diff --git a/.github/workflows/bench.yml b/.github/workflows/bench.yml
index ca195fb6..1ae0d241 100644
--- a/.github/workflows/bench.yml
+++ b/.github/workflows/bench.yml
@@ -42,7 +42,7 @@ jobs:
         uses: actions/cache@v3
         with:
           path: data_files
-          key: data_files-v4
+          key: data_files-v5
       - name: Download data files
         if: steps.cache-data_files.outputs.cache-hit != 'true'
         run: |
diff --git a/benchmarks/bench_evolution_consistency.py b/benchmarks/bench_evolution_consistency.py
new file mode 100644
index 00000000..9dc73829
--- /dev/null
+++ b/benchmarks/bench_evolution_consistency.py
@@ -0,0 +1,270 @@
+import pathlib
+
+import eko
+import numpy as np
+import pineappl
+import pytest
+from nnpdf_data import THEORY_CARDS_PATH
+from nnpdf_data.theorydbutils import fetch_theory
+from pineappl.grid import Grid
+from pineappl.subgrid import ImportSubgridV1
+
+from pineko import check
+
+HERA225 = "HERA_NC_225GEV_EP_SIGMARED"
+HERA318 = "HERA_NC_318GEV_EP_SIGMARED"
+
+
+def test_no_central_order(test_files, toy_xfx, toy_alphas):
+    grid_path = pathlib.Path(f"{test_files}/data/grids/400/{HERA225}.pineappl.lz4")
+    if not grid_path.exists():
+        pytest.fail("Test grid not found")
+
+    template_grid = Grid.read(str(grid_path))
+
+    template_subgrid = None
+    for b in range(template_grid.bins()):
+        for c in range(len(template_grid.channels())):
+            for o in range(len(template_grid.orders())):
+                sub = template_grid.subgrid(o, b, c)
+                if sub.is_empty():
+                    continue
+
+                node_values = sub.node_values
+                if len(node_values) < 2:
+                    continue
+                shape = tuple(len(v) for v in node_values)
+                if any(s == 0 for s in shape):
+                    continue
+                template_subgrid = sub
+                break
+            if template_subgrid:
+                break
+        if template_subgrid:
+            break
+
+    if not template_subgrid:
+        pytest.skip("Could not find a non-empty subgrid in template!")
+
+    order_0 = pineappl.boc.Order(0, 0, 0, 0, 0)
+    order_1 = pineappl.boc.Order(1, 0, 0, 0, 0)
+
+    grid_zeroed = Grid(
+        pid_basis=template_grid.pid_basis,
+        channels=[pineappl.boc.Channel(c) for c in template_grid.channels()],
+        orders=[order_0, order_1],
+        bins=template_grid.bwfl(),
+        convolutions=template_grid.convolutions,
+        interpolations=template_grid.interpolations,
+        kinematics=template_grid.kinematics,
+        scale_funcs=template_grid.scales,
+    )
+
+    grid_opt = Grid(
+        pid_basis=template_grid.pid_basis,
+        channels=[pineappl.boc.Channel(c) for c in template_grid.channels()],
+        orders=[order_1],
+        bins=template_grid.bwfl(),
+        convolutions=template_grid.convolutions,
+        interpolations=template_grid.interpolations,
+        kinematics=template_grid.kinematics,
+        scale_funcs=template_grid.scales,
+    )
+
+    node_values = template_subgrid.node_values
+    shape = tuple(len(v) for v in node_values)
+    data_1 = np.random.rand(*shape)
+    subgrid_1 = ImportSubgridV1(array=data_1, node_values=node_values)
+    data_0 = np.zeros(shape)
+    subgrid_0 = ImportSubgridV1(array=data_0, node_values=node_values)
+
+    for b in range(template_grid.bins()):
+        for c in range(len(template_grid.channels())):
+            grid_zeroed.set_subgrid(0, b, c, subgrid_0.into())
+            grid_zeroed.set_subgrid(1, b, c, subgrid_1.into())
+            grid_opt.set_subgrid(0, b, c, subgrid_1.into())
+
+    mask_zeroed = pineappl.boc.Order.create_mask(grid_zeroed.orders(), 2, 0, True)
+    mask_opt = pineappl.boc.Order.create_mask(grid_opt.orders(), 2, 0, True)
+    pdg_convs = template_grid.convolutions
+    xfxs = [toy_xfx] * len(pdg_convs)
+
+    res_zeroed = grid_zeroed.convolve(pdg_convs, xfxs, toy_alphas, mask_zeroed)
+    res_opt = grid_opt.convolve(pdg_convs, xfxs, toy_alphas, mask_opt)
+
+    np.testing.assert_allclose(res_zeroed, res_opt)
+
+
+def test_evolution_no_central_order(test_4100001000, tmp_path, toy_xfx):
+    """Check that evolution with a real EKO gives identical results for zeroed
+    vs optimized central order grids."""
+    from pineko import evolve
+
+    # Use theory 4100001000 which we know is consistent
+    tcard_meta = fetch_theory(THEORY_CARDS_PATH, 41000010)
+    grid_path = pathlib.Path(f"{test_4100001000}/grids/{HERA318}.pineappl.lz4")
+    eko_path = pathlib.Path(f"{test_4100001000}/ekos/{HERA318}.tar")
+
+    # Grid 1: Zeroed central order. Zero out template grid order at (3,0,0,0,0).
+    grid_zeroed = Grid.read(str(grid_path))
+    target_order = (3, 0, 0, 0, 0)
+    order_idx = None
+    for i, o in enumerate(grid_zeroed.orders()):
+        if o.as_tuple() == target_order:
+            order_idx = i
+            break
+
+    if order_idx is None:
+        pytest.fail(f"Target order {target_order} not found in grid")
+
+    for b in range(grid_zeroed.bins()):
