IndisputableMonolith.Mathematics.ComputationalComplexityFromRS
The module Mathematics.ComputationalComplexityFromRS introduces definitions that tie computational complexity to Recognition Science, centering on the certification that DFT-8 size equals 8. This follows from the eight-tick octave with period 2^3 and the forcing of D=3 spatial dimensions. Researchers linking discrete transforms or complexity classes to the RS forcing chain would cite the module. The module is definitional, supplying ComplexityClass, ComputationalComplexityCert, and supporting size lemmas without deeper proofs.
claimThe discrete Fourier transform of size 8 has cardinality $2^D=8$, where $D=3$ is the spatial dimension forced by the Recognition Science framework.
background
Recognition Science derives all physics from one functional equation, with the forcing chain producing J-uniqueness, the phi-ladder, the eight-tick octave of period $2^3$, and D=3 spatial dimensions. This module operates in that setting by importing Mathlib and defining RS-native complexity objects. It introduces ComplexityClass for classifying computational structures, complexityClassCount for enumeration, dft8Size for the transform cardinality, and ComputationalComplexityCert for formal certification of the size equality.
proof idea
This is a definition module, no proofs. It consists of declarations for ComplexityClass, complexityClassCount, dft8Size, dft8Size_8, ComputationalComplexityCert, and computationalComplexityCert, together with the direct equality dft8Size_8 that records DFT-8 size = 2^D = 8.
why it matters in Recognition Science
The module supplies the computational layer that extends the Recognition Science forcing chain (T7 eight-tick octave and T8 D=3) into discrete transforms and complexity classes. It enables downstream connections between the phi-ladder, RCL, and information-processing structures, filling the gap between the core physical derivations and computational consequences of the framework.
scope and limits
- Does not derive or compare standard complexity classes such as P versus NP.
- Does not include runtime bounds, algorithms, or decidability results.
- Does not extend the DFT size certification beyond the single case of length 8.
- Does not address quantum or continuous computational models.