diff --git a/.github/workflows/pytest.yml b/.github/workflows/pytest.yml
index 536f7d53..50316b09 100644
--- a/.github/workflows/pytest.yml
+++ b/.github/workflows/pytest.yml
@@ -16,7 +16,7 @@ jobs:
       fail-fast: false
       matrix:
         os: [ubuntu-latest]
-        python-version: ["3.7", "3.8", "3.9", "3.10"]
+        python-version: ["3.7", "3.8", "3.9", "3.10", "3.11"]
         include:
           - os: macos-latest
             python-version: 3.9
@@ -40,6 +40,7 @@ jobs:
           pip install pytest
           pip install pytest-cov
           pip install pytest-benchmark
+          pip install hypothesis
           pip install py
           pip freeze
 
diff --git a/CONTRIBUTING.md b/CONTRIBUTING.md
index 98ab0c75..8d803e4a 100644
--- a/CONTRIBUTING.md
+++ b/CONTRIBUTING.md
@@ -25,7 +25,9 @@ For all pull requests tests are executed for the most recent python releases via
 pytest -vv --cov=pyerrors
 pytest -vv --nbmake examples/*.ipynb
 ```
-requiring `pytest`, `pytest-cov`, `pytest-benchmark` and `nbmake`. To get a coverage report in html run
+requiring `pytest`, `pytest-cov`, `pytest-benchmark`, `hypothesis' and `nbmake`. To install the test dependencies one can run `pip install pyerrors[test]`
+
+To get a coverage report in html run
 ```
 pytest --cov=pyerrors --cov-report html
 ```
diff --git a/pyerrors/__init__.py b/pyerrors/__init__.py
index a6fefe8d..981e0fd7 100644
--- a/pyerrors/__init__.py
+++ b/pyerrors/__init__.py
@@ -41,7 +41,7 @@ print(my_new_obs)                             # Print the result to stdout
 `pyerrors` introduces a new datatype, `Obs`, which simplifies error propagation and estimation for auto- and cross-correlated data.
 An `Obs` object can be initialized with two arguments, the first is a list containing the samples for an observable from a Monte Carlo chain.
 The samples can either be provided as python list or as numpy array.
-The second argument is a list containing the names of the respective Monte Carlo chains as strings. These strings uniquely identify a Monte Carlo chain/ensemble.
+The second argument is a list containing the names of the respective Monte Carlo chains as strings. These strings uniquely identify a Monte Carlo chain/ensemble. **It is crucial for the correct error propagation that observations from the same Monte Carlo history are labeled with the same name. See [Multiple ensembles/replica](#Multiple-ensembles/replica) for details.**
 
 ```python
 import pyerrors as pe
@@ -142,6 +142,8 @@ my_sum.details()
 >   · Ensemble 'ensemble1' : 1000 configurations (from 1 to 1000)
 >   · Ensemble 'ensemble2' : 500 configurations (from 1 to 500)
 ```
+Observables from the **same Monte Carlo chain** have to be initialized with the **same name** for correct error propagation. If different names were used in this case the data would be treated as statistically independent resulting in loss of relevant information and a potential over or under estimate of the statistical error.
+
 
 `pyerrors` identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar `|` in the name of the data set.
 
diff --git a/setup.py b/setup.py
index 3aa4d889..37a56f51 100644
--- a/setup.py
+++ b/setup.py
@@ -25,8 +25,8 @@ setup(name='pyerrors',
       license="MIT",
       packages=find_packages(),
       python_requires='>=3.7.0',
-      install_requires=['numpy>=1.19', 'autograd>=1.5', 'numdifftools>=0.9.41', 'matplotlib>=3.5', 'scipy>=1.7', 'iminuit>=2.17', 'h5py>=3.7', 'lxml>=4.9', 'python-rapidjson>=1.9', 'pandas>=1.1'],
-      extras_require={'test': ['pytest', 'pytest-cov', 'pytest-benchmark']},
+      install_requires=['numpy>=1.21', 'autograd>=1.5', 'numdifftools>=0.9.41', 'matplotlib>=3.5', 'scipy>=1.7', 'iminuit>=2.17', 'h5py>=3.8', 'lxml>=4.9', 'python-rapidjson>=1.9', 'pandas>=1.1'],
+      extras_require={'test': ['pytest', 'pytest-cov', 'pytest-benchmark', 'hypothesis']},
       classifiers=[
           'Development Status :: 5 - Production/Stable',
           'Intended Audience :: Science/Research',
diff --git a/tests/obs_test.py b/tests/obs_test.py
index 5fbedf98..b01ed034 100644
--- a/tests/obs_test.py
+++ b/tests/obs_test.py
@@ -4,9 +4,25 @@ import copy
 import matplotlib.pyplot as plt
 import pyerrors as pe
 import pytest
+from hypothesis import given, strategies as st
 
 np.random.seed(0)
 
+@given(st.lists(st.floats(allow_nan=False, allow_infinity=False, width=32), min_size=5),
+       st.text(),
+       st.floats(allow_nan=False, allow_infinity=False, width=32, min_value=0))
+def test_fuzzy_obs(data, string, S):
+    my_obs = pe.Obs([data], [string])
+    my_obs * my_obs
+    my_obs.gamma_method(S=S)
+
+
+@given(st.floats(allow_nan=False, allow_infinity=False, width=16))
+def test_sin2_cos2(value):
+    Obs = pe.pseudo_Obs(value, value * 0.123, "C0")
+    iamzero = np.sin(Obs) ** 2 + np.cos(Obs) ** 2 - 1
+    assert iamzero.is_zero(atol=1e-6)
+
 
 def test_Obs_exceptions():
     with pytest.raises(Exception):
@@ -59,7 +75,7 @@ def test_Obs_exceptions():
         one.plot_piechart()
     plt.close('all')
 
-def test_dump():
+def test_dump_pickle():
     value = np.random.normal(5, 10)
     dvalue = np.abs(np.random.normal(0, 1))
     test_obs = pe.pseudo_Obs(value, dvalue, 't')
@@ -68,6 +84,12 @@ def test_dump():
     new_obs = pe.load_object('test_dump.p')
     os.remove('test_dump.p')
     assert test_obs == new_obs
+
+
+def test_dump_json():
+    value = np.random.normal(5, 10)
+    dvalue = np.abs(np.random.normal(0, 1))
+    test_obs = pe.pseudo_Obs(value, dvalue, 't')
     test_obs.dump('test_dump', dataype="json.gz", path=".")
     test_obs.dump('test_dump', dataype="json.gz")
     new_obs = pe.input.json.load_json("test_dump")