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.

ashvale/dashboard.py

@@ -489,6 +489,22 @@ DASHBOARD_HTML = r"""
           <p class="text-[9px] text-slate-600 leading-snug mt-1.5">Closing a door changes how strongly the sensor couples to outside. The heads carry about 55 hours of memory, so tell them rather than waiting two days.</p>
         </div>
       </div>
+      <div class="mt-3 pt-3 border-t border-slate-800">
+        <div class="flex items-center justify-between mb-1.5">
+          <div>
+            <span class="text-[11px] font-semibold text-slate-300">Heated or cooled to a setpoint</span>
+            <p class="text-[9px] text-slate-600 leading-snug">A thermostat makes the room a closed loop: it returns to the setpoint instead of drifting. Persistence is the wrong baseline for that, so this adds a fourth ensemble member and lets the Hedge weights decide if it earns its place. Humidity follows at constant vapour pressure, which is why a heated house is dry.</p>
+          </div>
+          <button id="s-heat" class="shrink-0 ml-3 px-2.5 py-1 rounded-lg border text-[10px] font-mono">--</button>
+        </div>
+        <div class="grid grid-cols-2 gap-2 font-mono text-[10px]">
+          <label class="block"><span class="text-slate-600 uppercase text-[9px]">setpoint &deg;C</span>
+            <input id="s-setpoint" type="number" step="0.5" class="w-full mt-0.5 bg-slate-950/70 border border-slate-800 rounded-lg px-2 py-1.5 text-white"></label>
+          <label class="block"><span class="text-slate-600 uppercase text-[9px]">time constant h</span>
+            <input id="s-tau" type="number" step="0.1" class="w-full mt-0.5 bg-slate-950/70 border border-slate-800 rounded-lg px-2 py-1.5 text-white"></label>
+        </div>
+      </div>
+
       <div class="flex gap-2 mt-3">
         <input id="s-note" placeholder="what changed, e.g. doors shut, felt chilly"
                class="flex-1 min-w-0 bg-slate-950/70 border border-slate-800 rounded-lg px-2.5 py-1.5 text-[11px] font-mono text-white">
@@ -1111,6 +1127,10 @@ async function loadSettings() {
   el('s-lon').value = site.longitude;
   el('s-psy').innerText = sen.hum_psychrometric ? 'on' : 'off';
   el('s-psy').className = sen.hum_psychrometric ? PILL_ON : PILL_OFF;
+  el('s-heat').innerText = site.heating ? 'on' : 'off';
+  el('s-heat').className = site.heating ? PILL_ON : PILL_OFF;
+  el('s-setpoint').value = site.heating_setpoint_c;
+  el('s-tau').value = site.thermal_time_constant_h;
 }
 loaders.settings = loadSettings;
 
@@ -1147,6 +1167,13 @@ el('s-led').addEventListener('click', () =>
   postSettings({led_enabled: !(settingsDoc.server||{}).led_enabled}, 's-msg'));
 el('s-psy').addEventListener('click', () =>
   postSettings({hum_psychrometric: !(settingsDoc.sensor||{}).hum_psychrometric}, 's-msg'));
+el('s-heat').addEventListener('click', () =>
+  postSettings({heating: !(settingsDoc.site||{}).heating}, 's-msg'));
+for (const id of ['s-setpoint','s-tau']) {
+  el(id).addEventListener('change', () => postSettings({
+    heating_setpoint_c: Number(el('s-setpoint').value),
+    thermal_time_constant_h: Number(el('s-tau').value)}, 's-msg'));
+}
 el('s-fps').addEventListener('input', e => el('s-fps-val').innerText = e.target.value + ' fps');
 el('s-fps').addEventListener('change', e =>
   postSettings({led_fps: Number(e.target.value)}, 's-msg'));