Heated environment: a thermostat member in the forecast ensemble

A room held at a setpoint is a different process from one left to drift. It is
a closed loop, and persistence, the baseline everything here is scored against,
is the wrong statement about it: the truth is not that it stays where it is, it
is that it returns to the setpoint.

So site.heating adds a fourth ensemble member, first order because that is what
a controlled system is:

    dT_set(h) = (T_set - T_now) * (1 - exp(-h / tau))

Humidity follows and is the part that is easy to get wrong. Heating adds no
moisture, so vapour pressure is conserved and not relative humidity:

    RH(h) = RH_now * es(T_now) / es(T_now + dT_set(h))

Warm the air and RH falls although nothing was dried, which is why a heated
house in winter is dry. The test asserts the dew point is unchanged to 1e-6.
Pressure gets zero: a thermostat cannot move the synoptic field.

Offered, not imposed. Hedge scores this member on realised error like any
other, so a wrong tau or a stale setpoint costs accuracy and gets down-weighted
rather than quietly biasing every forecast. Verified: on history with no
heating the ensemble assigned it weight 0.000. With heating off it returns zero
and is identical to persistence.

Going from three members to four means old saved heads must migrate.
from_dict reinitialises weights and member_mae. I missed member_mae first time
and it did not fail on load, it failed later inside learn() on a broadcast
error, which is a much worse place to find out; the migration test now covers
both and calls learn() to prove it.

Settings tab gains the toggle, setpoint and time constant. Turning heating on
or off is treated as a regime change like a door: discontinuity marker plus a
queued retrain.

tests/test_estimation.py

@@ -177,3 +177,74 @@ def test_kalman_state_round_trips_through_dict():
     back = KalmanCV.from_dict(kf.to_dict())
     assert back.level == pytest.approx(kf.level)
     assert back.rate == pytest.approx(kf.rate)
+
+
+# ---------------------------------------------------------------- thermostat
+
+def test_thermostat_reversion_is_first_order_and_preserves_dew_point():
+    """A heated room is a closed loop, and heating adds no moisture.
+
+    Two properties, both easy to get wrong. The temperature must close the gap
+    to the setpoint exponentially rather than jumping or drifting, and the
+    implied humidity change must leave the dew point exactly where it was: RH
+    falls only because es(T) rose, which is why a heated house in winter is dry.
+    """
+    import math
+
+    from ashvale.config import load_config
+    from ashvale.physics import dew_point, saturation_vapour_pressure
+    from ashvale.station import Station
+
+    cfg = load_config()
+    cfg.site.heating = True
+    cfg.site.heating_setpoint_c = 23.0
+    cfg.site.thermal_time_constant_h = 1.5
+    st = Station(cfg)
+    st.live = {"temp_smooth": 18.0}
+
+    tau = 1.5 * 3600.0
+    for h in (900, 3600, 10800, 86400):
+        expected = (23.0 - 18.0) * (1.0 - math.exp(-h / tau))
+        assert st._setpoint_delta("temperature", h, 18.0) == pytest.approx(expected, rel=1e-9)
+
+    # monotonic toward the setpoint, never past it
+    deltas = [st._setpoint_delta("temperature", h, 18.0)
+              for h in (900, 3600, 10800, 21600, 86400)]
+    assert all(a < b for a, b in zip(deltas, deltas[1:]))
+    assert deltas[-1] <= 5.0 + 1e-9
+
+    # dew point invariant
+    t0, rh0 = 18.0, 55.0
+    d_t = st._setpoint_delta("temperature", 86400, t0)
+    d_rh = st._setpoint_delta("humidity", 86400, rh0)
+    assert float(dew_point(t0 + d_t, rh0 + d_rh)) == pytest.approx(
+        float(dew_point(t0, rh0)), abs=1e-6)
+    assert d_rh < 0.0, "warming a room at constant moisture must lower RH"
+    assert float(saturation_vapour_pressure(t0 + d_t)) > float(
+        saturation_vapour_pressure(t0))
+
+    # a thermostat cannot move the synoptic field
+    assert st._setpoint_delta("pressure", 86400, 1013.0) == 0.0
+
+    # and off, the member is exactly persistence
+    cfg.site.heating = False
+    assert st._setpoint_delta("temperature", 86400, 18.0) == 0.0
+    assert st._setpoint_delta("humidity", 86400, 55.0) == 0.0
+
+
+def test_forecast_head_migrates_state_from_before_the_setpoint_member():
+    """An old save has three weights where there are now four."""
+    from ashvale.models.nowcast import MEMBERS, ForecastHead
+
+    h = ForecastHead(target="temperature", horizon_s=900, n_features=4)
+    state = h.to_dict()
+    state["weights"] = [0.2, 0.3, 0.5]          # a pre-setpoint save
+    state["member_mae"] = [0.4, 0.5, 0.6]
+    back = ForecastHead.from_dict(state)
+    assert back.weights.size == len(MEMBERS)
+    assert float(back.weights.sum()) == pytest.approx(1.0)
+    # member_mae must migrate too. Missing it did not fail on load, it failed
+    # later inside learn() on a broadcast error, which is a worse place to
+    # discover a migration bug.
+    assert back.member_mae.size == len(MEMBERS)
+    back.learn(np.zeros(4), 20.0, 20.5, 0.1, 0.2)      # must not raise