cert_to_inputs: wire §4 worksheet orchestrator into HW kWh derivation

Replaces the legacy `predicted_hot_water_kwh` cascade with a call into
`water_heating_from_cert` for the modal combi-gas-mains population. The
new helper `_hot_water_fuel_kwh_per_yr` chains the §4 cascade end-to-end
(occupancy → daily hot water → energy content → distribution + combi
loss → (62)m total → (64)m output) then divides by water-heater
efficiency to land annual fuel kWh — the slot CalculatorInputs expects.

Section-by-section validation across all 6 Elmhurst fixtures shows:
  §1 dimensions   exact (≤ 1e-4) on all 6
  §2 ventilation  exact (≤ 1e-4) on all 6
  §3 heat trans   exact on non-RR (000474, 000490) within 0.04 W/K
                  (display-rounding); RR fixtures under-count per the
                  formal SapRoomInRoof sub-area deferral.
  §4 hot water    exact on the 2 fixtures with LINE_42/LINE_64 lodged
                  (000474 PCDB override + 000490 cascade-default); 4 RR
                  fixtures emit plausible orchestrator values.

End-to-end SAP impact (legacy → new):
  000490  57=57 (cont 56.72 → 56.92, closer to worksheet 57.40)
  000474  55→56 (cont 55.39 → 55.59, expected 62, still 6pt under)

Caveats / future slices:
  - Cold water source defaults to mains (no domain-model field yet).
  - Shower flow rate defaults to 7 L/min vented (no shower_outlet_type
    plumbing yet); both fixtures actually lodge this so no false drift.
  - Cylinder + solar + WWHRS / PV / FGHRS branches default to zero.
  - PCDB Table 3b combi loss not implemented; orchestrator accepts a
    `combi_loss_monthly_kwh_override` for now but cert_to_inputs always
    falls to Table 3a row "time-clock keep-hot".
  - water_efficiency variable misnamed "pct" — it's a decimal (0.0-1.0).

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

packages/domain/src/domain/sap/rdsap/cert_to_inputs.py

@@ -68,6 +68,10 @@ from domain.sap.worksheet.ventilation import (
     MechanicalVentilationKind,
     ventilation_from_inputs,
 )
+from domain.sap.worksheet.water_heating import (
+    TABLE_J1_TCOLD_FROM_MAINS_C,
+    water_heating_from_cert,
+)
 
 
 # RdSAP 10 Table 27 — fraction of total floor area treated as the
@@ -741,6 +745,95 @@ def _ventilation_counts(vent: Optional[SapVentilation]) -> _VentilationCounts:
     )
 
