped_fixture])
+    def test_risk_score_in_range(self, invoices, late, days_late):
+        late = min(late, invoices) if invoices > 0 else 0
+        result = score_partner(
+            total_invoices=invoices, paid_late_count=late,
+            avg_days_late=days_late,
+            longest_overdue_days=int(days_late),
+            open_overdue_amount=invoices * 1000.0,
+            average_invoice_amount=1000.0,
+        )
+        self.assertGreaterEqual(result.score, 0)
+        self.assertLessEqual(result.score, 100)
+
+
+@tagged('post_install', '-at_install', 'property_based')
+class TestToneInvariants(TransactionCase):
+
+    @given(
+        sequence=st.integers(min_value=1, max_value=10),
+        risk=st.integers(min_value=0, max_value=100),
+    )
+    @settings(max_examples=50, deadline=1000,
+              suppress_health_check=[HealthCheck.function_scoped_fixture])
+    def test_tone_always_in_valid_set(self, sequence, risk):
+        tone = select_tone(level_sequence=sequence, risk_score=risk)
+        self.assertIn(tone, ('gentle', 'firm', 'legal'))