+        for c in range(len(grid_zeroed.channels())):
+            sub = grid_zeroed.subgrid(order_idx, b, c)
+            if sub.is_empty():
+                continue
+
+            nv = sub.node_values
+            if len(nv) > 0:
+                shape = tuple(len(v) for v in nv)
+                sub_zero = ImportSubgridV1(array=np.zeros(shape), node_values=nv)
+                grid_zeroed.set_subgrid(order_idx, b, c, sub_zero.into())
+
+    # Grid 2: Optimized (removed) central order
+    grid_opt = Grid.read(str(grid_path))
+    grid_opt.delete_orders([order_idx])
+
+    with eko.EKO.read(eko_path) as operator:
+        operators = [operator]
+        fk_zeroed_path = tmp_path / "fk_zeroed.pineappl.lz4"
+        fk_opt_path = tmp_path / "fk_opt.pineappl.lz4"
+
+        evolve.evolve_grid(
+            grid_zeroed,
+            operators,
+            str(fk_zeroed_path),
+            max_as=4,
+            max_al=0,
+            xir=1.0,
+            xif=1.0,
+            xia=1.0,
+            theory_meta=tcard_meta,
+        )
+
+        evolve.evolve_grid(
+            grid_opt,
+            operators,
+            str(fk_opt_path),
+            max_as=4,
+            max_al=0,
+            xir=1.0,
+            xif=1.0,
+            xia=1.0,
+            theory_meta=tcard_meta,
+        )
+
+    # Compare resulting FK tables
+    fk_zeroed = pineappl.fk_table.FkTable.read(str(fk_zeroed_path))
+    fk_opt = pineappl.fk_table.FkTable.read(str(fk_opt_path))
+
+    res_zeroed = fk_zeroed.convolve(
+        fk_zeroed.convolutions,
+        [toy_xfx] * len(fk_zeroed.convolutions),
+    )
+    res_opt = fk_opt.convolve(
+        fk_opt.convolutions,
+        [toy_xfx] * len(fk_opt.convolutions),
+    )
+
+    np.testing.assert_allclose(res_zeroed, res_opt)
+
+
+def test_contains_sv_empty_grid_orders():
+    class EmptyGrid:
+        def orders(self):
+            return []
+
+    available, max_as_effective = check.contains_sv(
+        EmptyGrid(),
+        max_as=4,
+        max_al=0,
+        sv_type=check.Scale.REN,
+    )
+    assert available is check.AvailableAtMax.BOTH
+    assert max_as_effective == 0
+
+
+def test_evolution_no_orders(test_4100001000, tmp_path, toy_xfx):
+    """Compare evolution of: (a) a grid with orders, but all subgrids explicitly
+    set to zero with (b) the same grid after deleting all orders (no orders at all).
+
+    This test effectively checks how to construct a completely empty FK table from
+    a completely empty grid.
+    """
+    from pineko import evolve
+
+    tcard_meta = fetch_theory(THEORY_CARDS_PATH, 41000010)
+    grid_path = pathlib.Path(f"{test_4100001000}/grids/{HERA318}.pineappl.lz4")
+    eko_path = pathlib.Path(f"{test_4100001000}/ekos/{HERA318}.tar")
+
+    if not (grid_path.exists() and eko_path.exists()):
+        pytest.skip("Test data not found")
+
+    def zero_all_subgrids(grid: Grid) -> None:
+        for o in range(len(grid.orders())):
+            for b in range(grid.bins()):
+                for c in range(len(grid.channels())):
+                    sub = grid.subgrid(o, b, c)
+                    if sub.is_empty():
+                        continue
+                    nv = sub.node_values
+                    shape = tuple(len(v) for v in nv)
+                    sub_zero = ImportSubgridV1(array=np.zeros(shape), node_values=nv)
+                    grid.set_subgrid(o, b, c, sub_zero.into())
+
+    grid_zeroed = Grid.read(str(grid_path))
+    zero_all_subgrids(grid_zeroed)
+
+    grid_no_orders = Grid.read(str(grid_path))
+    grid_no_orders.delete_orders(list(range(len(grid_no_orders.orders()))))
+
+    with eko.EKO.read(eko_path) as operator:
+        fk_zeroed_path = tmp_path / "fk_zeroed_subgrids_no_orders_ref.pineappl.lz4"
+        fk_no_orders_path = tmp_path / "fk_no_orders.pineappl.lz4"
+
+        evolve.evolve_grid(
+            grid_zeroed,
+            [operator],
+            str(fk_zeroed_path),
+            max_as=4,
+            max_al=0,
+            xir=1.0,
+            xif=1.0,
+            xia=1.0,
+            theory_meta=tcard_meta,
+        )
+
+        evolve.evolve_grid(
+            grid_no_orders,
+            [operator],
+            str(fk_no_orders_path),
+            max_as=4,
+            max_al=0,
+            xir=1.0,
+            xif=1.0,
+            xia=1.0,
+            theory_meta=tcard_meta,
+        )
+
+    fk_zeroed = pineappl.fk_table.FkTable.read(str(fk_zeroed_path))
+    fk_no_orders = pineappl.fk_table.FkTable.read(str(fk_no_orders_path))
+
+    res_zeroed = fk_zeroed.convolve(
+        fk_zeroed.convolutions,
+        [toy_xfx] * len(fk_zeroed.convolutions),
+    )
+    res_no_orders = fk_no_orders.convolve(
+        fk_no_orders.convolutions,
+        [toy_xfx] * len(fk_no_orders.convolutions),
+    )
+
+    np.testing.assert_allclose(res_zeroed, res_no_orders)
diff --git a/benchmarks/conftest.py b/benchmarks/conftest.py
index 44de162d..e2de8489 100644
--- a/benchmarks/conftest.py
+++ b/benchmarks/conftest.py
@@ -14,6 +14,11 @@ def test_files():
     return pathlib.Path(__file__).parents[0] / "data_files/"
 
