IndisputableMonolith.Mathematics.ElementaryRegularNumberSystems
This module defines elementary regular number systems for the Recognition Science framework. Researchers constructing the mathematical foundations would cite it when establishing number systems compatible with the RS time quantum. It is a definition module containing NumberSystem, numberSystem_count, NumberSystemCert, and numberSystemCert with no proofs.
claimThe module introduces structures NumberSystem and NumberSystemCert over the RS time quantum with associated counting and certification functions.
background
The module resides in the Mathematics domain and imports Mathlib together with IndisputableMonolith.Constants. The upstream Constants module supplies the fundamental RS time quantum, defined as τ₀ = 1 tick. Sibling declarations in the module introduce NumberSystem, numberSystem_count, NumberSystemCert, and numberSystemCert as the core objects.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies foundational number-system objects that support later developments in the Recognition Science mathematics layer and the forcing chain (T0-T8). It connects directly to the Constants module for the time quantum τ₀.
scope and limits
- Does not contain any theorems or proofs.
- Does not import modules beyond Mathlib and Constants.
- Does not define objects outside the listed siblings NumberSystem, numberSystem_count, NumberSystemCert, numberSystemCert.