semiconductorDopantCert
plain-language theorem explainer
This definition supplies the concrete witness that the dopant type set for silicon semiconductors has cardinality five under configDim D = 5. Researchers modeling solid-state devices in the Recognition Science framework would cite it when they require the enumerated categories for device-level calculations. The construction is a direct one-line wrapper that inserts the decidable cardinality result into the required structure field.
Claim. Let $S$ be the structure whose sole field requires that the finite set of dopant types has cardinality five. The definition instantiates $S$ by assigning to that field the value of the theorem that computes the cardinality of the dopant type enumeration as five.
background
The module treats semiconductor modeling at solid-state depth B15, where configDim D = 5 fixes silicon-type materials. It enumerates five canonical dopant categories: group-V donors (P, As, Sb), group-III acceptors (B, Al, Ga), deep-level impurities, compensating centers, and transition-metal scattering centers. The structure packages the single assertion that the dopant type set has cardinality five.
proof idea
The definition is a one-line wrapper that applies the upstream theorem establishing the cardinality of the dopant type set to populate the structure field.
why it matters
This definition closes the dopant enumeration for the B15 materials layer in the Recognition Science framework, where configDim D = 5 is set by the eight-tick octave and the spatial dimension count. It supplies the concrete certificate required for any later model that applies J-cost or phi-ladder formulas to doped semiconductors. No open questions remain; the result rests entirely on the decidable cardinality computation.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.