SemiconductorDevice
plain-language theorem explainer
SemiconductorDevice enumerates the five canonical device types in semiconductor physics as an inductive type with constructors for diode, BJT, MOSFET, JFET, and IGBT. Researchers modeling device physics from first principles in Recognition Science cite this to establish the count of five devices matching configDim D=5. The declaration is a direct inductive definition deriving decidable equality and finite type structure.
Claim. Let $D$ be the inductive type whose constructors are the five standard semiconductor devices: diode, bipolar junction transistor (BJT), metal-oxide-semiconductor field-effect transistor (MOSFET), junction field-effect transistor (JFET), and insulated-gate bipolar transistor (IGBT).
background
The module derives semiconductor physics from the Recognition Science phi-ladder, where band gaps appear as multiples of $φ^{-3}$ and carrier types equal $D-1$. Crystal symmetries are fixed at $2^D=8$ for the zincblende lattice. The local setting identifies five device types with configDim $D=5$, providing the base enumeration whose cardinality is later certified.
proof idea
The declaration is an inductive definition that introduces five constructors and derives the instances DecidableEq, Repr, BEq, and Fintype.
why it matters
This definition supplies the finite set whose cardinality is proven equal to 5 in the downstream theorem semiconductorDeviceCount. It anchors the SemiconductorPhysicsCert structure recording the two-carrier relation and eight symmetries. In the framework it realizes the five device types as configDim $D=5$, consistent with the eight-tick octave and $2^D=8$ symmetries.
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