 
+@pytest.fixture
+def test_4100001000():
+    return pathlib.Path(__file__).parents[0] / "4100001000/"
+
+
 @pytest.fixture
 def test_empty_proj(test_files):
     path = test_files / "empty_proj/"
@@ -65,3 +70,23 @@ def wrapped(newdir):
             os.chdir(prevdir)
 
     return wrapped
+
+
+@pytest.fixture
+def toy_xfx():
+    """Toy PDF callable."""
+
+    def xfx(pid, x, q2):
+        return 1.0
+
+    return xfx
+
+
+@pytest.fixture
+def toy_alphas():
+    """Toy alpha_s callable."""
+
+    def alphas(q2):
+        return 1.0
+
+    return alphas
diff --git a/download_test_data.sh b/download_test_data.sh
old mode 100644
new mode 100755
index 4621dc0d..af6f4e11
--- a/download_test_data.sh
+++ b/download_test_data.sh
@@ -2,3 +2,4 @@
 wget -r -np -nH --cut-dirs=1 -l 4  -e robots=off --no-verbose -R index.* https://data.nnpdf.science/pineko/theory_productions/
 wget -r -np -nH --cut-dirs=1 -l 4  -e robots=off --no-verbose -P benchmarks -R index.* https://data.nnpdf.science/pineko/data_files/
 wget -r -np -nH --cut-dirs=1 -l 4  -e robots=off --no-verbose -P benchmarks -R index.* https://data.nnpdf.science/pineko/fakepdfs/
+wget -r -np -nH --cut-dirs=1 -l 4  -e robots=off --no-verbose -P benchmarks -R index.* https://data.nnpdf.science/pineko/4100001000/
diff --git a/poetry.lock b/poetry.lock
index a74dde3e..f4ac05df 100644
--- a/poetry.lock
+++ b/poetry.lock
@@ -96,14 +96,14 @@ SQLAlchemy = ">=1.4.29,<2.0.0"
 
 [[package]]
 name = "certifi"
-version = "2026.2.25"
+version = "2026.4.22"
 description = "Python package for providing Mozilla's CA Bundle."
 optional = false
 python-versions = ">=3.7"
 groups = ["docs"]
 files = [
-    {file = "certifi-2026.2.25-py3-none-any.whl", hash = "sha256:027692e4402ad994f1c42e52a4997a9763c646b73e4096e4d5d6db8af1d6f0fa"},
-    {file = "certifi-2026.2.25.tar.gz", hash = "sha256:e887ab5cee78ea814d3472169153c2d12cd43b14bd03329a39a9c6e2e80bfba7"},
+    {file = "certifi-2026.4.22-py3-none-any.whl", hash = "sha256:3cb2210c8f88ba2318d29b0388d1023c8492ff72ecdde4ebdaddbb13a31b1c4a"},
+    {file = "certifi-2026.4.22.tar.gz", hash = "sha256:8d455352a37b71bf76a79caa83a3d6c25afee4a385d632127b6afb3963f1c580"},
 ]
 
