Distributions, not values

The second architectural move follows directly from the first. If we're going to solve under uncertainty, the inputs have to represent uncertainty. Every input driver in VYAN is a learned distribution fitted from the customer's own transaction history. Not a 14-day lead time. A shape with mean 14, σ 4, P85 19, P95 24, P99 31, updating incrementally as new arrivals land.

The drivers that are shapes: supplier lead times, plant capacities, scrap and yield rates, demand residuals, customer cancellation rates, foreign-exchange movements, commodity prices, supplier promise reliability. Even the supplier's own commit is a shape — how close to the committed date does this specific supplier actually deliver, conditional on its track record over the last eighteen months? Master-data scalars stay where they are in the ERP; VYAN reads them as initial seeds and lets the realized distributions take over within weeks.

Drivers don't move independently. Brent moves with FX. GDP softening propagates through specific customer segments. Substitution graphs activate. VYAN samples them jointly — trajectory-coherent sampling preserves the correlation structure across iterations through copulas fitted from history, so the solver never evaluates an implausible joint state (Brent at P95 while FX is at P5 independently). Each iteration is a coherent future, not a random draw from marginals.

The Decision Policy is the bridge between distributions and commitments. The deterministic operational commit consumes a percentile per driver derived from the risk posture; the stochastic answer — the full range — is always available on request. The customer always has both views: "what does the system recommend today" and "what's the shape of what could happen across the realistic distribution of futures."