IndisputableMonolith.Mathematics.ElementaryRegularNumberSystems
The module ElementaryRegularNumberSystems supplies foundational definitions for regular number systems in Recognition Science. It introduces the NumberSystem structure and related certification objects that rest on the RS time quantum τ₀. Researchers modeling discrete spacetime would reference these definitions when constructing number-theoretic components of the framework. The module consists entirely of definitions with no proof content.
claimThe module defines the type $NumberSystem$ of elementary regular number systems, along with $numberSystem_count$ and the certification predicate $NumberSystemCert$.
background
Recognition Science derives physics from a single functional equation, with the fundamental time quantum given by τ₀ = 1 tick in the Constants module. This module provides the elementary regular number systems that serve as the discrete foundation for subsequent constructions such as the phi-ladder and J-cost functions. It imports standard mathematical libraries from Mathlib and the RS constants to ensure compatibility with the eight-tick octave and spatial dimension D=3.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
This module provides the base definitions that feed into parent structures in the IndisputableMonolith, particularly those involving the Recognition Composition Law and the forcing chain from T0 to T8. It establishes the number systems used in mass formulas and Berry creation thresholds.
scope and limits
- Does not contain any theorems or proofs.
- Does not specify connections to physical observables beyond the imported time quantum.
- Does not include advanced or irregular number systems.