uv: error: No solution found when resolving dependencies

error: No solution found when resolving dependencies means uv could not find one set of versions that satisfies every requirement at once. The cause: lines that follow explain why, as a chain of Because ... we can conclude ... steps; the last step names the requirements that cannot both be true. Loosen or remove one of them (usually an explicit pin) and run uv lock again.

Reproduce it

requests 2.32.3 needs urllib3>=1.21.1,<3, but the project also pins urllib3==1.0:

cat > pyproject.toml <<'EOF'
[project]
name = "demo"
version = "0.1.0"
requires-python = ">=3.13"
dependencies = ["requests==2.32.3", "urllib3==1.0"]
EOF
uv lock --python 3.13 2>&1 | grep -v '^Using '
exit "${PIPESTATUS[0]}"

error: No solution found when resolving dependencies
  cause: Because requests==2.32.3 depends on urllib3>=1.21.1,<3 and your project depends on requests==2.32.3, we can conclude that your project depends on urllib3>=1.21.1,<3.
         And because your project depends on urllib3==1.0, we can conclude that your project's requirements are unsatisfiable.

The Using CPython ... line, which names the local interpreter, is filtered out.

Fix

Remove the conflicting pin and let uv choose a compatible urllib3:

cat > pyproject.toml <<'EOF'
[project]
name = "demo"
version = "0.1.0"
requires-python = ">=3.13"
dependencies = ["requests==2.32.3"]
EOF
uv lock --python 3.13 -q && echo "resolved"

resolved

Reading the explanation

Read the chain from the first Because to the final your project's requirements are unsatisfiable. Each step combines two facts; the two facts that cannot hold together are the ones to change.