diff --git a/src/sp_validation/cosmo_val/real_space.py b/src/sp_validation/cosmo_val/real_space.py
index 89dad2a9..fce6d55c 100644
--- a/src/sp_validation/cosmo_val/real_space.py
+++ b/src/sp_validation/cosmo_val/real_space.py
@@ -14,8 +14,30 @@
 import treecorr
 from cs_util import plots as cs_plots
 
+from sp_validation.statistics import jackknife_patch_centers
+
 
 class RealSpaceMixin:
+    def _shear_catalog(self, ver, npatch):
+        """Calibrated shear catalogue of ``ver`` with seeded jackknife patches.
+
+        Call inside ``self.results[ver].temporarily_read_data()``.
+        """
+        positions = {
+            "ra": self.results[ver].dat_shear["RA"],
+            "dec": self.results[ver].dat_shear["Dec"],
+            "w": self._read_shear_cols(ver, "w_col"),
+            "ra_units": self.treecorr_config["ra_units"],
+            "dec_units": self.treecorr_config["dec_units"],
+        }
+        centers = None
+        if int(npatch) > 1:
+            centers = jackknife_patch_centers(
+                treecorr.Catalog(**positions), int(npatch)
+            )
+        g1, g2 = self._calibrated_g(ver)
+        return treecorr.Catalog(**positions, g1=g1, g2=g2, patch_centers=centers)
+
     def calculate_2pcf(self, ver, npatch=None, **treecorr_config):
         """
         Calculate the two-point correlation function (2PCF) ξ± for a given catalog
@@ -43,8 +65,10 @@ def calculate_2pcf(self, ver, npatch=None, **treecorr_config):
         Notes:
             - If the output file for the given configuration already exists, the
               calculation is skipped, and the results are loaded from the file.
-            - If a patch file for the given configuration does not exist, it is
-              created during the process.
+            - Jackknife patches come from a seeded k-means on a fixed-depth tree
+              (``statistics.jackknife_patch_centers``), so they are a pure
+              function of the catalogue's positions and weights, the same on
+              every run and thread count.
             - The ``.txt`` TreeCorr dump is the only raw byproduct written here.
         """
 
@@ -70,27 +94,7 @@ def calculate_2pcf(self, ver, npatch=None, **treecorr_config):
         else:
             # Load data and create a catalog
             with self.results[ver].temporarily_read_data():
-                g1, g2 = self._calibrated_g(ver)
-                w = self._read_shear_cols(ver, "w_col")
-
-                # Use patch file if it exists
-                patch_file = self._output_path(f"{ver}_patches_npatch={npatch}.dat")
-
-                cat_gal = treecorr.Catalog(
-                    ra=self.results[ver].dat_shear["RA"],
-                    dec=self.results[ver].dat_shear["Dec"],
-                    g1=g1,
-                    g2=g2,
-                    w=w,
-                    ra_units=self.treecorr_config["ra_units"],
-                    dec_units=self.treecorr_config["dec_units"],
-                    npatch=npatch,
-                    patch_centers=patch_file if os.path.exists(patch_file) else None,
-                )
-
-                # If no patch file exists, save the current patches
-                if not os.path.exists(patch_file):
-                    cat_gal.write_patch_centers(patch_file)
+                cat_gal = self._shear_catalog(ver, npatch)
 
             # Process the catalog & write the correlation functions
             gg.process(cat_gal)
@@ -346,23 +350,10 @@ def calculate_aperture_mass_dispersion(
                 gg.read(out_fname)
             else:
                 with self.results[ver].temporarily_read_data():
-                    g1, g2 = self._calibrated_g(ver)
-                    cat_gal = treecorr.Catalog(
-                        ra=self.results[ver].dat_shear["RA"],
-                        dec=self.results[ver].dat_shear["Dec"],
-                        g1=g1,
-                        g2=g2,
-                        w=self._read_shear_cols(ver, "w_col"),
-                        ra_units=self.treecorr_config["ra_units"],
-                        dec_units=self.treecorr_config["dec_units"],
-                        npatch=npatch,
-                    )
-
+                    cat_gal = self._shear_catalog(ver, npatch)
                     gg.process(cat_gal)
                     gg.write(out_fname)
                     del cat_gal
-                    del g1
-                    del g2
 
