diff --git a/src/adaptiverg_qec/autocorr.py b/src/adaptiverg_qec/autocorr.py
index 5ff84eb..25493e9 100644
--- a/src/adaptiverg_qec/autocorr.py
+++ b/src/adaptiverg_qec/autocorr.py
@@ -55,6 +55,18 @@
 ]
 
 
+def _require_finite(values: np.ndarray, name: str) -> None:
+    """Fail closed on NaN/inf at a public entry (Issue #46).
+
+    Geordnete Vergleiche mit NaN sind immer False; ein Waechter der Form
+    ``if stat <= 0: raise`` liesse eine NaN-Reihe als "gueltig" durch und das
+    Ergebnis waere still NaN. Deshalb wird die Endlichkeit an JEDEM oeffentlichen
+    Eingang geprueft, nicht nur dort, wo sie zufaellig ueber einen Hilfsaufruf laeuft.
+    """
+    if not np.all(np.isfinite(values)):
+        raise ValueError(f"{name} must be finite (NaN/inf found)")
+
+
 def autocorr_function_fft(x: np.ndarray) -> np.ndarray:
     """Normierte Autokorrelationsfunktion rho(t), t=0..N-1, via FFT.
 
@@ -74,9 +86,13 @@ def autocorr_function_fft(x: np.ndarray) -> np.ndarray:
     n = x.size
     if n < 2:
         raise ValueError(f"need >=2 samples for an autocorrelation, got {n}")
+    _require_finite(x, "samples")
     xc = x - x.mean()
     var0 = float(np.dot(xc, xc) / n)  # = Var(x) (biased, = gamma(0))
-    if var0 <= 0.0:
+    if not np.isfinite(var0):
+        # endliche Samples, aber |x| ~ 1e308: die Quadratsumme laeuft ueber
+        raise ValueError("variance overflows float64; rescale the series")
+    if not (var0 > 0.0):  # positiv formuliert: jeder nicht-positive Fall faellt hier
         raise ValueError("constant series: Var(x)=0, autocorrelation undefined")
     # Null-Padding auf >= 2N-1 (verhindert zyklische Faltung); naechste 2er-Potenz.
     nfft = 1 << (2 * n - 1).bit_length()
@@ -143,10 +159,14 @@ def integrated_autocorr_time(
     """
     x = np.asarray(x, dtype=np.float64).ravel()
     n = x.size
-    if c_window <= 0:
+    _require_finite(x, "samples")
+    if not (c_window > 0):  # NaN-sicher (Issue #46)
         raise ValueError(f"c_window must be > 0, got {c_window}")
     if rho is None:
         rho = autocorr_function_fft(x)
+    else:
+        rho = np.asarray(rho, dtype=np.float64)
+        _require_finite(rho, "rho")
     # Kumulative tau_int(W) = 0.5 + cumsum(rho[1:]); tau_of_w[k] = tau_int(W=k+1).
     tau_of_w = 0.5 + np.cumsum(rho[1:])
     n_w = tau_of_w.size
@@ -231,6 +251,7 @@ def binning_error(x: np.ndarray, *, max_block: int | None = None) -> BinningResu
     """
     x = np.asarray(x, dtype=np.float64).ravel()
     n = x.size
+    _require_finite(x, "samples")
     if n < 64:
         raise ValueError(f"need >=64 samples for a meaningful binning curve, got {n}")
     if max_block is None:
@@ -321,6 +342,8 @@ def jackknife_ratio(
     den_terms = np.asarray(den_terms, dtype=np.float64)
     if num_terms.ndim != 2 or den_terms.ndim != 2:
         raise ValueError("num_terms and den_terms must be 2D (N, k)")
