computationalComplexityCert
plain-language theorem explainer
RS encodes computational complexity via a five-class taxonomy whose cardinality is fixed at five and whose DFT-8 size equals eight. A working mathematician auditing the RS mirror would reference this certificate when checking the structural claim that DFT computation lies in P. The definition is a direct record construction that pulls the two field values from the theorems complexityClassCount and dft8Size_8.
Claim. The certificate asserts that the cardinality of the set of complexity classes equals five and that the size of the discrete Fourier transform on eight points equals eight.
background
Recognition Science derives five canonical complexity classes (P, NP, coNP, PSPACE, EXP) from the configuration dimension D = 5. The module formalizes the conjecture that P ≠ NP because NP-complete problems possess an exponential number of J = 0 basins in the recognition-cost landscape. The upstream theorem complexityClassCount establishes that the cardinality of ComplexityClass is five, while dft8Size_8 shows that the DFT size for eight points is eight.
proof idea
The definition is a direct record construction. It sets the five_classes field to the value supplied by complexityClassCount and the dft_poly field to the value supplied by dft8Size_8. Both source theorems are proved by the decide tactic.
why it matters
This definition supplies the concrete certificate required by the RS account of computational complexity. It supports the claim that DFT computation over eight points lies in P because |ℤ/8ℤ| = 8 = 2^D. The parent discussion in the module notes that a full proof of P ≠ NP lies beyond the present formalization and would require Clay-level effort.
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