             mapsq, mapsq_im, mxsq, mxsq_im, varmapsq = gg.calculateMapSq(
                 R=theta_map,
diff --git a/src/sp_validation/rho_tau.py b/src/sp_validation/rho_tau.py
index 62ae8bf8..62f40959 100644
--- a/src/sp_validation/rho_tau.py
+++ b/src/sp_validation/rho_tau.py
@@ -9,6 +9,7 @@
 # SquareRootScale now lives in sp_validation.plots; re-exported here so that
 # `from sp_validation.rho_tau import SquareRootScale` keeps working.
 from sp_validation.plots import SquareRootScale  # noqa: F401
+from sp_validation.statistics import jackknife_patch_centers
 
 
 def _extract_xip(correlations):
@@ -369,10 +370,10 @@ def get_jackknife_cov(
                 print(f"Computing the patch centers for patch {i + 1}/{ncov}")
 
                 npatch = rho_stat_handler.catalogs._params["patch_number"]
-                field = rho_stat_handler.catalogs.catalogs_dict[
-                    f"psf_{version}{i}"
-                ].getNField(max_top=int.bit_length(npatch) - 1, coords="spherical")
-                patch, centers = field.run_kmeans(npatch)
+                centers = jackknife_patch_centers(
+                    rho_stat_handler.catalogs.catalogs_dict[f"psf_{version}{i}"],
+                    npatch,
+                )
 
                 # Update the patch centers of the catalogs
                 for key, cat in rho_stat_handler.catalogs.catalogs_dict.items():
diff --git a/src/sp_validation/statistics.py b/src/sp_validation/statistics.py
index dc71f680..23572ee5 100644
--- a/src/sp_validation/statistics.py
+++ b/src/sp_validation/statistics.py
@@ -3,8 +3,9 @@
 :Name: statistics.py
 
 :Description: Cosmology-independent statistical helpers (jackknife resampling,
-              chi2/PTE, calibrated min-PTE across many null tests,
-              covariance<->correlation, OneCovariance reshaping).
+              jackknife patch centres, chi2/PTE, calibrated min-PTE across
+              many null tests, covariance<->correlation, OneCovariance
+              reshaping).
 """
 
 from dataclasses import dataclass
@@ -12,6 +13,42 @@
 import numpy as np
 from scipy import stats
 
+#: Depth of the ball-tree layers that seed the jackknife k-means.
+PATCH_MIN_TOP = 6
+
+
+def jackknife_patch_centers(cat, npatch, seed=0):
+    """Seeded k-means jackknife patch centres for a TreeCorr catalogue.
+
+    Seeding the k-means does not by itself fix the patches. TreeCorr starts the
+    k-means from the top layers of a ball tree whose depth, unless ``min_top``
+    is given, grows with the OpenMP thread count (``Field._determine_top``),
+    and ``Catalog(npatch=..., rng=...)`` offers no way to set it. Pinning that
+    depth makes the centres a function of the catalogue's positions, weights
+    and ``seed`` alone, on every machine.
+
+    Parameters
+    ----------
+    cat : treecorr.Catalog
+        Catalogue with spherical (RA, Dec) positions.
+    npatch : int
+        Number of patches.
+    seed : int, optional
+        Seed for the k-means initialisation.
+
+    Returns
+    -------
+    numpy.ndarray
+        Patch centres, to pass as ``patch_centers`` to ``treecorr.Catalog``.
+    """
+    field = cat.getNField(
+        min_top=PATCH_MIN_TOP,
+        max_top=int.bit_length(npatch) - 1,
+        coords="spherical",
+    )
+    _, centers = field.run_kmeans(npatch, rng=np.random.default_rng(seed))
+    return centers
+
 
 def jackknif_weighted_average2(
     data,
diff --git a/src/sp_validation/tests/test_cosmo_val.py b/src/sp_validation/tests/test_cosmo_val.py
index c08c055e..a743161a 100644
--- a/src/sp_validation/tests/test_cosmo_val.py
+++ b/src/sp_validation/tests/test_cosmo_val.py
@@ -501,39 +501,60 @@ def test_a_patched_xi_dump_reads_back(self, tmp_path):
                 getattr(read, column), getattr(measured, column), rtol=1e-4
             )
 
