research: Dütsch driver — periodic Morison bases from step mod T

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

research/duetsch_re100_kc5/protocol.py

@@ -53,7 +53,7 @@ def interval_bases(n, T, points=16):
     """Single-step interval averages over [n, n + 1] of cos phi |cos phi| and sin phi
     (phi in radians = 2 pi s / T - pi / 2), Gauss-Legendre quadrature."""
     x, w = np.polynomial.legendre.leggauss(points)
-    s = n + 0.5 * (x + 1.0)
+    s = int(n) % T + 0.5 * (x + 1.0)  # periodic: identical bases in every cycle
     phi = 2.0 * np.pi * s / T - 0.5 * np.pi
     c = np.cos(phi)
     return 0.5 * float(np.sum(w * c * np.abs(c))), 0.5 * float(np.sum(w * np.sin(phi)))

tests/unit/test_duetsch_protocol.py

@@ -73,6 +73,7 @@ def test_geometry_repeats_exactly_across_cycles():
             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
+    assert p.interval_bases(123 + 7 * T, T) == p.interval_bases(123, T)
 
 
 def test_exact_point_inside_body_is_missing_even_with_fluid_corners():