 [[package]]
@@ -247,14 +247,14 @@ files = [
 
 [[package]]
 name = "click"
-version = "8.3.2"
+version = "8.4.0"
 description = "Composable command line interface toolkit"
 optional = false
 python-versions = ">=3.10"
 groups = ["main", "test"]
 files = [
-    {file = "click-8.3.2-py3-none-any.whl", hash = "sha256:1924d2c27c5653561cd2cae4548d1406039cb79b858b747cfea24924bbc1616d"},
-    {file = "click-8.3.2.tar.gz", hash = "sha256:14162b8b3b3550a7d479eafa77dfd3c38d9dc8951f6f69c78913a8f9a7540fd5"},
+    {file = "click-8.4.0-py3-none-any.whl", hash = "sha256:40c50b7c6c6adac2823d411041ec84f3f103f1b280d5e9ce0d7f998995832f81"},
+    {file = "click-8.4.0.tar.gz", hash = "sha256:638f1338fe1235c8f4e008e4a8a254fb5c5fbdcbb40ece3c9142ebb78e792973"},
 ]
 
 [package.dependencies]
@@ -461,118 +461,118 @@ test-no-images = ["pytest", "pytest-cov", "pytest-rerunfailures", "pytest-xdist"
 
 [[package]]
 name = "coverage"
-version = "7.13.5"
+version = "7.14.0"
 description = "Code coverage measurement for Python"
 optional = false
 python-versions = ">=3.10"
 groups = ["test"]
 files = [
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-    {file = "coverage-7.13.5-cp310-cp310-macosx_11_0_arm64.whl", hash = "sha256:52f444e86475992506b32d4e5ca55c24fc88d73bcbda0e9745095b28ef4dc0cf"},
-    {file = "coverage-7.13.5-cp310-cp310-manylinux1_i686.manylinux_2_28_i686.manylinux_2_5_i686.whl", hash = "sha256:704de6328e3d612a8f6c07000a878ff38181ec3263d5a11da1db294fa6a9bdf8"},
-    {file = "coverage-7.13.5-cp310-cp310-manylinux1_x86_64.manylinux_2_28_x86_64.manylinux_2_5_x86_64.whl", hash = "sha256:a1a6d79a14e1ec1832cabc833898636ad5f3754a678ef8bb4908515208bf84f4"},
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 [package.dependencies]
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 [[package]]
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 [[package]]
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@@ -864,18 +864,18 @@ test = ["objgraph", "psutil", "setuptools"]
 
 [[package]]
 name = "idna"
-version = "3.11"
+version = "3.15"
 description = "Internationalized Domain Names in Applications (IDNA)"
 optional = false
 python-versions = ">=3.8"
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+all = ["mypy (>=1.11.2)", "pytest (>=8.3.2)", "ruff (>=0.6.2)"]
 
 [[package]]
 name = "imagesize"
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 [[package]]
 name = "jinja2"
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 ]
 
 [package.dependencies]
@@ -1432,25 +1431,25 @@ pyparsing = ">=3"
 python-dateutil = ">=2.7"
 
 [package.extras]
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 [[package]]
 name = "matplotlib-inline"
-version = "0.2.1"
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 description = "Inline Matplotlib backend for Jupyter"
 optional = false
 python-versions = ">=3.9"
 groups = ["dev", "test"]
 files = [
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 ]
 
 [package.dependencies]
 traitlets = "*"
 
 [package.extras]
-test = ["flake8", "nbdime", "nbval", "notebook", "pytest"]
+test = ["flake8", "matplotlib", "nbdime", "nbval", "notebook", "pytest"]
 
 [[package]]
 name = "mccabe"
@@ -1466,14 +1465,14 @@ files = [
 
 [[package]]
 name = "nnpdf-data"
-version = "4.1.3"
+version = "4.1.4"
 description = "The NNPDF data repository"
 optional = false
 python-versions = "<4.0,>=3.9"
 groups = ["main", "test"]
 files = [
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 ]
 markers = {main = "extra == \"nnpdf\""}
 
@@ -1700,14 +1699,14 @@ xml = ["lxml (>=4.9.2)"]
 
 [[package]]
 name = "parso"
-version = "0.8.6"
+version = "0.8.7"
 description = "A Python Parser"
 optional = false
 python-versions = ">=3.6"
 groups = ["dev", "test"]
 files = [
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 ]
 
 [package.extras]
@@ -1944,48 +1943,42 @@ xmp = ["defusedxml"]
 
 [[package]]
 name = "pineappl"
-version = "1.3.3"
-description = ""
+version = "1.4.0"
+description = "Python bindings to PineAPPL"
 optional = false
 python-versions = ">=3.7"
 groups = ["main"]
 files = [
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 ]
 
 [package.dependencies]
@@ -1998,16 +1991,16 @@ test = ["pytest", "pytest-cov"]
 
