IndisputableMonolith.Mathematics.NumericalAnalysisFromRS
The module Mathematics.NumericalAnalysisFromRS supplies RS-derived numerical definitions centered on DFT-8 modes. Researchers modeling discrete transforms within the eight-tick octave cite these objects. The module organizes sibling definitions around the relation DFT-8 modes = 2^3 = 8 without containing proofs.
claimThe module defines objects satisfying DFT-8 modes = $2^3 = 8$.
background
Recognition Science obtains the eight-tick octave at T7 of the forcing chain, with period $2^3$. This module introduces numerical analysis tools from RS, including NumericalMethod, dft8Modes, fftOps, and NumericalAnalysisCert. The module doc-comment states DFT-8 modes = 2^3 = 8, anchoring the discrete Fourier transform to the RS octave.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
This module feeds the numerical certification layer of the Recognition framework by supplying DFT-8 modes that realize T7. It supports downstream objects such as NumericalAnalysisCert for validating computations on the phi-ladder.
scope and limits
- Does not implement general-purpose numerical libraries.
- Does not prove convergence theorems outside the RS context.
- Does not address continuous Fourier transforms.