fix(epc-prediction): size-representative template selection (ADR-0029)

Template (the comparable whose structure/geometry is copied wholesale)
was members[0] — an arbitrary draw from the API search order. With floor
area varying widely within a property_type cohort (NG71AA houses span
51-340 m2), this made the copied geometry noisy and systematically large.

Pick the member whose floor area is closest to the cohort median instead,
implementing ADR-0029 decision 4's unimplemented "closest on size"
criterion while keeping the structure coherent (it is still one real
property, so floor dims / windows / parts stay internally consistent for
the calculator).

Smoke corpus (29 leave-one-out predictions):
  floor_area  mean|.| 68.0 -> 37.9 m2  (bias +46.8 -> -3.9)
  window_area mean|.| 11.1 -> 7.3 m2
  parts       mean|.| 1.00 -> 0.38
  SAP |pred-calc - calc(actual)| MAE 7.19 -> 4.86

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

domain/epc_prediction/epc_prediction.py

@@ -10,6 +10,7 @@ logic — deterministic neighbour synthesis, not ML.
 from __future__ import annotations
 
 import copy
+import statistics
 from collections import Counter
 from typing import Iterable, Optional, Union
 
@@ -41,8 +42,19 @@ class EpcPrediction:
 
     @staticmethod
     def _template(comparables: ComparableProperties) -> Comparable:
-        """The representative comparable whose structure seeds the prediction."""
+        """The representative comparable whose structure seeds the prediction:
-        return comparables.members[0]
+        the member whose floor area is closest to the cohort median. A single
+        neighbour's geometry is copied wholesale, so a size-representative
+        template keeps the prediction off the cohort's size outliers (ADR-0029
+        decision 4: closest on size)."""
+        members: tuple[Comparable, ...] = comparables.members
+        median_area: float = statistics.median(
+            c.epc.total_floor_area_m2 for c in members
+        )
+        return min(
+            members,
+            key=lambda c: abs(c.epc.total_floor_area_m2 - median_area),
+        )
 
     @staticmethod
     def _apply_categorical_modes(

tests/domain/epc_prediction/test_epc_prediction.py

@@ -59,6 +59,27 @@ def test_predicts_a_picture_by_copying_a_representative_template() -> None:
     assert predicted is not template
 
 
+def test_template_is_the_member_closest_to_the_cohort_median_size() -> None:
+    # Arrange — the cohort spans a wide range of sizes; members[0] is an atypical
+    # tiny 20 m² outlier. A single neighbour's geometry is copied wholesale, so
+    # the template must be the size-representative member (closest to the median),
+    # not whoever happens to come first (ADR-0029 decision 4: closest on size).
+    cohort = _cohort(
+        _epc(floor_area=20.0),
+        _epc(floor_area=80.0),
+        _epc(floor_area=200.0),
+    )
+
+    # Act
+    predicted: EpcPropertyData = EpcPrediction().predict(
+        PredictionTarget(postcode="LS6 1AA", property_type="2"), cohort
+    )
+
+    # Assert — the 80 m² member (the median) seeds the structure, not the 20 m²
+    # outlier sitting at members[0].
+    assert predicted.total_floor_area_m2 == 80.0
+
+
 def test_sets_main_wall_construction_to_the_cohort_mode() -> None:
     # Arrange — the template (members[0]) is solid brick (2), but the cohort
     # majority is cavity (1). The homogeneous categorical should follow the mode,