research: Dütsch driver — exact-point body mask, periodic geometry from step mod T

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

tests/unit/test_duetsch_protocol.py

@@ -62,3 +62,25 @@ def test_interval_bases_and_morison_fit_recover_known_coefficients():
     assert np.allclose(b[:, 1], np.sin(phi), atol=1e-5)          # midpoint ~ interval mean
     f = 2.09 * b[:, 0] - (math.pi ** 2 * 1.45 / p.KC) * b[:, 1]
     assert p.morison_fit(f, b[:, 0], b[:, 1]) == pytest.approx((2.09, 1.45), abs=1e-9)
+
+
+def test_geometry_repeats_exactly_across_cycles():
+    A = p.amplitude(20)
+    for m in (0, 1, T // 4, T // 2 - 1, 7 * T // 12):
+        for c in (1, 5, 11):
+            assert p.position(m + c * T, T, A) == p.position(m, T, A)
+            assert p.phase(m + c * T, T) == p.phase(m, T)
+            v0 = p.position(m + 1, T, A) - p.position(m, T, A)
+            assert p.position(m + 1 + c * T, T, A) - p.position(m + c * T, T, A) == v0
+    assert p.cycle(T // 4 + 5 * T, T) == 6  # unwrapped index stays separate
+
+
+def test_exact_point_inside_body_is_missing_even_with_fluid_corners():
+    field = np.zeros((6, 6))
+    fluid = np.ones((6, 6), bool)
+    fluid[3, 3] = False                         # only one corner solid
+    centre, radius = (3.0, 3.0), 0.3
+    value, used, total = p.sample(field, fluid, 3.2, 3.1, centre, radius)   # inside the circle
+    assert value is None and used == () and total == 0.0
+    value, used, total = p.sample(field, fluid, 3.35, 3.0, centre, radius)  # just outside
+    assert value is not None and total > 0.0