IndisputableMonolith.Mathematics.NumericalAnalysisFromRS
The module NumericalAnalysisFromRS supplies definitions for numerical methods derived from Recognition Science, centered on the DFT-8 with exactly 8 modes fixed by the relation 2^3. It includes supporting objects for methods, FFT operations, and certification. Researchers working on discrete transforms in RS-derived physics models would reference these constructs. The module is a collection of definitions with no proof bodies.
claimThe module defines the 8-mode discrete Fourier transform satisfying $8=2^3$ together with NumericalMethod, fftOps, and NumericalAnalysisCert.
background
Recognition Science obtains an eight-tick octave (period $2^3$) at forcing-chain step T7. This module translates that structure into numerical tools by importing Mathlib and introducing sibling definitions for numerical methods, the DFT-8, FFT operations, and a certification object. The module DOC_COMMENT states directly that DFT-8 modes equal 2^3 equals 8.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the numerical-analysis layer that supports discrete computations tied to the eight-tick octave (T7) in the Recognition Science framework. It feeds the certification objects and related siblings that enable RS-native numerical implementations.
scope and limits
- Does not treat DFT sizes other than 8.
- Does not prove correctness or convergence of the defined operations.
- Does not incorporate RS constants such as phi or alpha into the numerical objects.
- Does not address floating-point or hardware implementation.