+    _require_finite(num_terms, "num_terms")
+    _require_finite(den_terms, "den_terms")
     n = num_terms.shape[0]
     if den_terms.shape[0] != n:
         raise ValueError(f"num/den sample count mismatch: {n} vs {den_terms.shape[0]}")
diff --git a/src/adaptiverg_qec/clt.py b/src/adaptiverg_qec/clt.py
index 1a23e15..db48f4e 100644
--- a/src/adaptiverg_qec/clt.py
+++ b/src/adaptiverg_qec/clt.py
@@ -74,7 +74,7 @@
 import numpy as np
 from scipy import stats
 
-from .autocorr import integrated_autocorr_time
+from .autocorr import _require_finite, integrated_autocorr_time
 
 __all__ = [
     "CLTResult",
@@ -133,6 +133,7 @@ def obm_variance(x: np.ndarray, *, batch_size: int | None = None) -> float:
     n = x.size
     if n < 4:
         raise ValueError(f"need >=4 samples for OBM, got {n}")
+    _require_finite(x, "samples")
     if batch_size is None:
         batch_size = max(1, int(np.floor(np.sqrt(n))))
     b = int(batch_size)
@@ -195,10 +196,13 @@ def confidence_interval(
     """
     if not (0.0 < alpha < 1.0):
         raise ValueError(f"alpha must be in (0,1), got {alpha}")
-    if n < 1:
+    if not (n >= 1):  # NaN-sicher (#46)
         raise ValueError(f"n must be >= 1, got {n}")
-    if sigma2_g < 0.0:
-        raise ValueError(f"sigma2_g must be >= 0, got {sigma2_g}")
+    # Issue #46: positiv formuliert und endlich -- ``sigma2_g < 0.0`` liess NaN durch.
+    if not (np.isfinite(sigma2_g) and sigma2_g >= 0.0):
+        raise ValueError(f"sigma2_g must be finite and >= 0, got {sigma2_g}")
+    if not np.isfinite(mean):
+        raise ValueError(f"mean must be finite, got {mean}")
     z = float(stats.norm.ppf(1.0 - alpha / 2.0))
     half = z * np.sqrt(sigma2_g / n)
     return (mean - half, mean + half)
@@ -221,8 +225,8 @@ def ar1_clt_variance(phi: float, sigma_eps: float = 1.0) -> dict[str, float]:
     """
     if not (-1.0 < phi < 1.0):
         raise ValueError(f"AR(1) requires |phi| < 1, got {phi}")
-    if sigma_eps <= 0.0:
-        raise ValueError(f"sigma_eps must be > 0, got {sigma_eps}")
+    if not (np.isfinite(sigma_eps) and sigma_eps > 0.0):  # NaN/inf-sicher (#46)
+        raise ValueError(f"sigma_eps must be finite and > 0, got {sigma_eps}")
     var_marg = sigma_eps**2 / (1.0 - phi**2)
     sigma2_g = sigma_eps**2 / (1.0 - phi) ** 2
     tau_int = (1.0 + phi) / (2.0 * (1.0 - phi))
diff --git a/tests/test_autocorr.py b/tests/test_autocorr.py
index 5ba7cb0..deb74c3 100644
--- a/tests/test_autocorr.py
+++ b/tests/test_autocorr.py
@@ -170,3 +170,67 @@ def test_record_configs_default_off() -> None:
 def test_invalid_inputs_raise(bad) -> None:
     with pytest.raises((ValueError, TypeError)):
         bad()
+
+
+# --- Issue #46: non-finite samples must fail closed ---------------------------
+# ``if var0 <= 0.0: raise`` rejected a constant series but let NaN through
+# (nan <= 0.0 is False); integrated_autocorr_time then returned all-NaN results.
