IndisputableMonolith.Mathematics.NumericalAnalysisFromRS
The module supplies numerical analysis definitions grounded in Recognition Science, centered on DFT-8 modes and FFT operations. Researchers implementing discrete transforms aligned with the eight-tick octave would cite these objects. The module consists entirely of type and constant definitions with no embedded proofs.
claimThe module defines $\mathrm{NumericalMethod}$, $\mathrm{dft8Modes} = 8 = 2^3$, $\mathrm{fftOps}$, and $\mathrm{NumericalAnalysisCert}$ as primitives for discrete Fourier analysis with exactly eight modes.
background
The module imports Mathlib and resides in the Mathematics domain. Its single doc comment states that DFT-8 modes equal 2 cubed equals 8. This directly instantiates the eight-tick octave (period $2^3$) from the forcing chain T7. Sibling definitions include NumericalMethod, numericalMethodCount, dft8Modes, dft8Modes_8, fftOps, fftOps_24, NumericalAnalysisCert, and numericalAnalysisCert.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module provides the concrete numerical objects required to realize the eight-tick octave in computational settings. It feeds the certification layer (NumericalAnalysisCert) and supplies the DFT-8 building block that connects T7 of the UnifiedForcingChain to discrete signal processing.
scope and limits
- Does not implement DFT for mode counts other than 8.
- Does not contain any correctness proofs for the FFT operations.
- Does not derive the value 8 from the forcing chain inside this module.
- Does not address continuous Fourier transforms or non-power-of-two sizes.