diff --git a/datatypes/epc/domain/epc.py b/datatypes/epc/domain/epc.py
index ae4fd8241..6c65cf0a9 100644
--- a/datatypes/epc/domain/epc.py
+++ b/datatypes/epc/domain/epc.py
@@ -46,3 +46,6 @@ class Epc(Enum):
             Epc.G: 1,
         }
         return bounds[self]
+
+    def sap_lower_bound_continuous(self) -> float:
+        raise NotImplementedError
diff --git a/tests/datatypes/epc/domain/test_epc.py b/tests/datatypes/epc/domain/test_epc.py
index 474c5e890..062a4d78b 100644
--- a/tests/datatypes/epc/domain/test_epc.py
+++ b/tests/datatypes/epc/domain/test_epc.py
@@ -4,6 +4,8 @@ target)."""
 
 from __future__ import annotations
 
+from decimal import ROUND_HALF_UP, Decimal
+
 import pytest
 
 from datatypes.epc.domain.epc import Epc
@@ -24,3 +26,27 @@ def test_sap_lower_bound_returns_the_band_floor() -> None:
 def test_band_floor_round_trips_through_from_sap_score(band: Epc) -> None:
     # Act / Assert — a band's floor scores back to that band.
     assert Epc.from_sap_score(band.sap_lower_bound()) is band
+
+
+@pytest.mark.parametrize("band", list(Epc))
+def test_continuous_band_floor_is_where_the_published_rating_enters_the_band(
+    band: Epc,
+) -> None:
+    # Arrange — the Optimiser judges "reached band X" on the calculator's
+    # *continuous* SAP, but a dwelling is in a band by its *published* rating
+    # (the half-up-rounded integer). The continuous floor is the point those two
+    # agree: the lowest continuous score whose published rating is in the band.
+    # Asserted against the real publishing path (round half up → from_sap_score)
+    # rather than an arithmetic literal, so the two cannot drift apart.
+    def published_band(continuous: float) -> Epc:
+        rounded = int(Decimal(continuous).quantize(Decimal("1"), rounding=ROUND_HALF_UP))
+        return Epc.from_sap_score(rounded)
+
+    # Act
+    continuous_floor: float = band.sap_lower_bound_continuous()
+
+    # Assert — at the floor the dwelling publishes into the band; a hair below
+    # it publishes into a worse one. (Band G has no worse band to fall into.)
+    assert published_band(continuous_floor) is band
+    if band is not Epc.G:
+        assert published_band(continuous_floor - 0.01) is not band