IndisputableMonolith.Mathematics.NumberSystemsFromRS
The module NumberSystemsFromRS defines number systems grounded in Recognition Science and establishes that the rational system contains the J-cost domain on positive rationals. Researchers building RS-derived constants or mass ladders would cite it to fix the base number system. It is a definitions module with no proofs.
claimThe positive rationals $\mathbb{Q}^+$ form the J-cost domain inside the rational NumberSystem, with NumberSystemCert certifying the embedding.
background
The module sits in the Mathematics domain and imports Mathlib for standard number theory. It introduces NumberSystem as the structure carrying a number system and NumberSystemCert as its certificate object. The central statement is that the rational system contains the J-cost domain consisting of positive rationals, providing the setting where the J function from the forcing chain can act.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the number-system layer required by downstream Recognition Science constructions such as the phi-ladder and mass formula. It anchors the rational base before T5 J-uniqueness and T6 phi fixed-point steps are applied.
scope and limits
- Does not treat irrational or real number systems.
- Does not derive the J function itself.
- Does not compute explicit constants such as alpha or G.