 
+# SAP 10.2 Table J4 — default mixer-shower flow rate for an existing
+# dwelling with a vented hot water system (the existing-dwelling minimum).
+# Both validation worksheets (000474 + 000490) lodge this value. Combi-
+# pumped showers (11 L/min) and instantaneous-electric showers (handled
+# via line (64a)m, not here) need shower-outlet-type plumbing in a later
+# slice.
+_SHOWER_FLOW_VENTED_L_PER_MIN: Final[float] = 7.0
+
+
+def _mixer_shower_flow_rates_from_cert(
+    epc: EpcPropertyData,
+) -> tuple[float, ...]:
+    """Pull mixer-shower flow rates from the cert.
+
+    The cert lodges flow rate per shower outlet (Elmhurst worksheets
+    show "Vented hot water system, 7.00"). The domain model doesn't
+    surface that field yet; until it does, every cert defaults to the
+    SAP10.2 Table J4 "Vented hot water system" row at 7 L/min — the
+    existing-dwelling minimum and what both validation fixtures
+    (000474 + 000490) actually lodge. Combi-pumped showers (11 L/min)
+    or electric showers (handled via (64a)m, not here) will need
+    proper shower-outlet-type plumbing in a later slice.
+    """
+    return (_SHOWER_FLOW_VENTED_L_PER_MIN,)
+
+
+def _has_bath_from_cert(epc: EpcPropertyData) -> bool:
+    """True iff cert lodges ≥ 1 bath. `number_baths is None` is treated as
+    bath present (modal UK lodging — bathless dwellings are rare and
+    typically explicitly lodged as 0)."""
+    n = epc.sap_heating.number_baths
+    return n is None or n >= 1
+
+
+def _hot_water_fuel_kwh_per_yr(
+    *,
+    epc: EpcPropertyData,
+    water_efficiency_pct: float,
+    is_instantaneous: bool,
+    primary_age: Optional[str],
+) -> float:
+    """Annual hot water FUEL kWh (the slot calculator.CalculatorInputs
+    expects). Wires the SAP10.2 §4 worksheet orchestrator into the cert→
+    inputs adapter.
+
+    For combi gas (the dominant population) the orchestrator handles the
+    full Appendix J cascade including Table 3a row "time-clock keep-hot"
+    combi loss. Cylinder + solar + WWHRS / PV diverter / FGHRS branches
+    default to zero — extension slices will populate them as needed.
+
+    Annual output (Σ (64)m) is divided by `water_efficiency_pct / 100`
+    to convert delivered heat to fuel kWh, mirroring the worksheet's
+    (219) line. Falls back to legacy `predicted_hot_water_kwh` if the
+    TFA is missing (the orchestrator requires it for occupancy).
+    """
+    if epc.total_floor_area_m2 is None:
+        return predicted_hot_water_kwh(
+            total_floor_area_m2=epc.total_floor_area_m2,
+            seasonal_efficiency_water=water_efficiency_pct,
+            cylinder_size=None if is_instantaneous else _int_or_none(epc.sap_heating.cylinder_size),
+            cylinder_insulation_thickness_mm=(
+                None if is_instantaneous else epc.sap_heating.cylinder_insulation_thickness_mm
+            ),
+            cylinder_insulation_type=(
+                None if is_instantaneous
+                else _int_or_none(epc.sap_heating.cylinder_insulation_type)
+            ),
+            age_band=None if is_instantaneous else primary_age,
+            has_wwhrs=False,
+            has_solar_water_heating=epc.solar_water_heating,
+        )
+    result = water_heating_from_cert(
+        epc=epc,
+        mixer_shower_flow_rates_l_per_min=_mixer_shower_flow_rates_from_cert(epc),
+        has_bath=_has_bath_from_cert(epc),
+        # Cold water source isn't on the domain model yet; default to mains
+        # (the dominant UK lodging — 95%+). Header-tank dwellings will need
+        # a domain-model field + plumb-through in a future slice.
+        cold_water_temps_c=TABLE_J1_TCOLD_FROM_MAINS_C,
+        low_water_use=False,
+    )
+    if water_efficiency_pct <= 0:
+        return 0.0
+    # `water_efficiency_pct` is misnamed in the calling code — the value
+    # is a decimal (0.0–1.0), not a percent. Divide the orchestrator's
+    # delivered-heat output by the decimal efficiency to land fuel kWh.
+    return result.output_kwh_per_yr / water_efficiency_pct
+
+
 def cert_to_inputs(
     epc: EpcPropertyData, *, prices: PriceTable = SAP_10_2_SPEC_PRICES
 ) -> CalculatorInputs:
@@ -848,23 +941,11 @@ def cert_to_inputs(
         # = q_generated, matching the per-kWh-generated unit price.
         water_eff = 1.0 / _heat_network_dlf(primary_age)
     is_instantaneous = epc.sap_heating.water_heating_code in _INSTANTANEOUS_WATER_CODES
-    hw_kwh = predicted_hot_water_kwh(
-        total_floor_area_m2=epc.total_floor_area_m2,
-        seasonal_efficiency_water=water_eff,
-        # Instantaneous HW systems (codes 907/909) have no cylinder and
-        # no primary circuit — pass None for both to suppress storage
-        # and primary losses in the demand model.
-        cylinder_size=None if is_instantaneous else _int_or_none(epc.sap_heating.cylinder_size),
-        cylinder_insulation_thickness_mm=(
-            None if is_instantaneous else epc.sap_heating.cylinder_insulation_thickness_mm
-        ),
-        cylinder_insulation_type=(
-            None if is_instantaneous
-            else _int_or_none(epc.sap_heating.cylinder_insulation_type)
-        ),
-        age_band=None if is_instantaneous else primary_age,
-        has_wwhrs=False,
-        has_solar_water_heating=epc.solar_water_heating,
+    hw_kwh = _hot_water_fuel_kwh_per_yr(
+        epc=epc,
+        water_efficiency_pct=water_eff,
+        is_instantaneous=is_instantaneous,
+        primary_age=primary_age,
     )
     lighting_kwh = predicted_lighting_kwh(
         total_floor_area_m2=epc.total_floor_area_m2,