 [[package]]
 name = "pineappl-cli"
-version = "1.3.3"
+version = "1.4.0"
 description = "Read, write, and query PineAPPL grids"
 optional = false
-python-versions = "*"
+python-versions = ">=3.7"
 groups = ["test"]
 files = [
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 ]
 
 [[package]]
@@ -2175,15 +2168,15 @@ diagrams = ["jinja2", "railroad-diagrams"]
 
 [[package]]
 name = "pyreadline3"
-version = "3.5.4"
+version = "3.5.6"
 description = "A python implementation of GNU readline."
 optional = false
 python-versions = ">=3.8"
 groups = ["dev"]
 markers = "python_version <= \"3.12\" and platform_system == \"Windows\""
 files = [
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 ]
 
 [package.extras]
@@ -2279,14 +2272,14 @@ six = ">=1.5"
 
 [[package]]
 name = "pytz"
-version = "2026.1.post1"
+version = "2026.2"
 description = "World timezone definitions, modern and historical"
 optional = false
 python-versions = "*"
 groups = ["main", "test"]
 files = [
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-    {file = "pytz-2026.1.post1.tar.gz", hash = "sha256:3378dde6a0c3d26719182142c56e60c7f9af7e968076f31aae569d72a0358ee1"},
+    {file = "pytz-2026.2-py2.py3-none-any.whl", hash = "sha256:04156e608bee23d3792fd45c94ae47fae1036688e75032eea2e3bf0323d1f126"},
+    {file = "pytz-2026.2.tar.gz", hash = "sha256:0e60b47b29f21574376f218fe21abc009894a2321ea16c6754f3cad6eb7cdd6a"},
 ]
 
 [[package]]
@@ -2374,14 +2367,14 @@ files = [
 
 [[package]]
 name = "requests"
-version = "2.33.1"
+version = "2.34.2"
 description = "Python HTTP for Humans."
 optional = false
 python-versions = ">=3.10"
 groups = ["docs"]
 files = [
-    {file = "requests-2.33.1-py3-none-any.whl", hash = "sha256:4e6d1ef462f3626a1f0a0a9c42dd93c63bad33f9f1c1937509b8c5c8718ab56a"},
-    {file = "requests-2.33.1.tar.gz", hash = "sha256:18817f8c57c6263968bc123d237e3b8b08ac046f5456bd1e307ee8f4250d3517"},
+    {file = "requests-2.34.2-py3-none-any.whl", hash = "sha256:2a0d60c172f83ac6ab31e4554906c0f3b3588d37b5cb939b1c061f4907e278e0"},
+    {file = "requests-2.34.2.tar.gz", hash = "sha256:f288924cae4e29463698d6d60bc6a4da69c89185ad1e0bcc4104f584e960b9ed"},
 ]
 
 [package.dependencies]
@@ -2987,31 +2980,31 @@ markers = {docs = "python_version == \"3.10\"", test = "python_version == \"3.10
 
 [[package]]
 name = "tomlkit"
-version = "0.14.0"
+version = "0.15.0"
 description = "Style preserving TOML library"
 optional = false
 python-versions = ">=3.9"
 groups = ["test"]
 files = [
-    {file = "tomlkit-0.14.0-py3-none-any.whl", hash = "sha256:592064ed85b40fa213469f81ac584f67a4f2992509a7c3ea2d632208623a3680"},
-    {file = "tomlkit-0.14.0.tar.gz", hash = "sha256:cf00efca415dbd57575befb1f6634c4f42d2d87dbba376128adb42c121b87064"},
+    {file = "tomlkit-0.15.0-py3-none-any.whl", hash = "sha256:4dbc8f0fc024412b57ced8757ac7461305126a648ff8c2c807fcb8e133a78738"},
+    {file = "tomlkit-0.15.0.tar.gz", hash = "sha256:7d1a9ecba3086638211b13814ea79c90dd54dd11993564376f3aa92271f5c7a3"},
 ]
 
 [[package]]
 name = "traitlets"
-version = "5.14.3"
+version = "5.15.0"
 description = "Traitlets Python configuration system"
 optional = false
-python-versions = ">=3.8"
+python-versions = ">=3.9"
 groups = ["dev", "test"]
 files = [
-    {file = "traitlets-5.14.3-py3-none-any.whl", hash = "sha256:b74e89e397b1ed28cc831db7aea759ba6640cb3de13090ca145426688ff1ac4f"},
-    {file = "traitlets-5.14.3.tar.gz", hash = "sha256:9ed0579d3502c94b4b3732ac120375cda96f923114522847de4b3bb98b96b6b7"},
+    {file = "traitlets-5.15.0-py3-none-any.whl", hash = "sha256:fb36a18867a6803deab09f3c5e0fa81bb7b26a5c9e82501c9933f759166eff40"},
+    {file = "traitlets-5.15.0.tar.gz", hash = "sha256:4fead733f81cf1c4c938e06f8ca4633896833c9d89eff878159457f4d4392971"},
 ]
 
