ComputationalComplexityCert
plain-language theorem explainer
ComputationalComplexityCert is a structure that records two numerical facts in the RS model of complexity: the finite type of complexity classes has cardinality exactly 5, and the DFT size over the eight-tick cycle equals 8. Researchers deriving P versus NP from recognition cost landscapes would cite this to anchor the class count to the spatial dimension D = 5. The declaration is a bare structure definition with no computational content or proof steps.
Claim. Let $C$ be the finite type whose elements are the five classes $P$, $NP$, $coNP$, $PSPACE$, $EXP$. Then $|C| = 5$ and the size of the discrete Fourier transform on eight points equals $8$.
background
ComplexityClass is the inductive type with constructors p, np, coNP, pspace, exp, equipped with Fintype so that its cardinality is well-defined. The constant dft8Size is defined as $2^3$, reflecting the eight-tick octave in the RS forcing chain where the period is $2^D$ with $D = 3$. The module states that these five classes correspond to configDim $D = 5$ and that DFT computation over this size lies in P.
proof idea
This declaration is a structure definition. It simply declares two fields whose types are the propositions Fintype.card ComplexityClass = 5 and dft8Size = 8. No lemmas or tactics are invoked; the structure serves as a container for these facts.
why it matters
This structure supplies the concrete certificate used by computationalComplexityCert to witness the RS claim that exactly five complexity classes exist and that DFT-8 is polynomial-time. It directly supports the module's statement that |Z/8Z| = 8 = 2^D and ties the P vs NP distinction to the J-cost landscape having exponentially many zero basins. The declaration closes the numerical side of the complexity model before any deeper conjecture is addressed.
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