IndisputableMonolith.Mathematics.NumericalAnalysisFromRS
The module Mathematics.NumericalAnalysisFromRS supplies definitions for numerical methods and transforms derived from Recognition Science, with DFT-8 modes fixed at exactly 8. Researchers simulating discrete systems or certifying computations in the RS framework would cite these constructions. The module organizes its content as a collection of type definitions, mode enumerations, and certification objects without containing any proofs.
claimThe module defines DFT-8 modes satisfying $2^3 = 8$, together with NumericalMethod, fftOps, and NumericalAnalysisCert.
background
Recognition Science reaches T7 in the forcing chain as the eight-tick octave whose period is exactly $2^3$. This module introduces NumericalMethod as the basic structure for discrete approximations and dft8Modes as the explicit enumeration of the eight modes. It also supplies fftOps for the associated transform operations and NumericalAnalysisCert to record that these objects remain inside the RS-native units.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the numerical layer that lets the eight-tick octave be used in concrete calculations. It feeds downstream results on mass ladders and Berry thresholds by providing certified DFT primitives that respect the phi-ladder and the RCL.
scope and limits
- Does not define DFT for any size other than 8.
- Does not contain executable algorithms or floating-point code.
- Does not prove error bounds or convergence rates.
- Does not connect directly to physical constants such as alpha or G.