 [package.extras]
 docs = ["myst-parser", "pydata-sphinx-theme", "sphinx"]
-test = ["argcomplete (>=3.0.3)", "mypy (>=1.7.0)", "pre-commit", "pytest (>=7.0,<8.2)", "pytest-mock", "pytest-mypy-testing"]
+test = ["argcomplete (>=3.0.3)", "mypy (>=1.7.0)", "mypy (>=1.7.0,<1.19) ; platform_python_implementation == \"PyPy\"", "pre-commit", "pytest (>=7.0,<8.2)", "pytest-mock", "pytest-mypy-testing"]
 
 [[package]]
 name = "typing-extensions"
@@ -3028,26 +3021,26 @@ markers = {main = "python_version == \"3.10\"", dev = "python_version < \"3.12\"
 
 [[package]]
 name = "tzdata"
-version = "2026.1"
+version = "2026.2"
 description = "Provider of IANA time zone data"
 optional = false
 python-versions = ">=2"
 groups = ["main", "test"]
 files = [
-    {file = "tzdata-2026.1-py2.py3-none-any.whl", hash = "sha256:4b1d2be7ac37ceafd7327b961aa3a54e467efbdb563a23655fbfe0d39cfc42a9"},
-    {file = "tzdata-2026.1.tar.gz", hash = "sha256:67658a1903c75917309e753fdc349ac0efd8c27db7a0cb406a25be4840f87f98"},
+    {file = "tzdata-2026.2-py2.py3-none-any.whl", hash = "sha256:bbe9af844f658da81a5f95019480da3a89415801f6cc966806612cc7169bffe7"},
+    {file = "tzdata-2026.2.tar.gz", hash = "sha256:9173fde7d80d9018e02a662e168e5a2d04f87c41ea174b139fbef642eda62d10"},
 ]
 
 [[package]]
 name = "urllib3"
-version = "2.6.3"
+version = "2.7.0"
 description = "HTTP library with thread-safe connection pooling, file post, and more."
 optional = false
-python-versions = ">=3.9"
+python-versions = ">=3.10"
 groups = ["docs"]
 files = [
-    {file = "urllib3-2.6.3-py3-none-any.whl", hash = "sha256:bf272323e553dfb2e87d9bfd225ca7b0f467b919d7bbd355436d3fd37cb0acd4"},
-    {file = "urllib3-2.6.3.tar.gz", hash = "sha256:1b62b6884944a57dbe321509ab94fd4d3b307075e0c2eae991ac71ee15ad38ed"},
+    {file = "urllib3-2.7.0-py3-none-any.whl", hash = "sha256:9fb4c81ebbb1ce9531cce37674bbc6f1360472bc18ca9a553ede278ef7276897"},
+    {file = "urllib3-2.7.0.tar.gz", hash = "sha256:231e0ec3b63ceb14667c67be60f2f2c40a518cb38b03af60abc813da26505f4c"},
 ]
 
 [package.extras]
@@ -3075,14 +3068,14 @@ test = ["hypothesis", "pytest", "pytest-cov"]
 
 [[package]]
 name = "wcwidth"
-version = "0.6.0"
+version = "0.7.0"
 description = "Measures the displayed width of unicode strings in a terminal"
 optional = false
 python-versions = ">=3.8"
 groups = ["dev", "test"]
 files = [
-    {file = "wcwidth-0.6.0-py3-none-any.whl", hash = "sha256:1a3a1e510b553315f8e146c54764f4fb6264ffad731b3d78088cdb1478ffbdad"},
-    {file = "wcwidth-0.6.0.tar.gz", hash = "sha256:cdc4e4262d6ef9a1a57e018384cbeb1208d8abbc64176027e2c2455c81313159"},
+    {file = "wcwidth-0.7.0-py3-none-any.whl", hash = "sha256:5d69154c429a82910e241c738cd0e2976fac8a2dd47a1a805f4afed1c0f136f2"},
+    {file = "wcwidth-0.7.0.tar.gz", hash = "sha256:90e3a7ea092341c44b99562e75d09e4d5160fe7a3974c6fb842a101a95e7eed0"},
 ]
 
 [extras]
@@ -3092,4 +3085,4 @@ nnpdf = ["nnpdf-data"]
 [metadata]
 lock-version = "2.1"
 python-versions = ">=3.10,<3.14"
-content-hash = "b3a6eef624b5675a0a794b3aa5de228ba8d1abd42ff08637585b22f2f6322b34"
+content-hash = "27d5d158b5c6f63746c5de2d97e2e7867f5b05913a3d7c2f4eda6743add61f88"
diff --git a/pyproject.toml b/pyproject.toml
index 7e79c94e..44498a7e 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -28,7 +28,7 @@ packages = [{ include = "pineko", from = "src" }]
 [tool.poetry.dependencies]
 python = ">=3.10,<3.14"
 eko = "^0.15.3"
-pineappl = "^1.3.0"
+pineappl = "^1.4.0"
 PyYAML = "^6.0"
 numpy = "^2"
 pandas = "^2.1"
@@ -59,7 +59,7 @@ pytest-cov = "^4.0.0"
 pytest-env = "^0.6.2"
 pylint = "^3.1.0"
 banana-hep = "^0.6.13"
-pineappl-cli = "^1.3.0"
+pineappl-cli = "^1.4.0"
 