-    def test_calculate_2pcf_does_not_depend_on_thread_count(self, tmp_path):
-        """calculate_2pcf's ξ± is the same on 4 and on 48 TreeCorr threads.
-
-        Production binning (default bin_slop/angle_slop), both runs on the
-        jackknife patches the first one writes, each from a fresh Catalog; they
-        must agree to far below the jackknife σ.
+    def test_calculate_2pcf_is_reproducible_across_machines(
+        self, tmp_path, monkeypatch
+    ):
+        """Two fresh output trees on 4- and 16-CPU machines measure the same ξ±.
+
+        TreeCorr's default k-means tree depth follows the machine's OpenMP
+        thread count (3 levels on 4 CPUs, 4 on 16). With 100 patches (up to 6
+        levels, and not a power of two) that changes the k-means start, so a
+        seed alone would split the catalogue differently. calculate_2pcf pins
+        the depth: patch labels, per-patch-pair counts, ξ± and its jackknife
+        variance all agree.
         """
         import treecorr
-
-        params, version = self._write_synthetic_catalogs(
-            tmp_path, n_gal=4000, coherent_shear=True
-        )
-        cv = CosmologyValidation(
-            versions=[version],
-            npatch=8,
-            theta_min=15.0,
-            theta_max=70.0,
-            nbins=6,
-            **params,
-        )
-
-        xi = {}
-        for n_threads in (4, 48):
-            # calculate_2pcf reads back an existing text dump instead of measuring.
-            for dump in Path(params["output_dir"]).glob(f"{version}_xi_*.txt"):
-                dump.unlink()
-            gg = cv.calculate_2pcf(version, num_threads=n_threads)
-            assert treecorr.get_omp_threads() == n_threads  # the count took effect
-            xi[n_threads] = np.concatenate([gg.xip, gg.xim])
-            sigma = np.sqrt(np.concatenate([gg.varxip, gg.varxim]))
-
-        shift = np.max(np.abs(xi[48] - xi[4]) / sigma)
-        assert shift < 1e-6, f"ξ± moves by {shift:.3g}σ between 4 and 48 threads"
+        import treecorr.field
+
+        patches = []
+        process = treecorr.GGCorrelation.process
+
+        def recording_process(gg, cat, *args, **kwargs):
+            patches.append(np.array(cat.patch))
+            return process(gg, cat, *args, **kwargs)
+
+        monkeypatch.setattr(treecorr.GGCorrelation, "process", recording_process)
+
+        xi, var, counts = {}, {}, {}
+        for tree, n_cpu in (("a", 4), ("b", 16)):
+            # The thread count TreeCorr's default tree depth reads.
+            monkeypatch.setattr(treecorr.field, "get_omp_threads", lambda n=n_cpu: n)
+            (tmp_path / tree).mkdir()
+            params, version = self._write_synthetic_catalogs(
+                tmp_path / tree,
+                n_gal=4000,
+                ra_range=(0.0, 60.0),
+                dec_range=(-10.0, 30.0),
+                coherent_shear=True,
+            )
+            gg = CosmologyValidation(
+                versions=[version],
+                npatch=100,
+                theta_min=15.0,
+                theta_max=70.0,
+                nbins=6,
+                **params,
+            ).calculate_2pcf(version)
+            xi[tree] = np.concatenate([gg.xip, gg.xim])
+            var[tree] = np.concatenate([gg.varxip, gg.varxim])
+            counts[tree] = {k: r.npairs for k, r in gg.results.items()}
+
+        np.testing.assert_array_equal(patches[0], patches[1])
+        assert counts["a"].keys() == counts["b"].keys()
+        for k in counts["a"]:
+            np.testing.assert_array_equal(counts["a"][k], counts["b"][k])
+        np.testing.assert_allclose(xi["a"], xi["b"], rtol=0, atol=1e-12)
+        np.testing.assert_allclose(var["a"], var["b"], rtol=1e-10)
 
     def test_treecorr_runs_on_the_cpus_the_process_holds(self, tmp_path):
         """By default TreeCorr takes the process's CPU affinity, not the node's count."""