diff --git a/src/matchbox/common/hash.py b/src/matchbox/common/hash.py
index aa2a279..8b6f2f8 100644
--- a/src/matchbox/common/hash.py
+++ b/src/matchbox/common/hash.py
@@ -1,6 +1,5 @@
 import base64
 import hashlib
-from functools import lru_cache
 from typing import TYPE_CHECKING, Any, TypeVar
 from uuid import UUID
 
@@ -112,38 +111,48 @@ def columns_to_value_ordered_hash(data: DataFrame, columns: list[str]) -> Series
     return Series(hashed_records)
 
 
-@lru_cache(maxsize=None)
-def combine_integers(*n: int) -> int:
+class IntMap:
     """
-    Combine n integers into a single negative integer.
-
-    Used to create a symmetric deterministic hash of two integers that populates the
-    range of integers efficiently and reduces the likelihood of collisions.
-
-    Aims to vectorise amazingly when used in Arrow.
-
-    Does this by:
-
-    * Using a Mersenne prime as a modulus
-    * Making negative integers positive with modulo, sped up with bitwise operations
-    * Combining using symmetric operations with coprime multipliers
-
-    Args:
-        *args: Variable number of integers to combine
-
-    Returns:
-        A negative integer
+    A data structure taking unordered sets of integers, and mapping them a to an ID that
+    1) is a negative integer; 2) does not collide with other IDs generated by other
+    instances of this class, as long as they are initialised with a different salt.
+
+    The fact that IDs are always negative means that it's possible to build a hierarchy
+    where IDs are themselves parts of other sets, and it's easy to distinguish integers
+    mapped to raw data points (which will be non-negative), to integers that are IDs
+    (which will be negative). The salt allows to work with a parallel execution
+    model, where each worker maintains their separate ID space, as long as each worker
+    operates on disjoint subsets of positive integers.
     """
-    P = 2147483647
-
-    total = 0
-    product = 1
-
-    for x in sorted(n):
-        x_pos = (x ^ (x >> 31)) - (x >> 31)
-        total = (total + x_pos) % P
-        product = (product * x_pos) % P
-
-    result = (31 * total + 37 * product) % P
 
-    return -result
+    def __init__(self, salt: int):
+        self.mapping: dict[frozenset[int], int] = {}
+        if salt < 0:
+            raise ValueError("The salt must be a positive integer")
+        self.salt: int = salt
+
+    def _salt_id(self, i: int) -> int:
+        """
+        Use Cantor pairing function on the salt and a negative int ID, and minus it.
+        """
+        if i >= 0:
+            raise ValueError("ID must be a negative integer")
+        return -int(0.5 * (self.salt - i) * (self.salt - i + 1) - i)
+
+    def index(self, *values: int) -> int:
+        """
+        Args:
+            values: the integers in the set you want to index
+
+        Returns:
+            The old or new ID corresponding to the set
+        """
+        value_set = frozenset(values)
+        if value_set in self.mapping:
+            return self.mapping[value_set]
+
+        new_id: int = -len(self.mapping) - 1
+        salted_id = self._salt_id(new_id)
+        self.mapping[value_set] = salted_id
+
+        return salted_id
diff --git a/src/matchbox/common/results.py b/src/matchbox/common/results.py
index 9416a50..ff97e5c 100644
--- a/src/matchbox/common/results.py
+++ b/src/matchbox/common/results.py
@@ -26,8 +26,8 @@
 
 from matchbox.common.db import Cluster, Probability
 from matchbox.common.hash import (
+    IntMap,
     columns_to_value_ordered_hash,
-    combine_integers,
     list_to_value_ordered_hash,
 )
 from matchbox.server.base import MatchboxDBAdapter, inject_backend
@@ -303,7 +303,7 @@ def to_clusters(results: ProbabilityResults) -> ClusterResults:
     )
 
     # Get unique probability thresholds, sorted
-    thresholds = edges_df["probability"].unique()
+    thresholds = sorted(edges_df["probability"].unique())
 
     # Process edges grouped by probability threshold
     for prob in thresholds:
@@ -367,7 +367,7 @@ def attach_components_to_probabilities(probabilities: pa.Table) -> pa.Table:
     graph = rx.PyGraph(node_count_hint=n_nodes, edge_count_hint=n_edges)
     graph.add_nodes_from(range(n_nodes))
 
-    edges = tuple(zip(left_indices.to_numpy(), right_indices.to_numpy(), strict=False))
+    edges = tuple(zip(left_indices.to_numpy(), right_indices.to_numpy(), strict=True))
     graph.add_edges_from_no_data(edges)
 
     components = rx.connected_components(graph)
@@ -413,6 +413,7 @@ def find(self, x: T, parent_dict: dict[T, T] | None = None) -> T:
                 self._shadow_parent[x] = x
                 self._shadow_rank[x] = 0
 
+        # TODO: Instead of being a `while`, could this be an `if`?
         while parent_dict[x] != x:
             parent_dict[x] = parent_dict[parent_dict[x]]
             x = parent_dict[x]
@@ -512,7 +513,9 @@ def diff(self) -> Iterator[tuple[set[T], set[T]]]:
         self._shadow_rank = self.rank.copy()
 
 
-def component_to_hierarchy(table: pa.Table, dtype: pa.DataType = pa.int32) -> pa.Table:
+def component_to_hierarchy(
+    table: pa.Table, dtype: pa.DataType = pa.int32, salt: int = 1
+) -> pa.Table:
     """
     Convert pairwise probabilities into a hierarchical representation.
 