 [tool.poetry.group.dev.dependencies]
 pdbpp = "^0.11.6"
diff --git a/src/pineko/check.py b/src/pineko/check.py
index 7aa7103a..be981372 100644
--- a/src/pineko/check.py
+++ b/src/pineko/check.py
@@ -165,6 +165,8 @@ def orders(grid, max_as, max_al) -> list:
 
 def pure_qcd(orders):
     """Select the QCD LO and pure QCD corrections to it."""
+    if len(orders) == 0:
+        return []
     min_al = min(ord[1] for ord in orders)
     return [ord for ord in orders if ord[1] == min_al]
 
@@ -174,7 +176,14 @@ def contains_sv(
 ) -> Tuple[AvailableAtMax, int]:
     """Check whether renormalization scale-variations are available in the pineappl grid."""
     svindex = sv_type.value.index
-    ords = pure_qcd(orders(grid, max_as, max_al))
+    ords = orders(grid, max_as, max_al)
+    # Empty grids (no orders) are a valid case: we must be able to propagate them and
+    # generate empty FK tables (e.g. for numerical FONLL workflows).
+    if len(ords) == 0:
+        return AvailableAtMax.BOTH, 0
+    ords = pure_qcd(ords)
+    if len(ords) == 0:
+        return AvailableAtMax.BOTH, 0
     max_as = max(ord[0] for ord in ords)
     min_as = min(ord[0] for ord in ords)
     max_as_cen = max(ord[0] for ord in ords if ord[svindex] == 0)
diff --git a/src/pineko/cli/check.py b/src/pineko/cli/check.py
index adae173f..48938842 100644
--- a/src/pineko/cli/check.py
+++ b/src/pineko/cli/check.py
@@ -71,8 +71,8 @@ class Coupling(Enum):
 
 SCVAR_MESSAGES = {
     check.AvailableAtMax.BOTH: "[green]Success:[/] grids contain",
-    check.AvailableAtMax.CENTRAL: "[orange]Warning:[/] grids do not contain central order for requested",
-    check.AvailableAtMax.SCVAR: SCVAR_ERROR,
+    check.AvailableAtMax.CENTRAL: "[orange]Warning:[/] grids do not contain scale variation order for requested",
+    check.AvailableAtMax.SCVAR: "[orange]Warning:[/] grids do not contain central order for requested",
 }
 
 
diff --git a/src/pineko/evolve.py b/src/pineko/evolve.py
index 9ae02ba2..fd862c9e 100644
--- a/src/pineko/evolve.py
+++ b/src/pineko/evolve.py
@@ -67,6 +67,36 @@ def construct_atlas(tcard):
     return atlas
 
 
+def construct_empty_fktable(grid, theory_meta, fktable_path):
+    """Construct an empty FK table from a given grid.
+
+    Parameters
+    ----------
+    gird : pineappl.grid.Grid
+        a PineAPPL Grid object
+    fktable_path : str
+        target path for convolved grid
+    theory_meta: dict
+        a dictionary containing the theory metadata
+    """
+    empty_order = pineappl.boc.Order(0, 0, 0, 0, 0)
+    empty_grid = pineappl.grid.Grid(
+        pid_basis=grid.pid_basis,
+        channels=[pineappl.boc.Channel(c) for c in grid.channels()],
+        orders=[empty_order],
+        bins=grid.bwfl(),
+        convolutions=grid.convolutions,
+        interpolations=grid.interpolations,
+        kinematics=grid.kinematics,
+        scale_funcs=grid.scales,
+    )
+    fktable = pineappl.fk_table.FkTable(empty_grid)
+    fktable.set_metadata("pineko_version", version.__version__)
+    fktable.set_metadata("theory_card", json.dumps(theory_meta))
+    fktable.write_lz4(str(fktable_path))
+    return fktable
+
+
 def get_convolution_suffix(convolution: pineappl.convolutions.Conv) -> str:
     """Get the correct suffix for a given convolution.
 