+@pytest.mark.parametrize("bad", [float("nan"), float("inf"), float("-inf")])
+@pytest.mark.parametrize("position", [0, -1])
+def test_autocorr_rejects_non_finite_samples(bad: float, position: int) -> None:
+    x = np.random.default_rng(46).standard_normal(64)
+    x[position] = bad
+    with pytest.raises(ValueError, match="finite"):
+        autocorr.autocorr_function_fft(x)
+    with pytest.raises(ValueError, match="finite"):
+        autocorr.integrated_autocorr_time(x)
+
+
+@pytest.mark.parametrize("c_window", [float("nan"), 0.0, -1.0])
+def test_integrated_autocorr_time_rejects_invalid_window(c_window: float) -> None:
+    x = np.random.default_rng(46).standard_normal(64)
+    with pytest.raises(ValueError, match="c_window"):
+        autocorr.integrated_autocorr_time(x, c_window=c_window)
+
+
+# --- #46/#47 review: every public entry, not only autocorr_function_fft -------
+def _series_with(bad: float, n: int = 256) -> np.ndarray:
+    x = np.random.default_rng(47).standard_normal(n)
+    x[n // 2] = bad
+    return x
+
+
+@pytest.mark.parametrize("bad", [float("nan"), float("inf")])
+def test_binning_error_rejects_non_finite_samples(bad: float) -> None:
+    with pytest.raises(ValueError, match="finite"):
+        autocorr.binning_error(_series_with(bad))
+
+
+def test_integrated_autocorr_time_checks_x_even_with_precomputed_rho() -> None:
+    good = np.random.default_rng(47).standard_normal(256)
+    rho = autocorr.autocorr_function_fft(good)
+    with pytest.raises(ValueError, match="finite"):
+        autocorr.integrated_autocorr_time(_series_with(float("nan")), rho=rho)
+
+
+def test_integrated_autocorr_time_rejects_non_finite_rho() -> None:
+    x = np.random.default_rng(47).standard_normal(256)
+    rho = autocorr.autocorr_function_fft(x)
+    rho[5] = float("nan")
+    with pytest.raises(ValueError, match="finite"):
+        autocorr.integrated_autocorr_time(x, rho=rho)
+
+
+def test_jackknife_ratio_rejects_non_finite_terms() -> None:
+    num = np.random.default_rng(47).standard_normal((64, 1))
+    den = np.ones((64, 1))
+    num[10, 0] = float("nan")
+    with pytest.raises(ValueError, match="finite"):
+        autocorr.jackknife_ratio(num, den, block_size=4, combine=lambda a, b: a[0] / b[0])
+
+
+def test_autocorr_overflowing_series_is_not_reported_as_constant() -> None:
+    x = np.array([1e308, -1e308] * 32)
+    with pytest.raises(ValueError) as exc:
+        autocorr.autocorr_function_fft(x)
+    assert "constant" not in str(exc.value)
diff --git a/tests/test_clt.py b/tests/test_clt.py
index a5ae538..f1ecd6b 100644
--- a/tests/test_clt.py
+++ b/tests/test_clt.py
@@ -119,3 +119,38 @@ def test_clt_edge_inputs_raise() -> None:
         clt.ar1_clt_variance(1.0)  # |phi|>=1
     with pytest.raises(ValueError):
         clt.ar1_clt_variance(0.5, sigma_eps=0.0)  # sigma_eps<=0
+
+
+# --- Issue #46: NaN must not pass the sigma2_g guard -------------------------
+@pytest.mark.parametrize(
+    ("mean", "sigma2_g"),
+    [(0.0, float("nan")), (0.0, -1.0), (float("nan"), 1.0), (0.0, float("inf"))],
+)
+def test_confidence_interval_rejects_non_finite_or_negative_inputs(
+    mean: float, sigma2_g: float
+) -> None:
+    with pytest.raises(ValueError):
+        clt.confidence_interval(mean, sigma2_g, 10)
+
+
+def test_confidence_interval_accepts_zero_variance() -> None:
+    assert clt.confidence_interval(1.5, 0.0, 10) == (1.5, 1.5)
+
+
+# --- #46/#47 review: remaining silent-NaN entries ---------------------------
+def test_obm_variance_rejects_non_finite_samples() -> None:
+    x = np.random.default_rng(47).standard_normal(256)
+    x[100] = float("nan")
+    with pytest.raises(ValueError, match="finite"):
+        clt.obm_variance(x)
+
+
+@pytest.mark.parametrize("sigma_eps", [float("nan"), float("inf"), 0.0, -1.0])
+def test_ar1_clt_variance_rejects_invalid_sigma_eps(sigma_eps: float) -> None:
+    with pytest.raises(ValueError, match="sigma_eps"):
+        clt.ar1_clt_variance(0.5, sigma_eps)
+
+
+def test_confidence_interval_rejects_nan_n() -> None:
+    with pytest.raises(ValueError):
+        clt.confidence_interval(0.0, 1.0, float("nan"))  # type: ignore[arg-type]