Each layer emits impulses — drift tilts with their own clock: a(t) = amp · (1 − e^(−t/rise)) · e^(−t/τ). Short-lived things (technicals, crowd mood, analyst notes) have τ of days; news events persist by type (earnings ~40d, legal ~90d, policy ~120d); political/resource pressure builds over ~45 days and persists for years; long-run growth comes from a CAPM prior blended with the stock's own 30-year CAGR.

Drift μ(t) = μ_LR + seasonal(month) + Σ a_i(t). Volatility mean-reverts: σ(t)² = σ_LR² + (σ_now²·VIXmult − σ_LR²)·e^(−t/60). Prices follow log S(t+1) = log S(t) + μ dt + σ √dt · ε + J with fat-tailed Student-t(5) shocks ε and Poisson jumps J whose intensity rises with black-swan news, VIX stress and political stress. 1,500 Monte-Carlo paths × 10 years are re-simulated on every live update with fixed random numbers, so the fan only moves when the inputs move.

P(up) is the share of simulated paths above today's price. Confidence combines how many data layers are live, how strongly the layers agree, signal-to-noise of the median move, and a penalty for distance into the future.