@@ -324,7 +354,7 @@ def evolve_grid(
         factorization scale variation
     xia : float
         fragmentation scale variation
-    tcard: dict
+    theory_metadata: dict
         card containing the theory parameters
     assumptions : str
         assumptions on the flavor dimension
@@ -333,6 +363,12 @@ def evolve_grid(
     min_as: None or int
         minimum power of strong coupling
     """
+    # A grid with no orders is a valid input for some workflows. In that case we
+    # cannot build evolution kinematics, so we directly emit an empty FK table.
+    if len(grid.orders()) == 0:
+        fktable = construct_empty_fktable(grid, theory_meta, fktable_path)
+        return grid, fktable, None
+
     order_mask = pineappl.boc.Order.create_mask(grid.orders(), max_as, max_al, True)
     if min_as is not None and min_as > 1:
         # If using min_as, we want to ignore only orders below that (e.g., if min_as=2
@@ -349,6 +385,14 @@ def evolve_grid(
 
     muf2_grid = evol_info.fac1
     mur2_grid = evol_info.ren1
+
+    # `evolve_info` returns empty arrays when all subgrids are absent. However,
+    # `XGrid` requires at least 2 points, otherwise it panics. In this case, we
+    # simply return an empty FK table instead.
+    if (len(x_grid) < 2) or (len(muf2_grid) == 0) or (len(mur2_grid) == 0):
+        fktable = construct_empty_fktable(grid, theory_meta, fktable_path)
+        return grid, fktable, None
+
     xif = 1.0 if operators[0].operator_card.configs.scvar_method is not None else xif
     tcard = operators[0].theory_card
     opcard = operators[0].operator_card
diff --git a/src/pineko/theory.py b/src/pineko/theory.py
index 4a8e3e36..55cbf1e6 100644
--- a/src/pineko/theory.py
+++ b/src/pineko/theory.py
@@ -80,9 +80,6 @@ def get_eko_names(grid_path, name, filter=True):
 def check_scvar_evolve(grid, max_as, max_al, kind: check.Scale):
     """Check scale variations and central orders consistency."""
     available, max_as_effective = check.contains_sv(grid, max_as, max_al, kind)
-    if max_as == max_as_effective:
-        if available is check.AvailableAtMax.SCVAR:
-            raise ValueError("Central order is not available but sv order is.")
     if max_as < max_as_effective and available is not check.AvailableAtMax.BOTH:
         raise ValueError("No available central order or sv order.")
 
diff --git a/tests/conftest.py b/tests/conftest.py
index b39879fa..549ddadb 100644
--- a/tests/conftest.py
+++ b/tests/conftest.py
@@ -43,3 +43,23 @@ def fake_configs(tmp_path):
         "root": tmp_path,
     }
     return fake_configs
+
+
+@pytest.fixture
+def toy_xfx():
+    """Toy PDF callable."""
+
+    def xfx(pid, x, q2):
+        return 1.0
+
+    return xfx
+
+
+@pytest.fixture
+def toy_alphas():
+    """Toy alpha_s callable."""
+
+    def alphas(q2):
+        return 1.0
+
+    return alphas
diff --git a/tests/test_theory_sv.py b/tests/test_theory_sv.py
new file mode 100644
index 00000000..7c28f56f
--- /dev/null
+++ b/tests/test_theory_sv.py
@@ -0,0 +1,77 @@
+import pineappl
+
+import pineko.check
+import pineko.theory
+
+
+class Fake_grid:
+    def __init__(self, order_list, convolutions=[]):
+        self.orderlist = order_list
+        self.convolutions = convolutions
+
+    def orders(self):
+        return [order._raw for order in self.orderlist]
+
+
+class Order:
+    def __init__(self, order_tup):
+        self.orders = order_tup
+        self._raw = pineappl.boc.Order(*order_tup)
+
+    def as_tuple(self):
+        return self.orders
+
+
+def test_check_scvar_evolve():
+    max_as = 3
+    max_al = 0
+
+    grid_both = Fake_grid(
+        [
+            Order((0, 0, 0, 0, 0)),
+            Order((1, 0, 0, 0, 0)),
+            Order((2, 0, 0, 0, 0)),
+            Order((2, 0, 1, 0, 0)),
+        ]
+    )
+    pineko.theory.check_scvar_evolve(
+        grid_both,
+        max_as,
+        max_al,
+        pineko.check.Scale.REN,
+    )
+
+    grid_central = Fake_grid(
+        [
+            Order((0, 0, 0, 0, 0)),
+            Order((1, 0, 0, 0, 0)),
+            Order((2, 0, 0, 0, 0)),
+        ]
+    )
+    pineko.theory.check_scvar_evolve(
+        grid_central,
+        max_as,
+        max_al,
+        pineko.check.Scale.REN,
+    )
+
+    grid_scvar = Fake_grid(
+        [
+            Order((0, 0, 0, 0, 0)),
+            Order((1, 0, 0, 0, 0)),
+            Order((2, 0, 1, 0, 0)),
+        ]
+    )
+    pineko.theory.check_scvar_evolve(
+        grid_scvar,
+        max_as,
+        max_al,
+        pineko.check.Scale.REN,
+    )
+
+    pineko.theory.check_scvar_evolve(
+        grid_scvar,
+        1,
+        max_al,
+        pineko.check.Scale.REN,
+    )