@@ -526,6 +529,7 @@ def component_to_hierarchy(table: pa.Table, dtype: pa.DataType = pa.int32) -> pa
     """
     hierarchy: list[tuple[int, int, float]] = []
     uf = UnionFindWithDiff[int]()
+    im = IntMap(salt=salt)
     probs = pc.unique(table["probability"])
 
     for threshold in probs:
@@ -537,24 +541,24 @@ def component_to_hierarchy(table: pa.Table, dtype: pa.DataType = pa.int32) -> pa
         for row in zip(
             current_probs["left"].to_numpy(),
             current_probs["right"].to_numpy(),
-            strict=False,
+            strict=True,
         ):
             left, right = row
             uf.union(left, right)
-            parent = combine_integers(left, right)
+            parent = im.index(left, right)
             hierarchy.extend([(parent, left, threshold), (parent, right, threshold)])
 
         # Process union-find diffs
         for old_comp, new_comp in uf.diff():
             if len(old_comp) > 1:
-                parent = combine_integers(*new_comp)
-                child = combine_integers(*old_comp)
+                parent = im.index(*new_comp)
+                child = im.index(*old_comp)
                 hierarchy.extend([(parent, child, threshold)])
             else:
-                parent = combine_integers(*new_comp)
+                parent = im.index(*new_comp)
                 hierarchy.extend([(parent, old_comp.pop(), threshold)])
 
-    parents, children, probs = zip(*hierarchy, strict=False)
+    parents, children, probs = zip(*hierarchy, strict=True)
     return pa.table(
         {
             "parent": pa.array(parents, type=dtype()),
@@ -635,8 +639,8 @@ def to_hierarchical_clusters(
 
         with ProcessPoolExecutor(max_workers=n_cores) as executor:
             futures = [
-                executor.submit(proc_func, component_table, dtype)
-                for component_table in component_tables
+                executor.submit(proc_func, component_table, dtype, salt)
+                for salt, component_table in enumerate(component_tables)
             ]
 
             for future in futures:
diff --git a/test/client/test_hierarchy.py b/test/client/test_hierarchy.py
index 6396a7b..4f73820 100644
--- a/test/client/test_hierarchy.py
+++ b/test/client/test_hierarchy.py
@@ -9,7 +9,6 @@
 import pyarrow.compute as pc
 import pytest
 
-from matchbox.common.hash import combine_integers
 from matchbox.common.results import (
     attach_components_to_probabilities,
     component_to_hierarchy,
@@ -119,22 +118,6 @@ def test_attach_components_to_probabilities(parameters: dict[str, Any]):
     assert len(pc.unique(with_components["component"])) == parameters["num_components"]
 
 
-@pytest.mark.parametrize(
-    ("integer_list"),
-    [
-        [1, 2, 3],
-        [9, 0],
-        [-4, -5, -6],
-        [7, -8, 9],
-    ],
-    ids=["positive", "pair_only", "negative", "mixed"],
-)
-def test_combine_integers(integer_list: list[int]):
-    res = combine_integers(*integer_list)
-    assert isinstance(res, int)
-    assert res < 0
-
-
 @pytest.mark.parametrize(
     ("probabilities", "hierarchy"),
     [
@@ -195,9 +178,9 @@ def test_combine_integers(integer_list: list[int]):
 def test_component_to_hierarchy(
     probabilities: dict[str, list[str | float]], hierarchy: set[tuple[str, str, int]]
 ):
-    with patch(
-        "matchbox.common.results.combine_integers", side_effect=_combine_strings
-    ):
+    with patch("matchbox.common.results.IntMap") as MockIntMap:
+        instance = MockIntMap.return_value
+        instance.index.side_effect = _combine_strings
         probabilities_table = (
             pa.Table.from_pydict(probabilities)
             .cast(
@@ -340,8 +323,10 @@ def test_hierarchical_clusters(input_data, expected_hierarchy):
             "matchbox.common.results.ProcessPoolExecutor",
             lambda *args, **kwargs: parallel_pool_for_tests(timeout=30),
         ),
-        patch("matchbox.common.results.combine_integers", side_effect=_combine_strings),
+        patch("matchbox.common.results.IntMap") as MockIntMap,
     ):
+        instance = MockIntMap.return_value
+        instance.index.side_effect = _combine_strings
         result = to_hierarchical_clusters(
             probabilities, dtype=pa.string, proc_func=component_to_hierarchy
         )
diff --git a/test/common/test_hash.py b/test/common/test_hash.py
new file mode 100644
index 0000000..7556ef7
--- /dev/null
+++ b/test/common/test_hash.py
@@ -0,0 +1,48 @@
+from matchbox.common.hash import IntMap
+
+
+def test_intmap_basic():
+    im1 = IntMap(salt=10)
+    a = im1.index(1, 2)
+    b = im1.index(3, 4)
+    c = im1.index(a, b)
+
+    assert len({a, b, c}) == 3
+    assert max(a, b, c) < 0
+
+
+def test_intmap_same():
+    im1 = IntMap(salt=10)
+    a = im1.index(1, 2)
+    b = im1.index(3, 4)
+    c = im1.index(a, b)
+
+    im2 = IntMap(salt=10)
+    x = im2.index(1, 2)
+    y = im2.index(3, 4)
+    z = im2.index(a, b)
+
+    assert (a, b, c) == (x, y, z)
+
+
+def test_intmap_different():
+    im1 = IntMap(salt=10)
+    a = im1.index(1, 2)
+    b = im1.index(3, 4)
+    c = im1.index(a, b)
+
+    im2 = IntMap(salt=11)
+    x = im2.index(1, 2)
+    y = im2.index(3, 4)
+    z = im2.index(a, b)
+
+    for v1, v2 in zip([a, b, c], [x, y, z], strict=True):
+        assert v1 != v2
+
+
+def test_intmap_unordered():
+    im1 = IntMap(salt=10)
+    a = im1.index(1, 2, 3)
+    b = im1.index(3, 1, 2)
+
+    assert a == b