§7 slice 2: two-main case 1 weighted-R per Table 9b

Adds secondary_fraction (203) + secondary_responsiveness orchestrator
params. When both main systems heat the whole house (Table 9c case 1),
the u-formula consumes a weighted responsiveness:
  R_eff = (1 - (203)) × R_primary + (203) × R_secondary

Synthetic equivalence test pins the contract: any (frac, R_primary,
R_secondary) call lands the same MIT as a single-main call with the
weighted R. No fixture exercises case 1 (all 6 Elmhurst = single combi),
so secondary_fraction defaults to 0 → identity behaviour.

Case 2 (different parts heated separately) deferred — needs (203) >
1-(91) branch + conditional T_2 averaging + per-system Table 4e
adjustment. No fixture data to drive.

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

packages/domain/src/domain/sap/worksheet/mean_internal_temperature.py

@@ -237,6 +237,8 @@ def mean_internal_temperature_monthly(
     responsiveness: float,
     living_area_fraction: float,
     control_temperature_adjustment_c: float = 0.0,
+    secondary_fraction: float = 0.0,
+    secondary_responsiveness: float = 1.0,
 ) -> MeanInternalTemperatureResult:
     """SAP 10.2 §7 orchestrator — chain Table 9c steps 1–9 for all 12 months.
 
@@ -255,7 +257,16 @@ def mean_internal_temperature_monthly(
       control_temperature_adjustment_c (93) Table 4e adj (defaults 0 — all 6
                           Elmhurst fixtures have (93) = (92), so this is a
                           known shortcut; cert-side mapping is a future slice).
+      secondary_fraction  (203) fraction of main heat from second main system
+                          when both heat the whole house (Table 9c case 1).
+                          Defaults 0 (single-main); used to compute weighted R
+                          per Table 9b: R_eff = (1-frac)·R_primary + frac·R_secondary.
+                          Case 2 (different parts heated) deferred — no fixture.
     """
+    effective_responsiveness = (
+        (1.0 - secondary_fraction) * responsiveness
+        + secondary_fraction * secondary_responsiveness
+    )
     elsewhere_off_hours = (
         _ELSEWHERE_OFF_HOURS_TYPE_3 if control_type == 3 else _ELSEWHERE_OFF_HOURS_TYPE_12
     )
@@ -285,7 +296,7 @@ def mean_internal_temperature_monthly(
             heating_temperature_c=_T_H1_C,
             off_hours_first=_LIVING_AREA_OFF_HOURS[0],
             off_hours_second=_LIVING_AREA_OFF_HOURS[1],
-            external_temp_c=ext, responsiveness=responsiveness,
+            external_temp_c=ext, responsiveness=effective_responsiveness,
             total_gains_w=gains, heat_transfer_coefficient_w_per_k=h,
             time_constant_h=tau,
         )
@@ -301,7 +312,7 @@ def mean_internal_temperature_monthly(
             heating_temperature_c=t_h2_m,
             off_hours_first=elsewhere_off_hours[0],
             off_hours_second=elsewhere_off_hours[1],
-            external_temp_c=ext, responsiveness=responsiveness,
+            external_temp_c=ext, responsiveness=effective_responsiveness,
             total_gains_w=gains, heat_transfer_coefficient_w_per_k=h,
             time_constant_h=tau,
         )

packages/domain/src/domain/sap/worksheet/tests/test_mean_internal_temperature.py

@@ -65,6 +65,46 @@ def test_mean_internal_temperature_monthly_reproduces_000490_line_92_jan() -> No
     assert result.mean_internal_temp_monthly[0] == pytest.approx(15.1899, abs=5e-3)
 
 
+def test_two_main_systems_case_1_uses_weighted_responsiveness_per_table_9b() -> None:
+    # Arrange — SAP10.2 Table 9b weighted-R formula when both main systems
+    # heat the whole house (same control type, shared T_h2 + Th-time grid):
+    #     R = (203) × R_system2 + [1 - (203)] × R_system1
+    # Equivalent-R contract: passing secondary_fraction + secondary_R must
+    # produce the same MIT as a single-main run with the weighted R.
+    secondary_fraction = 0.3   # (203)
+    primary_r = 1.0            # gas wet system (Table 4d)
+    secondary_r = 0.0          # extreme — exaggerates the weighting effect
+    expected_r = (1.0 - secondary_fraction) * primary_r + secondary_fraction * secondary_r
+
+    common_kwargs = dict(
+        monthly_external_temp_c=_W000490_EXT_TEMP_C,
+        monthly_total_gains_w=_W000490_TOTAL_GAINS_W,
+        monthly_heat_transfer_coefficient_w_per_k=_W000490_HTC_W_PER_K,
+        thermal_mass_parameter_kj_per_m2_k=_W000490_TMP_KJ_PER_M2_K,
+        total_floor_area_m2=_W000490_TFA_M2,
+        control_type=_W000490_CONTROL_TYPE,
+        living_area_fraction=_W000490_LIVING_AREA_FRACTION,
+    )
+
+    # Act
+    two_system = mean_internal_temperature_monthly(
+        responsiveness=primary_r,
+        secondary_fraction=secondary_fraction,
+        secondary_responsiveness=secondary_r,
+        **common_kwargs,
+    )
+    equivalent_single = mean_internal_temperature_monthly(
+        responsiveness=expected_r,
+        **common_kwargs,
+    )
+
+    # Assert — every month identical to floating-point precision
+    for m in range(12):
+        assert two_system.mean_internal_temp_monthly[m] == pytest.approx(
+            equivalent_single.mean_internal_temp_monthly[m], abs=1e-12
+        ), f"(92) month {m+1} weighted-R contract"
+
+
 def test_elsewhere_temperature_control_type_2_uses_quadratic_drop() -> None:
     # Arrange — Table 9 elsewhere formula for control type 2 (programmer +
     # room thermostat, default for boiler systems with reasonable control):