Stats for Nerds tab, KaTeX methods, weather icons, outlook to top

New Stats for Nerds tab over a new read-only /api/nerd endpoint: Kalman NIS
and covariance per signal, both compensators, all 18 RLS heads with trace(P)
against the cap, |theta|, EWMA RMSE, conformal alpha against target, realised
coverage and ensemble weights, plus per-head feature attribution over the 33
standardised weights, the Mahalanobis and Page-Hinkley detector state,
climatology harmonics and precipitation coefficients.

Methods overhaul: KaTeX now renders the equations. They were previously passed
through .replace(/[{}\\]/g,' '), which stripped every brace and backslash and
turned real mathematics into mush. Stages 2, 3, 5, 6 and 7 gained full
derivations (RLS normal equations and the trace cap, Joseph-form Kalman with
NIS, adaptive conformal with its coverage limit, ridge harmonic regression with
anomaly decay) and a per-symbol legend rendered inline.

Conditions ahead gains weather icons chosen from measured cloud index, solar
elevation and temperature rather than the barometric class alone, so a fine
barometer under overcast draws a cloud and after sunset draws a moon. Snow is
selected on temperature.

Seven day outlook moves to the top of Live, directly under the nav. Tab renamed
Models and Calibration.

Verified in Chromium at 1600x900: Live, History, Models and Nerd all report
zero scrollbars, zero clipping, no page scroll, zero console errors. Methods
keeps its documented prose scroller. Backtest numerically unchanged.
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## The dashboard
Four tabs, one viewport, no scrolling on desktop. Below 1024 px the constraint is
released, because pinning four panels into a phone viewport produces unreadable
Five tabs, one viewport, no scrolling on desktop. Below 1024 px the constraint is
released, because pinning five panels into a phone viewport produces unreadable
eight-pixel type.
| Tab | Answers |
| --- | --- |
| **Live** | What is it doing now, what it expects next, how sure it is, and the week ahead |
| **Live** | The week ahead, current readings, the forecast with its band, and conditions |
| **History** | What did it do, over any timeframe you ask for |
| **Models and calibration** | Has the model earned its confidence, and the calibration inputs |
| **Models and Calibration** | Has the model earned its confidence, and the calibration inputs |
| **Stats for Nerds** | Every internal the estimator and the 18 learners are carrying |
| **Methods** | How the whole thing is wired, and how each stage fails |
Live carries the current readings, the observed-and-forecast chart with its 90%