diff --git a/.github/workflows/_checks.yml b/.github/workflows/_checks.yml
index 9eae5c6..e0913a6 100644
--- a/.github/workflows/_checks.yml
+++ b/.github/workflows/_checks.yml
@@ -56,7 +56,9 @@ jobs:
           cache-dependency-glob: "**/pyproject.toml"
       - run: uv python install ${{ matrix.python-version }}
       - run: uv venv --python ${{ matrix.python-version }}
-      - run: uv pip install --resolution lowest-direct --only-binary PyYAML ".[yaml]"
+      - name: Pin every declared floor
+        run: uv run --no-project --with packaging --with tomli python scripts/floor_constraints.py > floors.txt
+      - run: uv pip install --resolution lowest-direct --constraints floors.txt --only-binary PyYAML ".[yaml]"
       - run: uv run --no-project python -c "import compose2pod, yaml; print(yaml.__version__)"
 
   pytest:
diff --git a/pyproject.toml b/pyproject.toml
index d5265cc..1982dea 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -51,8 +51,10 @@ module-root = ""
 
 [dependency-groups]
 dev = [
+    "packaging",
     "pytest",
     "pytest-cov",
+    "tomli",
 ]
 lint = [
     "ruff",
diff --git a/scripts/__init__.py b/scripts/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/scripts/floor_constraints.py b/scripts/floor_constraints.py
new file mode 100644
index 0000000..8287fbe
--- /dev/null
+++ b/scripts/floor_constraints.py
@@ -0,0 +1,63 @@
+"""Usage: python scripts/floor_constraints.py [pyproject.toml] > floors.txt."""
+
+import collections.abc
+import pathlib
+import sys
+import typing
+
+import tomli
+from packaging.requirements import Requirement
+from packaging.utils import canonicalize_name
+from packaging.version import Version
+
+
+_FLOOR_OPERATORS: collections.abc.Set[str] = frozenset({">=", "==", "~="})
+
+
+class UnboundedError(ValueError):
+    pass
+
+
+def _declared_floor(requirement: Requirement) -> Version | None:
+    floors = [Version(spec.version) for spec in requirement.specifier if spec.operator in _FLOOR_OPERATORS]
+    return max(floors, default=None)
+
+
+def declared_requirements(project: collections.abc.Mapping[str, typing.Any]) -> list[str]:
+    requirements = list(project.get("dependencies", []))
+    for extra_requirements in project.get("optional-dependencies", {}).values():
+        requirements.extend(extra_requirements)
+    return requirements
+
+
+def floor_constraints(requirements: collections.abc.Iterable[str]) -> list[str]:
+    floors: dict[tuple[str, str], tuple[str, Version]] = {}
+    unbounded: list[str] = []
+    for line in requirements:
+        requirement = Requirement(line)
+        floor = _declared_floor(requirement)
+        if floor is None:
+            unbounded.append(requirement.name)
+            continue
+        key = (canonicalize_name(requirement.name), str(requirement.marker or ""))
+        name, known = floors.get(key, (requirement.name, floor))
+        floors[key] = (name, max(known, floor))
+    if unbounded:
+        raise UnboundedError("declares no floor: " + ", ".join(unbounded))
+    return [f"{name}=={floor}" + (f"; {marker}" if marker else "") for (_, marker), (name, floor) in floors.items()]
+
+
+def main(argv: collections.abc.Sequence[str]) -> int:
+    path = pathlib.Path(argv[0] if argv else "pyproject.toml")
+    project = tomli.loads(path.read_text(encoding="utf-8")).get("project", {})
+    try:
+        constraints = floor_constraints(declared_requirements(project))
+    except UnboundedError as error:
+        print(error, file=sys.stderr)  # noqa: T201
+        return 1
+    print("\n".join(constraints))  # noqa: T201
+    return 0
+
+
+if __name__ == "__main__":
+    sys.exit(main(sys.argv[1:]))
diff --git a/tests/test_floor_constraints.py b/tests/test_floor_constraints.py
new file mode 100644
index 0000000..bacfe4d
--- /dev/null
+++ b/tests/test_floor_constraints.py
@@ -0,0 +1,78 @@
+import pathlib
+import runpy
+import sys
+
+import pytest
+
+from scripts import floor_constraints
+
+
+def test_a_lower_bound_becomes_an_exact_pin() -> None:
+    assert floor_constraints.floor_constraints(["PyYAML>=6,<7"]) == ["PyYAML==6"]
+
+
+def test_a_marker_is_kept_so_the_resolver_evaluates_it() -> None:
+    assert floor_constraints.floor_constraints(["PyYAML>=6.0.1; python_version == '3.12'"]) == [
+        'PyYAML==6.0.1; python_version == "3.12"',
+    ]
+
+
+def test_compatible_release_and_exact_pins_are_floors() -> None:
+    assert floor_constraints.floor_constraints(["a~=1.4", "b==2.0.1"]) == ["a==1.4", "b==2.0.1"]
+
+
+def test_the_same_requirement_declared_twice_pins_the_higher_floor() -> None:
+    assert floor_constraints.floor_constraints(["a>=1", "A>=1.2"]) == ["a==1.2"]
+
+
+def test_differently_marked_declarations_each_keep_their_floor() -> None:
+    assert floor_constraints.floor_constraints(
+        ["a>=1; python_version < '3.12'", "a>=2; python_version >= '3.12'"],
+    ) == ['a==1; python_version < "3.12"', 'a==2; python_version >= "3.12"']
+
+
+def test_an_unbounded_requirement_is_refused() -> None:
+    with pytest.raises(floor_constraints.UnboundedError, match=r"^declares no floor: a, b$"):
+        floor_constraints.floor_constraints(["a<2", "b", "c>=1"])
+
+
+def test_every_extra_contributes_its_requirements() -> None:
+    project = {"dependencies": ["a>=1"], "optional-dependencies": {"x": ["b>=2"], "y": ["c>=3"]}}
+
+    assert floor_constraints.declared_requirements(project) == ["a>=1", "b>=2", "c>=3"]
+
+
+def test_a_project_without_dependencies_declares_none() -> None:
+    assert floor_constraints.declared_requirements({}) == []
+
+
+def test_main_prints_this_repos_constraints(capsys: pytest.CaptureFixture[str]) -> None:
+    assert floor_constraints.main([str(pathlib.Path(__file__).parent.parent / "pyproject.toml")]) == 0
+    assert capsys.readouterr().out.splitlines() == [
+        'PyYAML==6; python_version < "3.12"',
+        'PyYAML==6.0.1; python_version == "3.12"',
+        'PyYAML==6.0.2; python_version == "3.13"',
+        'PyYAML==6.0.3; python_version >= "3.14"',
+    ]
+
+
+def test_main_fails_on_an_unbounded_requirement(
+    tmp_path: pathlib.Path,
+    capsys: pytest.CaptureFixture[str],
+) -> None:
+    pyproject = tmp_path / "pyproject.toml"
+    pyproject.write_text('[project]\ndependencies = ["a"]\n', encoding="utf-8")
+
+    assert floor_constraints.main([str(pyproject)]) == 1
+    assert capsys.readouterr().err == "declares no floor: a\n"
+
+
+def test_running_the_script_exits_with_the_verdict(monkeypatch: pytest.MonkeyPatch, tmp_path: pathlib.Path) -> None:
+    pyproject = tmp_path / "pyproject.toml"
+    pyproject.write_text('[project]\ndependencies = ["a>=1"]\n', encoding="utf-8")
+    monkeypatch.setattr(sys, "argv", ["floor_constraints.py", str(pyproject)])
+
+    with pytest.raises(SystemExit) as exit_info:
+        runpy.run_path(str(pathlib.Path(floor_constraints.__file__)), run_name="__main__")
+
+    assert exit_info.value.code == 0