diff --git a/experiments/audit_density_order.py b/experiments/audit_density_order.py
index dac3d22..d208eb9 100644
--- a/experiments/audit_density_order.py
+++ b/experiments/audit_density_order.py
@@ -609,11 +609,24 @@ def audit_case(campaign, name):
                             "linear_iterations": sum(int(r["linear_iterations"]) for r in history)}
         fine = totals[("stored_density", degree, 30)]
         physical18 = result["physical"]["18"]["metrics"]
-        for region_key, physical_key in (("mass", "mass"), ("volume", "volume"), ("inertia_z", "moment_of_inertia_z")):
+        for region_key, physical_key in (("mass", "mass"), ("volume", "volume")):
             close(fine[region_key], physical18[physical_key], "Sliced/physical " + region_key, rtol=2e-9, atol=1e-13)
+        # Position factors raise the normal polynomial degree beyond the
+        # eight-point sliced rule's exactness. Tangential refinement does not
+        # test that error, so moment differences are observations, not identities.
+        radius = float(meta["R_reference"])
+        require(math.isfinite(radius) and radius > 0, "Invalid reference radius")
+        moment_comparisons = {"scope": "Order14 normal slicing versus unsliced q18; first moments and inertia may have normal quadrature error."}
+        values = [("inertia_z", physical18["moment_of_inertia_z"], 2)]
         for j, axis in enumerate("xyz"):
-            close(fine[f"first_moment_{axis}"], physical18[f"center_of_mass_{j}"] * physical18["mass"],
-                  "Sliced/physical first moment", atol=2e-12)
+            values.append((f"first_moment_{axis}", physical18[f"center_of_mass_{j}"] * physical18["mass"], 1))
+        for key, reference, power in values:
+            require(math.isfinite(fine[key]) and math.isfinite(reference), "Nonfinite moment observation")
+            difference = fine[key] - reference
+            mass_radius_scale = abs(physical18["mass"]) * radius ** power
+            moment_comparisons[key] = {"sliced": fine[key], "physical_q18": reference, "difference": difference,
+                "difference_over_mass_radius_power": difference / mass_radius_scale if mass_radius_scale else None}
+        result["sliced_vs_physical_moments"] = moment_comparisons
     return result
 
 
@@ -733,6 +746,7 @@ def main():
               "scope": __doc__, "limitations": ["Local projection M,b and mapped weights are not exported.",
                   "Complete negative partitions are checked only on lines with exported negative intervals; no global positivity claim.",
                   "Shallow unresolved witnesses remain recorded; root position tests have coefficient-scaled allowances.",
+                  "Tangential convergence does not establish accuracy of the fixed eight-point normal rule; sliced first moments and inertia are compared observationally with q18.",
                   "Coupled timing and convergence gates are producer observations, not independent equation evaluations."],
               "campaigns": {}, "consumed_sha256": {str(Path(common.__file__).resolve()): digest(Path(common.__file__))}}
     comparable = defaultdict(list)