diff --git a/pixi.lock b/pixi.lock
index 46f046e7..5ba1b013 100644
--- a/pixi.lock
+++ b/pixi.lock
@@ -5232,7 +5232,7 @@ packages:
 - pypi: .
   name: array-api-extra
   version: 0.7.2.dev0
-  sha256: ac4ddf62fc1119c489439a90bb7cdd847926d5462cf7cffaaf2f9bcd8a2ef831
+  sha256: 9caaf6a80751c89c1693ce901b4d31202552ea7af0cd3f37564d406d6565c051
   requires_dist:
   - array-api-compat>=1.11.2,<2
   requires_python: '>=3.10'
diff --git a/pyproject.toml b/pyproject.toml
index a542faf8..1e93cbe4 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -64,7 +64,7 @@ numpydoc = ">=1.8.0,<2"
 array-api-strict = ">=2.3.1"
 numpy = ">=1.26.4"
 pytest = ">=8.3.5"
-hypothesis = "*"
+hypothesis = ">=3.88.3"
 dask-core = ">=2025.3.0"  # No distributed, tornado, etc.
 # NOTE: don't add jax, pytorch, sparse, cupy here
 # as they slow down mypy and are not portable across target OSs
@@ -80,7 +80,7 @@ lint = { depends-on = ["pre-commit", "pylint", "mypy", "pyright"] }
 [tool.pixi.feature.tests.dependencies]
 pytest = ">=8.3.5"
 pytest-cov = ">=3"
-hypothesis = "*"
+hypothesis = ">=3.88.3"
 array-api-strict = ">=2.3.1"
 numpy = ">=1.22.0"
 
@@ -134,7 +134,7 @@ numpy = "=1.22.0"
 # Backends that can run on CPU-only hosts
 # Note: JAX and PyTorch will install CPU variants.
 [tool.pixi.feature.backends.dependencies]
-pytorch = "*"
+pytorch = ">=1.13.1"
 dask = ">=2025.3.0"
 numba = ">=0.61.0"  # sparse dependency
 llvmlite = ">=0.44.0"  # sparse dependency
@@ -143,13 +143,13 @@ llvmlite = ">=0.44.0"  # sparse dependency
 sparse = { version = ">=0.16.0" }
 
 [tool.pixi.feature.backends.target.linux-64.dependencies]
-jax = "*"
+jax = ">=0.5.2"
 
 [tool.pixi.feature.backends.target.osx-64.dependencies]
-jax = "*"
+jax = ">=0.5.2"
 
 [tool.pixi.feature.backends.target.osx-arm64.dependencies]
-jax = "*"
+jax = ">=0.5.2"
 
 [tool.pixi.feature.backends.target.win-64.dependencies]
 # jax = "*"  # unavailable
@@ -165,8 +165,8 @@ system-requirements = { cuda = "12" }
 
 [tool.pixi.feature.cuda-backends.target.linux-64.dependencies]
 cupy = ">=13.4.1"
-jaxlib = { version = "*", build = "cuda12*" }
-pytorch = { version = "*", build = "cuda12*" }
+jaxlib = { version = ">=0.5.2", build = "cuda12*" }
+pytorch = { version = ">=1.13.1", build = "cuda12*" }
 
 [tool.pixi.feature.cuda-backends.target.osx-64.dependencies]
 # cupy = "*"  # unavailable
@@ -181,7 +181,7 @@ pytorch = { version = "*", build = "cuda12*" }
 [tool.pixi.feature.cuda-backends.target.win-64.dependencies]
 cupy = ">=13.4.1"
 # jaxlib = { version = "*", build = "cuda12*" }  # unavailable
-pytorch = { version = "*", build = "cuda12*" }
+pytorch = { version = ">=1.13.1", build = "cuda12*" }
 
 [tool.pixi.environments]
 default = { features = ["py313"], solve-group = "py313" }